Developments in the Theory of Cationoid Polymerisations

Developments in the Theory of Cationoid Polymerisations P. H. Plesch

Developments in the Theory of Cationoid Polymerisations (1946 - 2001)

Peter H. Plesch

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Contents 1

General Introduction ....................................................................................... 1

2

Developments in the Cationic Polymerisation of Alkenes - A Personal View (1994) ................................................................................ 5

3

Reviews ......................................................................................................... 31

4

3.1

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) ..... 33

3.2

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) ...... 95

3.3

Some Considerations Concerning Energetics (1955) .......................... 159

3.4

Theoretical Attempts at Improving Initiators for Cationic Polymerisation of Alkenes (1982) ...................................................... 175

3.5

Thermochemical Aspects of the Initiation of Cationic Polymerisations by Organic Cations. Conflation of Two Unpublished Conference Contributions (1999) .................................. 195

3.6

The Relation Between Reduction Potential and Solvation Energy for some Aryl Methylium Ions (1989) ............................................... 203

Theorising about Reaction Mechanisms...................................................... 215 4.1

Suggestions Concerning the Ionic Polymerisation of Vinyl Ethers (1950) ..................................................................................... 217

4.2

Developments in the Theory of Cationic Polymerization, Part I (1951) ...................................................................................... 223

4.3

Developments in the Theory of Cationic Polymerization, Part II (1954) ..................................................................................... 233

4.4

The Mechanism of Cationic Polymerisations Catalysed by Metal Halides (1959) ......................................................................... 243

4.5

A New Theory of Initiation by Aluminium Halides (1972) ............... 249

4.6

Approaches Towards a Comprehensive Theory of the Cationic Polymerisation of Olefins (1974) ....................................................... 269 i

Developments in the Theory of Cationoid Polymerisations

4.7

The Initiation of Polymerisations by Aluminium Halides (1980) ....... 281

4.8

Some Effects of the Complex Formation Between Cations and Monomers (1990) .............................................................................. 315

4.9

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) .............................................................................. 325

4.10 A General Theory Explaining Discontinuous Variations of the Degree of Polymerisation with the Concentration of the Reagents (1964) ................................................................................. 379 5

6

About Propagating Species and Propagation Rate-Constants in Cationic Polymerisations ............................................................................. 399 5.1

The Propagation Rate-Constants in Cationic Polymerisations (1971) ................................................................................................ 401

5.2

Nature of the Propagating Species in Cationic Polymerisations (1973) ................................................................................................ 421

5.3

Propagation Rate-Constants in the Cationic Polymerisation of Alkenes (1984) ................................................................................... 437

5.4

An Account of the Propagating Species in Cationic Polymerisations (1989) ................................................................................................ 451

5.5

The Propagation Rate Constants of the Cationic Polymerisation of Alkenes - Part III. Indene, Two Vinyl Ethers and General Discussion (1990) .............................................................................. 455

5.6

The Propagation Rate-Constants of the Cationic Polymerisation of Some Alkenes in Nitrobenzene - IV. Not the Real kp+ (1993) ......... 479

5.7

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) ................................................................................... 489

5.8

Rate Constants of Cationic Polymerisations and Mayr’s Rate Constants Reconciled (2001) ............................................................. 577

Pseudocationic Polymerisation (Ψ Cat), Renamed ca. 1998 ‘Cationoid Insertion Polymerisation’ (CIP) ................................................................... 589 6.1

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The Interaction Between Perchloric Acid and Styrene in Methylene Dichloride (1964) .............................................................................. 591

Contents

6.2

Pseudocationic and True Cationic Polymerisation of Styrene with Various Catalysts (1965) .................................................................... 599

6.3

Cationic and Pseudocationic Polymerisation of Aromatic Olefins Part I. Kinetics and Mechanism of the Pseudocationic Polymerisation of Styrene by Perchloric Acid (1965) ......................... 603

6.4

New Views on Cationic Polymerisation (1966) ................................. 613

6.5

Reaction Mechanism in Cationic and Pseudocationic Polymerisations (1966) ................................................................................................ 623

6.6

Cationic and Pseudocationic Polymerisation of Aromatic Olefins-II. The Reactions Following Polymerisation of Styrene by Perchloric Acid (1968) ....................................................................... 635

6.7

Cationic and Pseudocationic Polymerisation of Aromatic Olefins III. A Re-investigation of the Polymerisation of Styrene by Perchloric Acid in Methylene Dichloride (1976) ................................ 661

6.8

Pseudo-Cationic Polymerisation After 24 Years (1988) ..................... 671

6.9

Kinetics of Living Polymerisations (1988) .......................................... 685

6.10 Cationoid Living Polymerisations (1992) ........................................... 689 7

8

The Polymerisation of 1,3-Dioxacycloalkanes ............................................ 713 7.1

The Mechanism of the Polymerisation of Cyclic Formals (1971) ....... 715

7.2

The Propagating Species in the Polymerisation of 1,3-Dioxacycloalkanes by Perchloric Acid (1975).............................. 725

7.3

Some Aspects of the Polymerisation of 1,3-Dioxacycloalkanes (1976) ........................................................... 741

The Chemical Publications of P. H. Plesch in Chronological Order, 1946 - 2001 ................................................................................................ 757

Abbreviations and Acronyms............................................................................. 771

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Developments in the Theory of Cationoid Polymerisations

iv

Foreword

I first met Peter Plesch in the late 1950s when he had established his vacuum techniques in Keele and I was embarking on my PhD. My visit to Keele was to seek advice (freely given) on handling sensitive reaction systems. I rapidly came to appreciate that Peter operated on a somewhat higher intellectual plane than many academics. All might claim a common goal in achieving an understanding of how reactions or other processes work. But, while some are happy with an easy, sensible-sounding explanation, Peter took no easy line and needed to know how things really worked. Throughout his scientific career, Peter worked on cationic and related polymerisation processes for which he coined the collective term cationoid polymerisations. Compared to free-radical or living anionic polymerisations, in the earlier days cationoid polymerisations were theoretically and experimentally difficult and constituted a Cinderella field limited to a few aficionados; most of us positively avoided the subject. A feature of meetings of the High Polymer Research Group in the 1960s and 70s, held in a room with a small balcony at the Manor House Hotel in Mortonhampstead, was that Plesch and Pepper, two of those aficionados, inhabited the balcony. When relevant, they contributed enthusiastically to discussions (often disagreeing with each other) and their mutual discussion on detailed and probably obscure mechanistic features descended as ‘from on high’. Solving the detailed reaction mechanisms to produce rational explanations of cationoid polymerisations and reliable values of kinetic parameters has been Peter’s consistent goal for over 50 years. Unlike many people who devote their lives to a single topic, if, in order to advance the subject, some new experimental technique was required he and his group developed it; over the years they developed several devices and procedures to generate more-reliable data. Peter, therefore, was a serious experimentalist as well as a careful analyser and scrutinizer of data, data of his and of others. Over the years he freely criticised not only the work of others but also his own work (as is apparent in this volume) in order to develop a more complete understanding of systems. Thus, this book reports his contributions ‘warts and all’ where one paper may criticise a preceding paper. Lord Dainton, in his Foreword to Peter’s first book on cationic polymerisation, used the Latin phrase for ‘a crude and confusing mass’, my less-erudite phrase in the early days

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Developments in the Theory of Cationoid Polymerisations might have been ‘What a mess!’. Now we see a more coherent picture emerging in no small measure due to Peter’s intellectual pursuits. In this somewhat distinctive volume it is possible to trace Peter’s thought processes over the years as well as the development of cationoid polymerisations. While much current emphasis in polymer chemistry is on so-called ‘controlled, living polymerisation processes’, an emphasis I consider exaggerated, the contents of this volume are concerned with the broader aspects of cationoid polymerisations and not of selected modern developments. Peter’s latest book is not a textbook of cationoid polymerisations which distils all contributions and presents the reader with the current state of understanding in the field. Nor is it an historical account of the development of the subject or an account of the final outcome of the discussions from the 1960s. The book is a collection of Peter’s papers, organised in groups, which trace developments in cationoid polymerisations as seen from his own studies and his analyses of the works of others; contributions of other groups are seen in discussions of their works within Peter’s papers. Each group of papers or individual papers have associated commentaries which explain the overall aims and the significance of individual studies as steps in the development of the subject. Thus, progress in the subject can be plotted from the early days of confusion to current understanding. This volume, therefore, allows the reader to trace the development of this subject through Peter’s thought processes and provides an insight into the workings of an individual mind and exemplifies Peter’s rigorous approach to developing an understanding of his subject and his genuine pursuit for truth. True to Peter’s ways, to obtain the maximum from the book the reader must put in some effort to trace this progress.

Professor Geoff Eastmond Liverpool University 2002

vi

Authors’ Foreword

Why this book was made What is usually left to the end of a Foreword, I choose to make my beginning. It was the enterprise of Frances Powers, the Commissioning Editor of Rapra Technology Ltd, which provided me with the opportunity of putting together the record of much of my life’s work in the present volume, and for that I am deeply grateful. Re-living old campaigns, savouring past triumphs and mulling over the ‘might-have-beens’ are enjoyable for the not-so-young, but together they are not an adequate reason for an enterprise such as the present book. The curious seeker for motives may be interested to know that this volume is actually the logical outcome of my life-long urge to share knowledge, to pass on skills and to draw lessons from hard-won experiences. Thus the Prologues to each paper or group of papers set the scene and put the work recorded here into the context of contemporary chemistry; in short, they show why even the oldest of theses papers are still worth reading. A strong contributory reason for gathering together the record of what I did and thought is that many of the papers first appeared in Conference Proceedings and other venues that were not widely known or not readily accessible.

What is not in this book and why An inspection of my Publications List and a comparison with the Contents List of this book indicates that many papers are not here. A short explanation of some of these absences is that they lack any theoretical novelty, for example the group of three (83, 84, 85)* debunking by ingenious experimentation several allegations of abnormal isomerisation-polymerisations. They originated from an old family saying: ‘Rather than be astonished I prefer not to believe it’ (much pithier in the original German: ‘Eh ich mich wund’re glaub’ ich’s nicht.’). Other absences have a rather more profound origin. I have always felt the need to know as much as possible about any materials and systems, i.e., combinations of materials, *The numbers in () refer to the numbers in the Publications List at the end.

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Developments in the Theory of Cationoid Polymerisations such as solutions with which I am working. This was particularly appropriate for the highly reactive metal halides. As so little reliable information on their solutions was available and there were so many speculations about how they react with different solvents, I decided that what I wanted to know, I would have to find out myself. With the help of top-quality research students we did, and these researches, stretching over several decades had two important consequences: they enabled us to explain the age-old mystery of the polymerisations initiated by aluminium halides, and the relevant papers are of course included here (Section 5); and from them arose an entirely new area of physical chemistry, that of Binary Ionogenic Equilibria, and theses papers with one exception are not found here (25, 30, 33, 36, 89, 104, 111, 122, 127, 138). Similarly, my efforts to find an alternative to spectroscopy for investigating cationoid polymerisations resulted in our polarographic work, which is also not included in this volume (66, 75, 79, 81, 86, 100, 101, 105, 107, 108, 109, 113, 121, 137).

The title Some explanation is required why my title involves the adjective ‘cationoid’ instead of the traditional ‘cationic’. As most of those familiar with the subject have known for some years, I use this term to include both the cationic polymerisations by carbenium ions and also those polymerisations in which an alkene is inserted into the strongly polarised covalent bond of an ester, the cationoid insertions; I have seen no convincing reason for changing my well known opinion that these are different types of reactions, and that a clear distinction between them is heuristically useful.

Acknowledgements To my more than 50 fellow-researchers, from recent graduates to Senior Lecturers on study-leave, I owe much for their part in the master-apprentice collaboration which for me has always been one of the most interesting of human relations. All of them, and their quirks, I remember with varying degrees of irritation and admiration, and with gratitude for their hard working, hard thinking and loyalty. Next, I wish to record the great debt, which I owe to the many facilitators, from teenage technicians to the successive departmental heads who favoured me with benevolent neglect, and especially those who after my official retirement, continued to make me welcome in their Department. The only one of these facilitators whom I will name here is our nonpareil glass blower, Chris Cork, who for over 30 years taught us his skills, built the impossible and finally, in 1985, when I retired, helped me to dismantle it all, both of us very sad.

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Finally, my sincere appreciation to the succession of ladies who, over the decades, helped my manuscripts into print, and especially to Pauline Weston, the untiring and resourceful ‘midwife’ at the birth of this present volume. Professor G. C. Eastmond very kindly agreed to scrutinise this book after its completion, and for this act of friendship to an old colleague and for his Foreword, I am truly grateful. I am greatly indebted to the staff at Rapra, especially to Claire Griffiths, Sandra Hall and Steve Barnfield who were involved in the production of this book. I hope that the present juxtaposition of past work will act as an encouraging reminder to younger readers that making new science requires both bold, but well-founded, experiments and imaginative, but rigorous, thought.

Peter H Plesch In his 84th year in this world and in his 51st year at Keele March 2002

ix

Developments in the Theory of Cationoid Polymerisations

x

General Introduction

1

General Introduction

The main purpose of the present volume is to bring together the ideas about the nature of cationoid polymerisations, which I developed over several decades, and to show how they have helped me to provide a coherent theoretical framework for this particularly difficult area of chemistry. The Summing-up by Lord Dainton at the end of my first book ‘Cationic Polymerisation and Related Complexes’ [14] begins with the rather depressing phrase: ‘rudis indigestaque moles’ (a crude and confused mass) which is how the subject appeared to many in 1952; but now, after nearly fifty years, cationoid polymerisations no longer present such a dismal and discouraging picture. This progress in understanding is mainly due to two developments. One is the improved quality of the experimental results, which came from understanding that a successful study of these reactions requires especially meticulous techniques. The second is that a fairly coherent body of theory was developed by means of which many of the apparently diverse phenomena could be interpreted. I have been involved in this evolution from the earliest times [8, 9] and most of the papers which are presented here show how my quest for unifying and simplifying ideas has helped in the construction of a self-consistent theory of the phenomena. Actually, most of my papers contain a theoretical section, partly because of my driving curiosity to ‘rerum cognoscere causas’ (to know the causes of things), and partly because of an intellectual meanness. Let me explain this: The experimental procedures developed by the Keele research group were extremely rigorous, and therefore elaborate and time-consuming; in other words, the results we got had involved considerable intellectual effort and hard physical labour. That is why I always attempted to extract from them the absolute maximum of information, to squeeze them dry. Anything less, would in my view, have been to short-change those who had laboured and - ultimately - those who had provided the funds. In other words, the harvest of new science would not have been maximised. For this reason it always pained me when I had to read or - even worse - referee papers in which only the most obvious fruits had been gathered from the experimental results. One example can suffice - if, in a study of a polymerisation I had recorded only the molecular weights (MW) of the polymers, I would have considered it incomplete. Having the information on how the MW depended on the reaction parameters, it was essential for me to find out by means of Mayo plots what it was that had stopped the chains from growing further, for example [65]; and after that it was ever only a short step to drawing theoretical conclusions.

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Developments in the Theory of Cationoid Polymerisations The same urge to maximise intellectual profits, to exploit the rich veins discovered, and then often abandoned, by others and sometimes not even recognised, has also given me some very notable successes. One of the earliest of these insights originated from me recognising that Norrish and Russell’s curve relating the rate of polymerisation of isobutene by SnCl4 to the concentration of water is a parabola, whence I could prove that the dominant propagating species must be unpaired cations [44]. If the quality of those results had not been so good I would not have taken the trouble to analyse them so much more closely than the original authors had done. Actually, at that time (early 1950s) it was probably not yet appropriate to apply the theory of ionic solution equilibria and the associated electrochemistry in that context, which is what I eventually did [44]. This same ability to recognise hidden, unexploited treasure induced me to develop the first comprehensive theory of the polymerisations by ionising radiations [146]. None of the original researchers had stood back from their own findings, seen that their rather primitive theory was incompatible with the results of others, and set about constructing the general theory that was evidently needed. My effort [146] eventually produced a much-refined model of the propagating carbenium ion in solution and its different modes of reaction. One rather depressing feature of this present review of things done, is the realisation how slowly new ideas diffuse into the mass of shared views and of accepted paradigms that form the bedrock of a mature science. This seems to be a universal phenomenon: for example, even now few of those who have dabbled amateurishly with cationic polymerisations by using boron fluoride or its etherate as initiator realise that many years ago the true initiator had been shown to be the monohydrate of BF3 which is a protonic acid (A), and that as long ago as 1935 the dihydrate was proved to be hydroxonium hydroxyfluoroborate, H3O+BF3OH¯ (B). Some of the many instances of my findings being ignored by colleagues will be given where appropriate. However, having been alert from earliest times to this phenomenon of intellectual inertia, I always tried to link my results to the existing body of knowledge. For that reason almost all my papers contain a section with a title such as ‘Comparison with results of other workers’, e.g., [115], which enabled the reader to put our new results into the context of existing knowledge and beliefs. On looking over this collection of new findings and insights, I count myself fortunate in having cultivated a modest competence in mathematics, kinetics, thermodynamics and, especially electrochemistry. Without those skills I would not have been able to do what I did. In other words, it was essential for success - and to avoid gross solecisms - to be multifacetted, and polymer chemistry as usually understood would just not have been enough. Finally, a warning about what this book is not: my collection of papers is not a textbook or a monograph on cationoid polymerisations. My contributions to that subject, though

2

General Introduction substantial, are - just contributions to a large, diverse construct, which has benefited from the efforts of many very different chemists over many years.

Nomenclature, symbols and other formalities, attributions and references 1. Nomenclature and symbols • When this author realised that the pseudo-cationic polymerisations (now called cationoid insertion polymerisations) were a distinct reaction category, he started using the term cationoid to comprise both these insertions into a highly polar bond and the original cationic polymerisations which involve classical carbenium ions. • In the older papers the inaccurate old word carbonium ion, which originated from organic chemistry, has not been replaced by the semantically correct term carbenium ion. The appearance of this term marks the time when Oláh’s discovery of quinquevalent carbon in super-acid solution, the true carbonium ion, made the change of nomenclature essential and urgent. • The temptation to replace and bring up to date the somewhat bizarrely chosen symbols in my earlier papers has been resisted. 2. The papers that are reproduced here appear essentially in their original form except for the correction of (we hope, most) misprints and errors. 3. I feel the need for some comment on the quite frequently used word ‘proof’ in the present context. Amongst philosophers of science there is now wide-ranging support for Popper’s thesis that, in principle, one cannot prove any scientific proposition, because it is always possible that progress will make available some other interpretation of the phenomena in question; only disproof is possible. However, as I have explained elsewhere [152], in chemistry, a very mature subject, it is often appropriate for practical purposes to use the terms proof and proving without excuses or qualifications. 4. Realising that the correct attribution of ideas is very difficult in any fast-moving subject, I have always attempted to be fair without being pedantic. There is, however, one colleague to whose shade and to whose surviving colleagues I owe more than the usual apologies; it is Guenther Heublein, and, because I am fluent in German, I do not even have the linguistic excuse of my colleagues ignorant of German for neglecting his work. It is to my own detriment that I have done much less than justice to the results and the theoretical suggestions from his school, many of which are closely relevant to some of the ideas, which I have developed (C). My omission is the more 3

Developments in the Theory of Cationoid Polymerisations harmful because through my command of the language I could have helped their incorporation into the mainstream of theoretical evolution.

References The references to the author’s own works carry the serial number of that work in his Publications List, which is at the end of this book. References to other papers are lettered and are given at the end of each piece.

References to Introduction (A) A. Gandini and A. Martinez, Die Makromolekulare Chemie - Macromolecular Symposia, 1988, 13/14, 211. (B) L. J. Klinkenberg and J. A. A. Ketelaar, Recueil des Travaux Chimiques des PaysBays, 1935, 54, 959. (C) See for example G. Heublein, Zum Ablauf ionischer Polymerisationsreaktionen, Akademie-Verlag, Berlin, 1975.

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2

Developments in the Cationic Polymerisation of Alkenes - A Personal View (1994) P. H. Plesch

This paper was first published in Makromekulare Chemie, Macromolecular Symposia, 1994, 85, 1-31. Reproduced here by kind permission of Wiley-VCH Verlag GmbH, copyright 1994.

Abstract In this paper the author presents some of his contributions to the theory and practice of the cationic polymerisation (CP) of alkenes since 1944. The first phase of his work at the University of Manchester comprises the discovery of co-catalysis by water with TiCl4, the invention of the pseudo-Dewar reaction vessel, the use of trichloroacetic acid as co-catalyst, and the disproof of the alleged cationic isomerisation of cis-stilbene. The second phase at Keele (1951-1985) involved the construction and progressive improvement of the vacuum reaction calorimeter and its use in a variety of kinetic studies with many monomers and initiators. Reactive researches were concerned with disproving the alleged isomerisation-polymerisation of various alkylstyrenes and the participation of radical-cations in the polymerisation of N-vinylcarbazole by electron acceptors. The disproof of direct initiation (i.e., without a co-catalyst) by metal halides MtXn was eventually followed by the demonstration that the MtXn can initiate CP by the cationation of the monomer by the cation MtXn-1+. The very detailed studies of the binary ionogenic equilibria by which these cations are formed were part of pro-active researches into various equilibria including some between alkyl halides RX and MtXn and between monomers and MtXn. Other pro-active work showed that styrene and isobutene behave completely differently when polymerised by the same syncatalytic system TiCl4 + H2O in CH2Cl2. The rates and degree of polymerisation (DP) obtained with isobutene were explained by the idea that at higher temperatures the principal propagators are paired cations and that as the temperature is reduced the unpaired cations become progressively more kinetically important. This first use of these concepts in CP could also account very naturally for numerous observations by others with other initiators and solvents. The discovery of the pseudocationic polymerisations by means of kinetic, conductimetric and spectroscopic studies led eventually to a fairly comprehensive theory of living CP.

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Developments in the Theory of Cationoid Polymerisations A side-effect was the spectroscopic hunt for the elusive styryl cation which resulted in the identification of the principal cations formed by the action of acids on styrene; the subsequent quest for a non-spectroscopic method to identify organic cations led to the development of the polarography of carbenium and oxonium ions. The last experimental work was aimed at measuring the propagation rate-constant, kp+, for various monomers under the ‘ideal’ conditions which, it was hoped, would be provided by the solvent nitrobenzene. This was frustrated by the complexing of the propagating carbenium ions with the solvent; but the mechanistic insight resulting from a detailed examination of the results provided useful new understanding of previously unexplained anomalies. After the author’s retirement in 1985 there followed several theoretical researches. The larger enterprises include a new theory to account for the hitherto unexplained features of the CP induced by ionising radiations, and a critical analysis of the alleged propagation rate-constants kp+. This has shown that the great majority of such claims are ill-founded, and the author explained in detail why he considers only 17 rateconstants to be reliable.

1 Introduction Several friends suggested that for my lecture at this 11th Symposium on Cationic and other Ionic Polymerisations I should review the changes in the understanding of cationic polymerisations with emphasis on my contributions. One reason given was that - apart from David Pepper - I am the oldest worker still active in this area and that I have contributed new experimental methods, results, and ideas continuously over more than four decades, my first (joint) publication [1] having been in 1946, my first single-author paper in the following year [2], and my latest one earlier this year [3]. I was hesitant about such an egocentric enterprise until I read Otto Vogl’s account of his work with aldehydes [4] which is fascinating and instructive, and so I decided to adopt a similar format. I will try, as I have always done, to acknowledge the contributions of others, but it seems unlikely that I will succeed in giving appropriate credit with regard to every innovation, and for such lapses I apologise in advance. Historically, the work consists of three sections: The period at the University of Manchester, 1944-1950; the studies at Keele with many co-workers from 1951 until my retirement in 1985, and my subsequent theoretical writings. I will deal only marginally with the three independent physico-chemical developments which originated from my studies on alkenes, although they engaged a major part of my energies. These are the polymerisations of dioxacycloalkanes, the polarography of carbenium and oxonium ions, and the binary ionogenic equilibria (BIE). Those stories might be told on other occasions.

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Developments in the Cationic Polymerisation of Alkenes - A Personal View (1994) It will be obvious from my account that although I consider myself primarily a physical chemist, my concern was always with finding the most efficient solution to a problem. If that meant doing phase-rule studies with a vacuum line (hardly ever attempted before), or getting infra-red spectra of polymers to identify end-groups when the only IR instrument in the City of Manchester at that time was in the ICI laboratories at Blackley, or synthesising new model compounds or super-pure AlCl3, we just overcame the practical obstacles and got on with it. This attitude often evoked a response, mainly from non-British colleagues: ‘I could not do that! I am an x-chemist and don’t know anything about y-chemistry and z-chemistry’.

2 Manchester, 1944-1950

2.1 The start After graduating from Cambridge in 1940 and war-related work in industry, I joined the Department of Physical Chemistry at the University of Manchester in November 1944 as a research assistant to the head of the Department, Michael Polanyi. He set me to work under a newly appointed Assistant Lecturer, H. A. Skinner, to help with a problem related to the Synthetic Rubber Programme which had been assigned to him some years earlier. The aim was to make the rate and yield of the polymerisation of isobutene and the molecular weight of the product controllable and reproducible. Several lecturers in physical chemistry, but mainly A. G. Evans, and an inorganic lecturer, F. Fairbrother, whose speciality was ‘Friedel-Crafts’-type metal halides, with numerous research students had experimented extensively with isobutene without making any significant advances, except perhaps the discovery that amongst the many metal halides tried, TiCl4 seemed to offer the best prospects in terms of the control of reaction rate and yield. Also, since the polymerisation of isobutene by AlCl3 at low temperatures (which were needed to obtain high molecular weights) is - in a favourite text-book phrase - ‘the fastest organic reaction known’, Polanyi drew upon his experience of catalytic reactions to circumvent some of the inherent difficulties. He replaced isobutene by the readily available mixture of its sterically hindered dimers 2,2,4-trimethylpentene-1 and -2(di-isobutene), which at about room temperature are converted quite slowly to a mixture of oligomers under the influence of Friedel-Crafts halides, especially the favourite BF3 and its complexes. The results from Evans and his research students included two phenomena which, with hindsight, could be seen to contain a clue to understanding these erratic polymerisations. It was found that the oligomerisations of the dimers were of first order internally but with respect to an asymptote which was not the monomer concentration and which was irreproducible from one experiment to another; and occasionally a reaction which had stopped

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Developments in the Theory of Cationoid Polymerisations would continue when the reaction vessel was opened to the atmosphere and the contents stirred. Amongst the research students this was known as the ‘Allen effect’ after its discoverer. This was the situation when I joined Polanyi’s group in November 1944 and the first entry in my laboratory notebook (dated 7.11.44 - 20.12.44) reads as follows: ‘The polymerisation of isobutene is so far a repeatable, but not a reproducible reaction. Following on from the work of Seymour et al., in this department, and work at ICI and in America, we are attempting to elucidate the reaction mechanism of this polymerisation. In particular, we want to find out how it is that decreasing the temperature increases the reaction rate and within what limits that holds. It is also of considerable interest to discover why it is that under certain conditions catalyst and monomer can co-exist without reaction taking place.’

2.2 The discovery of co-catalysis On the basis of the previous work, Polanyi, Skinner and I decided to use hexane as solvent and TiCl4 as catalyst (what we now call initiator). The experimental technique was crude, but its essential feature, retained thereafter, was to use the temperature rise of the reaction mixture, due to the exothermicity of the polymerisations, to measure the rate and the extent (yield Y) of the reactions. The entry in my notebook for 23rd July 1945, recording my polymerisation experiment No.55 is followed by one of 10th October 1945 which reads as follows:

History 23.7.45 to 10.10.45 ‘During this period several notable events took place: 1. Use of Atomic Bombs against Japan. 2. End of Asiatic War. 3. My engagement and marriage. 4. Widespread unrest all over the world.’ This is followed by a specification for a new apparatus which includes the description of the ‘pseudo-Dewar’, reaction vessel [5]. This is a Dewar vessel, the Dewar-space of which can be filled with air or evacuated through a side-arm. Thus the contents can be cooled

8

Developments in the Cationic Polymerisation of Alkenes - A Personal View (1994) and then, by the evacuation of the Dewar-space, the device can be converted into an adiabatic reaction calorimeter. It was the first advance on the Dewar vessel since Dewar invented it, and it formed the basis of all subsequent developments [6, 7], especially the magnificent apparatus of Sigwalt’s group. By means of this device it was possible to introduce the reagents into the reaction vessel and to cool them to the required temperature without their extensive exposure to the atmosphere which had been necessary previously. The first few experiments with the new device showed that with starting temperatures below approximately –30 °C the polymerisations of isobutene by TiCl4 in hexane stopped with the yield (Y) less than 100%, that Y and the reaction rate increased as the starting temperature decreased, and that below approximately –80 °C the reactions were very fast and went to completion. By the end of November, after approximately 20 experiments it had been established that the incomplete polymerisations at the higher temperatures could be restarted by atmospheric moisture. By analogy with the term co-enzyme I named water a co-catalyst to the catalyst TiCl4. These findings established a link with and an explanation for the ‘Allen effect’ mentioned above. The necessity for a co-catalyst with BF3 was subsequently confirmed rigorously by Evans and Meadows [8-10] by means of an all-glass vacuum apparatus which established a characteristic style of experimentation which I adopted and adapted. They showed that under rigorously anhydrous conditions isobutene and BF3 could be mixed without the isobutene polymerising, and that the addition of water did initiate a polymerisation. Fairbrother and Frith [11] reported very briefly that the polymerisation of isobutene by (Ta-Nb)F5 ‘required a co-catalyst’ - without stating which one they used. Shortly afterwards Norrish and Russell [12] showed the effect of water on the polymerisation of isobutene by SnCl4 in C2H5Cl. Evans and Meadows also showed that for the polymerisation of gaseous isobutene by BF3, acetic acid and tert-butanol could act as co-catalysts and they claimed that diethyl ether (Et2O) was a weak co-catalyst. Unfortunately, this was not a valid claim, and many subsequent investigators postulated initiation by Et+ from BF3OEt2 before Gandini and his collaborators showed that the alleged activity was due to residual water [13, 14]. The acidity of the monohydrates of the electron-deficient metal halides was well known and treated as analogous to that of the monohydrate of SO3. The first soluble co-catalyst for the system isobutene + TiCl4 + hexane was CCl3CO2H (2) [15]. The enhancement of the acidity of CCl3CO2H by TiCl4 - because that is what was involved - was treated as analogous to the increase of acidity from H2SO4 to H2S2O7. However, at that time ideas on the nature of acidity were still evolving. One still found the bare proton H+ in equations as a reagent because it was not yet widely realised that for energetic reasons the proton needs to find an energetically more favourable location (a stronger base such as another water molecule) to combine with before it can leave the non-ionic monohydrate complex [16]:

9

Developments in the Theory of Cationoid Polymerisations MtXn.OH2 + H2O → MtXnOH- + H3O+

(1)

The analogous reaction (2) in which the base is an alkene MtXn.OH2 + CH2:C(Me)2 → Me3C+ + MtXnOH-

(2)

was now regarded as the general initiation step, and the fate of the trimethylcarbenium ion Me3C+ and of the analogous propagating cations and the effects of solvents on ionpairing became matters of interest. The apparent simplicity of this theory of co-catalysis made it tempting to believe that all CP were initiated in this way, and for several decades the less rigorously executed polymerisations in which apparently the addition of a co-catalyst was not required were ‘explained’ by the invocation of a mythical ‘adventitious co-catalyst, probably water’ - a phrase which became a ritual incantation to ward off any too searching enquiries concerning techniques. This practice persisted even after my group had shown by rigorous vacuum technique that water does not affect the polymerisation of isobutene by AlCl3 [17], which goes well in the driest systems. The working hypothesis then was that the alkyl halide solvent acted as co-catalyst, but there were also strong indications that it was dangerous to generalise from one metal halide to another.

3 Vivat Popper

3.1 Popper said... The philosopher of science Karl Popper propagated the useful and now almost selfevident notion that it is not possible to prove any theory because, at least in principle, more than one theoretical explanation can be devised to explain any one set of observations. However, for many groups and types of observations one particular theory may be so efficient in explanation and powerful in prediction, that the existence of alternatives can be ignored, especially in the absence of discordant, i.e., inexplicable, facts. Such theories then came to be regarded as facts or ‘the truth’. I have always avoided the pitfalls implicit in the word ‘truth’ by telling my students that truth is the concern of lawyers and theologians, and that I, like many scientists, am content to regard my ideas about the behaviour of matter as more or less useful to the extent that they produce coherent, economical explanations and valid predictions. It is an essential part of Popper’s thesis that any theory which claims to be scientific must be sufficiently precise to be falsifiable. This means that the theory must be able to make

10

Developments in the Cationic Polymerisation of Alkenes - A Personal View (1994) predictions of the type: ‘If the experimental procedure A is carried out, then the result A´ will be observed’. If a result other than A´ is found, then either the theory is not valid, i.e., wrong, or the experiment was not done correctly. This alternative is particularly relevant to chemistry, but it has been neglected by many philosophers because most of them, whilst familiar with (some) physics, are ignorant of chemistry, where impurities in chemicals, the catalytic effects of surfaces, and many other features may influence a result in an unknown manner and may therefore be difficult or impossible to incorporate in a theory. (The most notable exception was Michael Polanyi.) Another important difference between physical and chemical theories is that a theory about chemical reactions must be compatible with many different measurable effects. For example, a theory about the intermediates in a chemical reaction must be compatible not only with the common rules of valency, but with spectroscopic, electrochemical, kinetic, and other observations. Thus the tests for the acceptability of chemical ideas are very stringent. Much of my research effort has been concerned with showing that some quite popular ideas (theories) have been wrong, that is they were not compatible with the observations or with some of the established parts of chemistry, or that certain theories were inadequate because they failed to explain some important facts. In the following sections I will present some examples of these researches which helped to clarify our subject.

3.2 Falsification in practice

3.2.1 The isomerisation of cis-stilbene This example involves a wrongly interpreted observation, i.e., an alleged but wrong fact, upon which a theoretical superstructure concerning ionic reaction paths had been built. When Michael Polanyi relinquished the Chair of Physical Chemistry at the University of Manchester in 1948, he was followed by M. G. Evans from Leeds. By that time I was an Assistant Lecturer and M. G. Evans took a kindly interest in my activities. I was pestering him for a research student, and a final year student, D. S. Brackman, was pestering him to do research for a higher degree. So he got rid of two pests by setting Brackman to work with me, and he suggested that we look at a report by the well-known physical-organic chemist C. C. Price that cis-stilbene could be isomerised to the trans-isomer by BF3 [18]. Since an attempt to reproduce this result [19] had been unsuccessful, and since the possibility of such an isomerisation was interesting at that time for the developing views on reaction mechanisms, the enterprise seemed worthwhile, and I had by then developed a superior vacuum technique suitable for such a study. The results which we obtained under high vacuum showed that when either isomer was mixed with BF3 or TiCl4 there was a reversible formation of coloured complexes but no reaction, and when a co-catalyst was added the

11

Developments in the Theory of Cationoid Polymerisations ensuing reaction yielded a mixture of oligomers, but there was no isomerisation [20, 21]. When I visited Charlie Price in 1952 he explained that the report had originated from a less-than-thorough vacation student mistaking the solid mixture of oligomers obtained from the liquid cis-stilbene for the crystalline trans-stilbene. Since I had met Price first when he visited Manchester in the late 1940s, we established a very friendly relationship which has lasted. My results marked the end of ‘ionic cis-trans isomerisation’. In the course of these studies we extended the list of complexes formed by metal halides (MtXn) and arylalkenes, and we found that when cis- or trans-stilbene was oligomerised by TiCl4 + CCl3CO2H in bulk or in benzene or hexane, the oligomeric products contained considerable quantities of indane end-groups, formed by an internal Friedel-Crafts reaction; this finding served to generalise the observations of several earlier workers, especially those of Dainton and Tomlinson [22] with α-methylstyrene. When the oligomerisation was attempted in toluene, trans-stilbene formed some, and cis-stilbene formed exclusively ‘p-stilbyl toluene’, i.e. 1,2-diphenyl-2-(4-tolyl)ethane. Our finding that an ordinary-Friedel-Crafts alkylation played an important part in a CP generalised my finding p-tolyl end-groups in polystyrenes which had been prepared in toluene [23]. This alkylation reaction, which Overberger unfortunately named ‘molecular termination’, involves a proton transfer reaction, and it was subsequently studied in considerable detail by Overberger’s and Okamura’s groups [for References see [24]]. It can be represented schematically by equations (3) and (4): -CH2.CHZ+ + ArH → -CH2.CHZ.ArH+

(3)

-CH2.CHZ.ArH+ + M → -CH2.CHZ.Ar + HM+

(4)

3.2.2 The alleged isomerisation-polymerisation of alkylstyrenes The work to be described is concerned with alleged observations by Russian and Japanese chemists, which could not be reproduced. In the 1960s, after Kennedy and Thomas [25] had established the isomerisation polymerisation of 3-methylbutene-1, this became a popular subject. From Krentsel’s group in the USSR and Aso’s in Japan there came several claims to have obtained polymers of unconventional structure from various substituted styrenes by CP. They all had in common that an alleged hydride ion shift in the carbenium ion produced a propagating ion different from that which would result from the cationation of the C:C of the monomer and therefore a polymer of unconventional structure; the full references are in our papers. The monomers concerned are the 2-methyl-, 2-isopropyl-, 4-methyl-, 4-isopropyl-styrenes. The alleged evidence consisted of IR and proton magnetic resonance (PMR) spectra, and the hypothetical reaction scheme which the spectra were claimed to support can be exemplified thus:

12

Developments in the Cationic Polymerisation of Alkenes - A Personal View (1994)

(5)

This reaction would give polymers with the structure shown in which the benzene ring is part of the chain, instead of the normal polystyrenes. It happened that I heard of Kennedy’s attempts at checking the Russian claims - at the time when Magagnini in my laboratory was doing the same thing, and I also found that in Darmstadt a student of D. Braun had done similar work. I organised the pooling of our results and they were published in three papers [26, 27, 28]. It is obvious from the apparatus diagrams in these papers that a large part of our evidence was obtained by Magagnini who extended considerably the scope of our vacuum techniques, and these papers are amongst the best illustrations of what one can do with them. The short conclusion from the long quest was that all these alleged isomerisationpolymerisations proved to be entirely mythical, and that therefore the relevant Russian and Japanese claims are invalid.

3.2.3 Direct initiation ‘Direct initiation’ is the term used for the initiation of a CP by a metal halide without a co-catalyst (co-initiator in modern terminology). 3.2.3.1 How it does not go One of the earliest theories concerning the initiation of the CP of CH2:CHZ by MtXn, due to Hunter and Yohé [29] formulates the initiation as the formation of the zwitter-ion MtXn-CH2-CHZ+. I had shown that in solvents of low polarity the energy required to separate the ions would be prohibitively large [15], but Medvedev and Gantmakher [30] revived the theory in order to explain some claims that CP could be initiated in solvents of intermediate polarity without a co-catalyst. By exploiting the implications of the very thorough work of Colclough and Dainton with styrene and SnCl4 in various solvents [31] and by means of several experiments especially designed by us for the purpose [32], we showed that with TiCl4 or SnCl4 there was no evidence for any CP of styrene or isobutene in alkyl chlorides being initiated without a co-catalyst, and that the revival of the old theory was not helpful. I had our paper translated into Russian and asked S. S.

13

Developments in the Theory of Cationoid Polymerisations Medvedev, the ‘Grand Old Man’ of polymer science in the USSR, to communicate it to the Doklady [33]. I had no doubt, such were the ethics of science at the time, that he would do this, although we were claiming a disproof of his own theory. Of course he did, and when I met him subsequently at a conference he dismissed my thanks briefly with the remark ‘But that was the natural thing to do. That is what a scientist owes to his colleagues’. As the Romans used to say ‘O si sic omnes’ (if only everyone were like that!). The ‘pre-cocatalysis’ theories were reviewed by me in 1949 [34]. Various other theories of ‘direct’ initiation proposed subsequently by various authors have also proved to be untenable in the face of hard evidence. 3.2.3.2 How it does go When discussing how metal halides initiate the polymerisation of alkenes it is essential to realise that we know a little about BF3, BCl3, the AlX3 (X = Cl or Br), (EtAlCl2 + Cl2), TiCl4, and SnCl4 and virtually nothing about any of the others; and that ‘little’ has taught us that they all behave differently, except AlCl3 and AlBr3 which do seem to be very similar. This individualism also implies that different potential co-catalysts may react differently with the different MtXn. Here is not the place for a treatise on this complicated subject, but it is the occasion to describe how we established the manner in which the AlX3 initiate polymerisations in the most rigorously purified systems. In Section 4 there is an account of our exploration of the self-ionisation of the AlX3. Having established that phenomenon [35, 36], I could pursue with Grattan [37] the idea that it is the inorganic cation AlX2+ which initiates the polymerisations by cationating the monomer: AlX2+ + CH2:CHZ → X2Al-CH2.CHZ+

(6)

This idea had been proposed and used by several authors, but none had attempted to test it experimentally. We did this by killing the polymerising mixtures with tritiated water and then hydrolysing the polymers. We determined quantitatively the C-T groups formed from the C-Al initial groups, and the tertiary end-groups and found that their numbers were equal - as they should be if the growth of every polymer is started either by AlX2+ or by H+ from transfer and is terminated either by transfer of H+ or by reaction of the growing carbenium ions with water. The extremely low initiation efficiency in terms of the Al consumed was explained by the smallness of the ionic concentration which we had measured in the initiating AlX3 solutions; and the coexistence of the excess of AlX3 with unpolymerised monomer was explained by the AlX3 being prevented from further participation in the BIE by being complexed with the monomer, which we demonstrated as described in Section 4. Thus we had resolved the oldest problem in the subject and

14

Developments in the Cationic Polymerisation of Alkenes - A Personal View (1994) answered the question at the end of my notebook entry quoted in Section 2.1. No facts incompatible with our theory have come to my notice. However, it must be remembered that in less pure systems other forms of initiation may occur.

3.2.4 The elusive styryl cation When I became interested in the spectrum of the styryl (1-phenylethyl) cation, MeC+HPh, the literature concerning its UV-vis absorption spectrum and its λMax and εMax was discordant, and therefore Gandini and I decided to investigate it [38]. We fell into the same trap that had caught previous investigators, but our assignments were challenged and doubts about them also emerged from the work of others [see References 2-6 in [30] and References 9-12 in [40]]. Therefore I planned a full-scale attack on the problem of the species generated by the interaction of styrene with acids. V. Bertoli succeeded in determining the number and nature of the species generated in these reactions by numerous syntheses and by devising subtle methods of generating the cations from the compounds thus obtained, and then characterised the ions by UV-vis and PMR spectroscopy [39, 40, 41]. Whilst others had pointed out that our early spectroscopic work, like that of our predecessors, lacked verisimilitude, we ourselves proved it wrong and replaced it with results which mostly seem to be supported by subsequent work. It was the very great difficulty of characterising carbenium ions spectroscopically which led me to develop their polarographic identification and estimation.

3.2.5 Radical-cations and NVC In the 1960s various authors [Scott, Ellinger and others, see References in [42]] suggested that the polymerisation of N-vinylcarbazole (NVC) by organic electron acceptors is propagated by radical-cations or chemically equivalent species. These suggested mechanisms were unsupported by adequate chemical or kinetic evidence, but because of the exceptionally great reactivity of NVC there seemed to be here an interesting set of phenomena worth investigating. Therefore we undertook a very thorough and wideranging study of polymerisations of NVC initiated by C(NO2)4 and by chloranil in various solvents [42]. Amongst other novel features this involved determinations of formation constants of charge-transfer complexes, the preparation of NVC oligomers for end-group studies by means of transfer agents, the determination of transfer coefficients by a very thorough exploitation of the Mayo plots, and detailed kinetic measurements. Our conclusions, which have not been challenged, were that these polymerisations are cationic and are initiated by the cations formed from the ionic dissocation of charge-transfer complexes; and that our evidence is not compatible with any reaction mechanism other than a normal CP.

15

Developments in the Theory of Cationoid Polymerisations

4 Keele 1951 - 1985 4.1 Introduction In the previous section I have described some researches which originated from me wishing to test certain alleged observations and various ideas which seemed questionable, and therefore that work has mainly a reactive character. In the present section I will outline some proactive researches, that is investigations which started with me at Keele and which initiated new lines of enquiry. It so happens that many of the researches of this type were concerned with the polymerisation of dioxacycloalkanes, the properties of oxonium ions, the polarography of carbenium and oxonium ions and various kinds of BIE, and they therefore fall outside the scope of this review; but there were enough proactive researches on alkenes to make a story of steadily evolving ideas.

4.2 The start at Keele, Cationic Symposium 2 and the numbering of Cationic Polymerisation Symposia When, in January 1951, I went to the newly founded University College of North Staffordshire, which in 1960 became the University of Keele, as a Lecturer in Physical Chemistry and second-in-command to the Head of Department, Professor H. D. Springall, there was no departmental building, i.e., no labs. So M. G. Evans allowed me to keep my laboratory in Manchester. When I acquired a laboratory at Keele, he allowed me to take away the whole contents of my Manchester laboratory and since at Keele we had virtually no money for research, it was this generosity alone which enabled me to restart my experimental work. However, before that happened, I decided to occupy myself with organising the ‘Second Symposium on Cationic Polymerisation and Related Complexes’ in March 1952, which would also be the first conference of any kind to be held at Keele. I did this because the first such symposium organised by D. C. Pepper in Dublin in 1949 [43] had been outstandingly successful in bringing together people and ideas, and it seemed time to create another such occasion (see Note at the end of this section). The proceedings and discussions appeared in 1953 [24]. The successive Symposia became important to all of us concerned with CP, and the development of the subject can be traced in the titles of the papers presented. The title of my Symposium shows that then, as for a long time thereafter, complexes of various kinds were thought to be important in the mechanism of what was still generally known as ‘Friedel-Crafts’ polymerisations. One of the most interesting parts of this publication is a report by G. Salomon of Delft on a Symposium on ‘Carbonium Ion Reactions’ held at Leiden in March 1952, just a few days before our symposium. It is clear that this marks, as nearly as can be, the general

16

Developments in the Cationic Polymerisation of Alkenes - A Personal View (1994) recognition of what we now call the carbenium ion as a stable reaction carrier of welldefined structure and properties [see also Chapter 1 in [44]].

Note on the numbering of Cationic Polymerisation Symposia Strictly, Pepper’s Symposium was not the first, because on 15th September 1945, that is one month after the end of World War II, Polanyi convened a one-day ‘Symposium on Friedel Crafts Catalysts and Polymerisation’ at the University of Manchester. A typed version of the lectures and discussions was circulated to the participants by Polanyi in July 1946; I possess a copy of this very interesting document, which awaits publication. The seven lecturers included Sir Harry Melville and the 10 discussants included Sir Robert Robinson. Unfortunately, I do not have a list of participants, but I recall that there were more than 50. Further, one might reasonably designate as the third ‘Cationic Symposium’ the ‘Symposium on Catalysis in Hydrocarbon Chemistry’ organised by the American Chemical Society in 1952 [45]. A re-reading of the papers there by Schmerling, Szwarc, H. C. Brown, and Langlois will put the advances, which we believe to have made, in proper perspective.

4.3 Complexes I In chemistry, the term ‘complex’ can mean many things. The belief, which I shared, that complexes of the metal halides with monomers or with alkyl halides are important in CP induced me to undertake several difficult but fruitful investigations. Complexes between RX and MtXn were well known [see References in [24]] and they were being studied at about that time by several workers, such as H. C. Brown at Purdue University with regard to the Al halides; and Fairbrother at Manchester University was concerned with similar systems and with the ionisation of trityl halides by metal halides. I was concerned with TiCl4, my then favourite ‘catalyst’, and its interaction with the alkyl chlorides which were used as solvents for CP. The theory first suggested by Pepper [46] and adopted by us was that if a CP was initiated in an alkyl chloride RCl, and there was no evident effect of water, then the initiation was most likely akin to a Friedel-Crafts alkylation. This was represented by the equations (7) and (8): RX + MtXn → ← RX.MtXn

(7)

RX.MtXn + CH2:CHZ → R-CH2-CHZ+ + MtX-n+1

(8)

The cationation (8) introduces R as an initial group into the polymers. The activity of various RX as co-catalysts was apparently supported by the finding of terminal R groups

17

Developments in the Theory of Cationoid Polymerisations in polymers until it was realised rather later that whilst this may be possible, the R groups might also appear in the polymers as a result of transfer reactions, possibly involving halonium ions: -CHX+ + RCl → ← -CHX.Cl+.R

(9)

-CHX.Cl+.R + CH2:CHX → -CHXCl + R.CH2-CHX+

(10)

Our subsequent much more rigorous work showed that with TiCl4 and isobutene or styrene, CH3CHCl2, CH2:CCl2, Me2CHCl do not act as co-catalysts, although with SnCl4 the last two RX do appear to act as co-catalysts [31]. I decided to ‘demythologise’ the subject by the most direct method that I knew, namely by freezing-point phase rule studies which should reveal the formation of complexes of any considerable stability. To do this we constructed a high-vacuum freezing point apparatus without taps or joints to determine the freezing point-composition curves of the whole range of mixtures of TiCl4 with six alkyl halides. However, we found no evidence for the formation of any complexes [47]. This made solvent co-catalysis with TiCl4 by reactions (7) and (8) seem very unlikely.

4.4 The origins of the BIE studies Suspecting that there may be an ionisation without complex formation, we then did a conductimetric study on TiCl4 in CH2Cl2 and EtCl [48]. This gave the useful result that there was no evidence for an ionisation yielding R+ and MtX-n+l, and it thus made solvent co-catalysis by the ionisation of the solvent very unlikely. A further useful outcome from these conductimetric studies was the realisation that the observed rectilinear dependence of the conductivity, κ, on the concentration of TiCl4 could only be explained reasonably as due to the self-ionisation of TiCl4, for which reaction (11) seemed most likely: 2 TiCl4 → ← TiCl3+ + TiCl5-

(11)

but the possibility that it might be due to reaction (12) was recognised: + 3 TiCl4 → ← 2 TiCl3 + TiCl 6

(12)

The important feature was the recognition that because the relation between κ and [TiCl4] was rectilinear, the number of concentration terms on each side of the equilibrium had to be the same, which ruled out the involvement of ion-pairs. Our work opened up the new field of binary ionogenic equilibria (BIE) which was to prove an essential preliminary to unravelling the mechanism of the polymerisation of isobutene by AlCl3. We also showed

18

Developments in the Cationic Polymerisation of Alkenes - A Personal View (1994) that earlier results of Fairbrother and of Kraus on aluminium halides and alkyls could be interpreted much more plausibly in terms of BIE. It was not until 1972 that I resumed studies in this area, because I was ‘pushed’ in that direction by our studies on ion-pairing. It happened like this: I had been interested in paired cations as the chain-carriers ever since I calculated the dissocation constant KD for the ion-pair poly(isobutyl)+ TiCl4.O2CCCl-3 in hexane (15). My first experimental study of ion pairing was with the model system MeEt3N+Iin CH2Cl2 over the unprecedentedly great temperature range 0 to –95 °C, the KD going from (0.9 to 2.8) x 10-5 mol/dm3 [49]. The subject became topical when various workers suggested that, as in the anionic polymerisations, unpaired cations might propagate more rapidly than paired ions. As there were few data on the dissociation of ion-pairs involving carbenium ions, and none on the oxo-carbenium ions, RCO+, which were of special interest to me at the time, I got O. Nuyken to study the conductivity of the salt MeCO+ SbF6- in CH2Cl2 [50] in order to determine by standard methods the dissociation constant KD of the ion-pairs. However, the κ - c0 (c0 = total concentration of the salt) plots were linear and we concluded that in these solutions the salt gave a BIE: ← MeCO+ + SbF6MeCOF + SbF5 →

(15)

Detailed studies showed that the concentration of ions was much smaller than c0, and therefore that of ion-pairs was negligible. I had thus been reminded of the BIE and could respond appropriately when shortly afterwards Grattan at the other end of the same laboratory found linear κ - c0 plots in his work with AlX3 in alkyl halides RX [35, 36]. This indicated that in adequately pure systems the aluminium halides ionise thus: ← AlX2+ + AlX42 AlX3 →

(16)

These systems were fully characterised in terms of the rates of the ionisations and the equilibrium constants; the BIE work has been summarised more recently [51].

4.5 Complexes II The involvement in CP of complexes between the MtXn and the monomer had been discussed by several authors. This was because even in 1952 several such complexes were known, we had found the complexing of TiCl4 with the stilbenes, AlCl3 was known to be more soluble in alkenes than in alkanes, etc. So, having devised a technique for doing freezing point phase diagrams under vacuum, I decided to investigate whether TiCl4 and isobutene form a complex. We found that they form certainly a one-to-one complex and probably a second one (2 isobutene : 1 TiCl4), but the formation of these complexes does not result in polymerisation [52, 53]. There is here an unresolved conflict with the observations by Cheradame, Sigwalt et al. on the ‘condensation polymerisation’

19

Developments in the Theory of Cationoid Polymerisations which results when various alkenes and metal halides are condensed together at low temperatures. Our second detailed study of this type of complex concerns the interaction of isobutene with AlX3 [37], to which I have referred in Section 2.3.2. The experiments are sufficiently unusual to merit description here in outline. (i) Procedure and observations: An ampoule of specially purified AlX3 (X = Cl or Br) was broken into exhaustively purified RX (EtCl or MeBr) and when solution was complete, a quantity of isobutene several times greater than that of AlX3 was admitted very slowly over 2 h. The κ fell asymptotically to a value which was much lower than the initial κ. The solution was colourless and clear. Vacuum distillation yielded only chromatographically pure solvent and isobutene; and in the vessel was left colourless crystalline AlX3 and no polymer. If more isobutene was added rapidly after the slow addition was complete, there was no polymerisation. If isobutene was added rapidly at first, a 100% yield of high polymer was obtained. (ii) Explanations: Our measurements of the self-ionisation of both AlX3 in the appropriate RX showed that [AlX2+]/[AlX3] ≈ 10-3 to 10-5. Thus when isobutene enters the solution, the probability of a molecule meeting AlX3 is much greater than that of meeting AlX2+. Hence IB.AlX3 forms and the self-ionisation equilibrium is driven to the left as shown by the fall in κ, so that there are insufficient ions to start polymerisations. If the isobutene is added rapidly, the addition of AlX2+ to the monomer is much faster than the recombination of the ions and therefore polymerisation ensues. The final κ was due to inert ions formed from AlX3 and the residual impurities. On the basis of these experiments we could explain at last what had puzzled all investigators of the polymerisation of isobutene by AlX3, namely that when a solution of AlX3 is added to one of isobutene there is a fast reaction which stops at incomplete conversion and which can be restarted by the addition of more AlX3 solution, but not by water or any other ionogenic compound. The reason is that the AlX2+ ions formed in the AlX3 solution by the self-ionisation of the AlX3 initiate a fast polymerisation which then is terminated; and the AlX3 is complexed by the excess of isobutene, and can then generate ions only very slowly. Thus the question posed at the end of my note-book entry quoted above had been answered at last. The idea that one of the partners on one side of an equilibrium reaction (say A or B) can react rapidly and irreversibly with a reagent M to give AM, whilst the participants on the other side, say Q and R (which may be the same) are also removed by reacting with M to give QM and/or RM, is new to kinetics. I have found it useful also in accounting 20

Developments in the Cationic Polymerisation of Alkenes - A Personal View (1994) quantitatively for the very low yield of carbenium ions obtained when a solution of a strong acid is added to a solution of a monomer, because strong acids in non-basic solvents also ionise by a BIE [54, 55].

4.6 Polymerisation kinetics By the time I went to Keele I realised that to make progress with the mechanism of CP one would need a vacuum reactor and that this development would require two new devices. One was a pseudo-Dewar which could be charged and operated under vacuum, the other was an all-metal vacuum valve containing no organic materials, so as to resist attack by metal halides and solvents, to replace glass taps. A research grant from the Polymer Corporation of Canada in 1953 (Keele’s first industrial grant) enabled me to take on a research student, and I was enormously fortunate in finding R. H. Biddulph with whose help I could solve both the above-mentioned problems and many more, including the construction of a high-speed temperature recorder (6). With the BiddulphPlesch adiabatic reaction calorimeter and its successors we did the first kinetic studies (17), [56-58] and the last [59-62]. The first kinetic work was concerned with a comparative study of isobutene and styrene, both in CH2Cl2 with TiCl4 + H2O over the range +20 to –90 °C, and a study of isobutene with AlCl3. The first useful lesson was that with the same initiator the kinetic behaviour of these two monomers was different in every respect. The behaviour of styrene indicated the coexistence of two initiating mechanisms, one of which involved water, and another (independent of water) which became dominant at the lowest temperatures. There was no evidence for or against the propagators being ionic. It now seems likely that the very complicated phenomenology of this system is due to it being (at least) di-eidic. For isobutene, water was found to be essential; the dependence of the rate on the temperature showed a minimum, and that of the DP showed a marked inflection. These findings and related, hitherto unexplained, results of others with different initiators and solvents could be explained in detail by the theory that at higher temperatures the main propagating species are paired cations and that as the temperature is reduced, unpaired cations become progressively dominant. In CP this was a novelty. In response to a new phenomenon, we coined the –eidic terminology: enieidic for several forms of co-existing propagators, monoeidic if there is only one, etc. One of the few examples in the older literature of a polymerisation system which is clearly monoeidic is provided by Norrish and Russell’s results for the polymerisation of isobutene by SnCl4 in EtCl at –78 °C. Examining these remarkably self-consistent results from the point of view of ionic equilibria, I found clear evidence that the propagation is by unpaired ions [p.181-182 [44]].

21

Developments in the Theory of Cationoid Polymerisations My last kinetic work was aimed at determining the kp+ of a range of monomers by what I believed to be a reliable method. For kinetic and electrochemical reasons I chose nitrobenzene as the solvent, and I chose carbenium and carboxonium salts as initiators so as to achieve a clean and fast initiation. The rate-constants were adequately reproducible, but it turned out that they were not the kp+. The project was flawed because I had been unaware of the reversible cationation of the solvent by the carbenium ions. A careful analysis of the kinetic, analytical and thermochemical results gave a new insight into the reaction mechanisms in nitrobenzene, but the main objective had eluded me.

4.7 Pseudo-cationic polymerisation Probably the most controversial amongst my chemical innovations is the idea of pseudocationic polymerisation developed with Gandini [63, 67] and with Dunn et al., [68], and it was summarised [69] and extended by me to explain living CP [70]. It arose as follows: Protonic acids, HA, had been used since the 18th Century to polymerise alkenes, but it was D. C. Pepper who took the logical step of using the strongest acid available in the early 1960s, namely HClO4. The kinetics of the polymerisation of styrene by this acid at around room temperature were apparently simple and seemed interpretable on the basis that the concentration of growing chains was equal to that of the acid. With Gandini we repeated this work, and we found Pepper’s interpretation incompatible with our kinetic, spectroscopic, and conductimetric measurements. Pepper’s own latest views on these reactions are presented at this Symposium. We developed a theory according to which any initiator whose anionic moiety can form an ester with the monomer may under appropriate conditions produce two types of chain carriers. One of these is the conventional carbenium ion, the other is an ester whose reactivity may need to be modified, that is enhanced (positive modifier) or reduced (negative modifier) [70] according to the circumstances. In many systems the carbenium ions and the modified esters co-exist, but they are generally not in equilibrium, their propagation and chain-breaking constants are different, and therefore they produce a product containing polymers with two different molecular weight distributions. The theory of pseudo-cationic polymerisations is closely related to established organic-chemical theory, especially the mechanism of the addition of esters to alkenes, and few, if any, well-established facts are in conflict with it. Therefore the reasons for the vociferous opposition is obscure. It would be inappropriate to continue the discussion here, when what is needed is more, and more rigorous, experimental evidence. The theory has proved useful because by means of it I could formulate a simple, self-consistent interpretation of a new range of phenomena, namely the many types of living polymerisation systems which have appeared in the recent past [70], and it will have done its job when it eventually generates a better theory.

22

Developments in the Cationic Polymerisation of Alkenes - A Personal View (1994)

5 Theoretical work after 1985 The theoretical work on pseudo-cationic polymerisation, although done after my retirement, arose from the earlier experimental studies; by contrast, the two pieces of work forming this last section were started after my retirement.

5.1 The rate-constants of the cationic polymerisation of alkenes What for brevity I will refer to as the kp+ study was undertaken at the request of an Editor, and the more gladly because I had previously published relatively brief and rather simplistic pieces on this subject and had wanted for a long time to review it thoroughly and critically. The resulting work [55] involved me scrutinising the original papers and applying the critical apparatus which I had developed out of my own experience to the experimental methods and to the authors’ interpretations of their results. As far as it was possible, I examined all the original results, replotted them in different ways when necessary, and thence drew my own conclusions. The great majority of the alleged kp+ proved to lack verisimilitude, and the most common reasons were lack of certainty about the nature and concentration of the chain-carriers and inadequate establishment of the kinetics. The total yield of a mere 17 values which I consider reliable should be a warning about just how difficult this subject has proved to be; it must be said that the numerous rejected results include those from my own group but, as mentioned above, their rejection resulted from a useful new insight into the mechanism of cationoid reactions in nitrobenzene [62].

5.2 New views on the cationic polymerisations induced by ionising radiations During my work on the kp+ review I also examined critically the many papers on the kinetics of polymerisations of alkenes (in the strict sense) and of alkyl vinyl ethers. Several insights resulted, including the realisation that the polymerisations of bulk monomers must be unimolecular reactions, that these are isomerisations of a complex between the growing carbenium ion and the monomer, that the polymerisation mechanism changes as the monomer is diluted, and that the nature of this change depends on the relative polarity of the monomer and the solvent. By means of these ideas I could account for the numerous and diverse observations and calculate some new rate-constants [3, 71]. This was one of the largest and most original theoretical researches I had undertaken since I succeeded in making sense of the discontinuous variations of DP with the concentrations of reagents which had puzzled researchers for many years [72].

23

Developments in the Theory of Cationoid Polymerisations

6 Conclusion The reviewing of this part of my work has been partly melancholy from the realisation of missed opportunities, partly satisfactory, and all of it stimulating because it revealed so much unfinished business. Maybe some of my audience and readers will feel impelled now actually to read some of my papers, and I hope that they will derive enjoyment and profit from them, for they have all been written with very great care to achieve clarity and precision. Further, unlike some of my colleagues, I have usually tried to relate my findings and ideas to those of other workers, because I hoped to contribute in this way to a discussion and thus to advance our understanding of the subject; and because presenting results and ideas without setting them in context and without reference to ‘prior art’ is not very helpful.

Acknowledgement This article is what in the fine arts would be called a ‘retrospective exhibition’. In order to make it more useful, I obtained from the Editor-in-Chief permission to quote in the references the full titles of my papers, and for this I am most grateful.

References 1.

A. G. Evans, D. Holden, P. H. Plesch, M. Polanyi, H. A. Skinner, M. Weinberger, Friedel-Crafts Catalysts and Polymerisation, Nature (London), 1946, 157, 102.

2.

P. H. Plesch, The Low-temperature Polymerisation of Isobutene by Friedel-Crafts Catalysts, Nature (London), 1947, p.160, 868.

3.

P. H. Plesch, New Views on the Cationic Polymerisations initiated by Ionising Radiations, (Developments in the Theory of Cationic Polymerisation, Part XI), Phil. Trans. R. Soc. Lond., 1993, A342, 469. - Part I of this series is P. H. Plesch, Developments in the Theory of Cationic Polymerisation, J. Applied Chem., 1951, 1, 269.

4.

O. Vogl, J. Macromol. Sci. 1992, A29, 1085.

5.

P. H. Plesch, M. Polanyi, H. A. Skinner, The Low-temperature Polymerisation of Isobutene by Friedel-Crafts Catalysts, J. Chem. Soc., 1947, 257.

6.

R. H. Biddulph, P. H. Plesch, A New Versatile Apparatus for Measuring the Rates of Fast Liquid-Phase Reactions, Chem. and Ind., 1959, 1482.

24

Developments in the Cationic Polymerisation of Alkenes - A Personal View (1994) 7.

S. D. Pask, P. H. Plesch, An Improved Vacuum Reaction Calorimeter, Chem. and Ind. (Lond.), 1981, 331.

8.

A. G. Evans, G. W. Meadows, M. Polanyi, Nature (London), 1946, 158, 94; 1947, 160, 869.

9.

A. G. Evans, G. W. Meadows, J. Polym. Sci., 1949, 4, 359.

10. A. G. Evans, G. W. Meadows, Trans. Farad. Soc. 1950, 4-6, 327. 11. F. Fairbrother, W. C. Frith, J. Chem. Soc., 195, 3051. 12. R. G. W. Norrish, K. E. Russell, Trans. Farad. Soc., 1952, 48, 91. 13. J. M. Moulis, J. Collomb, A. Gandini, H. Cheradame, Polymer Bull., 1980, 3, 197. 14. A. Gandini, A. Martinez, Makromol. Chem., Macromol. Symp., 1988, 13/14, 211. 15. P. H. Plesch, The Low-temperature Polymerisation of Isobutene, Pt. II, J. Chem. Soc., 1950, 543. 16. L. J. Klinkenberg, J. A. A. Ketelaar, Rec. Trav. Chim., 1935, 54, 959. 17. J. H. Beard, P. H. Plesch, P. P. Rutherford, The Low-temperature Polymerisation of Isobutene, Part V, Polymerisation by Aluminium Trichloride in Methylene Dichloride, J. Chem. Soc., 1964, 2566. 18. C. C. Price, M. Meister, J. Am. Chem. Soc., 1939, 61, 1595. 19. D. C. Downing, G. F. Wright, J. Am. Chem. Soc., 1946, 68, 141. 20. D. S. Brackman, P. H. Plesch, Some Reactions of the Stilbenes in the Presence of Metal Halides, J. Chem. Soc., 1953, 1289. 21. D. S. Brackman, P. H. Plesch, The Cationic Oligomerisation of the Stilbenes, J. Chem. Soc., 1958, 3563. 22. F. S. Dainton, R. H. Tomlinson, J. Chem. Soc., 1953, 151. 23. P. H. Plesch, The Polymerisation of Styrene by Titanic Chloride, Parts I, II, III, J. Chem. Soc., 1953, 1653, 1659, 1662. 24. P. H. Plesch, Ed., Cationic Polymerisation and Related Complexes, Heffer and Son, Cambridge, 1953.

25

Developments in the Theory of Cationoid Polymerisations 25. J. P. Kennedy, R. M. Thomas, Makromol. Chem., 1962, 53, 28. 26. P. L. Magagnini, P. H. Plesch, J. P. Kennedy, Studies on the Cationic Polymerisation of o-Methylstyrene, Europ. Polym. J., 1971, 7, 1161. 27. J. P. Kennedy, P. L. Magagnini, P. H. Plesch, Criticisms of Claims in the Field of Isomerisation Polymerisation, Pt. I. Polymerisation of p-Methylstyrene, J. Polymer Sci. A-1, 1971, 9, 1635. 28. J. P. Kennedy, P. L. Magagnini, P. H. Plesch, Claims in the Field of Isomerisation Polymerisation, Pt. II. Polymerisation of o-Isopropylstyrene, J. Polymer Sci., A-1, 1971, 9, 1647. 29. W. H. Hunter, R. V. Yohé, J. Am. Chem. Soc., 1933, 55, 1248. 30. S. S. Medvedev, A. R. Gantmakher, Doklady Akad. Nauk S.S.S.R., 1956, 106, 1031. 31. R. O. Colclough, F. S. Dainton, Trans. Faraday Soc., 1958, 54, 886, 894, 901. 32. W. R. Longworth, P. H. Plesch, P. P. Rutherford, Co-catalysis by Alkyl Halides in Cationic Polymerisation, Proc. Chem. Soc., 1960, 68. 33. W. R. Longworth, P. H. Plesch, P. P. Rutherford, The Mechanism of Cationic Polymerisations Catalysed by Metal Halides, Doklady Akad. Nauk U.S.S.R., 1959, 12-7, 97. 34. P. H. Plesch, Friedel-Crafts Polymerisation, Research, 1949, 2, 267. 35. D. W. Grattan, P. H. Plesch, Binary Ionogenic Equilibria, J. Electroanal. Chem., 1979, 103, 81. 36. D. W. Grattan, P. H. Plesch, Ionisation of Aluminium Halides in Alkyl Halides, J. Chem. Soc. Dalton Trans., 1977, 1734. 37. D. W. Grattan, P. H. Plesch, The Initiation of Polymerisations by Aluminium Halides, Makromol. Chem., 1980, 181, 751. 38. A. Gandini, P. H. Plesch, Spectroscopic Studies on Carbonium Ions Derived from Aromatic Olefins, Pt. I. Styrene and related Olefins, J. Chem. Soc., 1965, 4765. 39. V. Bertoli, P. H. Plesch, Origin of the Alleged, and Position of the Real, U.V. Absorption of the 1,3-Diphenyl-n-butyl Cation, Chem. Comm., 1966, 625.

26

Developments in the Cationic Polymerisation of Alkenes - A Personal View (1994) 40. V. Bertoli, P. H. Plesch, Spectroscopic Studies on Carbonium Ions derived from Aromatic Olefins, Part III, Ions derived from Styrene and Cognate Compounds, J. Chem. Soc. (B), 1968, 1500. 41. V. Bertoli, P. H. Plesch, The U.V. and P.M.R. Spectra of Ten Related Diaryl Carbonium Ions, Spectrochimica Acta, 1969, 25A, 447. 42. J. Pàc, P. H. Plesch, The Polymerisation of N-Vinylcarbazole by Electron Acceptors, Part I, Kinetics, Equilibria, and Structure of Oligomers; Part II, Discussion, Polymer, 1967, 237. 43. D. C. Pepper, (Ed.), Proc. Roy. Dublin Soc., 1950, 25NS, 131. 44. P. H. Plesch, Ed., The Chemistry of Cationic Polymerisation, Pergamon Press, 1963. 45. A.C.S. Symposium on Catalysis in Hydrocarbon Chemistry, No. 24, Sept. 1952. 46. D. C. Pepper, Trans. Faraday Soc., 1949, 45, 404. 47. W. R. Longworth, P. H. Plesch, The Interaction of Organic Chlorides with Metal Chlorides, Pt. I. Freezing-point Phase Diagrams of Titanium Tetrachloride with some Alkyl Chlorides, J. Chem. Soc., 1958, 451. 48. W. R. Longworth, P. H. Plesch, The Interaction of Organic Chlorides with Metal Chlorides, Pt. II. Electrochemical Studies of Titanium Tetrachloride in some Alkyl Chlorides, J. Chem. Soc., 1959, 1887. 49. J. H. Beard, P. H. Plesch, The Ionic Dissociation of Methyltriethylammonium Iodide in Methylene Dichloride between 0° and –95°, J. Chem. Soc., 1964, 4879. 50. O. Nuyken, P. H. Plesch, Binary Ionogenic Equilibria exemplified by Acetyl Hexafluoroantimonate and their Implications for Cationic Polymerisation, Chem. and Ind., 1973, 379. - See also F. R. Jones, P. H. Plesch, The Association Constants of Triethyloxonium Salts and their Solvation by Diethyl Ether, Chem. Comm., 1970, 1018. 51. P. H. Plesch, Binary Ionogenic Equilibria, Education in Chemistry, 1990, 27, 75. 52. W. R. Longworth, P. H. Plesch, P. P. Rutherford, Complex Formation between Isobutene and Titanium Tetrachloride, International Conference on Coordination Chemistry, 1959, Chem. Soc. Special Publ., No. 13, 115.

27

Developments in the Theory of Cationoid Polymerisations 53. P. H. Plesch, Discussion contribution to International Colloquium on Synthetic Polymer Chemistry, J. Macromol. Sci., 1972, A6, 979. 54. Kabir-ud-Din, P. H. Plesch, Polarography of some Protonic Acids in Methylene Chloride, J. Electroanal. Chem., 1978, 93, 29. 55. P. H. Plesch, The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes, Progress in Reaction Kinetics, 1993, 18, 1. 56. W. R. Longworth, C. J. Panton, P. H. Plesch, The Polymerisation of Styrene by Titanium Tetrachloride, Part IV. Kinetics of Polymerisation in Methylene Dichloride, J. Chem. Soc., 1965, 5579. 57. R. H. Biddulph, P. H. Plesch, The Low-temperature Polymeriation of Isobutene, Pt. IV, Exploratory Experiments, J. Chem. Soc., 1960, 3913. 58. R. H. Biddulph, P. H. Plesch, P. P. Rutherford, The Low-temperature Polymerisation of Isobutene, Part VI. Polymerisation by Titanium Tetrachloride and Water in Methylene Dichloride, J. Chem. Soc., 1965, 275. - See also C. J. Panton, P. H. Plesch, P. P. Rutherford, The Fractionation of Polyisobutene by Gradient Elution, J. Chem. Soc., 1964, 2586; and R. R. Biddulph, W. R. Longworth, J. Penfold, P. H. Plesch, P. P. Rutherford, The Heat of Polymerisation of Isobutene and of Styrene, Polymer, 1960, 1, 521. 59. S. D. Pask, P. H. Plesch, S. B. Kingston, The Polymerisation of Acenaphthylene by Carbocation Salts in Nitrobenzene, Makromol. Chem., 1981, 182, 3031. 60. G. E. Holdcroft, P. H. Plesch. The Propagation Rate-Constants for the Cationic Polymerisation of Acenaphthylene and Styrene in Nitrobenzene, Makromol Chem., 1984, 185, 27. 61. P. H. Plesch, S. H. Shamlian, The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes Part III. Indene, two Vinyl Ethers, and General Discussion, Europ. Polym. J., 1990, 26, 1113. 62. P. H. Plesch, The Propagation Rate-Constants of the Cationic Polymerisation of some Alkenes in Nitrobenzene - Part IV. Not the real kp+, (Developments in the Theory of Cationic Polymerisation, Part XII), European Polym. J., 1993, 29, 121. 63. A. Gandini, P. H. Plesch, The Interaction between Perchloric Acid and Styrene in Methylene Dichloride, Proc. Chem. Soc., 1964, 240.

28

Developments in the Cationic Polymerisation of Alkenes - A Personal View (1994) 64. A. Gandini, P. H. Plesch, Cationic and Pseudocationic Polymerisation of Aromatic Olefins. Part I. Kinetic and Mechanism of the Pseudocationic Polymerisation of Styrene by Perchloric Acid, J. Chem. Soc., 1965, 4826. 65. A. Gandini, P. H. Plesch, Pseudocationic and True Cationic Polymerisation of Styrene by Various Catalysts, J. Polym. Sci., B, 1965, 3, 127. 66. A. Gandini, P. H. Plesch, New Views on Cationic Polymerisation, Society of Chemical Industry Monograph No. 20, London, 1966, 107. 67. A. Gandini, P. H. Plesch, Cationic and Pseudocationic Polymerisation of Aromatic Olefins Part II, The Reactions following Polymerisation of Styrene by Perchloric Acid, European Polymer J., 1968, 11, 55. 68. D. J. Dunn, E. Mathias, P. H. Plesch, Cationic and Pseudocationic Polymerisation of Aromatic Olefins. Part III. A Re-investigation of the Polymerisation of Styrene by Perchloric Acid, European Polymer J., 1976, 12, 1. 69. P. H. Plesch, Pseudo-Cationic Polymerisation after 24 years, Makromol. Chem., Macromol. Symp., 1988, 13/14, 375 and 393. 70. P. H. Plesch, Cationoid Living Polymerisations, (Part X), Makromol. Chem., Macromol. Symp., 1992, 60, 11. 71. P. H. Plesch, A Theory of the Cationic Polymerisations Initiated by Ionising Radiations, (Developments in the Theory of Cationic Polymerisations, Part XI, Phil. Trans. Roy. Soc. Lond. 1993, A342, 469. 72. P. H. Plesch, Developments in the Theory of Cationic Polymerisation, Pt. IV, A General Theory Explaining Discontinuous Variations of the Degree of Polymerisation with the Concentration of the Reagents, J. Chem. Soc., 1964, 104.

29

Developments in the Theory of Cationoid Polymerisations

30

3

Reviews

31

Developments in the Theory of Cationoid Polymerisations

32

3.1

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) P. H. Plesch

This paper was first published in Chemistry of Cationic Polymerisation, Ed., P. H. Plesch, Pergamon, London, 1963, Chapter 4.

Prologue Since this writer has always regarded the reviewing of a subject to be an occasion for criticism and for explanatory theorising, this review contains much new thinking. Therefore it seemed pointless to reproduce here only those parts of the chapter which contain major innovations. However, the one section to which he wants to draw particular attention is his discussion of Norrish and Russell’s work of the late 1940s to early 1950s. The quality of that research has never been surpassed and it is deeply regrettable that there is no more of it. Because it is so self-consistent, this writer could extract from it the unequivocal deduction that in their system (isobutene + SnCl4 in EtCl at –78 ºC) the preponderant propagating species must be the unpaired cations. As will be seen, this has proved to be extremely valuable. Another innovation is the reinterpretation of the significance of the various chain-breaking constant ratios which several workers had determined by means of Mayo plots. In retrospect one notes that at least some of the mysteries of the polymerisation of isobutene noted here have been explained by the subsequent researches. The Appendix to this chapter, which is not reproduced here, is a slightly abridged version of Section 4.10 in this book.

1 Introduction The oligomerisation of isobutene, with and without isomerisation or fragmentation, and its polymerisation and co-polymerisation are industrial processes of considerable

33

Developments in the Theory of Cationoid Polymerisations importance. Good surveys of the polymerisation, especially its technical aspects, have been given by Schildknecht [1, 2]. A very detailed account, also from the technological point of view, of the oligomerisations, polymerisations, co-polymerisations and the properties of the polymers is given by Gueterbock [3]; this, probably the most complete account which has been published, contains useful tabulations of most of the important patents concerning solvents, catalysts, promoters, etc. A rather uncritical, largely technological, review has been compiled by Eidus and Nefedov [4]; the coverage of the literature in this work is, however, very inadequate. In this chapter we will be concerned mainly with the formation of high polymers of isobutene, and with the fundamental studies aimed at the elucidation of this reaction. There is no doubt that many useful hints of fundamental interest are to be found in the patent literature, but in most cases the purity of the reagents and the reaction conditions are so ill defined, that no conclusions can be drawn from findings reported in patents. The ratio of scientifically valuable to dubious information in patents is so small that detailed survey of them, in the hope of discovering sound information, should be a most unrewarding occupation. This is more or less true of all chemical patents, but especially so in this particular field where minute traces of impurities can effect catastrophic changes in the reaction pattern. For this reason attention has been confined to work published in the scientific literature.

2 The peculiarity of isobutene Isobutene is one of the very small number of aliphatic hydrocarbons which form linear high polymers by cationic catalysis (see Section 5). The reason for this is that only in these few among the lower aliphatic olefins is there found the right balance of those factors which determine the path of a cationic polymerisation. For the formation of linear high polymers it is necessary that the propagation reaction should be much faster than all alternative reactions of the growing end of the chain; and for any appreciable numbers of chains to be formed at all, the initiation must be fast.* By the Polanyi principle the activation energy of the initiation reaction, Ei, will be related antibatically to the enthalpy change of the initiation reaction, which can be represented by equation 1: +

AH + R1R 2 C = CR 3 R 4 → HR1R 2 C – C R 3 R 4 + A -

(1)

* The energetic aspects of the ‘peculiarity’ of isobutene, and of the individual steps in cationic polymerisations have been discussed in detail by Plesch [4a]. A discussion of the energetics of the closely related ionic isomerisation and cracking reactions has been given by Greensfelder [4b]; see also Chapter 1.

34

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) The variation in the ΔH of this reaction for a series of olefins is essentially governed by the differences in the proton affinities of the olefins, and these are steeply graded according to the degree of substitution and the nature of the substituents in the vicinity of the double bond (Table 1). Common experience indicates that an olefin must have a proton affinity in excess of that of propene to give rapid initiation with the common catalytic systems. This however is not sufficient: for the growth of long linear polymers it is also necessary that neither the ion formed by addition of a proton to the monomer, nor the subsequently formed oligomeric ions, be capable of other reactions having rates which are comparable to that of the propagation. The importance of this point is shown by the behaviour of butene-1 which gives branched oligomers with most cationic catalysts (see Chapter 5). Not only can the monomeric ion undergo an exo-energetic rearrangement:

Table 1 Proton affinities X(g) + H+(g) → XH+(g), ΔH°298 kcal/mole X

XH+

—Δ ΔH°298

C2H4

C2H5+

153*

C3H6

n-C3H7+

165

C3H6

i-C3H7+

181

C2H5CH:CH2

n-C4H9+

163

C2H5CH:CH2

i-C4H9+

189

s-C4H9+

187

(CH3)2C:CH2

i-C4H9+

166

(CH3)2C:CH2

t-C4H9+

196

CH3•C3H4+

(185)

cis- and transCH3.CH:CH.CH3

CH2:CH•CH:CH2

) )

+

C6H5•CH:CH2

C6H5•CH•CH3

(180)

(C6H5)2C:CH2

CH3•C(C6H5)2+

> 200

Notes: The uncertainty in the proton affinities of the alkylenes is probably ± 3 kcal/mole, in those of butadiene and styrene rather greater The proton affinities of multiply alkyl substituted ethylenes probably all lie within ± 3 kcal/mole of that of isobutene [4c]

35

Developments in the Theory of Cationoid Polymerisations +

CH 3CH 2 C HCH 3 → (CH 3 )3 C +

(2)

but if the simple dimer were formed, it could be attacked by a monomeric or oligomeric secondary ion and, by transfer of a hydride ion, give an oligomer and a tertiary ion which would then produce a branched structure:

+ CH3CHCHCH3 + CH3CH2CHCH3 R

CH2CH:CHCH3 + CH3CHCH2CH3 + CH3CH2CCH3 R

(3)

CH2CH:CHCH3

This type of transfer cannot happen with the oligomers of isobutene: The reaction 4 +

–CH 2 C(CH 3 )2 + –CH 2 C(CH 3 )2 CH 2 C(CH 3 )2 – → +

–CH 2 CH(CH 3 )2 + –CH 2 C(CH 3 )2 C HC(CH 3 )2

(4)

would be endothermic and, moreover, the —CH2 -groups in the polymer are shielded by the crowded methyl groups. It is this steric effect which also prevents the polymerisation of tri- and tetramethyl ethylene and also of the dimers of isobutene, 2,4,4-trimethyl pentene-1 and -2. The reasons for the peculiar reactivity of isobutene among the lower aliphatic olefins can be summarised thus: ethylene is insufficiently basic; ethylene, propene and the n-butenes offer reaction paths which can compete effectively with propagation; and most of the more heavily substituted ethylenes are sterically inhibited. (See also Appendix to Chapter 5.)

3 The structure of polyisobutene i. The polymer chain Polyisobutene has a regular head-to-tail structure, and the crowding of the methyl groups is so great that the molecule can only be built from conventional atomic models with great

36

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) difficulty. Such a model shows that the methyl groups are staggered along the chain so that a helical structure results [5]. One consequence of this crowding is that the heat of polymerisation (–13.0 kcal/mole) [6] is much smaller than the theoretical value calculated for an unstrained structure [5]. For this reason the polymerisation of isobutene has a relatively low ceiling temperature. At one time it was thought that the steep decrease of the DP of polyisobutenes, as the temperature of their formation approaches 0° from below, was due to this effect. This is now known to be wrong - the effect is due to kinetic, not thermodynamic causes. If one assumes a value of ΔS°ss = –30 e.u. at 25° (the same as for methylmethacrylate [7] and takes ΔH°ss = –13 kcal/mole [6], Tc for a 1 molar solution of isobutene is found to be 160°. This is probably rather too high because the extrapolation of various plots of log DP against 1/T, the slope of which depends upon the conditions of the polymerisation, indicates upper limits for Tc of the order of 140° (see Section 5, iii, (d), p.183).

ii. The end-groups The nature and proportions of different kinds of end-groups in polyisobutenes depend upon the catalytic system and the solvent used in their preparation. When oligoisobutenes are formed from gaseous isobutene at ambient temperature by BF3 and H2O the initial group is CH3, formed by addition of a proton to the monomer [8]. The predominant terminal groups are double bonds [8] formed by transfer reactions involving elimination of a proton from the growing carbonium ion:

CH3 –CH2 • C+ CH3 –H+

–H+ (a)

–CH = C(CH3)2

(b)

CH3

(5)

–CH2 • C = CH2

There are also some hydroxyl groups formed by combination of the carbonium ion with the OH- from the anion BF3OH- in a termination reaction: +

–CH 2 ⋅ C(CH 3 )2 BF3OH − → –CH 2 ⋅ C(CH 3 )2 OH + BF3

(6)

37

Developments in the Theory of Cationoid Polymerisations When isobutene is polymerised in an inert solvent such as n-hexane by a metal halide with water as co-catalyst, the same end-groups are formed [9, 10] However, with other solvents, especially alkyl halides, transfer reactions may also introduce end-groups derived from the solvent [11, 12], for example:

CH3 –CH2 • C+

CH3 C4H8 RCl

CH3

–CH2 • C • Cl + R • CH2 • C+

CH3

(7)

CH3

CH3

When a transfer agent is added deliberately to the reaction mixture, this turns up as an end-group in the polymer [13], for example:

CH3 –CH2 • C+

CH3 C4H8 C6H5 • O • CH3

CH3

–CH2 • C • C6H4 • O • CH3 + (CH3)3C+ (8)

CH3

(See also Section 5, iii, (d) below.) With co-catalysts other than water, a part of the co-catalyst may also form an end-group by a termination reaction. When trichloroacetic acid was used as co-catalyst with titanium tetrachloride, trichloroacetate end-groups were found on the polyisobutenes [9, 10]. The proportions of the different end-groups depend upon the relative rates of the various chain-breaking reactions by which they are formed. These are determined by the temperature, the solvent, the nature of the catalyst and co-catalyst, and the concentration of the chain-breaking agents. These features will be discussed below. The proportions of the different kinds of initial groups depend on the nature and rate of the different transfer reactions by which they are formed; and the proportion of initial groups derived from the catalyst will depend on the ratio of the rate of initiation to the sum of the rates of the transfer reactions. Finally, although the main chain of the polyisobutene molecule is very resistant to chemical attack [14], by virtue of its chemical structure and configuration, the end-groups are readily attacked by atmospheric oxidation.

38

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) This is obvious from the prominent carbonyl bands in the IR spectra of polyisobutenes which have been heated in air [15]. This indicates how important it is to handle carefully polymers which are to be used for end-group studies.

4 Catalytic systems i. Radicals Attempts to polymerise isobutene by free radical catalysis have all failed [16, 17] and copolymerisation experiments show that the t-butyl radical has no tendency to add to isobutene. The reasons for these facts are not at all obvious. Evidently, they cannot be thermodynamic and therefore they must be kinetic. One factor is probably that the steric resistance to the formation of polymer brings with it a high activation energy [17], and that the abstraction by a radical of a hydrogen atom from isobutene, to give the methallyl radical, has a much smaller activation energy. This reaction will also be accelerated statistically by the presence of six equivalent hydrogen atoms. The fact that replacement of one methyl group by carboxyl or carboxylate changes the situation drastically, in that methacrylic acid and its esters are readily polymerised by radicals, may be due to the introduction of a high degree of polarity, which reduces the activation energy for the reaction of a radical with the monomer.

ii. Anionic catalysts Isobutene is unaffected by metallic sodium [18], by sodamide in liquid ammonia [19] and by naphthyl sodium in tetrahydrofuran [20]. This means either that anions or radical anions are not formed from isobutene, or that, if they are formed, they do not react with monomer.

iii. Cationic catalysts Isobutene is renowned for the ease with which it reacts and, under suitable conditions, polymerises in the presence of reactive cations or of compounds from which such cations can be formed. In this context the word ‘reactive’ designates those cations which can react with isobutene to give a tertiary carbonium ion, and excludes those, such as R4N+ and R4B+ which cannot. The inertness of isobutene to radicals and anions, and its ready reaction with cations have produced a conviction that the activity of every catalyst which will polymerise 39

Developments in the Theory of Cationoid Polymerisations isobutene must be based on the presence or the generation of a reactive cation. So far this belief has served well enough, and the game of ‘chercher le cation’ has been fruitful in the interpretation of polymerisations induced by radiations and by some rather enigmatic catalysts. The use of isobutene as a discriminant to diagnose modes of catalytic activity is discussed in Chapter 3.

(a) Conventional acids We use the term ‘conventional acid’ to designate stable acids such as the hydrogen halides and the common mineral and organic acids, in order to distinguish them from the complex acids such as the hydrates of metal halides and the adducts formed from, for example, trichloroacetic acid and titanium tetrachloride. The nature of the products formed from isobutene in the presence of conventional acids depends on the concentration of the acid, the temperature and the solvent. The products are always of relatively low molecular weight, they may contain fragments of catalyst, and, due to methyl shifts, branching and fragmentation, their structure may not be that of a simple linear oligomer formed by addition of monomers one to another (conjunct polymerisation [21]). There is no record of high polymers having been formed from isobutene under the influence of a conventional acid only, and for this reason these reactions will not be discussed here in detail.

(b) Complex acids Isobutene is not polymerised by metal halides unless an ionogenic substance, the cocatalyst, is present [9, 18, 22-23]. The patent literature contains a great many combinations of a metal halide and a co-catalyst (often called promoter, especially in American patents), most of which are substances which can combine with the metal halide to form a protonic acid. Almost all the co-catalysts which have been studied in any detail belong to this class (see Table 2). The discovery of the phenomenon of co-catalysis brought the reactions catalysed (allegedly) by metal halides alone into the same category as those catalysed by conventional acids, so that for both types of catalysts the initiation can be represented by the equation

AH + CH 2 = C(CH 3 )2 → (CH 3 )3 C + A −

(9)

where A- may be either the anion of a conventional acid, such as HSO4-, or that of a complex acid, such as BF3OH-.

40

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) A ubiquitous co-catalyst is water. This can be effective in extremely small quantities, as was first shown by Evans and Meadows [18] for the polymerisation of isobutene by boron fluoride at low temperatures, although they could give no quantitative estimate of the amount of water required to co-catalyse this reaction. Later [11, 13] it was shown that in methylene dichloride solution at temperatures below about –60° a few micromoles of water are sufficient to polymerise completely some decimoles of isobutene in the presence of millimolar quantities of titanium tetrachloride. With stannic chloride at –78° the maximum reaction rate is obtained with quantities of water equivalent to that of stannic chloride [31]. As far as aluminium chloride is concerned, there is no rigorous proof that it does require a co-catalyst in order to polymerise isobutene. However, the need for a co-catalyst in isomerisations and alkylations catalysed by aluminium bromide (which is more ‘active’ than the chloride) has been proved [34-37], so that there is little doubt that even the polymerisations carried out by Kennedy and Thomas with aluminium chloride (see Section 5, iii, (a)) under fairly rigorous conditions depended critically on the presence of a co-catalyst - though whether this was water, or hydrogen chloride, or some other substance, cannot be decided at present.

Table 2a Summary of studies on the polymerisation of isobutene at low temperatures Aluminium chloride Temperature

‘Additive’

Solvent

References

‘alkyl halide’

43

–78

CH3Cl

53, 58, 61

–30 to –125

C2H5Cl

52

–78

C2H5Cl + CS2

56

–78

C2H5Cl + C2H6

63

–20° to –90°

–78

C2H5OH

C2H5Cl + C6H6

69

–78

C2H5OH

C2H5Cl + C6H14

69

–78

Various

C2H5Cl

63-69

–35 to –120

C2H3Cl

56

–78

CH2Cl2

56

C3H8, C5H12

52, 54, 60

–35 to –180

(a)

In all the studies recorded in this table the identity of the co-catalyst is doubtful (a) Alkyl halide was introduced as solvent for the catalyst

41

Developments in the Theory of Cationoid Polymerisations

Table 2b Summary of studies on the polymerisation of isobutene at low temperatures Titanium tetrachloride Temperature

Co-catalyst

*–50° to –80° –20 to –78

‘Additive’

Solvent

References

H2O

n-C6H14

9, 22, 28

?

n-C6H14

79

n-C6H14

9, 71

–80

H2O

*–75

CCl3CO2H

n-C6H14

9

–20 to –78

CCl3CO2H

n-C6H14

79

–60 to –80

CF3CO2H

n-C6H14

77

–38 to –103

?

C2H5Br

77

–30 to –112

?

C2H5Cl

77

–75

CF3CO2H

C2H5Cl

77

–78

?

C2H5Cl

65

–20 to –78

?

CHCl3

79

–20 to –78

CCl3CO2H

CHCl3

79

+ 5 to –70

H2O

i-C3H7Cl

33

+ 5 to –30

H2O

(CH2Cl)2

33

+ 5 to –90

H2O

CH3•CHCl2

33

*+ 18 to –95

H2O

CH2Cl2

32, 33, 79, 80

CO2

77

–50

i-C3H7Cl?

(a)

E t 2O

i-C3H7Cl

* denotes studies which include measurements of reaction rate (a) This work includes a study of various additives

Fairbrother and Frith [38] found that a mixture of niobium and tantalum pentafluorides would polymerise isobutene in hexane solution at –78° only in the presence of a cocatalyst, such as trichloroacetic acid.

42

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963)

Table 2c Summary of studies on the polymerisation of isobutene at low temperatures Miscellaneous catalysts Temperature

Catalyst

Co-catalyst

Solvent

References

50°

AlBr3

C2H5Br(?)

C O2

77

* 63 to 96

SnCl4

H2O (a)

C2H5Cl

30, 74, 76

–20 to –78

SnCl4

CCl3CO2H

n-C6H14

79

-20 to –78

SnCl4

CCl3CO2H

CHCl3

79

–20 to –78

SnCl4

CCl3CO2H

CH2Cl2

79

–65

BF3

? (a)

n-C6H14

49

–80

NbF5 + TaF5

CCl3CO2H

n-C6H14

38

n-C6H14

41, 42

* 0 to –30

Wichterle’s catalyst

For significance of * see Table 3.2b (a) See (a) Table 3.2b

Feeney, Holliday, and Marsden reported that when diboron tetrachloride and isobutene were mixed in a molar ratio of approximately 1:2, without solvent at –78°, the isobutene was polymerised to a rubbery polymer. It is likely that adventitious water, or a reaction product of water and the B2Cl4, was the co-catalyst in this reaction [39].

(c) Miscellaneous catalysts The initiation of polymerisation of isobutene by high energy radiation - which is not, strictly, a catalyst, - is discussed exhaustively in Chapter 17. The activity of the conventional and complex acids considered above depends on the transfer of a proton from the acid to the monomer. There are, however, some aprotonic catalysts the activity of which depends on the transfer of a positive organic ion from the catalyst to the monomer. Among aprotonic catalysts functioning in solution, the salt-like catalysts, such as acetyl fluoroborate, have received but little study. Longworth and Plesch [40], who first studied

43

Developments in the Theory of Cationoid Polymerisations these catalysts, were unable to induce the polymerisation of isobutene at ambient or low temperatures by acetyl, benzoyl or t-butyl perchlorate, acetyl fluoroborate, or acetyl chloride and zinc chloride, either with pure isobutene or with solutions of it in methylene dichloride. At best only liquid oligomers were obtained, even at –90°.

(d) Heterogeneous catalysis Very many acidic solids and liquids, immiscible with hydrocarbons, will catalyse the oligomerisation of isobutene at ambient temperatures. Among the more common are syncatalysts prepared from boron fluoride and a protonic substance BH (B = OH, CH3O, C2H5O, t-C4H9O, CH3CO2, etc.); mineral acids; natural and synthetic alumino-silicates, (e.g., Fuller’s earth, bentonite, attapulgite); and metal oxides containing small quantities of water. The reason for these catalysts giving only oligomers is mainly the dominance of transfer reactions at ambient and higher temperatures. All attempts to obtain high polymers with these catalysts by working at temperatures well below 0° failed, partly, at any rate, because the rate of reaction, and the rate of desorption of the polymer from the catalyst, become too small as the temperature is lowered. The only solid acidic catalyst which has given high polymers at an appreciable rate at low temperatures, and which has been studied in some detail, is that described by Wichterle [41, 42]. This was prepared as follows: A 10 per cent solution in hexane of aluminium tri-(s- or t-butoxide) was saturated with boron fluoride at room temperature, and excess boron fluoride was removed from the precipitate by pumping off about half the hexane. Two moles of boron fluoride were absorbed per atom of aluminium, and butene oligomers equivalent to two-thirds of the alkoxy groups were found in the solution; the resulting solid had hardly any catalytic activity. When titanium tetrachloride was added to the suspension in hexane, an extremely active catalyst was formed; but the supernatant liquid phase had no catalytic activity. The DP of the polymers formed by the catalyst prepared from the s-butoxide was much lower than that of polymers formed with a catalyst prepared from the t-butoxide.

5 Kinetic investigations The first extensive publication on the polymerisation of isobutene was the celebrated paper by Thomas et al. [43]. This is almost more remarkable for what it leaves out than for what it contains, but it did establish many of the important features of the reaction. The first serious attempts at a physicochemical (as opposed to organic-preparative) study were made by Polanyi’s school at Manchester, in the course of which the phenomenon of

44

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) co-catalysis was discovered [9, 18, 22-29]. This was followed by Dainton and Sutherland’s work [8] on the mechanism of initiation and by Norrish and Russell’s work on catalysis by stannic chloride-water [30, 31]. In 1955 the first of a series of studies by the Czechoslovak group headed by Vesely began to appear (see Section 5, iii, (b)). Publications by Plesch and his collaborators, and by the Esso group (Kennedy and Thomas) were not resumed until 1960. This long gap between publications, and the small number of groups involved are good indications of the difficulty of the problem.

i. Oligomerisations at ambient temperatures As was mentioned in Section 4, iii, at ambient and higher temperatures gaseous isobutene is converted to oligomers by many conventional and complex acids and other catalysts. These reactions are heterogeneous, involving a liquid or solid catalyst, the liquid oligomers (if the temperature is not too high), and the gaseous monomer; some of this, of course, is adsorbed on the catalyst and dissolved in the liquid oligomers which usually separate the actual catalyst from the gas phase. Thus, investigations of these systems could not provide much evidence on the kinetics of the reactions involved, but they did add considerably to our understanding of their chemistry. Evans, Meadows and Polanyi first showed that a mixture of highly purified gaseous isobutene and boron fluoride only reacts very slowly [18]; the initial pressure of the mixed gases was equal to the sum of the pressures of each gas [29], which proved that at ambient temperatures and at pressures of a few hundred mm no complex is formed between isobutene and boron fluoride. The addition of water [18, 27, 29], acetic acid [26, 29], or t-butanol [27, 29] to such a very slowly reacting mixture gave a very large increase in the rate of reaction - thus the co-catalytic activity of these compounds was proved. An indication was also obtained that diethyl ether is a weak co-catalyst [29], but it was not proved conclusively that the weak activity found was not due to impurities (water, methanol) in the ether. It was also shown that the catalytic complexes contained approximately equivalent quantities of boron fluoride and co-catalyst [29]; that the 1:2 complex BF3•2 CH3CO2H is not a catalyst; and that the reaction is heterogeneous, taking place on the surface of the solid catalytic complexes. The oligomer obtained from an initial isobutene pressure of 100 to 300 mm had a cryoscopically determined DP of 5, and approximately 2000 such pentamer molecules were formed per molecule of water added. When the initial pressure of isobutene was 1500 mm, the DP of the oligomer was 30. These observations show the dominance of transfer processes. It was also concluded that, since the first order rate constant for the

45

Developments in the Theory of Cationoid Polymerisations oligomerisation, obtained from the rate of fall of the isobutene pressure, did not appear to diminish with increasing conversion, there was no true termination involving destruction of the catalyst. However, this conclusion, although likely, is not entirely convincing, since the rate determining process governing the fall of pressure could well have been diffusion of monomer to the growing sites. Thus the rate constant could have stayed constant, despite possibly large variations in the (very high) rate of polymerisation, due to termination. Some light was shed on this question of termination by Dainton and Sutherland [8] who prepared oligoisobutenes by Evans and Meadows’ method, but used D2O as co-catalyst. Their investigation of the infra-red spectra of the oligomers showed the presence of tbutyl and vinylidene groups. This proved the occurrence of the initiation reaction 1 involving transfer of a proton from the catalyst or a growing chain to the monomer, and of a chain breaking reaction involving loss of a proton from a methyl group (reaction 5a). There were also indications of the presence of CH2D groups, due to initiation by BF3•D2O, of tri-substituted double bonds, due to loss of a proton from a CH2 group in a transfer reaction of type 5b, and of OH and OD groups. The presence of these supports the suggestion that in these reactions there is a termination reaction involving consumption of the co-catalyst by reaction 6. It is most unlikely that in this system the OH groups could have arisen from a reaction with ‘unengaged’ catalyst hydrate - though there is evidence that such reactions do occur in other systems. The kinetics of the oligomerisation of gaseous isobutene by boron fluoride and ether at 70° was investigated carefully by Vinnik et al. [44]. Unfortunately, they say nothing at all about the reaction products. At isobutene pressures up to about 150 mm, the reaction is of second order with respect to the olefin. The dependence of the second order rate constant on the pressures of boron fluoride and of ether, and on the quantity and composition of the condensed phase, consisting of the liquid complex BF3⋅Et2O together with excess ether or boron fluoride, is less clear, and the authors’ arguments are difficult to follow. They obtained a rate law which is formally the same as that which they had found for the oligomerisation of isobutene by sulphuric [45] and by phosphoric [46] acid, but they did not attempt to interpret this in terms of a mechanism. From indicator experiments similar to Wichterle’s [47] they concluded that the ‘acidity’ of BF3⋅Et2O is similar (H0 = –6⋅2) to that of 70 per cent sulphuric acid (H0 = –6⋅05). Their conclusion that initiation of the reaction involves the etherate functioning as a protonic acid is not well supported and seems very implausible. The only published kinetic investigation of the oligomerisation in solution [48] deals with the reaction in hexane at between +20° and –40°, catalysed by H2SO4 –H2O and by BF3 –H2O. The reactions were carried out in an adiabatic calorimeter and the temperature change accompanying oligomerisation was recorded automatically. By means of a careful

46

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) theoretical analysis and calibration experiments with ‘infinitely fast’ reactions (H2SO4 + KOH aq.) the corrections for imperfect adiabaticity and delays due to heat transfer were calculated, and with these the reaction curves were analysed to yield first order rate constants. This work can be criticised on the grounds that it was assumed that, since the slow reactions obtained under some conditions were of first order with respect to monomer, the fast reactions occurring under different conditions would also be of first order. Moreover, the mean DP of the products (which were not identified) varied from about 3 to about 4.5, but no allowance appears to have been made for the fact that for these very low oligomers the heat of polymerisation per base mole of monomer varies considerably with the DP. The main object of the investigation was to correlate the rate and DP with the acidity function, H0, of the catalyst. This was varied by altering the ratio [H2O]/[A], where A is sulphuric acid or boron fluoride, and H0 was determined for each such mixture. The reactions were carried out with a rate of stirring and a quantity of catalyst in the region in which the rate of reaction was independent of both these variables. Since there is not enough information to do anything else, we must take the authors’ results, especially the ‘first order rate constants’ k, as they are given. It appears that the reactions started with an accelerating phase and then became of first order. With 94.1 per cent H2SO4 (H0 = –8.62) the activation energy of the rate is about 3 kcal/mole. With the syncatalytic system BF3–H2O the plots of log k against H0 (in the range H0 = –7 to –9) at 0° and –20° were rectilinear and parallel. For the system H2SO4–H2O at 0° the plot of log k against H0 was rectilinear over the range H0 = –7 to –9, but steeper than that obtained with BF3–H2O; for more negative values of H0 (down to –10.5) the results were not closely reproducible, but showed k to be largely independent of H0; this was - quite plausibly - attributed to side reactions which were indicated by the strong colour of the reaction mixtures and the evolution of sulphur dioxide. The DP increased almost linearly with –H0, from about 3.5 at H0 = –7.5 to about 4.5 at H0 = –11. The information available is insufficient for any detailed kinetic conclusions to be drawn, but both the increase in rate and the increase in DP with increasing values of –H0 are quite intelligible - at least qualitatively - in terms of current theory.

ii. Polymerisation at near-ambient temperatures The only catalyst which has given high polymers of isobutene at ambient temperatures is Wichterle’s [41, 42] which has been described in Section 4, iii, (d). Some of the kinetic features

47

Developments in the Theory of Cationoid Polymerisations of the reaction were investigated. The catalyst used for these studies was that formed from aluminium t-butoxide. The rate of polymerisation and the DP of the polymers* were found to increase with the amount of titanium tetrachloride in the mixture, up to an Al:Ti ratio of 4:1, and beyond this they remained constant. Both rate and DP were independent of the order in which the B-Al complex, the TiCl4, and the isobutene were mixed. The initial rate was directly proportional to the quantity of catalyst, and was increased by vigorous stirring. The DP of the polymer formed was independent of the quantity of catalyst. Between 0° and –30° the initial rate of polymerisation gave a linear Arrhenius plot, with an ER = 7.0 kcal/mole. The most peculiar and interesting feature of the Wichterle catalyst is that the DP of the polymers is very much greater than that obtained with any other catalytic system, at the same temperature (see Figure 1).

Figure 1 The variation of DP with temperature for Wichterle’s catalyst [41] (line A) and for the syncatalyst TiCl4–CCl3CO2H in hexane [9] (line B). For line A: [i-C4H8] = 10 per cent by weight. [Al] = 3.2 x 10-3 mole/l, * [Ti]/[Al] = 0.5. For line B: [i-C4H8] = 1.25, [TiCl4] = 48 x 10-3, [CCl3CO2H] = 3.3 x 10-3 mole/l.

*Although it is not stated explicitly, it appears from the context that the DPs given are those for 100 per cent conversion

48

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) Another peculiar feature of this system is that the E DP changes with inonomer concentration*. Another way of presenting the same data shows that the dependence of the DP on the monomer concentration follows the unusual course shown in Figure 2. The fact that the DP becomes independent of [P1] when this is great, and the temperature low (–30°), is interpreted by the authors - quite plausibly - in terms of polymer gel inhibiting diffusion of monomer to the reaction sites, and a concurrent build-up of temperature. It was found that addition of only relatively large quantities of water affected the rate decreasing it, but that this did not affect the DP. The addition of di- and tri-isobutene also only affected the rate, but not the DP - this is a marked contrast to the homogeneous

Figure 2 The variation of DP with monomer concentration for Wichterle’s catalyst at various temperatures [42]. [Al] = 3.2 x 10-3 mole/l, [Ti]/[Al] = 0.5 *In references [41] and [42] the isobutene concentration is given in ‘per cent.’ Prof. Wichterle informed the author that this means ‘per cent by weight’

49

Developments in the Theory of Cationoid Polymerisations polymerisations in which the presence of higher olefins always reduces the DP of the polyisobutene [30, 43, 49]. This catalytic system is so complicated and the analytical information about it so incomplete, that it is not profitable to speculate about its detailed nature and mode of action. Since the polymerisation takes place at the surface of the catalyst, the variation of DP with monomer concentration cannot, reasonably, be interpreted by the Mayo equation. The very high DPs obtained at relatively high temperatures (–30° to 0°) could be due to an acceleration of the propagation reaction, or a deceleration of the chain-breaking reactions, or both, compared with the homogeneous polymerisation by for example, TiCl4–CCl3CO2H in hexane. The fact that EDP is negative and relatively large means that even the dominant chain-breaking reaction must have a large activation energy, but comparison with the homogeneous polymerisation by TiCl4–CCl3CO2H, which has about the same EDP (see Section 5, iii. (d)), shows that with the Wichterle catalyst the ratio of the entropies of activation for propagation and for chain breaking must be much in favour of propagation.

iii. Polymerisation at low temperatures The formation of high polymers from isobutene in solution has been investigated by only a few groups of workers, and each one of these has adhered to its own methods and its chosen catalyst, so that there has been virtually no cross-checking. The methods and concentration ranges of reagents used, and the phenomena observed by these different groups are so varied that a synoptic treatment of the results would be unprofitable, and therefore the various groups of investigations will be discussed separately.

(a) The work of the Esso group with AlCl3 as catalyst The first famous paper [43] on the polymerisation of isobutene by aluminium chloride was not followed by others on the same topic until twenty years later. In the interval there were occasional communications to scientific meetings [50], and one paper on copolymerisation [51], but a steady stream of patents revealed that much work was being devoted to the study of this and related reactions. Then, in 1960, there began to appear a series of papers by Thomas and his collaborators in which a wealth of fascinating results was presented. For this new series of experiments an elaborate dry-box technique was used in an attempt to obtain anhydrous conditions [61]. However, from the information given it can be calculated that even the quantity of residual atmospheric moisture was about equivalent to the number of moles of polymer formed in typical experiments - not taking into

50

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) account the moisture adsorbed on glass-ware and present in the reagents. Moreover, in some experiments ethyl chloride was used as the vehicle for aluminium chloride. Although these solutions were made up at –78°, such solutions are known to be unstable, and indeed they were reported to be yellow, so that the presence of traces of HCl and other, possibly co-catalytic, reaction products is probable. Thus none of these experiments shed any light on the vexed question of whether the system AlCl3–i-C4H8-alkyl chloride requires a co-catalyst, or whether the alkyl chloride, or a product formed from it, acts as co-catalyst. Polymerisation of undiluted monomer. The polymerisation of undiluted isobutene was studied by Kennedy and Thomas [52] by adding a 1.88 x 10-2 mole/l solution of AlCl3 in CH3Cl to isobutene at –35°, –50°, –78°, and –98°. They found that as the volume of catalyst solution added was increased from 0.2 to 1.0 ml the quantity of isobutene polymerised increased linearly from about 1 g, to 5.5 g at the first three temperatures, and to 3.5 g at –98°. The weight of polymer obtained for any given quantity of catalyst was the same when the original weight of isobutene was 7.10 g and 17.75 g; this showed that there were no chain terminating impurities in the monomer. The DP of the polymers too was independent of the quantity of monomer and of the amount of catalyst solution added, but increased with decreasing temperature from 103 at –35° to 2.8 x 103 at –98°, giving a linear Arrhenius plot with EDP = –1.3 kcal/mole. These observations indicate that the DP is controlled by transfer reactions, and it seems likely that under the conditions of these experiments the most important of these is monomer transfer. The fact that the DP was independent of conversion is difficult to interpret since the polymer was precipitated during the reaction and therefore the concept of ‘monomer concentration’ is ambiguous; if the growing chain ends remained in the unreacted monomer its concentration would remain effectively constant. These results are in apparent contradiction to others obtained by the same authors [53]. In this earlier paper* they reported that at –78°, with the same range of [AlCl3]:[i-C4H8] ratios, and at conversions of less than 10 per cent, the DP decreased from 5.4 x 103 at 4.8 x 10-3 wt.% AlCl3 on isobutene, to about 2.5 x 103 at concentrations greater than about 1.3 x 10-2 wt.% of AlCl3. The authors do not comment on this apparent discrepancy between their two series of results, which is rendered even more obscure by the different, but equally clumsy, concentration units which are used in the two papers. The matter * In many places in the text of Ref. [53] and in the caption to Table II, ‘isobutene’ is used erroneously in place of ‘polyisobutene’. On p. 487 ‘the DP of styrene’ should be ‘the DP of polystyrene’. - The following corrections should also be noted: Ref. 9. The last author should be M. Mueller-Cunradi, not M. Mueller-Conradi. Ref. 13. Norrish, R. G. W. and K. E. Russell, not Norris, R. G. W. and R. E. Russell. Ref 15. Mathieson, not Matheson. Ref. 22. Overberger, not Overgerger.

51

Developments in the Theory of Cationoid Polymerisations can be resolved thus: Recalculation of the results in the first column of Table 11 in Reference 53 shows that 1/DP increases linearly with [AlCl3] up to about 7 x 10-4 mole/ l, but thereafter it remains constant up to [AlCl3] = 16 x 10-4 mole/l. The concentration of aluminium chloride used in the work [52] referred to at the beginning of this section ranged from 1.5 x 10-4 to 7.5 x 10-4 mole/l, when 17.75 g of isobutene was used, and from 3.8 x 10-4 to 19 x 10-4 mole/l, when 7.71 g of isobutene was used. It thus fell just in that range of concentrations which in the earlier work had given the linear variation of 1/DP with [AlCl3]. The break in the 1/DP–[AlCl3] plot can be interpreted most plausibly by the supposition that aluminium chloride reacts with an impurity in the isobutene to give a chain-transfer agent, so that the concentration of this is proportional, or equal, to [AlCl3] as long as [AlCl3] < [impurity], and remains constant at all greater concentrations of AlCl3. (A closely analogous situation is discussed in detail in Section 5, iii, (c) below.) The discrepancy between the two sets of results can now be accounted for, at least tentatively, by assuming that in the earlier work [53] the concentration of the critical impurity was of the order of 7 x 10-4 mole/l, whereas in the later work [52] it was less than 1.5 x 10-4 mole/l. This matter is discussed in detail in the Appendix to this chapter. Polymerisations in n-pentane. Kennedy and Thomas, wishing to study the polymerisation of isobutene by aluminium chloride under homogeneous conditions, i.e., in a solvent in which even the highest polymers remained in solution at low temperatures, chose npentane [54]*. The specimen they used was stated to contain approximately 0.1 mole/l of branched and olefinic impurities which are known to reduce the DP and therefore the DPs obtained must be (slightly) lower than those which would have been obtained in pure n-pentane. All experiments were done at –78°, and the yield of polymer (per cent conversion) and the DPv, of the polymers are reported. When the catalyst, dissolved in methyl chloride, was added to the solution of isobutene in n-pentane, polymer was formed very rapidly, and in an amount which was proportional to the quantity of AlCl3 added and independent of the concentration of the catalyst solution itself. It was shown that the yield was not affected by the presence of methyl chloride. The yield from one monomer solution increased rectilinearly with the quantity * In this paper the caption to the top row of Table 1 should read ‘Mole % of n-pentane’ and not ‘Mole fraction of isobutene’. Also Reference 10 should have the date 1954, not 1956. Reference 13 should be to J. Chem. Soc., not J. Amer. Chem. Soc. Reference 14 should have the date 1949, not 1940. Reference 18 should be to J. Phys. Chem., not J. Amer. Chem. Soc. Reference 20 The last author should be Schneider, not Schnieder.

52

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) of catalyst solution added, i.e., the yield of polymer per mole of catalyst added was independent of the prevailing monomer concentration. For these experiments (Figure 1 of Reference 54) neither the initial monomer concentration nor the DP of the polymers is given, but correspondence with the authors elicited the information that they are the same as for Figure 4 of that paper. The limited conversion which is usually obtained when aluminium chloride in low concentrations is used to polymerise isobutene, has been attributed to the catalysts becoming embedded in the polymer which is precipitated. In these experiments this explanation is not relevant since the polymer remained in solution. Two obvious alternatives suggest themselves: (a) Inactivation of the catalyst by formation of stable ions carrying multiple positive charges, which would bind firmly the anionic moiety of the catalyst [55]. Although quite plausible for propene and other 1-enes, this explanation seems unattractive for isobutene, because of the far-reaching structural changes which would be required. (b) A rapid termination reaction between the carbonium ion and an anion derived from the anionic moiety of the catalyst, e.g., OH– from AlCl3OH–. This reaction commends itself because several analogous reactions with other metal halide catalysts are known. The variation of DP with initial monomer concentration in n-pentane solution at –78° was studied in a series of experiments [54] in which the catalyst concentration was so adjusted that the conversion was always below 10 per cent. However, these results and similar ones obtained with the same system presented in a later paper [56] are so scattered that no detailed correlation can be deduced. The only possible firm conclusion is that with increasing monomer concentration the DP declines from a peak of about 1.6 x 104 at [i-C4H8] ~ 1 mole/l to about 2.5 x 103 for the polymerisation of the undiluted monomer. It was found that the DP of the polymer formed varied in an unusual manner with the degree of conversion: At –78° in pentane solution with an initial [P1] of about 1.25 mole/ l the DP rose steeply to a maximum at about 25 per cent conversion and then fell off (Figure 3A). From such curves the ‘incremental’ DP formed at increasing conversion was calculated and found to follow a similar, but much steeper curve (Figure 3B). The authors suggest that the initial increase of DP with increasing conversion is due to the consumption of chain breaking impurities, which seems reasonable. The subsequent fall-off means that the DP decreases as the monomer concentration at which the polymer is being formed decreases. This is the ‘normal’ behaviour, but it appears to be in direct contradiction to the results obtained at very low conversion with different initial monomer concentrations. These, however, can also be explained by impurities present initially being progressively consumed.

53

Developments in the Theory of Cationoid Polymerisations Polymerisations in alkyl chlorides. In Figure 3 of Reference 43 it was shown that the DP of the polymers at first increased with monomer concentration, and then fell off steeply to a quite low value characteristic of the polymerisation of undiluted monomer. The exact nature of the diluent (‘alkyl halide’) and catalyst were not disclosed, but it is now known that the diluent was methyl chloride and the catalyst aluminium chloride. Kennedy and Thomas have investigated in some detail this interesting phenomenon [56] *. Experiments were carried out at –78° in a dry-box: To 7.1 g of isobutene and the appropriate quantity

Figure 3 The dependence of DP on monomer conversion. A cumulative, B incremental [54]. Temperature –78°. Solvent: pentane. Approximate concentrations: - [i-C4H8] ~ 1.5, [CH3Cl] ~ 1 mole/l. Catalyst: 4.12 x 10-2 mole/l AlCl3 in CH3Cl, introduced at the rate of 1 ml/min Footnote: In the captions to all the figures in this paper ‘DP of isobutene’ should read ‘DP of polyisobutene’. Note also the following corrections: Reference 3 The second author is Mathieson not Matheson. Reference 5 Williams, G., not Williams, A. Reference 28 T. Higashimura, not T.J. Higashimura. Reference 35 The third author is Heiligmann, not Heiligman; the date is 1945 not 1954.

54

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) of diluent, 1 ml of a 0.25 wt/vol % solution of AlCl3 in methyl chloride was added; the conversion was stated to have been always ‘low’ but no details are given. With all solvents except n-pentane, the polyisobutene came out of solution as it was formed. The results are presented as plots of DP against mole fraction of isobutene. With methyl chloride, methylene dichloride, or vinyl chloride as diluent the DP rises very steeply to a sharp peak with increasing monomer concentration, and then falls off in a curve of exponential type (Figure 4). With ethyl chloride there is apparently no maximum, the

Figure 4 The effect of monomer concentration on DP [56]. Temperature –78°. Solvent: CH3Cl. Catalyst: AlCl3 in CH3Cl

55

Developments in the Theory of Cationoid Polymerisations curve falling off from the highest DP at the lowest monomer concentration. However, it may occur at so low a monomer concentration as to have escaped detection in this work. The position and height of the maximum vary from one solvent to another, but there is no evidence to show whether they are truly a function of the solvent, or whether they are determined by impurities. Kennedy and Thomas attempted to construct a formal kinetic theory to account for these phenomena. They started from the assumption, for which there is no evidence, that the propagation reaction takes place with free ions only, but that the chain breaking reactions involve ion-pairs. Their algebraic formulation is inconsistent with their reaction scheme in that they represent the propagation step as kinetically of third order; they use a steady-state treatment despite the fact that the limited yields obtained in these reactions show that this is inappropriate; their equation for the DP as a function of [P1] is not of a form which has a maximum. For these and other reasons their treatment is not valid. (A simple explanation of the DP maximum is proposed in the Appendix to this Chapter.) The DP maximum is most prominent with alkyl halide solvents, and so it seemed that the change in the dielectric constant (DC) of the medium with changing monomer concentration might be at least partly responsible for it. This point was studied by Kennedy and Thomas in the following manner [56]. They determined the DP of polyisobutenes formed in solutions which contained a fixed ratio of one mole of methyl chloride to three moles of a mixture of isobutene and carbon bisulphide, the molar ratio of i-C4H8:CS2 being varied from 1/5 to 5; carbon disulphide was chosen, as it has approximately the same DC as isobutene. The DP again went through a maximum (Figure 5) at a mole fraction of i-C4H8 of ~ 0.20, as against ~ 0.18 with methyl chloride as the only solvent. Quite apart from the point (admitted by the authors) that the bulk DC of a solvent especially a mixed solvent - has little relevance to its effect on ionic reactions, the experiment would have been more significant had the volume fraction of the polar component been kept constant; however, there is no reason to doubt that the general trend would have been found to be the same. The experiment with CS2 showed up another extremely interesting effect. Over almost the whole range of compositions the DPs obtained were very significantly greater than those obtained without carbon bisulphide - with methyl chloride as sole diluent. This ‘CS2 effect’ has been reported previously for the cationic polymerisation of α-methylstyrene [57] and of isobutene [50]. It seems likely that it is due (at least partly) to the fact that CS2 does not act as a transfer agent, whereas most alkyl halides do. 56

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963)

Figure 5 The effect of monomer concentration on the DP in mixtures of CH3Cl and CS2 [56]. Temperature –78°. Catalyst: AlCl3 in CH3Cl The effect of the catalyst concentration on the DP of the polymer was investigated at –78° with methyl chloride as solvent at isobutene concentrations of 0.643 and 0.25 mole fraction (approximately 9.5 and 4.6 mole/l) [53]. The catalyst concentration, given as ‘wt.% AlCl3 on isobutene’ (sic!), covers the range 1.5 x 10-3 to 10-1 in these units. Recalculation of the results shows that 1/DP increases linearly with [AlCl3] up to a certain value* and at higher values remains constant. This corresponds closely to the behaviour reported for the polymerisations of undiluted monomer [53] and can be explained in the same way (see p.159). Experiments with radioactively labelled CH3Cl. One series of experiments [58] was aimed at finding out whether methyl chloride participated in the initiation of polymerisation by acting as co-catalyst, a reaction which can be represented by the equation +

i − C 4 H 8 + CH 3Cl + AlCl 3 → CH 3CH 2 C(CH 3 )2 AlCl 4−

(10)

Methyl chloride labelled with 14C was used both as vehicle for the catalyst and as solvent for the isobutene in reactions carried out at –78°. Polyisobutene equivalent to 82.2 per * At the higher monomer concentration this is not clearly discernible, but lies in the range (8 - 14) x 10-4 mole/l.; at the lower [P1] it is approximately 4 x 10-4 mole/l.

57

Developments in the Theory of Cationoid Polymerisations cent of the monomer was recovered and very carefully freed from entrained methyl chloride. The viscosity-average MW was 120,000, and DPn was taken as DPv/1.832 [59]; 5.1 per cent of the product was coloured and soluble in methanol, and was disregarded. From the radioactivity of the polymer and of the original methyl chloride it was found that if there was not more than one 14C atom per polymer molecule, 0.27 of the polymer molecules contained a methyl group derived from the solvent. The authors concluded that the formation of this fraction of molecules had been started by initiation according to equation 10, and that the remainder had been started by transfer with monomer. It has been admitted by the authors (private communication, and in press) that this conclusion is not warranted on this evidence, since alkyl halides such as methyl chloride, are known to act as transfer agents by a reaction which can be represented by Equation 7. At best, the evidence shows that methyl chloride was involved in starting - by initiation and/or transfer - about a quarter of the polymer molecules. The results of further studies with 14CH3Cl and CH336Cl are in process of publication [12]. Polymerisations at very low temperatures. The most spectacular feature of the cationic polymerisation of isobutene is the fact that it proceeds with great speed even at very low temperatures. Hitherto the lowest temperatures used were around –100°, but Kennedy and Thomas have extended the temperature range down to –185° in a series of highly ingenious experiments [60, 61]. Propane was selected as solvent for the isobutene; for experiments down to –145° the aluminium chloride was dissolved in ethyl chloride, for the work at lower temperatures a mixture of ethyl chloride and vinyl chloride was used. Although these catalyst solutions were made up at –78° they were yellow, and as stated above, they probably contained some hydrogen chloride and other catalytically active decomposition products. The polymerisations were carried out by running the cooled catalyst solution into the monomer solution. Polymer was formed, and came out of solution, almost immediately, and the reaction was very fast even at the lowest temperature (–185°) and lowest monomer concentration (0.6 mole/l). After the reaction was over, propanol at the reaction temperature was added to the reaction mixture to deactivate the catalyst. In one series of experiments the effect of temperature on DP was investigated using a 1.27 mole/l solution of monomer. To this was added dropwise 0.5 ml of a 1.85 x 10-2 mole/l solution of AlCl3 in ethyl chloride, for the experiments at –50° to –145°; for those at lower temperatures a lump of a frozen solution of AlCl3 in a mixture of ethyl and vinyl chloride was added to the isobutene solution in propane. The quantity of catalyst used in all these experiments was sufficiently great to give a yield of polymer of about 85 per cent.

58

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) The plot of log DP against 1/T was linear from –50° (DP ~ 2 x 103) to about –100° (DP ~ 2 x 104) and then curved to give a branch of much smaller slope between –145° and –185° (DP ~ 4 x 104). In a series of experiments at –180° the effect of monomer concentration on DP was investigated [61]. The catalyst concentration was much smaller than that used in the previous series, so that the reactions stopped at about 10 per cent conversion. It was found that the DP went from 1.75 x 105 at a monomer concentration of 0.6 mole/l through a shallow maximum of 2.17 x 105 at 1.9 mole/l and declined to 1.36 x 105, at 4.45 mole/l. The difference between the DPs obtained in this series of experiments and the DP obtained at –185° in the previous series, may have been due to the difference in the amounts of catalyst used in the two sets of experiments. If the DP is indeed independent of monomer concentration, the chain-breaking reactions which remain important at –180° must be of the same order with respect to monomer concentration as the propagation reaction. The most obvious conclusion is that monomer transfer is the dominant chain breaking reaction, so that DP = kp/km; it follows that the activation energy, EDP, characterising the low temperature branch of the Arrhenius plot is Ep – Em = –0.2 kcal/mole. A naive interpretation of the data on the assumption that the pre-exponential terms Ap and Am of the Arrhenius equations for kp and km are truly independent of temperature shows that Ap ~ 5 x 105 Am, and hence the prevalence of propagation over transfer appears to be due to the great difference between the corresponding pre-exponential factors, reflecting the difference in the corresponding entropies of activation. However, it is very doubtful whether the abovementioned assumption is even approximately valid under these circumstances. The higher EDP (–3.6 kcal/mole) at the higher temperatures cannot be interpreted without detailed kinetic information, but is probably associated with chain breaking reactions other than monomer transfer which gain in importance as the temperature is raised. The effect of monomer concentration on the dependence of the DP on temperature. Further studies [12, 52, 62] of the temperature dependence of the DP showed that the Arrhenius plot was approximately linear over the temperature range –5° to –78° for all concentrations of isobutene from about half-molar to undiluted monomer, and that the slope of the line increased with decreasing concentration in such a way that all the lines crossed at approximately the same temperature, –50°. This means that at –50°, the ‘inversion temperature’, the DP is independent of monomer concentration; at lower temperatures it decreases, at higher temperatures it increases with increasing monomer concentration. This behaviour was found for polymerisation in methyl, ethyl and vinyl chloride as solvents. 59

Developments in the Theory of Cationoid Polymerisations In honour of the discoverers we propose to name this phenomenon the ‘Kennedy-Thomas effect’. In the absence of more detailed information one can only guess qualitatively that this remarkable effect may be mainly due to the change of medium, which will affect not only the rate constants of propagation and chain breaking through changes in polarity, but will also effect the relative abundance of chain breaking reagents.

(b) The work of the Czechoslovak group with AlCl3 as catalyst A group of workers at the institute for Macromolecular Chemistry at Brno, under the leadership of Vesely, began to report in 1955 on investigations into the polymerisation of isobutene. Most of this work has been done with aluminium chloride as catalyst at –78°. The technique used in the earliest work was rather crude, but it was later refined so as to ensure a reasonable degree of dryness. A commendable feature of this work is the attention given to the purity of the reagents and the specification - for some of them, at least - of the nature and concentration of impurities. The most notable feature of these investigations is that, with a logic conspicuously absent from most other, related experiments, this group studied what is, after all, the most prominent feature of ionic systems - their electrical conductivity. It must be said at the outset that they discovered a most impressive inverse correlation between the specific conductivity of some catalyst solutions and the DP of the polyisobutenes obtained when monomer was added to these.* Regrettably, no other dependent variable, such as degree of conversion, was investigated (apart from some rough estimates of reaction rate), nor was the effect of monomer concentration studied (in one paper this is not even specified). None the less, the highly original attack has yielded most valuable and reliable information, but the interpretation given to it by the authors is open to some obvious criticisms, as will be shown below. The results of this group of workers are in many ways complementary to those of the Esso group discussed in the previous section, and they can validly be compared and combined with them because of the identity of the catalyst and the temperature, and the close similarity of the solvents which were used in both series of investigations.

Results In the first paper of this series [63] all the concentrations are given in such awkward terms that it is not possible to convert them accurately into mole/l units. The variation of DP * We propose that in recognition of its discoverers, Zlamal, Ambroz and Vesely, this important phenomenon be named the ‘ZAV Effect’.

60

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) with concentration of AlCl3 was investigated with a mixture of 54.3 per cent ethane and 45.7 per cent MeCl (by weight) as solvent. The isobutene concentration was 25 per cent by weight (approximately 3 mole/l). It was found that with increasing [AlCl3] the DP went through a very sharp peak, and the same behaviour was found with EtCl in place of MeCl. Variation of the composition of the C2H6–RCl mixture at constant [isobutene] (3 mole/ l) and [AlCl3] made the DP and the reaction rate (assessed semi-quantitatively) go through a very sharp maximum at about 20 wt.% of ethane, both with MeCl and EtCl. It was also shown that with ‘crude’ isobutene this peak was much broader and lower than with the purified monomer, and results were much less reproducible. These findings resemble very closely some of those obtained by Kennedy and Thomas. In the second paper [64] it was shown that for isobutene solutions in EtCl at –80°, the peak in the DP - [AlCl3] curve moved to lower values of [AlCl3] and became progressively sharper, as the purity of the EtCl was increased. However, the most important point in this paper is the first report of conductivity measurements. It was found that when acetonitrile was added to a solution of aluminium chloride in ethyl chloride, the specific conductivity rose rapidly with increasing concentration of acetonitrile, and the DP of the polyisobutenes formed subsequently in the solutions also rose (slowly) until the ratio [CH3CN]/[AlCl3] was about 0.5. Beyond this ratio the DP increased at an increasing rate with rising [CH3CN]/[AlCl3], but the conductivity fell, and reached a sharp minimum, coincident with a sharp maximum in the DP, at a [CH3CN]/[AlCl3] ratio of unity. A very similar behaviour was subsequently reported [66] for butyraldehyde in place of acetonitrile (Figure 6), and for many other compounds (all in EtCl at –80°). It was noted that with butyraldehyde there was a marked decrease of rate near the equivalence point. With diethyl ether and with anisole it was found [65, 67] that a sharp minimum in the specific conductivity curve, at an [ether]/[AlCl3] ratio of unity, was flanked by maxima, and that these were accompanied by a well defined maximum, and two minima, respectively, in the DP curve (see Figure 7). A maximum in the DP and a minimum in the specific conductivity, both at a ratio of [additive]/ [AlCl3] ranging from 0.8 to 1.0 (in EtCl at –78.5°) were also reported for a large range of ‘additives’, comprising various alcohols, acetone, methyl benzoate, acetic acid, 1-dodecanethiol, and tri-n-butylamine [66]. For all these additives no details are given, so that it is not known whether the relevant curves have more than one turning point. A more detailed investigation (EtCl, –78.5°) with ethanol [68] showed again a very striking antibatic correlation between DP and specific conductivity in the neighbourhood of [EtOH]/[AlCl3] = 1, with a very sharp peak in the DP curve and a corresponding sharp minimum in the conductivity curve. It was also shown that when the complex EtOH⋅AlCl3 was used as catalyst, the plots of conductivity and of 1/DP (after the subtraction of an

61

Developments in the Theory of Cationoid Polymerisations

Figure 6 The effect of n-butyraldehyde on the specific conductivity of 8.1 x 10-3 mole/l. AlCl3 in C2H5Cl at –80°; and on the DP of polyisobutenes formed in these solutions [66] ‘impurity correction’ from both quantities) against [EtOH⋅AlCl3] were straight lines through the origin. It is difficult to understand why the specific conductivity is rectilinearly related to [EtOH⋅AlCl3] up to 6 x 10-2 mole/l, as this means that the equivalent conductivity, Λ, is constant over this range of concentration. The naive interpretation of this constancy is that the complex is completely dissociated, and that ionic strength effects are negligible, which seems rather implausible. An alternative, rather more likely, explanation can be formulated in terms of the equilibrium 2EtOH⋅AlCl3 ↔ X+ + Y–, K = [X+][Y–]/[EtOH⋅AlCl3]2

62

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963)

Figure 7 The effect of diethyl ether on the specific conductivity of solutions of AlCl3 in C2H5Cl (2.5 x 10-2 mole/l) at –78.5°, and on the DP of polyisobutenes formed in these solutions [67] The nature of the ions X+ and Y– is obscure, but does not matter for this treatment. If [X+] = [Y–] ≡ i and [EtOH⋅AlCl3] ≡ A, then i = K1/2 A, provided that K is small, and in that case A is approximately equal to the analytical concentration of the complex. It follows that

63

Developments in the Theory of Cationoid Polymerisations

κ =2⋅i⋅Λr = 2K1/2⋅A⋅ΛT, where ΛT is the true equivalent conductance defined by Λr = κ/2i. At low ionic strengths this is reasonably constant, and therefore

Λ = κ/A = 2K1/2Λr will also be constant. For the complex n-Bu2O⋅AlCl3 both the specific conductivity plot and the 1/DP plot were convex to the concentration axis up to Bu2O⋅AlCl3 about 2 x 10-2 mole/l, and thereafter were rectilinear; but the plot of 1/DP against specific conductivity gave a straight line through the origin over the whole concentration range, thus showing that, however these two dependent variables may be related to the concentration of the catalyst, they are directly related to each other. These findings mean that Λ increases at first with increasing concentration of catalytic complex, and then becomes constant - which is more difficult to explain than the previous case, but might be accounted for in terms of more complicated equilibria. The effects of the non-polar additives benzene and cyclohexane were compared [69] by studying the effect (at –78.5°) of increasing concentrations of these compounds on the conductivity of solutions of AlCl3 and of EtOH⋅AlCl3 in ethyl chloride, and on the DP of the polyisobutenes formed in these solutions. With AlCl3 the DP went through a minimum and the conductivity through a maximum when the mixture contained about 5 per cent by weight of benzene. The addition of cyclohexane instead of benzene produced a steady increase in DP and a decrease in conductivity up to 25 per cent by weight of cyclohexane. With EtOH⋅AlCl3 the results were quite different, in that addition of benzene had no effect on the DP and produced only a slow, steady fall in conductivity. Cyclohexane produced only a very slight reduction of the DP which became independent of the quantity of cyclohexane once this exceeded 10 per cent by weight; the specific conductivity decreased continuously and quite steeply up to 30 per cent by weight of cyclohexane.

Discussion It is not possible to give here a detailed account of, nor to take issue with, every aspect of the interpretation which the authors give to their results. Their main conclusion is that the inverse correlation between DP and conductivity proves that the principal chain breaking reaction must be a bimolecular termination between free cations at the growing end of the chain and free anions in the solution. However, the arguments which lead to

64

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) this conclusion contain several errors. In the first place, it is logically impossible to draw firm conclusions about termination mechanisms from studies of DP alone, unless all transfer reactions have been identified and their kinetics and rate constants determined. This the authors have not done. In the absence of detailed information about transfer processes, evidence about the termination reaction can only be obtained from rate studies. The authors also frequently confuse termination with the various forms of transfer. The confusion arises partly through their use of the unfortunate term ‘molecular termination’ due to Endres and Overberger [85]. Moreover they formulate their mechanistic schemes in terms of reactions, some of which are known not to occur, such as the formation of ethyl ions from ethyl chloride and aluminium chloride. On the basis of their findings they contend that the effect of almost any compound hydrocarbons, alcohols, aldehydes, acids, amines, nitro-compounds, H2O, H2S, SO2, NH3 - can be co-catalytic or inhibitory, according to its concentration [66]. They extend quite unnecessarily the concept of co-catalyst to cover any substance which enhances the DP, and they thereby confuse and debase the originally perfectly precise meaning of the term ‘co-catalyst’: a substance the presence of which is essential for the functioning of the catalyst [22, 71]. It follows of course from this definition that evidence on co-catalytic activity can be obtained only from rate measurements, and never from studies of DP. Moreover, the theories of the authors do not account for certain important features of their results: that when the ratio [additive]/[AlCl3] is small, both the DP and the conductivity increase with increasing concentration of additive (alcohol, aldehyde, nitrile); and that with butyraldehyde the rate is markedly lower near the equivalence point where the DP is at a maximum, whereas in the alkyl halide-ethane mixtures both the rate and the DP went through a maximum at the same point. In our opinion the major part of these interesting results can be explained in the following terms, which coincide in part with the explanations given by the authors, but differ from theirs in two important respects. 1. It is known that the conducting species in solutions of aluminium halides in alkyl halides are complex; for instance solutions of aluminium bromide in ethyl bromide [70] contain the ions Al2Br5+ and Al2Br7-. 2. In the presence of highly polar organic oxygen or nitrogen compounds even larger complex ions are to be expected. 3. If the ions are large, it is to be expected that the ratio of free ions to ion-pairs will be relatively great. For instance, it follows from the Fuoss equation [72] that if the interionic distance is 10 Å, then in ethyl chloride at –78° (εT = 3.29 x 103) [73], the dissociation constant of ion-pairs is 2.5 x 10-3 mole/l. At a total concentration of electrolyte of 5 x 10-2 mole/l, the degree of dissociation is 0.2, and the ratio [cations]/ 65

Developments in the Theory of Cationoid Polymerisations [ion-pairs] = 0.25. Thus approximate proportionality between specific conductivity and concentration of complex is at least qualitatively intelligible. 4. There is no necessary relation between the electrical properties of the polymer cation, its anion, and the corresponding ion-pair, and those of the ions present in the solution before the isobutene is added. In fact, since the planar tertiary carbonium ion at the growing end of the polymer chain is much smaller than any cation (except the improbable AlCl2+) derivable from aluminium chloride, the dissociation constant of the carbonium ion - anion pair, whatever the anion, must be much smaller than that of the ion-pairs existing in the catalytic solutions before the addition of the monomer. 5. Since there is a close correlation between the specific conductivity of the catalytic solutions and the DP of the polymers formed in them, it follows that the electrochemical nature of the solutions must be largely unaffected by the polymerisation. Therefore at most a small fraction of the solute can be involved with the growing chain, and the remainder must be unaffected by the initiation of the polymerisation. This conclusion is strongly supported by the fact that in typical experiments the number of moles of polyisobutene formed was several powers of ten smaller than the number of moles of catalytic complex. 6. In the range of concentrations where the inverse correlation between specific conductivity of the catalytic solution and the DP of the polyisobutene formed in it prevails, the principal chain breaking agents must be free ions, the nature and concentration of which are probably very similar to those prevailing before the addition of the monomer. 7. It does not follow, as the authors affirm, that this chain-breaking reaction with free ions is a termination, nor that the entity at the growing end of the polymer chain, which reacts with the free ions, is itself a free ion. Unfortunately, we are still so ignorant of the electrochemistry of the systems involved, that it is not possible to construct a detailed, rigorous theory to explain these interesting phenomena, which certainly merit further investigation. A general discussion of the ‘peak phenomenon’ - the very sharp DP maximum found in many different systems, will be given in the Appendix to this chapter.

(c) Catalysis by SnCl4 The only quantitative work on the polymerisation of isobutene by stannic chloride, with water as co-catalyst, is that of Norrish and Russell [30, 74-76]. Further results, kindly

66

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) made available by Dr. Russell to the writer, were published and discussed by Biddulph and Plesch [77]. In this work all materials were most carefully purified and were handled entirely in a high-vacuum system. Ethyl chloride was used as solvent, and most of the experiments were done at –78.5°*. Rates were determined dilatometrically and DPs were measured viscosimetrically on polymers obtained at about 10 per cent conversion. The rate of polymerisation. It was found that at [isobutene] = 3.2 mole/l and [SnCl4] = 0.185 mole/l the dependence of the rate of polymerisation on the concentration of water varied with the degree of purification of the isobutene and of the ethyl chloride. When both had been subjected to two Podbielniak distillations (the usual procedure for most of the experiments) the rate varied rectilinearly with [H2O], but when both monomer and solvent had been subjected to six such distillations, the rate followed the curve shown in Figure 8. Under these conditions the rate at ‘zero added water’ corresponds to a concentration of the residual water of 5 x 10-4 mole/l. The authors concluded that the reaction would not go without a co-catalyst such as water.

Figure 8 The initial rate of polymerisation as a function of the concentration of water [3]. Temperature –78°. Solvent: C2H5Cl. [i-C4H8] = 20 mole% ~ 3.2 mole/l. [SnCll] = 1.15 mole% ~ 0.185 mole/l. [H2O] = 0.6 mole% corresponds to ~ 0.1 mole/l. o - Experimental points. Full line calculated from equation xv

* In Ref. 30 concentrations are given in ‘per cent’. Comparison with Ref. 74 shows that these are mole per cent. We have converted these to mole/l on the assumption that the volumes of isobutene and ethyl chloride are additive; see also Ref. 77.

67

Developments in the Theory of Cationoid Polymerisations Variation of the concentration of added water had a most interesting effect on the shape of the reaction curves, which are shown in Figure 9; even at the lowest water concentrations the reactions went to 100 per cent conversion; this is in marked contrast to the limited yields obtained with titanium tetrachloride as catalyst (see next section). At [isobutene] = 3.2 mole/l and [H2O] = 3 x 10-2 mole/l the rate increased steeply with [SnCl4] up to about 0.18 mole/l, and thereafter it was almost independent of this. The variation of polymerisation rate with monomer concentration was studied at a constant concentration of stannic chloride and water expressed in mole per cent, but this means that the molar concentrations of both were in fact decreasing slightly as the ratio of isobutene to ethyl chloride was increased. However, the effect of this was probably not significant. It was found that the rate increased approximately rectilinearly with the isobutene concentration up to 3 mole/l, reached a maximum at about 4.5 mole/l and declined to zero at about 8.5 mole/l. The authors recognised that the decrease in the dielectric constant of the reaction mixture with increasing concentration of isobutene was probably the main cause of the decrease in rate, and they suggested that the low solubility of the catalytic complex in mixtures of low DC might be a contributory factor. The variation of the polymerisation rate with temperature between –63.5° and –96.5° at [isobutene] = 3.2 mole/l corresponds to an activation energy ER = 7 kcal/mole. The degree of polymerisation. The variation of the DP with the concentrations of isobutene, stannic chloride, and water is best represented in the form of the Mayo plots shown in Figures 10, 11 and 12 which were constructed from Norrish and Russell’s

Figure 9 Reaction curves for polymerisation in ethyl chloride by SnCl4 + H2O at –78° [30]

68

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963)

Figure 10 The variation of DP with monomer concentration at –78° in ethyl chloride. Mayo plot

Figure 11 The variation of DP with [H2O] at –78° in ethyl chloride. [i-C4H8] = 3.22, [SnCl4] = 0.185 mole/l [31]. Mayo plot

69

Developments in the Theory of Cationoid Polymerisations

Figure 12 The variation of DP with [SnCl4] at –78° in ethyl chloride. [i-C4H8] = 3.22, [H2O] = 0.0306 mole/l [31]. Mayo plot. o Lower scale, • upper scale results. The first Mayo plot, 1/DP against 1/[P1] (Figure 10) has an intercept I1 = (2 ± 1) x 10-5 and a slope S1 = 5.4 x 10-4 mole/l. The second Mayo plot, (Figure 11), 1/DP against [H2O], has an intercept I1 = 3.78 x 10-5 and a slope S2 = 8.4 x 10-3 l/mole. The third Mayo plot, (Figure 12), 1/DP against [SnCl4], has a discontinuity at a stannic chloride concentration corresponding approximately to [SnCl4]/[H2O] = 1. The rising branch of the curve can be represented by a line of intercept I3 = 2 x 10-5 and slope S3 = 8 x 10-3 l/mole. The information contained in the Mayo plots can be interpreted as follows: The first Mayo plot shows that the rate of monomer transfer, km [Pn+] [P1], is small. The second and third Mayo plots show that there is a chain breaking agent, X, the concentration of which is proportional to [H2O] when this is less than [SnCl4], and proportional to [SnCl4] when [H2O] > [SnCl4]. It has been suggested [77] that these phenomena can be explained on the supposition that X is the stannic chloride monohydrate, but it will be shown below that this is probably erroneous. Assuming that the rate of chain propagation, Vp, is given by

[ ]

Vp = kp Pn+ [ P1 ] 70

(i)

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) and that the total rate of chain breaking, Vb, is given by

[ ]

Vb = Pn+ (kt + km [ P1 ] + kx [ X ])

(ii)

the equation governing the DP can be written in the form

1 k kt k [X] = m+ + x DP k p k p [ P1 ] k p [ P1 ]

(iii)

where kt is the rate constant of the unimolecular termination. From the values of the intercepts and slopes of the Mayo plots given above, and on the assumptions that

[X] = Q[SnCl 4 ⋅ H 2O]

(iv)

(where Q is a proportionality constant), and that the complex is not dissociated to an appreciable extent, the values of the relative chain breaking coefficients shown in Table 3 can be calculated [77].

Table 3 km/kp 2 x 10-5

kt/kp (mole/l) > 4.9 x 10-5

Qkx/kp 2.71 x 10-2

It is evident that by far the most effective chain breaking reaction is that involving the chain breaking agent X, the concentration of which is proportional to that of the monohydrate.

Discussion Only very few results are available on the variation of DP with temperature, but they indicate that between -63.5° and -95.5° the DP does not vary significantly and hence EDP = 0 ± 2 kcal/mole [76]. The obvious interpretation of the small EDP, and the large positive ER is that ER is essentially Ei, which means that initiation is slow compared with propagation and termination, and that one is dealing here with a system which has kinetics resembling those of free-radical polymerisations. Only one complete reaction curve without the acceleration anomaly has been published (the lowest curve in Figure 9). From this one finds t1/4: t1/2 = 0.43, t3/4: t1/2 = 1.76, where

71

Developments in the Theory of Cationoid Polymerisations t1/1, etc., is the time required for 25 per cent, etc. of the monomer to be polymerised. For a first order reaction these ratios are 0.42 and 2.0, respectively. In view of the inaccuracies inherent in taking the requisite measurements from a printed diagram, this is satisfactory confirmation that at least the major part of the reaction is of first order, overall. The reaction thus appears to obey a rate equation of the form

– d[ P1 ] / dt = k[ P1 ][Y] = kQ ′[ P1 ][SnCl 4 ⋅ H 2 O]

(v)

where [Y] = Q′[SnCl4] when [SnCl4] < [H2O], and [Y] = Q′[H2O] when [SnCl4] > [H2O]. Since the overall order of the reactions is unity, [Y] must be constant, so that we are dealing with a stationary system. Since there is a termination reaction, as will be shown below, the stationary state must be of the First Kind, i.e. the rates of initiation and termination are equal and finite, (Vi = Vt ≠ 0). In order to interpret the experimental rate equation in terms of a detailed kinetic scheme we must take cognisance of the sigmoid shape of the reaction curves obtained at low water concentration (Figure 9). Norrish and Russell [30] suggested that this acceleration is, as in radical polymerisations, due to the increasing viscosity reducing the rate of a bimolecular termination, and that this termination involved mutual neutralisation of cationic and anionic propagating centres. Later they abandoned this rather implausible idea in favour of the bimolecular prototropic reaction 11 (which is a variant of reaction 5) between the growing carbonium ion, assumed to be free, and the free anion [74]:

HPn+ + SnCl 4 OH − → M n + SnCl 4 ⋅ H 2 O

(11)

the dead polymer Mn has terminal unsaturation. Since the DP increases very rapidly with diminishing water concentration, this explanation is at least qualitatively plausible. The construction of a detailed kinetic analysis can now be approached in the following manner: We assume that only free ions propagate the reaction and take part in the transfer and the bimolecular termination reactions, we neglect the unimolecular termination, characterised by kt, which can only occur in an ion-pair, since the very small value of kt/ kp hardly exceeds the experimental uncertainty. As discussed above, we regard the termination as a bimolecular reaction between cations and anions (A-) of equal concentration, so that

[ ][ ]

[ ]

Vt = kt 2 Pn+ A − = kt 2 Pn+

72

2

(vi)

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) It is an obvious next step to identify this termination reaction with the second order chain breaking reaction involving the agent X, which was shown up by the Mayo plots. The rate of this is given by the third term of equation ii:

[ ]

Vt = kx Pn+ [ X ]

(vii)

Comparison of equations vi and vii shows that the agent X is the free anion A-, and it then follows that

Vt = kx Q 2 [SnCl 4 ⋅ H 2 O]

2

(viii)

and that kx = kt2. Concerning the initiation, we follow Russell [75a] in assuming that it is a second order reaction, the rate of which is independent of monomer concentration. Most probably it involves a complex of monomer with the stannic chloride monohydrate [75a]. In view of the well-known tendency of stannic chloride to form 6-co-ordinate rather than 5-coordinate structures, this idea does not seem too far-fetched. Since the monomer is in great excess over stannic chloride hydrate, the concentration of the complex, P1⋅SnCl4⋅H2O, will be sensibly equal to that of the monohydrate, i.e. of either the stannic chloride or the water, whichever is the scarcer. Therefore, the rate of initiation Vi, will be given by

Vi = ki [SnCl 4 ⋅ H 2 O]

2

(ix)

This is the only rate-law for initiation which, in combination with the expressions for Vp and Vt given by equations (i) and (vi-viii), will yield the correct overall rate equation. The reaction corresponding to equation ix can be written in the alternative forms

2 P1 ⋅ SnCl 4 ⋅ H 2 O → HP1+ SnCl 4 OH − + P1 ⋅ SnCl 4 ⋅ H 2 O or → HP2+ (SnCl 4 OH ⋅ H 2 O) + SnCl 4 −

(12)

or → HP2+ SnCl 4 OH − + SnCl 4 ⋅ H 2 O Since only a very small fraction of the stannic chloride hydrate appears to be involved in the reaction, there is no method at present of distinguishing between these, and possibly other, alternatives.

73

Developments in the Theory of Cationoid Polymerisations From the stationary state condition Vi = Vt and equations (i), (vi) and (ix) we obtain:

– d[ P1 ] / dt = Vp = k p ki 2 [ P1 ][SnCl4 ⋅ H2O] / kx 2 1

1

(x)

The rate equation (x) thus agrees with the experimental rate law given by equation (v). The overall rate constant was reported [75a] to have the value 0.35 l mole-1 min -1 at -78.5°. According to our interpretation this is kpki1/2/kx1/2. From the Mayo plots and equations (viii) and (ix) we have k i1/2kx1/2/k p= 2.71 x 10 -2. Hence ki = 9.5 x 10 -3 l mole-1 min-1. The coefficient in equation (v) is given by kQ′ = kpki1/2/kx1/2. If the very small term in kt is dropped, the Mayo equation (iii) can now be written in the forms

Qk [SnCl 4 ⋅ H 2 O] 1 k = m + x DP kp kp [ P1 ]

[ ]

− k m kx A = + kp kp [ P1 ]

(xi)

The same form of rate equation and Mayo equation can also be obtained, though with different constants, on the assumption, made by Biddulph and Plesch when first discussing this work [77], that the chain breaking agent is the stannic chloride hydrate itself. Since this reaction too would be subject to deceleration by increasing viscosity, it is also compatible with the curves of Figure 9. Fortunately, there is available a piece of evidence which helps to illuininate, if not to resolve entirely, this ambiguity. It will be recalled that when monomer and solvent had been purified with extreme rigour, the relation between initial rate and [H2O] was found to be no longer rectilinear, but to follow the curve shown in Figure 8. This experimental curve can be explained on the basis of Norrish and Russell’s ideas that the propagating species is the free cation and the terminating species the free anion, but not on any reasonable alternative assumptions, in particular the one that the terminating agent is the stannic chloride hydrate. The argument runs thus: If the dissociation of the ion-pairs is governed by the equilibrium

Pn+ A − ↔ Pn+ + A −

74

(13)

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) the dissociation constant, K, is defined by the relation

[ ][ ] [

K = Pn+ A − / Pn+ A −

]

(xii)

and

[ P ] = – K2 + 12 ( K + n

2

+ 4 Kc)

1

2

(xiii)

where

[ ] [

c = Pn+ + Pn+ A −

]

(xiv)

With the reasonable assumptions that c is proportional to the nominal concentration of water and that, as assumed earlier, the rate of polymerisation is given by equation i, we obtain the relation (xv), in which K1, K2, and K3 are composite, but constant, quantities.

Rate = –K1 + ( K2 + K3 [ H2O])

1

2

(xv)

The full line in Figure 8 represents this equation, and it gives a truly remarkable fit to the experimental points. It thus appears that at any rate in the purest systems of this kind the propagating species is the free ion, for the opposite assumption, that only the ion-pairs propagate the reaction, gives the mirror-image of the parabola in Figure 8. The reason why in the less rigorously purified systems the rate varied rectilinearly with the water concentration is not immediately obvious. It may be due to a ‘buffering’ equilibrium involving the impurities. Co-catalysts other than water. Trichloro- and monochloro-acetic acids, when used as cocatalysts, induced instantaneous polymerisation at –140°. With the following co-catalysts the rate of polymerisation at –78° decreased in the order: acetic acid > nitroethane > nitromethane > phenol > water [75a]. Since this is also the sequence of the acid dissociation constants of these substances in water, it appears that the ‘catalytic activity’, as shown by the rate of polymerisation, is correlated with the acidity of the cocatalyst in aqueous solution. However, there are two reasons for questioning the validity of this correlation. Theoretical considerations show that the free energy of dissociation of an acid in water, and hence the dissociation constant, is governed by the algebraic sum of the free energies for the solution of the undissociated acid in water, for vaporisation of the acid, for the formation of a free proton and an anion from the molecule of acid in the gas phase, and for hydration of the proton and anion. Thus the true acidity, given by the third of these

75

Developments in the Theory of Cationoid Polymerisations terms, is only fortuitously correlated with the aqueous acidity, and it is the true acidity which dominates the effective acidity in non-polar solvents. The second reason is that Satchell [78] has shown that in the protonation of m-xylene by catalysts composed of stannic chloride and acetic acid or the three chloroacetic acids as co-catalysts, the rate of reaction is inversely related to the aqueous acidity of these acids. Satchell rightly points out that, since the polymerisations are complicated reactions the rates of which are also affected by the terminating efficiency of the anion derived from the co-catalyst, no valid conclusions can be drawn from such studies about ‘catalytic efficiency’ in any fundamental sense. He interprets the order of effectiveness of the cocatalysts in terms of the stability of the complexes which they form with the metal halide. The DPs obtained in polymerisations catalysed by SnCl4-CCl3CO2H, with [SnCl4]/ [CCl3CO2H] ~ 3-4, [SnCl4] = (23-36) x 10-3 mole/l, at –20°, –50°, and –78° in n-hexane, chloroform, and methylene dichloride were studied by Imanishi, Higashimura, and Okamura [79]. They interpreted the results in terms of the Mayo equation in the form,

1 / DP = km / kp + J /[ P1 ]

(xvi)

The plots of 1/DP against 1/[P1] were linear, and the authors identified the term J, the slope of these plots, with kt/kp the unimolecular termination coefficient, without providing any evidence for the validity of this procedure. It seems plausible that indeed in hexane at the lowest temperature no chain breaking processes other than those characterised by km and kt are of importance, but at higher temperatures the existence of such reactions involving catalyst and/or co-catalyst and/or complexes formed from these is very probable. Moreover, in chloroform and methylene dichloride solution transfer with solvent seems likely to be important, especially again at the higher temperatures. For these reasons only the value of J for reactions in hexane at –78° can be accepted with confidence as kt/ kp. The fact that it is greater by a factor of 5 than that derived from Norrish and Russell’s results (Table 3) cannot be interpreted at present in view of the difference in both solvent and co-catalyst. The values of km/kp derived from the plots are shown in Table 4. At least at –78° they are almost independent of the nature of the solvent and thus the difference between these values and that derived from Norrish and Russell’s results (a factor of about 30) is probably due to the difference in the co-catalyst, and therefore in the structure of the anion. It is worth noting that with TiCl4 (in contrast to SnCl4) a change of co-catalyst from H2O to CCl3CO2H does not produce a significant change in km/kp (see Table 5). Inhibitors. Norrish and Russell found [30] that ethanol, t-butanol, diethyl ether, and acetone did not act as co-catalyst to stannic chloride in ethyl chloride. In the presence of

76

Temperature

104 km/kp 104 J

104 km/kp 104 J

104 km/kp 104 J

Solvent

n-C6H14

CHCl3

CH2Cl2

Catalyst

0.80 0.48 1.00 0.70 1.52 0.39

10.3 2.60 0.90

12.0 3.00 1.48

5.2

7.6 21.2 6.60 8.0 1.40

–78°

–50°

–20°

TiCl4

5.1

4.4

4.0

4.6

4.0

4.2

Activation energy differences (kcal/mol)

1.3

26.9

2.0

25.2

3.6

6.6

–20°

0.56

5.68

1.04

4.48

0.80

2.00

–50°

0.38

2.44

0.56

1.56

0.18

0.72

–78°

2.2

4.2

2.1

4.6

5.0

3.7

Activation energy differences (kcal/mol)

TiCl4•CCl3CO2H

54. 0

60.0

77.0

60.0

-

-

–20°

9.0

36.0

11.2

22.8

10.5

17.0

–50°

3.3

5.7

9.0

8.1

2.5

6.7

–78°

4. 8

3. 9

3. 4

3. 4

4. 3

2. 7

Activation energy differences (kcal/mol)

SnCl4•CCl3CO2H

Table 4. Results of Imanishi, Higashimura and Okamura [79]

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963)

77

Developments in the Theory of Cationoid Polymerisations

Table 5 Results of Plesch and collaborators on the DP of polyisobutenes Co-Catalyst

Solvent

H2O

Temperature

n-C6H14

EDP CCl3CO2H

Temperature 105 km/kp Temperature range EDP

CF3CO2H

20 8 –35° to –80°

–38° to –103°

–30° to –112°

–2

–5.5

–5.5

–75° 3.5 –5° to –75° –7.5 –75°

Temperature 105 km/kp Temperature range EDP

EtCl

–63° –71°

105 km/kp Temperature range

EtBr (a)

7 –60° to –80° –3.5

For References see text. EDP is in kcal/mole (a) In this system the main co-catalyst was probably water - see text

water they reduced the rate and the DP, as did butene-1 and -2. t-Butyl bromide is also not a co-catalyst, nor does it act as catalyst by itself [75b].

(d) Catalysis by TiCl4 Kinetic studies on the polymerisation of isobutene at low temperatures by titanium tetrachloride in various solvents form the subject of a series of papers by Plesch and his co-workers [9, 10, 13, 28, 32, 33, 71, 77, 80, 81]. The reactions were followed in an apparatus approximating to an adiabatic calorimeter by means of the temperature rise accompanying the polymerisation. In the early studies moisture was not rigorously excluded from the systems, but later [81] an elaborate vacuum technique was evolved and all reagents were carefully purified and dried. Titanium tetrachloride was also used as catalyst by Okamura and his collaborators [79] in a series of studies concerning the effects of solvent, catalyst, and co-catalyst on the DP of polyisobutene.

78

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) Polymerisations in hexane. The study of the reaction in hexane at low temperatures showed that it would not proceed in the absence of moisture [22, 28], and this was one of the observations which lead to the discovery of co-catalysis. The rates and DPs obtained when moist air was blown into a quiescent solution of isobutene and titanium tetrachloride in hexane were not very reproducible, and the reaction curves were S-shaped. Both the initial and maximum rates increased with increasing temperature [9], with ER = 8 ± 1 kcal/mole. The DP increased with decreasing temperature [22], such that EDP = –2 ± 0.5 kcal/mole. The relatively large, positive ER was taken to represent mainly Ei, which seems reasonable since micro-crystalline ice must have been involved in some way in the initiation reaction. A study by Imanishi, Higashimura, and Okamura [79] with [TiCl4] (3 - 48) x 10-3 mole/l, and unspecified quantities of water as the putative co-catalyst showed that at –20°, –50°, and –78° the variation of DP with monomer concentration obeyed the Mayo relation in the form shown in equation (xvi). Their results are shown in Table 4. As they did not prove that the DP is unaffected by, for instance, variations in [TiCl4] or [H2O], their derivation of kt/kp from the slopes of the plots cannot be accepted at face value. However, the values of km/kp obtained from the intercepts are valid. Plesch, Polanyi, and Skinner [28] found that HCl, SO2, CO2, EtOH, and Et2O were not cocatalysts, and the last two substances were shown to be inhibitors in that the addition of moist air to a solution containing them did not induce polymerisation. The search for co-catalysts other than water led to the discovery that trichloroacetic acid, sulphuric acid, and 20 percent oleum would act as a co-catalyst to titanium tetrachloride in hexane at about –75°, though none of these acids alone showed any catalytic activity under these conditions [9, 71]. Since trichloroacetic acid and its complexes with titanium tetrachloride are soluble in hexane, it was selected for further study [9]. The isobutene concentrations used were 0.62, 1.25 and 2.5 mole/l; [TiCl4] = (3 - 48) x 10-3 mole/l; [CCl3CO2H] = (0.3 - 6.6) x 10-3 mole/l; most experiments were done with [C4H8] = 1.25 mole/l at about –75°. The most notable difference between reactions co-catalysed by trichloroacetic acid and those cocatalysed by water is that the former give reactions with a rate decreasing monotonically from a maximum initial value, in contrast to the S-curves obtained with water. It was found that the initial rate increased linearly with [CCl3CO2H] at constant [TiCl4]. At constant [CCl3CO2H] the rate increased with [TiCl4] in an S-shaped curve up to [TiCl4]/ [CCl3CO2H] ~ 4, and thereafter remained constant. The variation of initial rate with [C4H8] was not investigated in detail, but the evidence points to a first-order dependence. The variation of rate with temperature gave ER = –7.5 kcal/mole. The variation of DP with temperature gave EDP = –7.5 kcal/mole. Since the DP was that of polymers obtained at high, or complete, conversion, and since large temperature rises

79

Developments in the Theory of Cationoid Polymerisations accompanied the reaction, no detailed conclusions can be drawn from the variation of DP with the concentrations of the reagents. It was found that variations in catalyst and cocatalyst concentration had only a small effect on the DP, but the DP did increase with increasing monomer concentration. An analysis of the rather scattered results by means of Mayo plots gives km/kp = 3.5 x 10-5, kt/kp = 5 x 10-5 mole/l, (both ± 20 per cent approx.) at –75°, and the term involving [CCl3CO2H] is negligibly small. These results are in reasonable agreement with those of Imanishi, Higashimura, and Okamura [79] (see Table 4). One of the most important observations made was that at low co-catalyst concentrations the polymerisation did not go to completion; further reaction could be induced by the addition of more trichloroacetic acid. It was concluded that the co-catalyst is consumed in a termination reaction, and this was confirmed by the detection of chlorine [9] and of trichloroacetate groups [10] in the polymers. It was also shown [9] that when [TiCl4]/[CCl3CO2H] was less than ~ 6, the reaction curves were S-shaped, and that this phenomenon was most probably due to a slow buildup of the concentration of growing chains; thereby a connection with the polymerisations co-catalysed by water was established. The detailed discussion of reaction mechanism [9] is of historical interest since it is one of the earliest expositions indicating the simultaneous occurrence of different chain breaking mechanisms. Imanishi, Higashimura, and Okamura [79] have reported on the DPs of polymers formed at –20°, –50°, and –78° with [TiCl4]/[CCl3CO2H] ~ 3-4, and [TiCl4] = (5-8) x 10-3 mole/ l. (see Table 4). As mentioned above their values of km/kp at –78° agree reasonably well with Plesch’s. The slope of the Mayo plots they interpret, as in all their work, as kt/kp. While there is some evidence from Plesch’s work [9] that this is approximately valid at -78°, it seems likely that at the higher temperatures chain breaking reactions other than the unimolecular termination characterised by kt will become more important, so that at –50°, and even more so at –20°, J can probably no longer be identified with kt/kp. A preliminary study of polymerisations co-catalysed by trifluoroacetic acid, with an improved technique [77], showed that at [C4H8] = 0.94 mole/l, [TiCl4] = 5.68 x 10-3 mole/l, and [CF3CO2H] = 0.81 x 10-3 and 1.22 x 10-3 mole/l, the variation of DP with temperature gave EDP = -3.5 ± 1.5 kcal/mole. Unfortunately, the large difference between this and the EDP obtained with trichloroacetic acid as co-catalyst cannot be interpreted in detail without a knowledge of the temperature dependence of the individual chainbreaking coefficients. Reactions in various alkyl halide solvents. A preliminary survey of polymerisations catalysed by titanium tetrachloride in various alkyl halide solvents was undertaken using highly purified materials and a vacuum technique. The most important qualitative result obtained was that in the solvents methylene dichloride, ethyl chloride, ethylene dichloride,

80

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) and isopropyl chloride, between 5° and the fp of the solvent, the polymerisation would not proceed in the absence of water, thus proving that these alkyl halides do not act as co-catalysts for titanium tetrachloride [32, 33, 77, 80]. It was possible to establish this point because in these solvents, as in hexane, the co-catalyst water is consumed during the polymerisation so that, if initially the residual water concentration was sufficiently low, the reactions would stop at low conversion. In the quiescent systems thus obtained polymerisation could be restarted by the addition of small quantities of water or trifluoroacetic acid. With ethyl bromide as solvent a brief, exploratory study [77] showed that the rates and DPs were more irreproducible than with other alkyl halides, and this was ascribed, at least partly, to the relatively high dissociation constant of ethyl bromide to ethylene and hydrogen bromide. No evidence was obtained whether ethyl bromide itself is a co-catalyst, and the putative co-catalyst in the reaction was residual water and possibly traces of t-BuBr formed from HBr and isobutene. Experiments with [C4H8] = 0.11-0.92 mole/l, [TiCl4] (2.7-11.2) x 10-3 mole/l, T = –38° to –103° showed that EDP = 5.5 ± 0.5 kcal/ mole; that below about –60° the DP is almost independent of monomer concentration; and that km/kp = 2 x 10-4 at –63° and 8 x 10-5 at –71°. A small number of experiments with ethyl chloride as solvent [77], before the most rigorous techniques had been developed, gave rather irreproducible rates, but quite consistent DPs. With water as the putative co-catalysts, [C4H8] = 0.173 mole/l, [TiCl4] = (2.5-7.5) x 10-3 mole/l, T = –30° to –112°, the DP was found to be independent of the titanium tetrachloride concentration and EDP = -5.5 ± 0.5 kcal/mole. With CF3CO2H as co-catalyst at –75°, and with [C4H8] = 0.09 - 0.18 mole/l, [TiCl4] = 5 x 10-3 mole/l, [CF3CO2H] = 0.01 x 10-3 mole/l, it was found that the DPs were the same as those obtained without CF3CO2H; that the DP was independent of monomer concentration; and that km/kp = 7 x 10-5. These results, summarised in Table 5, show that the behaviour of the DP is very similar in ethyl bromide and ethyl chloride, and suggest that the value or km/kp in polar solvents is approximately the same for the co-catalysts water and trifluoroacetic acid. Very similar conclusions are derivable from the results of Imanishi et al. [79] shown in Table 4, and from a comparison of these with those in Tables 5 and 6. With chloroform as solvent without added co-catalyst (water being the putative cocatalyst), and with [TiCl4] = (3 - 48) x 10-3 mole/l, and also with CCl3CO2H as cocatalyst ([TiCl4]/[CCl3CO2H] ~ 3-4, [TiCl4] = (5-8) x 10-3 mole/l) Imanishi et al. [79] found that the Mayo monomer plots were linear at –20°, –50°, and –78°. The values of km/kp calculated from these are shown in Table 4. With CCl3CO2H as co-catalyst km/kp is almost the same as with water*. * The slope of the Mayo plots was interpreted again as kt/kp and the reasons why this is probably invalid have been explained above.

81

Developments in the Theory of Cationoid Polymerisations

Table 6 Polymerisation of isobutene by titanium tetrachloride and water in methylene dichloride [80, 87] A. Chain breaking constants Temperature

18°

105 km/kp

420

kw/kp

5°

55

–14°

–32°

–48°

–60°

–75°

–90°

48

9.2

3.0

11

3.3

1.25

7.8

0.52

0.19

0.16

2040

313

25

0.4

107 (kt + J)/kp (mole/l)

B. Activation energy differences Activation energy difference (a)

Em - Ep

Ew - Ep

Ez - Ep (b)

Temperature range 18°

to –14°

10

–75° to –90°

1.4

to –32°

17

–60° to –90°

~0

5°

–14° to –90°

11

(a) In kcal/mole (b) Ez - Ep corresponds to the temperature coefficient of (kt + J)/kp

These authors also carried out a similar study with methylene dichloride as solvent, using the same concentrations as for the experiments in chloroform. The values of km/kp (Table 4) are very similar to those for chloroform solutions**. Kinetic studies in methylene dichloride solution. The most detailed kinetic study was carried out by Plesch and his collaborators with methylene dichloride as solvent and water as co-catalyst, but only a preliminary summary of the results has been published [80]; much of the information given below is taken from material which is being submitted for publication during 1963. This study showed for the first time in detail the influence of the water concentration on the whole pattern of the reaction, and it also revealed some unexpected effects of temperature on the reaction pattern. ** The slope of the Mayo plots was interpreted again as kt/kp and the reasons why this is probably invalid have been explained above.

82

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) The technique and apparatus used in this work have been described in detail [81]. The reaction vessel was made hydrophobic by exposure to the vapour of trimethylchlorosilane and evacuated for several hours. Then isobutene, dried by sodium, and methylene dichloride, stored over calcium hydride, were distilled into it, the temperature adjusted, and the reaction started by the breaking of a phial containing a solution of titanium tetrachloride in methylene dichloride and one containing water. These could be broken in this, or the reverse, order, or simultaneously. The ensuing reaction was registered as a time-temperature curve by an automatic recorder. The range of conditions studied was: [C4H8] = 0.05 –0.6 mole/l, [TiCl4] = (0.1-5) x 10-3 mole/l, [H2O] = (0.05-5) x 10-4 mole/l, T = 18°- –95°. The reaction mixtures were clear and colourless; at temperatures below about –15° the polymer came out of solution during the reaction. The half-lives of the reactions ranged from 2 to 60 s, the yield, rate, and DP were uninfluenced by the sequence in which the catalyst phial and water phial were broken, the DP of the polyisobutenes ranged from 20 to 2 x 105, and elementary and spectroscopic analyses showed the polymers to contain chlorine, OH-groups and vinyl and tri-substituted double bonds. The extent of reaction (yield). The yield obtained in the polymerisations depended on the water concentration in the manner illustrated in Figure 13, and from the intercepts of plots such as these the amount of residual water could be estimated as equivalent to about 10-5 mole/l. The water concentration just sufficient to give a yield of 100 per cent, [H2O]c, was found to fall with decreasing temperature, so that it could not be determined reliably below about

Figure 13 The variation of the yield, Y, with the concentration of added water [iC4H8] = 0.1 mole/l. [TiCl4] = (1.2 - 2.5) x 10-3 mole/l

83

Developments in the Theory of Cationoid Polymerisations –60°. In other words even with the most rigorous experimental procedure the amount of residual water could not be reduced significantly below [H2O]c at temperatures below –60°, so that in that temperature range only comparatively few incomplete reactions were achieved. Reactions which had stopped by consumption of water could always be re-started by the admission of moist air or the breaking of a phial containing water. It was found that at –60° the yield obeyed the relation

(

)

log [ P1 ]∞ /[ P1 ] ∝ [H 2 O]

2

0

(xvii)

where [P1]0 is the initial, and [P1]∞ the final monomer concentration. This is similar to Hayes and Pepper’s yield function for the polymerisation of styrene by sulphuric acid [82, 83]. The order and rate of the reactions. Above about –30° the reaction curves were rectilinear, i.e., the reactions were of zero order and ceased abruptly. Below –60° the reactions were of first order, and at intermediate temperatures they were initially of zero order and the extent of the zero order region increased with increasing temperature. This change of order with temperature and with conversion was a most striking and very reproducible feature. At all temperatures the initial rate R0, was proportional to the first power of the monomer concentration; for the zero order reactions this applied to the constant rate which prevails throughout the reaction:

Ro = k1[P1]0

(xviii)

When [H2O] > [H2O]c the variation of kl with [TiCl4] followed a curve of the type shown in Figure 14, at all temperatures, and k1 was independent of [H2O] provided that this was greater than [H2O]c. For [H2O] < [H2O]c, k1 varied with [H2O] as illustrated in Figure 15. A log-log plot showed that kl ∝ [H2O]2; the limiting value to which kl tends is proportional to [TiCl4]; and at very low [H2O], kl is almost independent of [TiCl4]. For the experiments in which the [TiCl4] lay in the range where R0 is directly proportional to [TiCl4] R0 = k2[TiCl4] [P1]0

(xix)

The way in which k2, defined by this equation, varies with temperature is shown in Figure 16. The DP of the polymers. The variation of the DP with [H2O] at T = –13° is shown in Figure 17 and similar curves were obtained at other temperatures. The DP was completely independent of [TiCl4]; the variation of DP with monomer concentration obeyed the Mayo equation down to –50°, but at –60° and –90° the DP was independent of monomer concentration down to

84

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963)

Figure 14 The variation of k1 with [TiCl4] at –35°; [H2O] > [H2O]c

Figure 15 The variation of kl with [H2O] at –60°. [TiCl4] = 2.1 x 10-3 mole/l

85

Developments in the Theory of Cationoid Polymerisations

Figure 16 The variation of k2 with temperature

Figure 17 The dependence of the DP on [H2O] at –13°⋅[i-C4H8] = 0.09 mole/l. [TiCl4] = 2.2 x 10-3 mole/l 0.05 mole/l; the plot of log DP against 1/T is rectilinear, with EDP = –8.2 kcal/mole, down to about –70°, and at lower temperatures it bends towards the 1/T axis. The shape of the DP distribution curves [84] changed with temperature in that those of polymers prepared at above about –50° show a well developed peak, whereas those of polymers prepared at lower temperatures fall off in a curve convex to the DP axis from a maximum at the lowest DP.

86

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963)

Discussion It has not been possible so far to construct a complete interpretation of these observations in terms of a mechanism and a corresponding kinetic scheme. However, a few conclusions appear to be fairly obvious. The role of water is two-fold. It is a co-catalyst, and its consumption during the reaction is, or is associated with, a kinetic termination. Moreover, there is evidence that the reaction in which water is consumed is of a lower order with respect to monomer than the propagation reaction, which therefore is most probably of first order with respect to monomer. The dependence of the DP on temperature indicates an upper limit of 140° for the ceiling temperature of polyisobutene in about 0.1 base-molar solution*. The curvature of this plot at low temperatures indicates that the DP is controlled by different processes at high and low temperatures; a similar curvature has been reported by Kennedy and Thomas [52]. The variation of DP with monomer concentration shows that monomer transfer is important at all temperatures, and dominant at the lower end of the range. The values of km/kp obtained from the Mayo plots, shown in Table 6, agree closely with those obtained by Imanishi et al. [79] (Table 4). The dependence of the DP on the water concentration shows that it attains a maximum, but at a water concentration which is so low that it could not be determined with any accuracy. At greater water concentrations the Mayo plots of 1/DP against [H2O] are linear. If the slopes of these are represented by kw/kp, i.e., if it is assumed that the concentration of chain breaking agent is equal to [H2O] the values shown in Table 6 are obtained. The Mayo equation for these reactions thus has the form

1 / DP = km / kp + kw [H 2 O] / kp [ P1 ] + ( kt + J ′) / kp [ P1 ]

(xx)

where the term J′ includes the rates of all unspecified chain breaking reactions and probably consists mainly of the solvent transfer term ks [S]. The values of (kt + J′)/kp are shown in Table 6. As far as the rate of reaction is concerned, the change of kinetic order with temperature, and the strange shape of the Arrhenius plot (Figure 16) indicate that the nature of the rate controlling processes changes with temperature. * It has been stated erroneously that the extrapolation of this plot to log DP = 0 gives the actual ceiling temperature [80].

87

Developments in the Theory of Cationoid Polymerisations The kinetic data may be summarised by the following empirical equation

(

R = ke [ X ][ P1 ] / 1 + kd [ P1 ] /[ P1 ]0

)

(xxi)

with the condition that at the higher temperatures kd is large, so that

R = ke [ X ][ P1 ]0 / kd

(xxii)

and at low temperatures kd is small, giving

R = ke[X][P1]

(xxiii)

The species X must fulfil the condition that when [H2O] > [H2O]c, [X] ∝ [TiCl4] and when [H2O] < [H2O]c, [X] ∝ [H2O]2. Chain-Transfer with anisole. The phenomenon of chain-transfer, especially with aromatic compounds, has been extensively investigated for the polymerisation of styrene, but there is only one such study with isobutene [13]. Isobutene (0.1 mole/l) was polymerised by titanium tetrachloride (3 x 10-3 mole/l) in methylene dichloride with a constant, low, but unknown concentration of water in the presence of anisole (0.02 to 0.15 mole/l) over the temperature range –9° to –90°. The reactions were stopped at 10–20 per cent conversion by the addition of methanol. Infrared and ultraviolet spectra showed the polymers to contain (presumably terminal) p-methoxyphenyl groups. From the Mayo plots (1/DP - [anisole]/[C4H8]) the relative transfer coefficient kr/kp was found to be 5.3 x 10-3, a value which did not vary significantly with temperature. The transfer reaction can be represented as follows:

HPn+ + Ph ⋅ O ⋅ CH 3

kr

+

→ HPn ⋅ C 6 H 5 ⋅ O ⋅ CH 3

fast → HPn ⋅ C 6 H 4 ⋅ O ⋅ CH 3 + HP1+ i − C 4 H8 (14)

Since the anisole also reduced the rate and the yield, it must be involved in a termination reaction; a plausible scheme for this involves the formation of an oxonium ion, which is too stable to propagate the reaction: +

+

HPn ⋅ C 6 H 5 ⋅ O ⋅ CH 3 → HPn ⋅ C 6 H 4 ⋅ O⋅ CH 3 | H

88

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) For the polymerisation of styrene (SnCl4-H2O-PhNO2-CCl4 at 0°) kr/kp for anisole was found [85] to be 1.62. It is highly probable that the big difference between this and the value for isobutene reflects mainly the difference between the kps for the two monomers. The very low value of kr/kp in the polymerisation of isobutene - or the very large kp of isobutene - accounts for the observation [86] that, whereas styrene polymerising cationically in the presence of preformed poly-p-methoxystyrene will form grafts by reacting with pendent rings, isobutene will not do so.

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Developments in the Theory of Cationoid Polymerisations 13. J. Penfold and P. H. Plesch, Proc. Chem. Soc., 311 (1961). 14. D. K. Thomas, Trans. Faraday Soc., 57, 511 (1961). 15. C. J. Panton and P. H. Plesch, unpublished. 16. A. S. Hoffmann, J. Polym. Sci., 34, 241 (1959). 17. E. Collinson, F. S. Dainton, and H. A. Gillis, J. Phys. Chem., 63, 909 (1959). 18. A. G. Evans and G. W. Meadows, Trans. Faraday Soc., 46, 327 (1950). 19. W. C. E. Higginson and N. S. Wooding; Thesis of N. S. Wooding, Leeds (1950). 20. M. Szwarc, private communication. 21. L. Schmerling and V. N. Ipatieff, ‘Advances in Catalysis’ Vol.2, Academic Press, New York (1950). 22. P. H. Plesch, Thesis, Manchester (1946). 23. A. G. Evans, D. Holden, P. H. Plesch, M. Polanyi, H. A. Skinner, and M. A. Weinberger, Nature, 157, 102 (1946). 24. A. G. Evans, G. W. Meadows and M. Polanyi, Nature, 158, 94 (1946). 25. A. G. Evans and M. A. Weinberger, Nature, 159, 437 (1947). 26. A. G. Evans, G. W. Meadows, and M. Polanyi, Nature, 160, 869 (1947). 27. A. G. Evans and M. Polanyi, J. Chem. Soc., 252 (1947). 28. P. H. Plesch, M. Polanyi, and H. A. Skinner, J. Chem. Soc., 257 (1947). 29. A. G. Evans and G. W. Meadows, J. Polym. Sci., 4, 359 (1949). 30. R. G. W. Norrish and K. E. Russell, Nature, 160, 543 (1947). 31. R. G. W. Norrish and K. E. Russell, Trans. Faraday Soc., 48, 91 (1952). 32. W. R. Longworth, P. H. Plesch and P. P. Rutherford, Doklady Akad. Nauk USSR, 127, 97 (1959). 33. W. R. Longworth, P. H. Plesch and P. P. Rutherford, Proc. Chem. Soc., 68 (1960).

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92

W. R. Longworth and P. H. Plesch, J. Chem. Soc., 1618 (1959).

Isobutene from the ‘Chemistry of Cationic Polymerisation’ (1963) 74. R. G. W. Norrish and K. E. Russell, Trans. Faraday Soc., 48, 91 (1952). 75a. K. E. Russell, Book, p. 114*. 75b.K. E. Russell, Book, p. 117*. 76. K. E. Russell, private communication. 77. R. H. Biddulph and P. H. Plesch, J. Chem. Soc., 3913 (1960). 78. D. P. N. Satchell, J. Chem. Soc., 1453 (1961); Proc. Chem. Soc., 296 (1962). 79. Y. Imanishi, T. Higashimura and S. Okamura, Chem. High Polymers (Japan), 18, 333 (1961). 80. R. H. Biddulph, P. H. Plesch and P. P. Rutherford, International Symposium on Macromolecules, Wiesbaden, 1959, paper III A 10. 81. R. H. Biddulph and P. H. Plesch, Chem. and Ind., 1482 (1959). 82. M. J. Hayes and D. C. Pepper, Proc. Chem. Soc., 228 (1958). 83. R. E. Burton and D. C. Pepper, Proc. Roy. Soc., A 263, 58 (1961). 84. C. J. Panton and P. H. Plesch, to be published. 85. G. F. Endres and C. G. Overberger, J. Amer. Chem. Soc., 77, 2201 (1955); J. Polym. Sci., 16, 283 (1955). 86. H. C. Haas, P. M. Kamath and N. W. Schuler, J. Polym. Sci., 24, 85 (1957). 87. P. H. Plesch, to be published. 88. R. O. Colclough and F. S. Dainton, Trans. Faraday Soc., 54, 894 (1958). 89. R. O. Colclough and F. S. Dainton, Trans. Faraday Soc., 54, 898 (1958). 90. R. Azami and N. Tokura, J. Polym. Sci., 42, 545 (1960). 91. S. Okamura, T. Higashimura and I. Sakurada, J. Polym. Sci., 39, 507 (1959). 92. S. Okamura, T. Higashimura and H. Yamamoto, J. Chem. Soc., (Japan) Ind. Chem. Section, 61, 1636 (1958). * Editor’s Note: No 14 in the Publications List

93

Developments in the Theory of Cationoid Polymerisations 93. T. Higashimura, Y. Sunaga and S. Okamura, Chem. High Polymers (Japan), 17, 257 (1960). 94. S. Okamura, T. Higashimura and Y. Imanishi, Chem. High Polymers (Japan), 16, 69 (1959).

94

Cationic Polymerisation from ‘Progress in High Polymers’ (1968)

3.2

Cationic Polymerisation from ‘Progress in High Polymers’ (1968)

Prologue The next chapter is a contribution to a collective volume containing detailed treatments of various themes in polymer science. The author took the opportunity to provide answers to some of the well-aimed questions about cationic polymerisations that had been put by two experienced polymer chemists (A) and from this the piece evolved into a conspectus of most parts of the subject. As such it is a useful snap-shot of this author’s thinking at that time. However, because of his familiarity with the subject, his piece turned out to be a rather daunting assembly of ‘worst case scenarios’, but for this very reason the article is also useful in showing just how complicated the subject can become. Amongst several other innovations there is here a demonstration of how the Mayo plots can reveal the kinetic order of a polymerisation with respect to the monomer. Another timely advance is the generalisation of the Mayo equation for the case of a dieidic polymerisation by unpaired and paired cations. This development was taken further in a very useful review that can be considered to be a follow-up or progress report from the work under discussion here (B). The thermochemical assessment of the feasibility of various possible reactions is developed further here, and there is a didactically useful example of this author being ‘taken in by his own propaganda’. In one calculation he shows thermochemically that the addition of the TiCl3+ ion to an alkene is unlikely, then shows that under different circumstances an initiation by the addition of an AlX2+ ion to a monomer is theoretically possible. That subject then did not surface again in his work until 1972 (92, 93) and it took until 1980 for the experimental solution of the problem of the initiation by aluminium halides to be published, in which the above-mentioned cationation is an essential feature (112). This paper also contains electrochemical considerations of the problem of ion-pairing and a fairly detailed discussion of dieidic propagation by complexed and uncomplexed cations. The equations for the latter system are then applied successfully to hitherto unexplained and unexploited observations by others.

95

Developments in the Theory of Cationoid Polymerisations In regard to the development of the subject as a whole, this Review is also useful because in it most of the older literature is given its due, before other, less scrupulous authors attempt to write reviews and textbooks without proper regard for precedents and priorities.

References (A) F. R. Mayo and M. Morton in Unsolved Problems in Polymer Science, National Academy of Science, NRC, Publication No.995, Washington, 1962. (B) D. J. Dunn in Developments in Polymerisation-1, Ed., R. N. Haward, Applied Science Publishers Ltd., London, 1979.

96

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) This chapter was first published in Progress in High Polymers, Volume II, Ed., J. C. Robb and F. W. Peake, 1968, Iliffe Books, London, 1968, 137-191.

1 Introduction This paper may be regarded as a sequel to my second book on Cationic Polymerisation [1]. I have aimed here at providing a fairly detailed discussion of some theoretical aspects of the subject which is still (or perhaps now more than ever before) in Dainton’s words rudis indigestaque moles (a crude and ill-digested, i.e., confused, mass) [2]. I also intend to discuss specifically some of the problems raised by Mayo and Morton in their article ‘Ionic Polymerization’ in the book Unsolved Problems in Polymer Science [3]. It needs to be said at the outset that my attempts at clarification have not been made easier by the discovery [4] of the pseudocationic polymerizations early in 1964. Since exploration and revaluation of these reactions are still only in their early stages, there are inevitably many loose ends and open questions and probably also some inconsistencies in the present work. Some aspects of pseudocationic polymerization have been reviewed [5-7]. It should be noted that this discovery makes many of the theoretical discussions in Reference 1 of purely historical interest. Since the publication of Reference 1 several reviews on, and relevant to, cationic polymerization [8] and on carbonium ions [9] have appeared.

1.1 Note on references It would make this article too cumbersome if I were to give detailed references for the factual bases of every generalization. Where such references are not given they will be found in Reference 1 and the subsequent reviews.

2 The nature of the propagating species: I

2.1 The origin and status of the carbonium ion theory The polymerizations of olefins catalysed by metal halides have been interpreted in terms of carbonium ions as the reactive species since the work of Hunter and Yohé (see p.109). Although the discovery of co-catalysis subsequently showed that their theory is not valid for many systems,

97

Developments in the Theory of Cationoid Polymerisations it did at the time provide some basis for the explanation of the reactions in terms of carbonium ions. The theoretical picture which was evolved from the discovery of co-catalysis saw the polymerizations entirely in terms of carbonium ions as the chain-propagating species. This theory became firmly established because it could account satisfactorily for most of the observations; because carbonium ions were used extensively and successfully in the interpretation of many organic reactions; and because the existence of carbonium ions and their characteristics were clearly demonstrated under many different conditions [1]. Later the polymerizations of cyclic oxygen compounds were interpreted successfully by an obvious extension of the theory involving oxonium and carboxonium ions. However, a search of the literature reveals that in fact there was until 1964 very little evidence concerning the presence of carbonium ions during polymerizations. At this point it is necessary to distinguish carefully between a demonstration that an olefin can form carbonium ions in the presence of a catalyst, (e.g., H2SO4) or a syncatalyst, (e.g., SnCl4·H2O), and a demonstration that these ions are present during the polymerization reaction, and necessarily connected with it. (See also reference 1, Chapter 1.) The systems for which the presence of ions during polymerization has been shown, and also those for which the absence of ions seems reasonably well established, have been listed (up to early 1965) [5]. Therefore only a brief summary will be given here of the early stages in the quest for ions. Evans and co-workers [10] showed that in the dimerization of 1,1-diphenylethylene and some of its derivatives in benzene by trichloroacetic acid, SnCl4 + H2O, and SnCl4 + HCl, the polymerizing solutions had an absorption spectrum indicating the presence of carbonium ions, though some of the spectral features have not been explained unambiguously. However, when SbCl3 + HCl was used as a syncatalyst the reacting solution did not show the spectrum characteristic of the carbonium ion, and this only appeared many hours after the monomer-dimer equilibrium had been attained [5]. Relatively few attempts have been made to demonstrate the presence of ions in the polymerization of styrene, the most extensively studied of all monomers. Pepper [11] made conductivity studies on stannic chloride solutions in various solvents with and without monomer and added water, using open systems. He concluded that his results shed little light on the question of whether chain-carrying cations were present (which, indeed, he presumed) or on their concentration. Brown and Mathieson [12] found that for the polymerization of styrene by chloroacetic acids in nitromethane, the conductivity was indistinguishable from zero when no water was added, although the reaction rate was appreciable, and with increasing amounts of added water the conductivity increased, but the polymerization rate decreased. Therefore their results gave no useful information on the question of the participation of carbonium ions.

98

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) Metz [13] made measurements of dielectric loss on CCl4-(CH2Cl)2 solutions in which styrene and stilbene were polymerised by stannic chloride. He concluded that ions were present during the polymerization, but since he worked with open systems and did not obtain rate measurements concurrently with the electric measurements, his findings too did not show clearly whether the ions are necessarily involved in the polymerization. A major effort in this field was made by Jordan and Treloar [14]. They showed that a yellow colour developed in the following systems: Time development of colour

Spec. measured

1. Styrene AlCl3

CCl4

not stated

time not stated

2. Styrene AlCl3

(CH2Cl)2

not stated

time not stated

3. Styrene SnCl4

(CH2Cl)2

CH3CHPhCl present: immediate, intense

0.5 h, peak at 401 μm

4. Styrene SnCl4

(CH2Cl)2

CH3CHPhCl present: slow

slowly developing peak at 440 μm

5. Styrene AlCl3

-

H2O added: immediate, intense

-

This information and details given in the paper would prove the case for the presence of carbonium ions during polymerization, were it not that non-polymerizing mixtures of styrene and some metal halides have a yellow colour which to the eye is very similar to that of the carbonium ion solution, that the spectra were not measured until a relatively long time had elapsed since the mixing of the reagents, and that the development of the spectra has not been correlated with the progress of polymerization. As it is, in view of the facts to be related in the next section, the case for the presence of carbonium ions during these polymerizations is not proven on the evidence as presented in the papers, although at least for systems 3 and 5 there are very strong indications in favour of this. At this point we must emphasise that the spectroscopic detection of ions does not mean necessarily that those same ions are the chain-carriers in polymerization. Up to 1965 it was believed by most workers that the absorption near 420 μm and 310 μm (with ε420 > ε310), which develops when styrene or 1-phenylethanol are treated with acid, was due to the 1-phenylethyl ion (see reference 15 and references quoted therein).

99

Developments in the Theory of Cationoid Polymerisations This assignment was queried [16-18] and detailed investigations [19a] showed that the principal originator of this spectrum is the 3-(1-methyl, 3-phenylindanyl) cation (I), and that, according to the conditions of the experiment, other ions of the diphenylmethyl type may contribute. The spectrum of the 1-phenylethyl ion has still not been identified but that of the homologous 1,3-diphenyl-n-butyl cation (II) was shown to have only a single important absorption, at 315 μm [19a].

CH3

H

CH2 Ph

(I)

+ +

CH 3 • CHPh • CH 2 C HPh

(II)

The position concerning aliphatic hydrocarbons has been summarised [5]. Some studies on the conductivity of catalytic solutions (mainly AlCl3 in EtCl with various oxygen compounds) have indeed shown that their conductivity is correlated with the degree of polymerisation (DP) of polyisobutenes subsequently formed in them. This is strong evidence that the chain-carriers are ions, and it has been shown that this correlation must mean that the number of ions concerned in the polymerization must be very much smaller than the number of ions derived from the catalyst [20, 21]. The kinetics of the polymerization of isobutene by SnCl4 + H2O in EtCl are difficult to explain on any theory other than that of propagation by free ions [22], and the polymerization of the same monomer by TiCl4 + H2O in CH2Cl2 shows features which can be explained reasonably satisfactorily on the basis of propagation by both free ions and ion-pairs, the relative importance of the two changing with temperature [23]. Thus, for isobutene with syncatalysts there is some circumstantial evidence for cations as the chain-carriers. For 3-methylbutene-1 and related monomers the occurrence of isomerizationpolymerisation (see sub-section 4.1) is strong evidence that the chain-carriers are ions. In the system cyclopentadiene-trichloroacetic acid-benzene the occurrence of ions during polymerization has been shown, but these arise from the protonation of conjugated double bonds in the polymer. However, there is also circumstantial evidence for the participation of carbonium ions in the growth reaction [24].

100

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) For the polymerization of alkyl vinyl ethers there is no direct evidence for or against the chain-carriers being ionic. Some aspects of this question are discussed in sub-section 4.4. A detailed study of the polymerization of N-vinylcarbazole by tetranitromethane has provided strong evidence that in this system the reaction is propagated by a very small concentration of carbonium ions [25]. Studies on the ‘cationic’ polymerization of cyclic ethers, cyclic formals, lactones and other heterocyclic compounds have proliferated so greatly in the last few years that a detailed review of the evidence concerning participation of oxonium and analogous ions in these reactions cannot be given here. Suffice it to say that there is firm evidence for a few, and circumstantial evidence for many such systems, that the reactive species are indeed ions; and there appears to be no evidence to the contrary. A few systems will be discussed in sub-sections 3.2 and 4.4. Thus we can say that in the whole field of cationic polymerization there are still very few studies which prove unambiguously the participation of ions as chain-carriers, that there are many more which provide strong circumstantial evidence, and that the theory has been accepted so widely in large measure because it fits in well with the current views on many types of organic reactions. This brief review of some important lines of evidence concerning the nature of the chain-carrier in cationic polymerizations has been occasioned by the new findings, to be described in subsection 2.2, which have made it necessary to reappraise the whole question.

2.2 Polymerization without carbonium ions The work of Pepper [26, 27] has shown that the polymerization of styrene by sulphuric, and especially perchloric, acid in certain polar solvents follows simple kinetics which can be interpreted by a fast initiation and a slow propagation. It was an obvious step to represent the initiation as a proton transfer from acid to olefin, and the propagation as a reaction between the resulting carbonium ion and the monomer; indeed, anything else would have been completely at variance with the then current ideas. The propagation rate constants deduced on this basis were much lower, and the corresponding activation energies much higher, than was generally. expected, but this was no obstacle to their acceptance. However, there are other features of the reactions which did give stronger cause for suspicion. Among these are that in nitrobenzene solution perchloric acid would not catalyse the polymerization and that in nitroethane the reaction was abnormally slow and not of first order; that the variation of rate with catalyst concentration in ethylene dichloride is strictly rectilinear, which is reconcilable with ionic chain-carriers only on the unlikely assumption that the propagation rate constants for free ions and

101

Developments in the Theory of Cationoid Polymerisations ion-pairs are very similar (see Section 6); and that water in concentrations up to 20 times that of the acid had no effect on the rate constant. Since the determination of absolute rate constants is one of the most urgent problems in cationic polymerization, and the styrene-perchloric acid system seemed to be so clean and simple, Gandini and Plesch set out first to check Pepper and Reilly’s results by determining spectroscopically the concentration of carbonium ions during polymerization, and they intended then to extend the method to other monomers. However, their findings were not as expected. A comparison of spectroscopic and conductivity measurements with rate measurements in an adiabatic calorimeter showed [4] that in methylene dichloride solution: a) During the polymerization the solution has a conductivity no greater than that of the acid solution only, and no absorption at the wavelength which was at that time believed to be characteristic of the styryl or poly-styryl ion (425 μm). b) When the polymerization is almost complete, conductivity and colour (owing to an absorption peak near 425 μm) appear simultaneously and increase to a maximum which remains constant. Addition of styrene at this stage instantaneously removes the colour and reduces the conductivity to its initial value, and polymerization sets in immediately with a rate constant equal to that of the first reaction. d) When polymerization is over, conductivity and absorption begin once more to rise. e) Water does not affect the rate, but prevents formation of an equivalent of carbonium ions at the end of the reaction, so that if [H2O] is greater than [HClO4] no ions at all are detectable spectroscopically at the end of the reaction. f) Pepper and Reilly’s kinetics were confirmed, and a propagation rate constant and activation energy were found which are in close agreement with theirs when allowance is made for the different dielectric constant (DC) of the solvents used in the two studies. g) There is evidence for equilibrium formation of a complex involving 4C8H8; when [C8H8] falls to less than 4[HClO4], ions are formed very rapidly; however, these are mainly the ion (I) and others of the diphenyl-methyl type [4d]. With sulphuric acid, also in methylene dichloride solution, no carbonium ions were visible throughout the polymerization, and none were formed at the end of the reaction.

102

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) Gandini and Plesch concluded that in these systems the chain-carriers are not ionic. Since they are certainly highly polar and in many respects behave as if they were ionic, we called the polymerizations propagated by them pseudo-cationic. Admittedly, in retrospect our original evidence for the non-ionic nature of the chain-carriers looks less convincing, but since that time many other phenomena have been found which support our view very forcibly [18]; the case for the reality of pseudo-cationic polymerizations has been presented in detail [7], and therefore the argument need not be repeated here. It appeared to us that the only reasonable non-ionic reaction product of an acid and an olefin would be an ester, and for this reason we put forward the idea that this is the active species in the pseudo-cationic polymerizations. Of course, the idea of an ester in this role has a respectable ancestry which has been discussed in this new context [6]. The ester mechanism of polymerization will be discussed in sub-section 3.3. It must be understood that our conclusion concerning the non-ionic nature of the chain-carriers in the pseudocationic polymerizations is quite independent of our view that the chaincarriers are esters; this is at present merely an hypothesis to explain our factual conclusion. The discovery of pseudo-cationic polymerizations has made it necessary to re-assess a very large part of the results in this field. The situation is in many ways similar to that created some 20 years ago by the discovery of co-catalysis, but whereas in the late 1940s there was only a handful of papers, there is now a vast body of information dealing with many monomers and catalysts which needs to be scrutinised.

3 The mechanism of catalysis ‘A general statement on the need for and function of promoters in conjunction with Friedel-Crafts catalysts is needed.’ Thus Mayo and Morton [3]. It has been shown for many metal halides and monomers that binary mixtures of these can be prepared (usually in a solvent) without any polymerization taking place. Such a quiescent mixture can be made to react by the addition of a suitable third compound, which is called the co-catalyst. This term is preferable to the word ‘promoter’, because in certain contexts a substance is called promoter which enhances the rate or yield of a reaction that will also go in the absence of the promoter; herein lies the true distinction between promoter and co-catalyst [28]. (For example, small quantities of epoxides or epichlorohydrin act as promoters in the cationic polymerization of tetrahydrofuran.) I will take it that in the above quotation the word ‘promoter’ was inadvertently used in place of ‘co-catalyst’, for only thus does it become really meaningful.

103

Developments in the Theory of Cationoid Polymerisations There are here two questions to be answered: (1) What is the function of the co-catalyst? (2) Is a co-catalyst required in every system?

3.1 The function of the co-catalyst Before the discovery of the pseudo-cationic reactions, one could say simply that the function of the co-catalyst is to provide cations which can initiate the polymerization [28b]. Although this is still valid for the true cationic polymerizations, it is more difficult to define the function of the co-catalyst in the pseudo-cationic reactions. Very tentatively one can suggest that the co-catalyst is the essential link in the formation of an ester which is the chain-carrier, as in the pseudo-cationic polymerizations catalysed by conventional acids; in other words, the co-catalyst and catalyst combine to form an acid, but this, instead of protonating the monomer, forms an ester with it, which is then the propagating species. [Note added in proof. In the context of co-catalysis in pseudo-cationic reactions the work of Giusti’s group is of great interest. They found that the polymerization of styrene [54a] and of acenaphthylene [54b] by iodine involves initial formation of organic iodides. Addition of hydrogen iodide, with [HI] = [I]0, removes the acceleration period in the polymerization because it forms 1-phenylethyl iodide rapidly. The order of the polymerisation with respect to iodine is smaller by one unit when hydrogen iodide is added to the reaction mixture than when it is not. The polymerisation is regarded as a pseudo-cationic one, in which the stable ester 1-phenylethyl iodide or oligo-styryl iodide is activated by co-ordination of two molecules of iodine. Thus one can regard the organic iodide as the catalyst, and the iodine as the co-catalyst.] The whole question of co-catalysis, even for true cationic polymerizations, is both conceptually and experimentally difficult. It can usefully be approached and illustrated by the following example. Experiment showed that carefully purified isobutene and boron fluoride do not react, but that on addition of water polymerization sets in [29]. It is known that boron fluoride and water react to give a highly acidic monohydrate and that isobutene can be oligomerised by strong acids. It was concluded that the polymerization involves the following reactions: C 4 H8

BF3 + H 2 O + C 4 H 8 → Me 3C + BF3OH − → H • (C 4 H 8 )n • CH 2 • CMe 2+ BF3OH − At this stage the question can be left open whether the initiation reaction is (a) or (b) below; or more complicated than either.

104

Cationic Polymerisation from ‘Progress in High Polymers’ (1968)

(a) BF3 + H 2 O → BF3 • H 2 O (b) H 2 O + BF3 • C 4 H 8

C 4 H8

Me 3C + BF3OH −

Many other compounds have been shown to act as co-catalysts in various systems, and their activity is interpreted by analogous reactions [30-33]. However, the confidence with which one previously generalised this simple picture has been shaken by some extremely important papers from Eastham’s group [34]. These authors have studied the isomerization of cis- and trans-but-2-ene and of but-l-ene and the polymerization of propene and of the butenes by boron fluoride with either methanol or acetic acid as cocatalyst. Their complicated kinetic results indicate that more than one complex may be involved in the reaction mechanism, and the authors have discussed the implications of their findings in some detail. Whenever it is possible, by suitable purification techniques, to prepare a non-reacting mixture of catalyst and monomer, and then to start reaction by addition of a third substance, the question as to the need for a co-catalyst in that particular system is settled, and the way is open for the investigation of various co-catalysts. This is the rationale behind the ‘stopping’ experiments which are such a characteristic feature of cationic polymerization studies. It is useful to note here a fundamental distinction between cationic and anionic polymerizations (including Ziegler-Natta systems). In the latter, residual water merely inactivates an equivalent quantity of catalyst, whereas in the former water may be a cocatalyst to the metal halide catalyst; in excess it may decrease the rate by forming catalytically inactive higher hydrates; and in very many systems it, or its reaction product(s) with a metal halide, act as extremely efficient chain-breakers, thus reducing the molecular weight of the polymers (see sub-section 5.4). In many systems, it is not possible to stop the reaction completely by purification and drying. We must then distinguish three cases. 1) Upon mixing the metal halide and the monomer there is no reaction, or reaction is slow and stops at low conversion. Polymerization can be started, or re-started, by addition of water. Examples: a) Isobutene-TiCl4-CH2Cl2 at from –20 ºC to –60 ºC [23]. b) Isobutyl vinyl ether-BF3-tetrahydrofuran [31].

105

Developments in the Theory of Cationoid Polymerisations This behaviour means that residual co-catalyst, usually assumed to be water, is very scarce and is consumed during the reaction, which stops when the supply of co-catalyst is exhausted; it implies a termination reaction. Evidently, the need for a co-catalyst other than one of the main components of the reaction mixture is satisfactorily proved by such an experiment. 2) The best drying techniques succeed only in reducing the reaction rate to a very low value, which is often rather irreproducible; the reactions go to completion. Examples: Styrene-SnCl4 in nitrobenzene [36], nitrobenzene-carbon tetrachloride mixture [37], or carbon tetrachloride [36]. Such behaviour has been attributed to co-catalysis by residual water (which is not consumed) and the concentration of this can be estimated from a plot of rate against added water concentration. The reasoning behind this interpretation was that no reaction between stannic chloride, styrene, and nitrobenzene and/or carbon tetrachloride was known, or indeed seemed plausible, which would give an ionic or ester-like product. (See, however, p.115.) 3) The most careful drying produces a relatively high, reproducible rate of reaction. The rate of reaction may or may not be affected (positively or negatively) by the addition of water. In some instances this type of behaviour may be difficult to distinguish from case (2) above. Examples: a) b) c) d)

Styrene-SnCl4-(CH2Cl2) at 25 ºC; addition of water increases rate [36]. Styrene-TiCl4-CH2Cl2 at –90 ºC; addition of water has no effect on rate [38]. Isobutene-AlCl3-CH2Cl2, from 0 ºC to –60 ºC; addition of water has no effect on rate [39]. Isobutene-AlBr3-heptane, from +22 ºC to –62 ºC; addition of water decreases the rate [40a].

This is certainly the most difficult case to interpret. A trivial explanation involves the hypothesis that there is present, (e.g., in the solvent), a co-catalytic impurity. However, in most of the examples quoted this is unlikely, since many different batches of reagents were used in each study, and it is hardly compatible with the kinetics. If the impurity explanation is ruled out, there remain the following possibilities for initiation: i) by a polar complex between metal halide and monomer;

106

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) ii) by addition of an ion derived from the metal halide by self-ionization; iii) by a ternary ionogenic reaction between metal halide, monomer, and alkyl halide solvent; iv) by an electron-transfer from olefin (giving a radical-cation) to metal halide. It will be shown in the following discussion that (i) and (ii) are extremely unlikely, but that (iii) and (iv) are at least possible under some conditions. Hunter-Yohé and MedvedevGantmakher mechanism (HY-MG). The first theory of cationic polymerization [41] was based on the supposition that metal halide and monomer form a complex which is so polar that it can be considered as a zwitterion, and that polymerization proceeds from the positive end of this complex −

+

M tX n ← CH 2 − C Me 2 This type of initiation, by reaction of monomer and catalyst only, is sometimes called ‘direct’ initiation, to distinguish it from an initiation which requires the intervention of a co-catalyst. The discovery of co-catalysis proved this view to be inapplicable for many systems, and theoretical reasons against it (at least for hydrocarbons) were also put forward [42]. Later, Gantmakher and Medvedev [43] revived the Hunter-Yohé mechanism with the addition that they supposed it to operate only in polar solvents, the idea being that the zwitterion would thus be stabilised by solvation. The experiments of Colclough and Dainton [36] with the system styrene-stannic chloride-nitrobenzene, and those of Longworth, Plesch and Rutherford [44] with isobutene-titanium tetrachloride-various alkyl chloride solvents, then showed that in these systems a co-catalyst is required and that therefore the HY-MG mechanism cannot be operative. It has in fact now been abandoned by its originators, who have conceded that in the styrene-SnCl4-EtCl system a co-catalyst is required [45]. It is, however, conceivable that this mechanism operates in one or other of the examples quoted on p.147, or in some other systems. For this reason it is useful to examine its energetics. The relevant equation is −

+

AlCl 3 (sol.) + C 4 H 8 (sol.) → A lCl 3 − CH 2 • C Me 2 (sol.) ΔHA This is split up for the calculation of ΔHA in the following way:

107

Developments in the Theory of Cationoid Polymerisations

ΔH AlCl 3 (sol.) + C 4 H 8 (sol.) → AlCl 3 (g) + C 4 H 8 (g) •

•

•

β1

→ C H 2 C Me 2 (g)

C 4 H 8 (g) •

C H 2 • C Me 2 (g) −

+

−

+

→ C H 2 • C Me 2 (g) −

+

AlCl 3 + C H 2 C Me 2 (g) → Al C l 3 • CH 2 • C Me 2 (g) −

+

−

ΔHS1

I1 − A1 – D1

+

A l Cl 3 • CH 2 • C Me 2 (g) → A l Cl 3 • CH 2 • C Me 2 (sol.) – ΔHS 2 ΔH A = ΔHS1 − ΔHS 2 + β1 − D1 + I1 − A1 Here, and in the following thermochemical schemes, ΔHS denotes solvation energy, D homolytic bond dissociation energy, I ionization potential, A electron affinity. We take the following values, all in kcal/mole:

β1, the ‘second half of the double bond’ = 50 D1, assumed the same as D(Me-AlMe2) = 60 I1, assumed the same as I(Me3C·) = 170 A1, assumed the same as A(Me3C·CH2·) = approximately 30 ΔHS1, approximately 2x latent heat of evaporation of CH2Cl2, 6.7, = 15 Therefore ΔHA = 145 – ΔHS2. Even though the figure of 145 kcal/mole may be uncertain by as much as ± 15 kcal/mole, it is evident that in order to make ΔHA negative, ΔHS2 would have to exceed at least 130 kcal/mole, which seems far too great; very similar figures are obtained for the styrenetitanium tetrachloride system. Moreover, the Coulombic energy required to separate the charges in the propagation steps has been left out of account. Thus there is a quite cogent thermochemical argument against the plausibility of this reaction mechanism, quite apart from the fact that there is no independent evidence for this, or any analogous, reaction. Initiation by ions derived from the metal halide. The question is sometimes asked why initiation of polymerization may not occur by addition to the olefin of one of the ions

108

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) known to be formed by the self-dissociation of the metal halide in solvents of moderate polarity, e.g. alkyl halides. The reactions concerned can be written thus:

2 TiCl 4 ↔ TiCl 3+ + TiCl 5− +

TiCl 3+ + C8H 8 → TiCl 3 • CH 2 • C H• C 6 H 5

ΔHB

The first of these reactions is known [46], the second is hypothetical; evidently, it is a variant on the theme of ‘direct’ initiation, i.e., without intervention of a co-catalyst. It is not difficult to show that ΔHB would be large and positive, and the corresponding reaction therefore very unlikely.

ΔH TiCl 3+ (sol.) + C8 H 8 (sol.)

→ TiCl 3+ (g) + C8H 8 (g)

ΔHS3

TiCl 3+ (g) + e

→ TiCl 3 (g)

– I2

C8 H 8 (g)

→ C H 2 ⋅ C H ⋅ C 6 H 5 (g)

•

•

•

•

β2

•

TiCl 3 (g) + C H 2 • C H • C 6 H 5 (g) → TiCl 3 • CH 2 • C H • C 6 H 5 (g) •

TiCl 3 • CH 2 • C H • C 6 H 5 (g) +

TiCl 3 • CH 2 • C H • C 6 H 5 (g)

+

→ TiCl 3 • CH 2 • C HvC 6 H 5 (g) + e +

→ TiCl 3 • CH 2 • C H • C 6 H 5 (sol.)

– D2 I3 – ΔHS 4

ΔHB = ΔHS3 − ΔHS4 + β2 − D2 − I2 + I3 We use the following magnitudes, all in kcal/mole:

β2, the ‘second half’ of the double bond,

40

I2, the first ionization potential of TiCl3,

157

I3, assumed the same as the ionisation potential of the α-phenylethyl radical,

189

D2, a C-Ti bond dissociation energy, not more than

10

ΔHB = 62 + ΔHS3 – ΔHS4

109

Developments in the Theory of Cationoid Polymerisations If we take the heat of solution of styrene in methylene dichloride as about –7 kcal/mole, ΔHS3 = –7 + ΔH′S3. Since ΔH′S3 and ΔHS4 are solvation energies of large positive ions, their difference cannot amount to more than a few kcal/mole, so that ΔHB must be large and positive, and the corresponding reaction therefore very improbable. [Note added in proof. Marek and Chmelir [40b, c] found that the polymerization of isobutene in heptane by aluminium bromide is greatly accelerated by addition of titanium tetrachloride. They suggested that the polymerization by aluminium bromide only is initiated by a cation such as AlBr2+ which adds to the isobutene and which is formed by self-dissociation of the catalyst. The enhancement of the rate by titanium tetrachloride they attribute to an increase in the concentration of ions by the reaction TiCl4 + AlBr3 → TiCl3+AlBr3Cl– and they provide evidence that the initiating species is TiCl+3, with Ti bound to the polymer: AlBr3Cl–TiCl3+ + C4H8 → TiCl3•CH2•CMe+2AlBr3ClTo obtain ΔH′B for the initiating reaction in this system, the above calculation must be modified as follows. Since reaction is in heptane, the initial and final species are ionpairs (possibly higher aggregates): ΔΗ′Β = ΔΔΗS + Δq + β1 + I1 – I2 + D2 = 27 + ΔΔΗS + Δq where ΔΔHS is the difference between the solvation energies of the initial and final ionpairs, and Δq is the difference between their Coulombic energies. Whereas the first of these is probably negligible, the second may well be negative and of the order of magnitude required to make ΔH′B approximately zero]. Solvent co-catalysis. It will be noticed that all but one of the reactions quoted on p.147 take place in an alkyl halide solvent. A list of most of the reactions belonging to this class is given in Table 1 (which, however, is not claimed to be exhaustive). Pepper [47] first suggested that alkyl halides could act as co-catalysts by a reaction which can be represented generally as MtXn + RX → MtX–n+1R+ This idea was based on the well-known analogous reactions of metal halides with triphenylmethyl halides, and thus seemed plausible. However, detailed studies have shown

110

Cationic Polymerisation from ‘Progress in High Polymers’ (1968)

TabIe 1. Co-catalysis by alkyl halides Catalyst

Monomer

Isobutene [ref.]

Styrene [ref.]

Propene [ref.]

Alkyl halide SnCl4

EtCl

-

[22]

(CH2Cl)2

+

[36]

t-BuCl

+

[36]

CH2Cl2

-

[44]

?+(a)

[38]

CH3CHCl2

-

[44]

–(a)

[44]

(CH2Cl)2

-

[44]

–(a)

[44]

i-PrCl

-

[44]

–(a)

[44]

AlCl3

CH2Cl2

?+

[39]

AlBr3

i-PrBr

TiCl4

+

[86]

+ Means that co-catalysis has been proved; - that it has been shown not to occur (a) All these compounds were reported not to be co-catalysts for the polymerization of styrene by TiCl4. In view of the more recent finding [38] that methylene dichloride may be a co-catalyst for this reaction at low temperatures, these claims need to be reexamined

that this is an over-simplification; there is in fact no evidence that carbonium salts are formed under polymerization conditions from the alkyl halides commonly used as solvents (methyl and ethyl chloride, methylene dichloride, ethylene dichloride) and the metal halides (aluminium trichloride, titanium tetrachloride, stannic chloride). It is not difficult to show that for such systems salt formation, as represented by the above equation, would be a highly endothermic process. None the less, co-catalysis by alkyl halide, commonly known as ‘solvent co-catalysis’, is at present one of the possible explanations for some of the reactions quoted on p.108 above. The theory of this initiation mechanism is based on the thermochemical argument that the reaction +

MtX n + RX + CR1R 2 : CR 3R 4 → RCR1R 2 • C R 3R 4 MtX −n +1 can be exothermic, because in comparison with the previous binary ionization reaction, one gains the enthalpy of addition of radical R to the olefin, and the difference between

111

Developments in the Theory of Cationoid Polymerisations the ionization potential of R and of the radical formed from the olefin. The kinetic objection to such a scheme, that it would involve a termolecular reaction, is not cogent, since in the systems under consideration binary complexes of olefin and metal halide are known to exist and there is some kinetic evidence for the participation of such complexes in the initiation reaction. It is also possible that in other systems the initiation takes place by attack on the olefin of a binary, polar, but not ionic, complex between alkyl halide and metal halide-as happens in many Friedel-Crafts alkylations. In order to provide a comparison with the thermochemical schemes given above, a detailed exposition of the thermochemistry of solvent co-catalysis may be useful. The relevant reaction is +

TiCl 4 (sol.) + C8 H 8 (sol.) + CH 2 Cl 2 (l) → CH 2 Cl ⋅ CH 2 ⋅ C H ⋅ C 6 H 5 TiCl 5− (sol.)

ΔHc

ΔH TiCl 4 (sol.) + C8 H 8 (sol.) + CH 2 Cl 2 (l) → TiCl 4 (g) + C 8 H 8 (g) + CH 2 Cl 2 (g) CH 2 Cl 2 (g)

→ CH 2 Cl ⋅ (g) + Cl ⋅ (g)

Cl ⋅ (g) + e

→ Cl − (g) −

TiCl 4 (g) + Cl (g)

→

– A2

TiCl 5− (g) •

– D4

•

→ C H 2 ⋅ C H ⋅ C 6 H 5 (g)

C8 H 8 (g) •

•

CH 2 Cl ⋅ (g) + C H 2 ⋅ C H ⋅ C 6 H 5 (g) •

CH 2 Cl ⋅ CH 2 ⋅ C H ⋅ C 6 H 5 (g)

ΔHS5

•

→ CH 2 Cl ⋅ CH 2 ⋅ C H ⋅ C 6 H 5 (g) +

→ CH 2 Cl ⋅ CH 2 ⋅ C H ⋅ C 6 H 5 (g) + e

+

β2 – D5 I3

+

CH 2 Cl ⋅ CH 2 ⋅ C H ⋅ C 6 H 5 (g) + TiCl 5− (g) → CH 2 Cl ⋅ CH 2 ⋅ C H ⋅ C 6 H 5 TiCl 5− (sol.) – q – ΔHS 6 ΔHc = ΔHS 5 – ΔHS 6 – q + β 2 + D3 – D5 – D4 – A2 + I3 The terms β2 and I3 have the values given above. Approximately, D3 = D5 = 80 kcal/ mole, and A2 = 88 kcal/mole. The value of D4 is unknown, but 70 kcal/mole is probably a realistic estimate. The Coulombic energy of the ion-pair is q, and assuming an interionic distance of 5 AU, this amounts to 70 kcal/mole. A value of ΔHS5 can be estimated as approximately three times the latent heat of vaporization of methylene dichloride (6.7 kcal/ mole), giving ΔHS5 = 20 kcal/mole. Thus ΔHc = 20 – ΔHS6 Although it is known that ΔHS6 would be relatively great, it is very difficult to obtain any idea of its magnitude, but a value greater than 20 kcal/mole seems quite plausible. Thus, there appear to be some grounds for believing that at least for some systems ΔHc may be

112

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) negative-and that is all that is required. Although this means that co-catalysis by an alkyl halide may be possible, such calculations cannot prove that it occurs, especially since it is not known whether in this reaction the chain-carrier is ionic or pseudo-ionic, and the latter possibility has been left out of account in these (and the earlier) calculations. The next question which presents itself is whether we can explain why in some systems solvent co-catalysis occurs, whereas in others, apparently similar, it does not. Let it be said first that in fact there is very little experimental evidence on this point. From the thermochemical point of view one can say that alkyl halide co-catalysis is the more probable, the lower the heterolytic bond dissociation energy of the alkyl halide, the more stable the cation derived from the monomer, and the smaller the anion derived from the metal halide. It must, however, be remembered that the non-occurrence of alkyl halide co-catalysis may be due to a kinetic prohibition, i.e., an excessively high activation energy for a reaction which is thermodynamically possible. It might be thought that the question whether a particular alkyl halide is a co-catalyst for a particular monomer-catalyst combination could be settled easily, by adding some of the compound in question to a non-reacting mixture of monomer and catalyst. This approach has been used [36, 44], but it must be carried out in a polar solvent which is itself not a co-catalyst, or only a very weak one. The ideal solvent for this kind of work remains to be found; it may be that SO2 or even CS2 (which behaves like a polar solvent) will provide the answer. If one wants to use alkyl chloride solvents without being troubled by the possibility of solvent co-catalysis, boron fluoride should be used as catalyst, since the ion BF3Cl- is not formed under the conditions generally used for polymerisations. Alkyl halide co-catalysis is taken to its logical conclusion when carboxonium or carbonium salts, such as CH3CO+BF4-, C6H5CO+ClO4- [48], Ph3C+SnCl5- [49], and Ph3C+SbCl6- [50-52], are used as catalysts. The trityl salts seem to be largely immune from interference by small quantities of impurities, but trityl perchlorate is sensitive to light [53]. In some systems the original ion probably starts the polymerization by adding onto the monomer [48]. In other systems it may abstract an electron from an unsaturated monomer to give a cation-radical [52], or it may abstract a hydride ion, e.g. from 1,3dioxolan to give a dioxolenium ion [55] which, however, does not initiate polymerisation of the dioxolan [93]. Electron-transfer initiation. Whereas co-catalysis by an alkyl halide has been established for some systems, there are others, e.g., examples (3b) and (3c) (p.108), and the polymerisations of isobutene [56] by AlCl3 in MeCl, for which it seems rather unlikely and at least one system, example (3d), for which it is impossible. In seeking an explanation for these reactions we must consider what has recently been discovered concerning

113

Developments in the Theory of Cationoid Polymerisations initiation of cationic polymerisation by way of radical cations formed from the monomer by electron transfer to the catalyst. In general terms the reaction can be represented thus: +

Cat + RCH : CH 2 ↔ Cx ↔ •Cat − R C H • CH 2 • Cx is a charge transfer complex; the position of the equilibria, and, hence, the importance of Cx, and the concentration of the radical ions, may differ greatly from one system to another. The radical cation then probably reacts in most systems in such a way that the radical function is rapidly inactivated and the cationic function then propagates a quite normal cationic polymerization. This idea was put forward first by Scott, Miller and Labes [57] for the polymerization of N-vinylcarbazole by organic electron-acceptors. It was then applied to initiation by the tropylium and other ions [52, 58]; by reducible metal ions but with emphasis on a possible radical reaction [59]; and by sodium chloroaurate in which Au(III) is reduced (see also Section 4.5) [60]. Then Plesch suggested [6] an application of the idea of catalysis by metal halides generally, giving as an example, the following hypothetical scheme:

2TiCl 4 + RCH : CH 2 +

•

TiCl 3 + TiCl 5− + R C H • C H 2 TiCl 3+ + TiCl 5− + RCH : CH 2 It is, of course, possible that the charge-transfer complex between metal halide and olefin, which is well known, is an intermediary in this reaction. There is here another variation on the theme of ‘direct’ initiation. The thermochemical analysis, analogous to the previous ones, goes as follows: +

•

2 TiCl 4 (sol.) + C8 H 8 (sol.) → TiCl 3 (sol.) + TiCl 5− (sol.) + C 6 H 5 C H C H 2 (sol.)

ΔHd ΔH

2 TiCl 4 (sol.) + C8 H 8 (sol.)

→ 2 TiCl 4 (g) + C8 H 8 (g)

ΔHS5

TiCl 4 (g)

→ TiCl 3 (g) + Cl(g)

D6

−

Cl(g) + e

→ Cl (g) −

− A2

− 5

TiCl 4 (g) + Cl (g)

→ TiCl (g)

C 8 H 8 (g)

→ C6 H 5 C H ⋅ C H 2 + e

+

+

•

C 6 H 5 C H ⋅ C H 2 (g) + TiCl 5− (g) + TiCl 3 (g) → solution ΔHd = ΔHS5 − ΔHS7 + D6 − A2 − D4 + I4 − q 114

− D4 •

I4 − q − ΔHS7

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) For ΔHS5, A2, D4, and q we take the values given previously: D6 = 80 kcal/mole and I4 = 200 kcal/mole. Thus ΔHd = 65 - ΔHS7. A value of 65 kcal/mole for ΔHS7, required to make ΔHd zero, is not excessively high, especially as it includes terms for the complexing of TiCl3 with one of the components of the reaction mixture, or its heat of crystallization, and for the destruction of the radical function. This type of reaction therefore appears feasible, at least for reducible metal halides.

3.2 Co-catalysis in the polymerization of oxygen compounds * The first study with an oxygen compound which was sufficiently rigorous to provide evidence on the question of co-catalysis was that of Farthing and Reynolds [61]. They showed that 3,3-bischloromethyl oxetan could be polymerised in methyl chloride solution by boron fluoride only in the presence of water. Later, Rose [62] obtained kinetic evidence for the need for a co-catalyst in the system oxetan—boron fluoride—methyl chloride, and he interpreted the low reaction rate when no water was added as due to residual water; he also showed that water and a hydroxyl-terminated polymer could act as co-catalysts. With ethylene oxide the situation is complicated. Worsfold and Eastham [63] showed that under anhydrous conditions in ethylene dichloride solution boron fluoride reacts slowly with the monomer to form a co-catalyst and that after the induction period during which this occurs the polymerization proceeds smoothly; and that the induction period can be eliminated if water, equivalent to the boron fluoride, is added to the system. With stannic chloride as catalyst apparently no co-catalyst is required [64], and the initiation reaction was represented thus:

CH 2 −

+

SnCl 4 + 2C 2 H 4 O → Sn Cl 4 • O • (CH 2 )2 • O CH 2 This is, of course, the Hunter-Yohé mechanism, involving a zwitterion, but with this monomer it does not seem implausible; in particular, the objection that it involves a large charge separation, which has some force in the case of a sterically hindered hydrocarbon such as isobutene, is probably not valid here, especially in view of the flexibility which the oxygen atom confers on the chain. * Since there is little evidence at present on whether any or all of these polymerisations are cationic or pseudocationic, the argument will be conducted on the former basis.

115

Developments in the Theory of Cationoid Polymerisations The same considerations apply to the explanation which Kern and Jaacks [65] put forward to account for their observation that the polymerization of trioxane by boron fluoride in methylene dichloride not only appears not to require a co-catalyst, but is retarded by water. They write the initiation reaction as

CH 2 — O −

BF3 + O

+

CH 2 → BF3 • O • CH 2 • O • CH 2 • O • C H 2 CH 2 — O

and regard the resonance stabilised carboxonium ion as the propagating species. This seems entirely plausible. A very detailed study of the polymerization of trioxane by boron fluoride etherate in n-hexane, ethylene dichloride, and nitrobenzene has come from Okamura’s school [66]. They consider that the zwitterion mechanism is not applicable in their systems and that in the absence of a protonogenic co-catalyst (water or methanol) initiation takes place by an ethyl ion from the syncatalyst in the polar solvents, but that in hexane solution water is an essential co-catalyst. The initiation reaction in the polymerization of vinyl ethers by BF3R2O (R2O = various dialkyl ethers and tetrahydrofuran) was shown by Eley to involve an alkyl ion from the dialkyl ether, which therefore acts as a (necessary) co-catalyst [35, 67]. This initiation by an alkyl ion from a BF3-ether complex means that the alkyl vinyl ethers are so much more basic than the mono-olefins, that they can abstract alkylium ions from the boron fluoride etherate. This difference in basicity is also illustrated by the observations that triethoxonium fluoroborate, Et 3O +BF 4 -, will not polymerise isobutene [68] but polymerises n-butyl vinyl ether instantaneously [69]. It was also shown [67] that in an extremely dry system boron fluoride will not catalyse the polymerization of alkyl vinyl ethers in hydrocarbons; thus, an earlier suggestion that an alkyl vinyl ether might act as its own co-catalyst [30] was shown to be invalid, at least under these conditions. However, Bawn et al., take the view that when polymerization of an alkyl vinyl ether is initiated by a stable ion, such as tropylium, the initiation involves electron abstraction from the monomer with formation of a radical cation and a tropyl radical [52]: •

+

C 7 H 7+ + CH 2 : CH ⋅ O ⋅ R → C H 2 • C H • O • R + C 7 H •7 In this reaction the monomer can be regarded as its own co-catalyst, since it generates the initiating ion.

116

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) Another reaction, related to this, is the initiation of the polymerization of tetrahydrofuran by the triphenymethyl cation. This involves H-abstraction from the monomer, but is certainly more complicated [70a] than was believed at one time [70b].

3.3 The mechanism of pseudo-cationic polymerization The phenomenology of pseudo-cationic polymerizations has been outlined in sub-section 2.2, and reasons were given there for our belief that in these reactions the chainpropagating species is an ester. However, it is not a normal ester, because experiment shows that the ester, 1-phenylethyl perchlorate, which one would expect to be formed from silver perchlorate and 1-phenylethyl bromide, does not in fact exist at room temperature. Instead of the ester, one obtains a complex mixture of oligomers, ions, and perchloric acid [4d]. The clue to the situation is the observation that ions are absent from polymerizing solutions of styrene and perchloric acid only so long as the styrene concentration is greater than 4x [HClO4]. We believe this to indicate that the ester can exist as such only so long as it is stabilised by complexing with four molecules of styrene [4d]. It may be that this stabilization of the ester, with respect to the ions which could be formed from it, is brought about by a reduction of the electron density at the anionic moiety through the co-ordination of the four molecules of styrene. The stabilization of the ester by co-ordination of monomer molecules would be closely analogous to the reduction of the equilibrium constant for ionization of tri(p-chlorophenyl) methyl chloride compared to that of triphenylmethyl chloride. We envisage the propagation step as the addition of the components of the ester across the double bond of the monomer; in modern terminology this is an insertion reaction. Whether this reaction occurs through a 4-centre or a 6-centre transition state, as shown below, is not clear.

However the rate constants and activation energies reported by Pepper and Reilly would be much more compatible with processes of this kind than with the attack of a carbonium ion on an olefin.

117

Developments in the Theory of Cationoid Polymerisations Whether or not our representation of the non-ionic chain-carrier as an ester is correct, the balance between the ionic and non-ionic forms for the system styrene—perchloric acid—methylene dichloride seems to be very delicate. Since the enthalpy terms affecting this balance must be small, and the entropy terms are likely to be important, it is not possible at present to analyse the situation in detail. However it is predictable that the factors which would favour the ionic form, as against the ester, are: lower ionization potential of the hydrocarbon radical, weaker ester bond, more polar solvent, and lower temperature.

4 Monomers Mayo and Morton, having pointed out the scarcity of information regarding the reactivities of monomers, write ‘…our greatest need is for generalisations which will correlate diverse observations with various monomers [3].’ This need has been met to some extent [1, 8], but there are further aspects which can be elaborated here with advantage. The following comments on various classes of monomers are aimed at illuminating from different points of view the general theme of reactivity. They are not intended to be exhaustive discussions, and are largely commentaries upon recent results.

4.1 Aliphatic mono-olefins The aliphatic mono-olefins present a particularly complicated picture at first sight. Only a few of them will give high polymers by cationic catalysis; most of these are either 1,1disubstituted ethylenes, or ethylenes with a single branched substituent, such as 3methylbutene-1 and vinylcyclohexane. The reasons why ethylene, propene, and the nbutenes do not give high polymers have been set out in detail [71]. Briefly, the ions derivable directly from all of these are either primary or secondary, e.g., +

AH + CH 2 : CH • Et → Et • C H • CH 3 A − and such cations can undergo exothermic hydride transfer reactions With the tertiary hydrogen atoms present in the oligomers, with formation of tertiary carbonium ions, leading to the growth of branched structures. There are also possibilities for energetically advantageous methide ion and proton transfer reactions, and the formation of allylic ions, all of which will tend to complicate the reaction and reduce the molecular weight [71, 34]. With isobutene and other 1,1-disubstituted alkenes [72, 73] the great stability of the tertiary carbonium ion ensures that propagation is energetically by far the most favourable reaction.

118

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) A most interesting case is 3-methylbut-l-ene. At about –80 ºC it gives high polymers with the expected structure (III):

C

C

C

C C

(III)

C

C

C

(IV)

C

C

This means that the isopropyl group stabilises the secondary ion sufficiently (compared to but-l-ene) for hydride transfer reactions to be suppressed, at least at low temperature. At about –120 ºC a high polymer of structure (IV) is formed. This is a true phantom polymer, since there exists no corresponding monomer. Evidently, at the very low temperature the propagation reaction which would lead to structure (III) becomes much slower than the isomerization reaction: +

+

— CH 2 C HCHMe 2 → — CH 2 CH 2 C Me 2 Vinyl cyclohexane and other similar monomers give analogous phantom polymers under similar conditions, and the reaction has been explored in great detail by Kennedy and his collaborators [9f, 74]. The occurrence of such relatively fast isomerizations makes it appear very likely that in these polymerizations the propagating species is a cation. Special interest attaches to the cyclic aliphatic hydrocarbons. Cyclopropane can be converted to oligomers by cationic catalysis [75, 76], and these appear to be essentially linear; but whether they are really different from the polypropenes formed under the same conditions from propene is not yet settled. The initiation most probably involves formation of a nonclassical cyclopropyl ion [77], as in alkylations with cyclopropane [78],

AlBr3 + HBr + (CH 2 )3 → H

+ AlBr4−

and presumably propagation proceeds through an analogous intermediate:

CH 3 (CH 2 )2

+

+ (CH 2 )3 → CH 3 (CH 2 )5

+

By contrast with the polymerization of propene, there seems little scope here for the formation of branched structures. Detailed elucidation of the polymer structure would provide evidence on the question whether a non-classical ion can act as chain-carrier.

119

Developments in the Theory of Cationoid Polymerisations Such evidence, pointing to the cyclopropylium ion as the chain-carrier, has been obtained from the polymerization of isopropylcyclopropane [79]. Cyclobutane has not been polymerised cationically (or by any other mechanism). Thermochemistry tells us that the reason is not thermodynamic; it is attributable to the fact that the compound does not possess a point of attack for the initiating species, the ring being too big for the formation of a non-classical carbonium ion analogous to the cyclopropyl ion, so that there is no reaction path for initiation. The oxetans in which the oxygen atom provides a basic site for protonation, are readily polymerizable. Methylenecyclobutane polymerises without opening of the cyclobutane ring [72, 73].

4.2 Aromatic mono-olefins The aromatic mono-olefins have been studied more extensively and intensively than any other class of monomers. Styrene, in particular, has received much attention, but nuclear and side-chain substituted styrenes are still largely unexplored, except in regard to copolymerization. The only other aromatic monomers which have been studied in any detail are α-methylstyrene [1] and 1,1-diphenylethylene and some of its derivatives [10]. It is strange that even readily available monomers, such as indene [80] and acenaphthylene [54b, 81], have hardly been investigated. Scanty though our information is, it indicates that most aromatic monomers show very similar kinetic behaviour under similar conditions. Moreover, it has recently been shown that the very simple kinetics of the polymerization of styrene by perchloric acid [27, 82] also apply to polymerization of p-chlorostyrene [83] by that catalyst. From concurrent studies of co-polymerization Brown and Pepper deduced that styrene gives a more reactive ‘active species’ than p-chlorostyrene, and that styrene is the more reactive monomer. The former conclusion is not easily compatible with an ion being the chain-carrier.

4.3 Comparison between aliphatic and aromatic mono-olefins A highly obscure feature of cationic polymerization is the great phenomenological difference between aliphatic and aromatic monomers. The survey by Brown and Mathieson [84] of the behaviour of a very wide range of monomers towards trichloroacetic acid is particularly illuminating in this respect. Unfortunately, there are so few studies with aliphatic olefins that detailed comparisons must be confined to isobutene. It is well known that isobutene cannot be polymerised by conventional acids, such as sulphuric, perchloric, hydrochloric, or by salt-like catalysts such as benzoyl perchlorate, whereas all these catalysts readily give at least oligomers from aromatic olefins. Even when the same catalytic system, (e.g., titanium

120

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) tetrachloride, or stannic chloride, and water in alkyl halide solvents), will polymerise both isobutene and styrene, the reactions present completely different kinetic patterns. At this point it is essential to emphasise that we have no basis whatever for comparing the rates of initiation for isobutene and styrene (or any other aromatic monomer) since even with syncatalytic systems, (e.g., stannic chloride-water), the mechanisms of initiation are probably different. What we need is information on the rates of protonation of the different monomers by the same simple acid, or of alkylation by the same carbonium or carboxonium salt, under identical conditions. As far as propagation is concerned, comparison of rates is hazardous because under some conditions the rate-determining step for isobutene [85], like propene [86], may be a unimolecular process, i.e., of zero order with respect to monomer (see sub-section 5.2). Moreover, comparison is complicated further by the consideration that in every system free cations and cations forming part of an ion-pair or higher aggregate may participate in the polymerization, and that therefore the extent of such participation must be ascertained before meaningful rate constants can be evaluated. This matter will be discussed in Section 6. In the light of our new knowledge about the pseudo-cationic polymerisation of styrene it appears that many, perhaps all, the main differences between aliphatic and aromatic monomers may be due to the fact that one is not comparing like with like; that is, the differences arise because under many of the most commonly used experimental conditions the two groups of monomers polymerise by different mechanisms. In order to make valid comparisons between two monomers it is necessary to ascertain first that they do both polymerise by the same mechanism under the same conditions. There remains, of course, the question why apparently isobutene (and perhaps other aliphatic olefins) do not polymerise by the pseudo-cationic mechanism - or do so much less readily than, say, styrene. Probably the short answer lies in the relative stabilities of the esters in the polymerisation conditions, (e.g., perchlorate stabilised by co-ordination of styrene). The long answer will have to be based on a detailed understanding of all the factors which determine this stability and thus govern the equilibrium between ester and ions.

4.4 Oxygen compounds When considering the numerous categories of oxygen-containing monomers there are two important rules to consider. 1) If a compound is to be polymerizable cationically, the reaction site must be the most basic point in the molecule (unless the concentration of the ‘catalyst’ exceeds that of the monomer).

121

Developments in the Theory of Cationoid Polymerisations 2) Almost any oxygen atom is more basic than almost any isolated olefinic double bond (obvious exceptions are, apparently, p-methoxystyrene [87] and 1-p-methoxyphenyl, 1-phenylethylene [88]). These principles can be illustrated by a few examples. The carbonyl oxygen of an ester group, (e.g., in acrylates or vinyl esters), is more basic than a vinyl group and it captures protons (or other cations) from the catalytic system to give a resonance-stabilised cation which does not involve the reaction site, namely the olefinic double bond. Hence, acrylates and vinyl esters do not polymerise cationically. On the other hand, in cyclic ethers (alkene oxides, oxetans, tetrahydrofuran) and formals the reaction site is a carbon–oxygen bond, the oxygen atom is the most basic point, and, hence, cationic polymerization is possible. The same considerations apply to the polymerization of lactones; Cherdron, Ohse and Korte showed that with very pure monomers polyesters of high molecular weight could be obtained with various cationic catalysts and syncatalysts, and proposed a very reasonable mechanism involving acyl fission of the ring [89]. The alkyl vinyl ethers present an interesting case in that the oxygen atom in a saturated dialkyl ether is certainly more basic than a vinyl group in a hydrocarbon (isobutene cannot be polymerised in diethyl ether). However, when the vinyl group is conjugated with the oxygen atom, the most exo-energetic process is not the protonation of the oxygen (V) but that of the vinyl group (VI), since the resulting cation is stabilised by charge delocalization: +

CH 2 : CH — O — R |

+

H + CH 2 : CH • O • R

(V)

H +

CH 3 • C H • O • R •

(VI)

Thus the reaction site, the double bond, participates in the charge and polymerization can take place. That the vinyl group conjugated with the oxygen atom is more basic than an ordinary ether oxygen is shown by the fact that alkyl vinyl ethers can be polymerised readily in dialkyl ethers as solvents. A number of publications purport to give values for the absolute propagation rate constant kp for the polymerization of isobutyl vinyl ether (Table 2). The values of Okamura et al., are derived by techniques and arguments which are of doubtful validity [54a] and they seem much too small. Eley’s value, derived from an analysis of non-stationary kinetics, is four orders of magnitude smaller than the kp deduced from studies of radiation

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Cationic Polymerisation from ‘Progress in High Polymers’ (1968)

Table 2 Propagation rate constant for the polymerisation of isobutyl vinyl ether Solvent

Temperature

kp(M-1 min-1)

Ref.

(CH2Cl)2

30 ºC

3.9 x 102

141

n-C6H14a

30 ºC

2.7

141

n-C6H14-Toluene

–40 ºC

4.6 x 102

109

Ph3CSbCl6-

CH2Cl2

0 ºC

2.2 x 105

52

C7H+7 +SbCl6-

CH2Cl2

0 ºC

2.7 x 105

52

Bulk

30 ºC

1.8 x 107

90b

Catalyst I2

BF3·Et2O

Radiation a

in Table 3 of Reference 141 this is given wrongly as CCl4

polymerization [90b]. Whereas the latter refers to propagation by free ions, Eley’s value must refer to ion-pairs, because of the low polarity of the solvent used, and the high positive Ep supports this view. It is encouraging that Chmelir and Marek’s value of kp for polymerization of isobutene in heptane by AlBr3 + TiCl4 (approximately 4 x 105 M-1 min-1 at –14 ºC) [40c] is of the same order of magnitude as Bawn’s value for the vinyl ether. In both systems there is probably propagation by free ions and ion-pairs. The unexpected variety found in cationic polymerizations is well illustrated by recent findings concerning the polymerization of dioxolan by perchloric acid. Gresham91 had been unable to find end-groups in polydioxolans made under anhydrous conditions and concluded that they were cyclic. His result has been confirmed by studies made with anhydrous perchloric acid as catalyst [92]. Since it is extremely unlikely that complete absence of chain ends can be achieved by a cyclization of long chains, and from other evidence, we concluded that the polymerization takes place without formation of chain ends, i.e. by a ring expansion mechanism:

H

H

O+

CH2—O—CH2—O—CH2 O

O

+

CH2—O—CH2—O—CH2 O

123

Developments in the Theory of Cationoid Polymerisations 1,3-Dioxepan seems to react in the same way [93]. Studies on the polymerization of various 4-methylene-1,3-dioxolans [94] by BF3Et2O or AlCl3 showed that 4-methylene-1,3-dioxolan itself polymerises mainly through the double bond; the 2-methyl and 2,2-dimethyl compounds gave polymers with a variable carbonyl content. This arises from a ‘co-polymerization’ in which units of type (VII) and (VIII) are incorporated in the chain in different proportions, according to the reaction conditions:

— —CH2—C— —

CH2= O

O

O

O

R1

—CH2.C.CH2.O.C— — R1

R1

O R2

R2

R2 n

n

(VII)

(VIII)

The relative reactivity of various cyclic oxygen compounds in copolymerization was correlated by Yamashita and his co-workers with the basicity of the monomers in a very convincing manner [95]. One of the questions raised by this work is why tetrahydrofuran is so much more basic and reactive than dioxolan. The clue to the solution comes from consideration of models which show that in dioxolan the two resultant dipoles bisecting the C—O—C angles almost neutralise each other, so that the net negative charge at each oxygen atom is very much smaller than it is in tetrahydrofuran [93]. It seems likely that this kind of consideration will also help to account for the ranking of the other cyclic oxygen compounds in the scale of basicities.

4.5 Nitrogen compounds One of the most interesting and original advances in cationic polymerisation is the polymerization of C ≡ N bonds and of pyridine reported by Kabanov et al., [96]. Starting from the fact that nitriles and heterocyclics are thermodynamically more stable than the conjugated polymers which could be formed from them, they argued that polymerization might be possible in the presence of a complexing agent which would lower the free energy of the polymer more than that of the monomer. This idea was realised by forming complexes of nitriles or pyridine with TiCl4, BF3, or ZnCl2 and acting on these with HPO3 or H3PO 4 at temperatures between 250 ºC and 300 ºC. It was found that benzonitrile with TiCl4 would give polymer even without added acid (experiments in vacuum apparatus), but that the complexes with BF3 or ZnCl2 would not. A cyclic trimer was formed initially, concurrently with the polymer, but was eventually converted to

124

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) linear polymer. Detailed structural studies on the linear polynitriles and polypyridines, as well as kinetic data are given, and reaction mechanisms are suggested, which seem very reasonable. This original and elegant method of circumventing thermodynamic prohibition should prove useful also with other monomers and work along these lines promises to be rewarding. The best-known nitrogen-containing monomer which is polymerizable cationically is undoubtedly N-vinylcarbazole (NVC). It is exceedingly sensitive to traces of acid and even suspensions of it in water can be polymerised. The discovery by Scott et al., [57] and Ellinger [97] that NVC can be polymerised by organic electron acceptors brought initiation by electron transfer, and the resulting radical cations, into this field. Detailed studies of the polymerization of NVC by tetranitromethane in nitrobenzene, and of some related systems, have elucidated the kinetics and mechanism and showed that initiation takes place by way of a charge-transfer complex between monomer and catalyst, and radical-cations formed from this [25].

5 Chain-breaking reactions*

5.1 Introduction Once a compound has been shown to polymerise, the most interesting question for me is: ‘What is stopping the chains from growing?’ When that question has been answered we must know much about the kinetics of the system and at least a little about its chemistry. Before entering into an account of the reactions which stop chains from growing, it is important to make once again a clear distinction between termination and transfer reactions. There is no reason for not adhering to the radical chemist’s definition of termination: a reaction in which the chain-carrier is destroyed. In cationic polymerizations there are two main types of termination reaction: a) Charge neutralization, as exemplified by the reaction

— — — CH 2 • CMe 2+ BF3OH − → — — — CH 2 • C(Me)2 OH + BF3

(IX)

b) Formation of a cation which is too stable to propagate the reaction; this can occur in several ways. For the polymerization of propene the following sequence of reactions has been suggested [86b]: * This question will be treated predominantly from the point of view of true cationic polymerisations, since too little is known about this aspect of the pseudo-cationic reactions.

125

Developments in the Theory of Cationoid Polymerisations

+

+

R ′ CHCH 3 AlBr4− + RCH(CH 3 )CH 2 CHCH 3 AlBr4− +

+

→ R ′CH 2 CH 3 + AlBr4− R C(CH 3 )CH 2 CHCH 3 AlBr4− +

CH 3CH : CH 2

(X)

( XI) R(CH 3 )⋅⋅⋅ CH⋅⋅⋅CHCH 3 + (CH 3 )2 CH + AlBr4− AlBr4−

The allylic ion (XI) is probably too stable to propagate the reaction. The inhibiting (poisoning) effect of oxygen, nitrogen, and sulphur compounds is also due to formation of stable ions (in so far as it is not due to sequestration of metal halide by complex formation), e.g., the reaction [98]:

R + + R ′3 N → RR ′3 N +

(XIa)

Most of the other important chain-breaking reactions are transfer reactions and much confusion has been created by authors failing to distinguish clearly; the introduction of the term ‘molecular termination’ [99] to designate the transfer by aromatic compounds [100] was not helpful. Since the condition for formation of high polymers is that the propagation reaction must be faster than all other reactions of the growing species, and since carbonium ions are highly reactive, it is evident that very special conditions are required for the formation of high polymers by cationic polymerization. The general conditions which must be satisfied are: a) Extreme purity to reduce the total rate of adventitious chain-breaking reactions. b) Low temperature to reduce the rate of inherent chain-breaking reactions. The adventitious chain-breaking reactions are those which involve the adventitious components of the polymerization system: in other words, the impurities. The inherent chain-breaking reactions are those which are characteristic of the system, such as reactions between cation and anion, monomer transfer, solvent transfer. Each system has its own inherent chain-breaking reactions and for any one monomer the relative importance of these can be changed by changing the solvent, catalyst or co-catalyst [27b, 101]. One interesting difference between vinyl compounds and cyclic oxygen compounds is that with some of the latter, e.g., tetrahydrofuran, all kinds of chain-breaking reactions

126

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) are of minor importance or entirely absent and with others, e.g., dioxolan, there may be extensive transfer, but no termination [93].

5.2 Algebraic treatment One object of molecular weight studies is to identify all the chain-breaking reactions and to measure their rate constants. As will be seen below, the relevant measurements yield the ratios of the chain-breaking rate constants to the rate constant of propagation, kp. From these ratios, known as the chain-breaking coefficients, the chain-breaking rate constants can only be found if kp is known. None the less, the chain-breaking coefficients themselves can be very informative. The method of obtaining the chain-breaking coefficients is based on that developed originally by Mayo for radical polymerisations. Let the rate of chain propagation be Vp, and the total rate of chain-breaking be Vb. Then the number average DP of the ‘instantaneous’ polymer is DPn = Vp/Vb

(1)

and if the polymer is isolated at low conversion, its DPn will be given by this equation if Vp and Vb are expressed in terms of the initial concentrations of all the reagents. In practice it is usually much easier to stop polymerizations at low conversion than to use the integrated form of the above equation which is required to represent the DPn obtained at high, or complete, conversional (See, however, reference 25.) When developing this equation in terms of the rate expressions for the individual reactions it has been the usual practice to assume that there is only one propagating species in the system - an assumption which will be discussed in Section 6, and that the propagation reaction is of second order: Vp = kp2[Pn+][P1]

(2)

where [P1] is the concentration of monomer and [Pn+] that of growing chains. However, evidence is accumulating that propagation reactions of first order may not be uncommon [85, 86]; in such reactions Vp = kp1[Pn+]

(3)

Therefore it will be useful to formulate the general case in terms of a propagation reaction written as Vp = kp[Pn+][P1]x

(4)

127

Developments in the Theory of Cationoid Polymerisations where x = 0 or 1, and then to derive the special cases. The total rate of chain-breaking can be written in the form

[ ](

)

Vb = Pn+ kt1 + ∑ kbi [ Xi ]

(5)

where kt1 is the rate constant for unimolecular termination, kbi is the rate constant for the reaction of growing ends with the ith chain-breaking agent Xi, and the summation comprises all chain-breaking reactions known and suspected. Thus:

∑ k [ X ] = k [ P ] + k [C] + k [ A] + k [S] + J bi

i

m

1

c

a

(6)

s

where C = catalyst, A = co-catalyst, S = solvent, and the term J is retained as a reminder of possible, as yet unidentified, chain-breaking reactions. A point which has been overlooked by most authors is that if the DP is found to depend on the concentration of a certain reagent, e.g., water, it does not follow that this reagent itself is the chain-breaking agent; one may only conclude that there is present a chain-breaking agent the concentration of which is proportional to that of the reagent being studied. From equations (1), (4), (5) and (6) we now obtain the general DP equation.

(

kp 1 1− x = km [ P1 ] + k + k [C] + ka [A ] + ks [S] + J DPn [ P1 ]x t1 c

)

(7)

The usefulness of this equation can be extended by making the substitution

[S] = (1 − [ P1 ]v m ) / v s

(8)

where vm and vs are the molar volumes of monomer and solvent in litres per mole, which are assumed to be additive. We thus obtain

⎞ k ks ks [ P1 ]v m 1 1 ⎛ 1− x = m [ P1 ] + − + J ′⎟ x ⎜ kt1 + DPn k p vs vs ⎠ k p [ P1 ] ⎝

(9)

where J’ includes J and the terms in kc and ka. Evidently, the term in [P1]vm will only become important at very high monomer concentrations. We will consider here only the range of [P1] over which [S] can be considered constant, because at higher [P1] and with

128

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) polar solvents complications due to the effect of changing polarity on the rate constants are to be expected. Case 1, x = 1

(

k 1 1 kt + kc [C] + ka [A ] + ks [S] + J = m + DPn k p 2 k p 2 [ P1 ] 1

)

(10)

The first Mayo plot, 1/DPn against 1/[P1] is, for many systems, a straight line, the intercept I1 of which gives km/kp2. The slope S1 gives the term in ( ), divided by kp2 and not, as has been assumed by several authors, kt1/kp2. Next, the second Mayo plot, 1/DPn against [C], has the slope S2 = kc/kp2[P1], and an intercept

I2 =

(

km 1 kt + ka [A ] + ks [S] + J + k p 2 k p 2 [ P1 ] 1

)

whence, by means of I1 a value of (kt1 + ka[A] + ks[S] + J)/kp2 can be calculated; and another value of this sum can be found from S1 and kc/kp2. In this way from appropriate plots other chain-breaking coefficients can be found - with corresponding cross-checks. It is evident that there is no way in which kt1 and J can be separated, and one can only hope to identify all chain-breaking reactions by exhaustive study and then take any chain-breaking effect which is independent of all concentrations as kt1. In many systems (most of which have been listed [21]) the DP goes through a maximum or minimum, or rises to a constant level, or falls to a constant level, as the concentration of one of the reagents is increased. Such behaviour is symptomatic of a more complicated chemical situation, (e.g., progressive neutralization or formation of one or more chainbreaking agents), and it must be analysed by the methods suggested by Plesch [21, 105]. This work goes some way towards answering Mayo and Morton’s query concerning ‘…some peculiar effects of concentrations on molecular weights…’ [3] Case 2, x = 0

(

k 1 1 = m [ P1 ] + kt + kc [C] + ka [A ] + ks [S] + J DPn k p1 k p1 1

)

(11)

It is evident that the usual first Mayo plot will not give a straight line, but that a plot of 1/DPn against [P1] will, with slope km/kp1, and an intercept given by the whole second term of the equation. The method of evaluating the other chain-breaking coefficients is obvious.

129

Developments in the Theory of Cationoid Polymerisations N.B. The important point to note is that, in favourable cases, the manner in which the DP depends on the monomer concentration can show unambiguously whether the propagation is a first- or a second-order reaction. This is very useful because often the evidence from rate measurements, especially the analysis of individual rate curves, may be uncertain and difficult to interpret.

5.3 Kinetic evidence concerning termination The termination reactions are probably more obscure than the other chain-breaking reactions in cationic polymerisation because in most systems they are unimportant compared to the transfer reactions. The only unambiguous evidence for the existence of a termination reaction can come from rate studies of the whole course of the reaction. Several types of behaviour can be distinguished: Case 1. If the polymerization reaction stops before all the monomer has been consumed, there must be a termination reaction. Examples of this behaviour are found in the following systems: Isobutene-TiCl4-H2O+n-C6H14 [106]. Isobutene-TiCl4-H2O-CH2Cl2 [23]. Isobutene-TiCl4-AlBr3-heptane [40b]. Styrene-H2SO4-(CH2Cl)2 [26, 107]. Ethylene oxide-SnCl4-(CH2Cl)2 [64]. Propene oxide-AlMe3-CH2Cl2 [108]. N-vinylcarbazole-tetranitromethane-toluene [25]. Vinyl isobutyl ether-BF3Et2O-toluene-hexane [109]. Trioxan-BF3(n-Bu)2O-cyclohexane [110]. If we apply the term ‘stationary state’ to those systems in which the concentration of growing chains does not vary throughout the reaction, then it is evident that none of the systems comprised under Case 1 can involve a stationary state. The population of growing chains is declining throughout most of the reaction and falls to zero before all the monomer has been consumed. The method of dealing with this type of kinetic behaviour, devised by Pepper et al., [26] has been used effectively by others [40b, 109, 110]. Case 2. If the dependence of DP on [P1] shows that the propagation is a second order reaction (equation (12)), and if the whole reaction curves are of first order, it follows that [Pn+] must be constant throughout the reaction, i.e., there is a stationary state. This can be of the First Kind, Vi = Vt ≠ 0, or of the Second Kind, Vi = Vt = 0. The diagnosis

130

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) may be difficult, but in some cases evidence from reaction under extreme conditions, (e.g., very low co-catalyst concentration), provides evidence for the existence of termination, in which case the stationary state must be of the First Kind; in other cases there is evidence for instantaneous and complete engagement of all the catalyst in the initiation reaction, so that during the reaction Vi = 0, and therefore Vt = 0 and the stationary state is of the Second Kind. It is unfortunate that many workers have not appreciated how essential a clue to the kinetics can be provided by the kinetic order of the whole reaction curve. The use of initial rates was carried over from the practice of radical polymerisation, and it can be very misleading. This was in fact shown by Gwyn Williams in the first kinetic study of a cationic polymerization, in which he found the reaction orders deduced from initial rates and from analysis of the whole reaction curves to be signfficantly different [111]. Since then several other instances have been recorded. The reason for such discrepancies may be that the initiation is neither much faster, nor much slower than the propagation, but of such a rate that it is virtually complete by the time that a small, but appreciable fraction of the monomer, say 5 to 20%, has been consumed. Under such conditions the overall order of the reaction will fall from the initial value determined by the consumption of monomer by simultaneous initiation and propagation, and of catalyst by initiation, to a lower value characteristic of the reaction when the initiation reaction has ceased. In some cases in which the rate of polymerization is of first order in monomer and for which there are reasons for believing a stationary state of the First Kind to prevail, it has been argued that Vt must be independent of [P1] (without, indeed, much evidence) and that therefore Vi must also be independent of [P1]. However, a termination reaction with monomer, though unlikely with most monomers, is not impossible, and in the Mayo plots it would be indistinguishable from monomer transfer. One possible mechanism for such a termination reaction is the formation of an allylic ion by abstraction of a hydride ion from the monomer [112]: + CH 2 : CMe 2 ⎧ ⎫ ⎧ (CH 2 : CMe • CH 2 ) ⎫ ⎪ ⎪ ⎪ ⎪ + Pn+ + ⎨ CH 2 : CMeX ⎬ → ⎨ (CH 2 : CX • CH 2 ) ⎬ + Pn H ⎪CH : CH • O • CH X ⎪ ⎪(CH : CX • O • CHX )+ ⎪ 2 2 ⎭ ⎩ 2 ⎩ ⎭

(XII)

This is related to reaction (X) for propene, but for isobutene this process is unlikely because it involves formation of a 2-methylallyl ion and destruction of a tertiary ion: in the gas phase this reaction would be highly endothermic [113] because the ionisation potential of the 2-methylallyl radical [114] is appreciably greater than that of the tertiary butyl radical [115], and the difference in the homolytic C—H bond dissociation energies is in the same

131

Developments in the Theory of Cationoid Polymerisations direction. Whether a possible difference in the solvation energies and Coulombic energies of the two ions could compensate for this in solution is an open question. Another mode of termination by monomer, which has been suggested for the polymerization of N-vinylcarbazole, is formation of a quaternary ammonium ion from the growing cation and the monomer [25] which is essentially the same as reaction (XIa). Case 3. If the propagation is a second-order reaction and the whole reaction curve is of second order, we have again necessarily a stationary state and this can only be of the First Kind. Thus, if we are dealing with formation of high polymers, such that rate = Vp, Vp = k2[P1]2 and Vi = Vt In many systems k2 = k3 [C]α or k4 [C]α [Cocat]β, where α and β may equal 1 or may be fractional. The polymerizations of alkyl vinyl ethers by iodine and some other catalysts obey these kinetics, with α = 1, β = 0 (see reference 35 and the preceding papers of that series). No general discussion of the multitude of behaviour patterns, especially as regards dependence on concentration of catalyst, or of components of a syncatalyst, can be profitable at this stage. As for the termination reactions - our special concern here - this kinetic pattern implies that Vi is of first order, Vt of zero order, with respect to monomer. This means that k3 or k4 contain a term kikp/kt; they may also contain one or more equilibrium constants - depending on the nature of the catalytic system.

5.4 Chemistry of chain-breaking reactions The number of chain-breaking reactions which have been identified in various systems is very great. They may be divided into at least four categories. a) The formation of ions too stable to propagate, e.g. reactions (X) and (XIa); these are terminations. b) Reactions in which a proton (or possibly some other cation) is lost to a base Bs from the growing chain, which then has an unsaturated end-group: –CH2 ⋅ CHR.CH2.CHR+ + Bs → –CH2.CHR.CH:CHR + HBs+

(XIII)

This reaction may be bimolecular, as shown, or unimolecular. i) If Bs is the anion, e.g., BF3OH-, this reaction is a catalyst regeneration and, in a system in which the initiation is slow, it is kinetically a termination.

132

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) ii) If Bs is monomer, the reaction is a monomer transfer (strictly, proton transfer to monomer). This is the most common type of transfer and few cationic polymerizations are known in which it does not occur; in many it is the dominant factor controlling the DP. Ever since the early work on butyl rubber it has been known that the DP of copolymers can be, and usually is, lower than that of either homopolymer made under the same conditions. This implies a preferential ‘cross-transfer’, which has been investigated in some detail [116-118]. Reactions in which a reagent is cloven: (i) The termination reactions of the type (IX) in which an anionic fragment is abstracted from the anion, so that the chain-carrier is neutralised. This type of termination has been claimed to occur in many systems; for example, in the polymerization of tetrahydrofuran by PF5 a terminal F from PF-6 was indeed found [119]. Zlamal, Ambroz, and Vesely [20] have found that in solutions of aluminium chloride in ethyl chloride, containing various quantities of, for example, ethanol, the electrical conductivity of the solution is antibatically related to the DP of the polyisobutene formed by addition of isobutene to the solution. The only reasonable interpretation of this phenomenon (the ZAV effect) is that the principal chain-breaking agent is an anion. There are some indications as to the nature of these anions and, although the nature of the end-groups resulting from the termination is unknown, it seems most likely that the termination involves cleavage of the anion and thus belongs into this class of reactions. ii) Transfer with an alkyl halide: Pn+ + RCl + P1 → PnCl + RP1+ This reaction, generally known as ‘solvent transfer’, probably involves a solvent molecule in the solvation shell of the cation and is thus not to be regarded as termolecular. For energetic reasons it is very unlikely to involve the formation of a free cation R+ as reaction intermediate, if RCl is any one of the alkyl chlorides which are commonly used as solvents; it may involve the species Pn+ClR [120]. Very little is known about this type of transfer reaction [118]; it is closely related to ‘solvent co-catalysis’ (see p.112). iii) Transfer with an aromatic compound: Pn+ + ArH + P1 → PnAr + HP1+

(XIV)

This reaction takes place in two stages, the rate-determining step (rate constant kr) being the alkylation of the aromatic compound; this is followed by a fast proton transfer to monomer [100]. The reaction is in fact a Friedel-Crafts alkylation: of all the transfer

133

Developments in the Theory of Cationoid Polymerisations reactions it has been most thoroughly studied, but mostly with styrene [99, 121]. It also occurs in the polymerization of isobutene, but kr/kp is much smaller than for styrene with the same transfer agent, anisole [122]. Okamura’s school has made a close study of the monomer transfer reaction, and they take the view that with at least some aromatic monomers this is not a direct proton transfer from a position α to the site of the charge (reaction (XIII)), but an alkylation of one monomer and subsequent proton transfer from the alkylated phenyl group to another monomer molecule [123]. Closely related to these alkylations is the following phenomenon. In the polymerization of aromatic monomers it is frequently found that at least a part of the end-groups is substituted indanes. In some systems these may be formed during the actual chain-breaking reaction; in others they are known to be formed by a relatively slow internal FriedelCrafts alkylation of a pendent phenyl group by the terminal olefinic group. With regard to pseudo-cationic polymerizations, Pepper and Reilly [27b] have made a start on the important task of correlating the kinetics of the chain-breaking reactions with the nature of the end-groups. They found that in the system styrene-perchloric acid-ethylene dichloride a chain-breaking reaction, the rate of which is independent of [P1] and which they write as the unimolecular version of reaction (XIII) (with Bs = ClO-4) gives the unsaturated end-groups, whereas monomer transfer gives indane end-groups; the actual mechanism of these reactions is obscure. iv) Transfer by hydride ion abstraction from polymer, discussed in sub-section 4.1; see also equation (X). Neutralization reactions in which the charge is destroyed. One version, equation (IX), has been mentioned at the beginning of sub-section 5.1. Whether there are neutralization reactions in which the whole of the anion combines with the active cation is at present not known, and such cases are likely to be rare because the very virtue of an effective polymerization catalyst resides in its having, or generating, an anion of very low nucleophilicity. Some obscurities. Each of the reactions mentioned has been identified in at least one system, but there are very many obscurities to be cleared up. For example, transfer by methyl vinyl ether, phenyl vinyl ether, vinyl acetate and some of the corresponding polymers in the polymerization of styrene by stannic chloride has been studied, but the mechanism is not at all clear [124]. In polymerizations catalysed by a metal halide and some others one of the most effective chain-breaking agents is a species, the concentration of which is proportional to the water concentration (see e.g., references 36, 37, 39, 69, 110, 125); but in most cases we know neither the exact nature of this species nor the type of reaction. 134

Cationic Polymerisation from ‘Progress in High Polymers’ (1968)

5.5 Factors influencing the chain-breaking reactions General considerations. The most obvious factors which may affect the magnitude of the chain-breaking rate constants, and, hence, of the chain-breaking coefficients for any one monomer, are (a) temperature, (b) solvent, (c) catalyst, (d) co-catalyst. It seems more useful to give here a general exposition of the effects involved than to attempt a summary of all the relevant studies. Information on chain-breaking coefficients is indeed contained in, or can be derived from, very many papers on cationic polymerization, but the largest single corpus of coherent data has been produced by Okamura’s school [32, 33, 101, 104, 126, 127]. Temperature. One of the rare generalizations about cationic polymerizations, to which very few exceptions are known [128, 129], is that as the temperature of reaction is reduced, the DP of the polymers increases. Furthermore, the corresponding Arrhenius plot, log DP against 1/T, is (approximately) rectilinear for most systems, and from it a formal ‘activation energy of DP’, denoted by EM, can be calculated. If in any one such system there is only one chain-breaking reaction, with a rate-constant kb, evidently EM = Ep-Eb. However, if there is more than one chain-breaking reaction, EM cannot be interpreted so simply. One can, indeed, write it formally as EM = Ep-Ez, where Ez is a composite quantity, which may in some cases be useful for comparisons, but this can be misleading. A real understanding of the effect of temperature on the chain-breaking reactions can only come from measurements of all the chain-breaking coefficients over a wide range of temperature; the operative word is ‘wide’. The danger of using too narrow a range of temperature is illustrated by the work of Imanishi, Higashimura, and Okamura [126] with the system isobuteneTiCl4-CH2Cl2 with water as the putative co-catalyst. From results obtained at –20 ºC, –50 ºC, and –70 ºC they deduced that log (km/kp) varied rectilinearly with 1/T, whereas the results of Plesch and collaborators obtained with the same system over the range from 18 ºC to –90 ºC showed that the Arrhenius plot for km/kp has a definite bend near –65 ºC and consists of two portions of very different slope [23]. The value of EM depends not only on solvent, catalyst, and co-catalyst but - at least for isobutene - also on the monomer concentration. Kennedy and Thomas [85] found that for isobutene-AlCl3-alkyl chloride the slope of the log DP-1/T plots increases with increasing monomer concentration in such a way that the family of lines all cross at approximately the same temperature, near –50 ºC which they called the inversion temperature. They interpreted this phenomenon in terms of a change in the relative importance of monomer transfer and solvent transfer with changing composition of the reaction mixtures. Solvent. The elementary reactions in cationic polymerizations are affected, like all other reactions, by the polarity of the medium in which they occur. Since there is at present no

135

Developments in the Theory of Cationoid Polymerisations other convenient measure of ‘polarity’ most workers continue to attempt correlations between kinetic constants, activation energies, etc., and the DC of the solutions concerned, although it has long been recognised that the DC is only a very inadequate measure of ‘polarity’. In fact, the logical validity of seeking any correlation between rate constants and DC has been seriously questioned [130]. The DPs obtained in cationic polymerizations are affected not only by the direct effect of the polarity of the solvent on the rate constants, but also by its effect on the degree of dissociation of the ion-pairs and, hence, on the relative abundance of free ions and ionpairs, and thus the relative importance of unimolecular and bimolecular chain-breaking reactions between ions of opposite charge (see Section 6). Furthermore, in addition to polarity effects the chain-transfer activity of alkyl halide and aromatic solvents has a quite distinct effect on the DP. The smaller the propagation rate constant, the more important will these effects be. Thus comparisons between the DPs obtained in different solvents are of little fundamental value, and only detailed information on the individual chain-breaking coefficients will advance our understanding. Catalysts and co-catalysts. The DPs, their temperature coefficients, and the individual chain-breaking constants are profoundly influenced by the nature of the catalyst and, in syncatalytic systems, of the co-catalyst. This was previously taken as one of the principal pieces of evidence adduced to support the view that in most cationic polymerisations the dominant growing species are ion-pairs. Although this interpretation may still be valid for some systems, namely those in which the chain-carriers are ions, one must now also consider that some of the observed differences may be due to a difference in mechanism. In pseudocationic reactions all the kinetic constants will necessarily change from one catalyst to another, and differ from those characterising truly ionic polymerizations of the same monomer. One of the few permissible generalisations is that for any one monomer, solvent, and temperature, syncatalysts give higher DPs than conventional acids. The explanation previously offered for this phenomenon [131, 132] must now be scrutinised from the point of view of the pseudo-cationic reactions (see also sub-section 4.3).

6 The nature of the propagating species: II

6.1 Multiplicity of chain-carriers Until recently most discussions of the mechanism of cationic polymerization have been based on the (usually tacit) assumption that in these reactions there is only one single

136

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) species of chain-carrier. However, elementary electrochemical considerations could have shown many years ago that this must be an over-simplification, except perhaps for reactions in non-polar solvents, such as hydrocarbons and carbon tetrachloride. For polar solvents the hypothesis that the chain-carriers are ions implies the existence of free cations as well as of cations forming part of ion-pairs, and possibly higher aggregates. Some authors have indeed recognised this, but evaded the question by supposing that even in alkyl halide solvents the predominant species would be ion-pairs. It will be shown below that for many systems this supposition may be quite fallacious; moreover, even if it were valid, it ignores the possibility that the propagation rate constant of the free ions may be so much greater than that of the paired cations that this could compensate for the smaller number of free ions and thus make their contribution to the total reaction rate appreciable. This situation appears to prevail in some anionic polymerizations [133]. (See also sub-section 4.4 and Table 2.) Only Norrish and Russell [22] based their interpretation of the isobutene-SnCl4-H2O-EtCl reaction explicity on propagation by free ions, and later work has given strong support to this idea. Since it is unreasonable to suppose a priori that the kinetic constants of free and paired cations are identical, equations need to be worked out which take into account the existence of two or more propagating species, the relative concentrations of which are governed by equilibria, and which have different propagation, transfer, and termination rate constants; this will be done below. We propose that polymerizations in which there are two or more propagating species be termed ‘enieidic’ (from Greek enioi meaning several and eidos meaning form) in order to avoid using the over-worked term ‘polymorphic’; the terms ‘monoeidic’ and ‘dieidic’ will also be found useful. Consideration of the whole field of cationic polymerization shows that simultaneous propagation by free ions and paired ions is only one of several types of enieidic polymerization. Another type of enieidic system is that in which the propagation is of the FontanaKidder type [86] in which the rate-determining step is isomerization of an associative complex. At very low monomer concentrations the rate of formation of this complex will become rate-determining and thus both the nature and the magnitude of the propagation rate constant will change, quite apart from the possibility of a slow direct reaction between the uncomplexed ion and the monomer. Thus, over a certain range of concentrations of monomer, two forms of propagation may coexist. This is somewhat similar to a compound reacting simultaneously by the SN1 and SN2 mechanisms. Systems in which several chemically different chain carriers coexist constitute another type of enieidic polymerization. One example of this would be a polymerization in which concurrent co-catalysis by water and by alkyl halide solvent produced anions MtXnOH– and MtX–n+1. In that case one must assume a priori that the cations forming pairs with the two different anions will have different kinetic constants.

137

Developments in the Theory of Cationoid Polymerisations Another possibility is that the reactivity of the active end would be influenced by complexing, e.g., with an added transfer agent. One example of this is the polymerization of styrene by stannic chloride in the presence of thiophene (T) [134] which can be interpreted on the supposition that there is equilibrium complex formation between the growing end and thiophene:

(Pn ,SnCl 4 ,H 2O) *

+ T ↔ ( Pn ,SnCl 4 ⋅ T,H 2 O) *

(XV)

and that the kinetic constants of the complexed and uncomplexed chaincarriers are different. Since it is now uncertain whether the chain-carriers are ions, the non-committal representation shown above has been used; this system will be discussed in detail in subsection 6.3. Co-polymerizations and homo-polymerizations of monomers such as dienes or 4methylene dioxolan, in which two or more types of ion may propagate simultaneously, are further examples of enieidic polymerizations. These dienes, of course, also provide examples of eniedic radical and anionic polymerizations. Indeed the idea of dieidic polymerization has been suggested by several authors in relation to anionic polymerizations; it arose from the aggregation in solution of the lithium alkyls [135], and similar phenomena. These considerations show that the determination of the number and nature of growing species in cationic polymerizations is, in general, not easy, and the alleged determinations of absolute rate constants need to be scrutinised most carefully from this point of view.

6.2 Free ions and ion-pairs Electrochemical considerations. There is so much evidence from electrical and also from non-electrical studies for the existence of ion-pairs in solvents of low polarity, that it cannot be ignored in discussing the reactions of ions in such systems [136]. The most detailed and comprehensive discussion of ion-pairs and related concepts has been given by Szwarc [137]. The next step after the recognition of the existence of ion-pairs is the estimation of their concentration as a function of the various experimental parameters, so that their importance relative to the free ions can be assessed. In order to do this, the dissociation constant of the ion-pairs under the relevant conditions is required.

Pn+ A − (solv.) ↔ Pn+ (solv.) + A − (solv.)

(XVI)

According to current theories the dissociation constant K of an ion-pair is determined by the DC of the solvent, ε, the temperature, T, and a term a which is interpreted by some

138

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) workers as the minimum interionic distance [138]. It is related to these quantities by the Bjerrum-Fuoss equation [139]

— log K = A – B/aεT

(12)

where A and B are calculable constants (except that A contains a term in log a). Many measurements, especially with quaternary ammonium salts, confirm the approximate validity of this equation for solvents having a DC greater than about 5. There are but few measurements of K for carbonium salts, and all of these are for triphenylmethyl salts, but by means of equation (12) the magnitude of K for other salts and for any required values of ε and T can be estimated with fair confidence. If the equilibrium (XVI) is the only one, the relation between K and the concentrations of free ions and ion-pairs is given by some elementary relations which, however, it is useful to set out in full. Let the concentrations be denoted by

[P A ] ≡ q, [P ] = [A ] ≡ p, p + q ≡ c + n

+ n

–

–

We assume that the activity coefficient of the ion-pairs is unity and denote the mean ionic activity coefficient by y±. The thermodynamic equilibrium constant for the dissociation is then given by the equation

K = p 2 y±2 /q = p 2 y±2 / (c − p)

(13)

on the assumption that K is independent of the polymer chain length. If, for simplicity, we denote K/y2± by Ky (which is the stoichiometric dissociation constant at finite concentration),

p=–

Ky + 2

1 2

(K

2 y

+ 4 Kyc

)

1/ 2

(14)

The degree of dissociation is α = p/c = 1 – q/c. We now consider the three special cases shown in Table 3. In order to ascertain which, if any, of the two approximations may be valid, we need to examine the magnitudes of K, Ky and c which are relevant to the systems under discussion. To determine a value of K which will be relevant to polymerizing systems, we need the dissociation constant of a carbonium salt with a large anion, in a solvent of ε about 10, at 25 ºC. The only relevant information is Longworth and Mason’s value of K for triphenylmethyl perchlorate in ethylene dichloride [53], and values of K for two quaternary ammonium perchlorates [140] (see Table 4).

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Developments in the Theory of Cationoid Polymerisations

Table 3 Ky

p

q

p/q

α

>> c

≈c

≈ c2/Ky

Ky/c

≈ 1–c/Ky≈ 1

c

c(51/2–1)/2

c(3–51/2)/2

1.62

0.6 2

<< c

≈ Ky1/2c1/2

≈c

Ky1/2/c1/2

≈ Ky1/2/c1/2≈ 0

Table 4 Dissociation constant K of perchlorates in ethylene dichloride A. Ph3C+ClO–4 [53] T (deg) 103K (mole/l)

21.5 1.26

10

0

1.48

1.66

B. 25° [140] Compound 104K (mole/l)

(n-Bu)4N+ClO4-

Me(n-Bu)3N+ClO4-

1.54

0.80

Since the anions derived from syncatalytic systems involving SnCl4 or TiCl4 are appreciably greater than the ClO4- ion, the corresponding values of K will also be greater. On the other hand, the tertiary butyl and other alkyl ions are smaller than the cations considered above, so that for such systems a K of the order of 10-4-10-3 mole/l is probably a realistic estimate, and at the concentrations of ions occurring in polymerizing systems Ky will be of the same order of magnitude. The magnitude of c is more difficult to determine. In most studies of cationic polymerizations the nominal catalyst concentration lies in the range 10-2-10-4 mole/l. However, in syncatalytic systems, such as SnCl4-H2O, the total concentration of cations, c, at any instant may be equal to the concentration of the scarcer of the two components (usually 10-3 to 10-5 mole/l) or it may be very much less than this. The main conclusion to be drawn from these considerations, despite their rather impressionistic character, is that in very many systems c and Ky are likely to be of the same order of magnitude. Therefore the facile assumption, made by many authors, that the dominant species are the ion-pairs, i.e., q ≈ c, is certainly not obviously justified and may be entirely incorrect for some systems. Indeed, as has been mentioned above, the

140

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) behaviour of the system isobutene SnCl4-H2O-EtCl at –78 ºC can only be interpreted reasonably on the basis that the principal propagating species is the free cations [142]. The kinetic equations. Having established from electrochemical considerations that the simultaneous presence of appreciable concentrations of free cations and ion-pairs can reasonably be expected in many of the systems of interest in the present context, the next task is to establish the shape of the curves relating p and q to c, and, hence, the curves to be expected for the dependence of rate on c under various conditions. These considerations are made much easier by the fact that the shapes of the curves are independent of the value of K. The curves of p against c and q against c (all in units of K) given by equation (14) are parabolas (curves A and B of Figure 1). Consider now a stationary system, i.e., one in which p and q are invariant with time. If the stationary state is of the Second Kind, c = [catalyst]; if it is of the First Kind, c is less than [catalyst]0, but proportional to it. The rate of polymerization is given by R ≡ –dm/dt = [kpp + kπq]m

(15)

Figure 1 The variation of the relative concentration of free ions, p/K (curve A), and of ionpairs, q/K (curve B), with total relative concentration of ions, c/K. For curve C see text

141

Developments in the Theory of Cationoid Polymerisations where m ≡ [P1], and kp and kπ are the rate constants for propagation by free ions and by ion-pairs. The term in brackets has the dimensions of a first-order rate constant. If propagation is by free ions only, kπ = 0, and this first order rate constant will show a dependence on c, and, hence, on [catalyst]0, given by curve A of Figure 1. This is identical in shape with the curve relating initial rate to water concentration which Norrish and Russell[22] found for the polymerization of isobutene by SnCl4-H2O in EtCl at –78 ºC, and on which the argument that free ions are dominant in this reaction is based [142]. If propagation is by ion-pairs only, i.e., kp = 0, the first-order rate constant will follow curve B of Figure 1. If kp = kπ, the rate constant is rectilinearly related to c (line C of Figure 1). Next we consider the general case in which, say, kp = βkπ, for different values of β. We substitute for kp and q in equation (15) and replace p and q in terms of α and c: R/kπm = c + (β – 1)αc

(16)

This equation is most conveniently handled in the dimensionless form R/Kkπm = (c/K)(1 + (β – 1)α)

(17)

so as to show up the dependence of R on c; of course, c, α, and K are related by the Ostwald Dilution Law K = α2c/(1 – α). The plots for β = 0.1, 0.5, 2, 11 are shown in Figure 2. These curves are a normalised form of the rate-[catalyst] plots obtained in the usual kinetic studies. It is evident from them that only very precise measurements would show any curvature in the plots of rate constant against catalyst concentration, unless β were less than about 0.1 or greater than about 10, and the catalyst concentration were varied by at least a factor of 10. The question arises why this phenomenon has so far escaped detection, except in the system isobutene-SnCl4-H2O-EtCl. One reason is that most studies in which it could have been found were conducted with syncatalytic systems, e.g., SnCl4-H2O, and curved plots obtained with such systems are usually ascribed, tacitly or explicitly, to equilibria between catalyst and co-catalyst. However, it is noteworthy that Colclough and Dainton [36] have presented curves relating rate to co-catalyst concentration for the polymerization of styrene by SnCl4 in ethylene dichloride at 25 °C with t-BuCl or water as co-catalyst, which have a very strong resemblance to those in Figure 2 for high values of β. If reinvestigation of this system shows the polymerization to be ionic, rather than pseudoionic, this would suggest that propagation by ion-pairs is dominant. It was stated in Section 2.2 that Pepper and Reilly’s findings concerning the dependence of the rate of polymerization of styrene on the perchloric acid concentration are difficult

142

Cationic Polymerisation from ‘Progress in High Polymers’ (1968)

Figure 2 The normalised polymerization rate, R/Kkπm, plotted against the total relative concentration of ions, c/K, according to equation (17). The value of β is shown against each curve

to reconcile with an ionic theory. The reaction has accurately first-order kinetics [27d], and the nine plots of first-order rate constant against [HClO4] can only be interpreted reasonably by straight lines through the origin. If the polymerization were ionic, this would mean that kp and kπ would be approximately equal (within a factor of about 10), a result which would be greatly at variance with all comparable cases, and very difficult to understand. For stationary systems of the First Kind and for non-stationary systems the rate equations are complicated, as they depend upon the kinetics of the initiation reaction. For such systems it is perhaps more profitable to concentrate attention upon the dependence of the DP on the reaction variables. Consider the following typical set of reactions, consisting of propagation, monomer transfer, and termination:

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Developments in the Theory of Cationoid Polymerisations

HPn+ A – + P1

→ HPn++1A –

kπ

HPn+ + P1

→ HPn++1

kp

HPn+ A – + P1

→ Pn + HP1+ A –

kμ

HPn+ + P1

→ Pn + HP1+

km

HPn+ A – HPn+ + A –

→ →

} HP A n

or Pn + HA

kτ11 kt 2

This selection of reactions, by way of example, is not meant to imply that, for instance, a second-order termination reaction of ion-pairs, say

HPn+ A – + A – → HPn A + A –

kτ2

is considered impossible, but for the purpose of developing the requisite equations it will suffice to consider the four chain-breaking reactions given above. With the previous notation, the rate of polymerization is given by R = m(kpp + kπq)

(18)

= kπm(βp + q)

(19)

= kπmp(β + pKy-1)

(20)

If it is assumed that the dissociation constant, Ky, of the ion pairs is independent of the length of the polymer chain attached to the cation, the Mayo equation takes the form

k p + kμ q kt2 p 2 + kτ1q + J p + Jq 1 + = m DP k p p + kπ q m k p p + kπ q

(

(21)

)

where Jp and Jq include unspecified chain-breaking reactions. This can be written in the form

(

)

kt2kτ1 K y−1 p k + kμ K y−1 p J p + Jq 1 = m + + DP kπ β + K y−1 p kπ m β + K y−1 p kπ mp β + K y−1 p

(

144

)

(

)

(

)

(22)

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) One important difference between these equations and those for monoeidic polymerizations is that they contain explicitly the concentrations of growing ends (p and q). Since these are related through equation (14) to c, and this depends upon the catalyst concentration, the DP depends upon this in an essential manner; in particular, the intercepts and slopes of the Mayo plots will depend upon it. Another important feature is that all the terms are composite, and therefore it is not to be expected that the Arrhenius plots for the intercepts and slopes of the Mayo plots will be rectilinear. In fact, historically, the nonlinearity of such Arrhenius plots obtained for the polymerization of isobutene by titanium tetrachloride and water gave the first clue to the existence of simultaneous propagation by free ions and ion-pairs in that system [23]. In non-stationary systems there is the added complication that c, and, hence, α and p and q, change throughout the reaction. The development of the requisite equations, though complicated, should not involve any fundamental difficulties. The full implications of the ideas and equations suggested here, and their applicability and heuristic value remain to be explored.

6.3 Complexed and uncomplexed chain-carriers General theory. Consider an ionic polymerization proceeding under conditions such that propagation by free ions can be neglected, and in the presence of a compound R which forms a complex with the ion-pair:

Pn+ A – + R ↔ Pn+ A – ⋅ R,

K1

Let the concentrations be denoted as follows:

[P A ] ≡ q, [R] ≡ r, [P A + n

–

[P1 ] ≡ m

+ n

–

]

⋅ R ≡ w, q + w ≡ c

The rate constants characterizing reactions of the uncomplexed ion pairs are given subscript 1, those of the complexed ion-pairs subscript 2. The rate of polymerization, Vp, is then given by Vp = m(kp1q + kp2w)

145

Developments in the Theory of Cationoid Polymerisations Since K1 = w/qr q = c/(1 + K1r) and, hence, Vp = mc(kp1 + kp2K1r)/(1 + K1r)

(23)

If c is constant, the system is stationary. In that case, provided that r does not change (significantly) throughout the reaction, this will have second-order kinetics, but the secondorder rate constant, the coefficient of mc, depends upon r. Two extreme cases can be usefully distinguished. When K1r << 1 Vp/mc = kp1 + kp2K1r

(24)

When K2r >> 1

k Vp = p1 + k p2 mc K1r

(25)

The second alternative is likely to be the more important in practice. The DP is given by equation (1) and Vp is given by equation (23). If R is a chain-breaking agent, then Vb is given by Vb = qJq + kr1qr + wJw where Jq and Jw include all terms representing chain-breaking reactions not involving R; kr1 is the rate constant for reaction of Pn+A- with R (which may be termination or transfer, see sub-section 5.4); and it is assumed that the complexed ion-pair Pn+A–. R does not react with free R. It follows that m/DP = (Jq + K1rJw + kr1r)/(kp1 + kp2K1r) If

K1r << kp1/kp2 m/DP = Jq/kp1 + r(K1Jw + kr1)/kp1

If

(27)

K1r >> kp1/kp2 m/DP = Jq/K1/kp2r + Jw/Kp2 + kr1/K1kp2

146

(26)

(28)

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) Consider now a pseudo-cationic polymerization in which the non-ionic chain-carrier can form a complex with the compound R. The algebra and resulting equations are the same as above, with the one difference that q now signifies the concentration of uncomplexed chain-carriers and w the concentration of those which are complexed with R. Application. The development of the foregoing train of thought was originally occasioned by some unpublished observations concerning the effect of anisole on the rate of polymerization of isobutene by titanium tetrachloride and water. Search of the literature for related observations revealed that Overberger and Endres [134] had found the polymerization of styrene by stannic chloride at 0 °C in nitrobenzene-carbon tetrachloride mixed solvent (with water as the putative co-catalyst) to be retarded by thiophene. The reaction had the following characteristics: the whole reaction curves were of first order (after an initial fast phase which was of short duration), the first-order rate constant k´ was proportional to [SnCl4]. This shows that this is a stationary system. The effect of thiophene on the DP obeyed the Mayo equation (1/DP proportional to [thiophene]), and the first-order rate constant decreased more rapidly than linearly with [thiophene] (Figure 3). This more than proportional effect was not explained by the authors in detail,

Figure 3 The first-order rate constant k´ for the polymerization of styrene by stannic chloride in the presence of thiophene [134]

147

Developments in the Theory of Cationoid Polymerisations but was ascribed qualitatively to the fact that thiophene caused kinetic termination. The authors pointed out that it could not be explained by the complexing of thiophene with stannic chloride. Since stannic chloride is known to form a complex with thiophene, and since the most favoured co-ordination number of Sn is 6, complex formation between the tin-containing moiety of the chain-carrier and thiophene is at least probable. Hence, we have the situation discussed above, and it remains to establish which, if any, of the simplified equations (24), (25), (27), and (28) is applicable. In equations (24) and (25) Vp/m is equivalent to Overberger and Endres’ k´. Examination of their data showed that a plot of k´-0.6 (min-1) against 1/r = [thiophene]-1 gave a straight line through the origin (Figure 4). This agreement with equation (25) shows the data to be compatible with the theory developed here, with the entirely reasonable condition that K1r >> 1. Unfortunately, since c is probably much less than [SnCl4], but unknown, kp2 and kp1/K1 cannot be calculated. As far as the DP is concerned, the author’s finding that its dependence on [thiophene] obeys the Mayo equation shows that equation (27) is the appropriate one. However, it follows from this that on our interpretation the slope of the Mayo plot is not, as the

Figure 4 Results of Overberger and Endres [134] plotted according to equation (25)

148

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) authors supposed, kr1/kp1 (kr/kp in their notation), but that given by equation (27). The conditions K1r >> 1 (equation 25) and K1r << kp1/kp2 (equation 27) are certainly compatible. The theory developed here can be extended and generalised in several ways, for instance by considering the monomer itself as the reagent which forms the complex with the chain carrier, and this leads towards the Fontana-Kidder theory of first-order propagation. The theory is also conceptually related to Eley’s ideas concerning sequestration of the catalyst iodine by complex formation with the vinyl ethers, by which he could account very elegantly for the phenomenology of the corresponding polymerisations.

7 Conclusion It is the author’s hope that the foregoing detailed discussion has helped to clarify some features of cationic polymerizations. Many other aspects, such as co-polymerization and radiation polymerization, which I have not been able to discuss here, deserve equal attention. But perhaps the most urgent task, and one which is much more widely relevant, is the elucidation of details of reaction mechanism, and in particular the identffication of the chain-carriers in many widely differing systems. The next problem then is to measure their concentration, its variation throughout the reaction, and, hence, the absolute rate constants. It is essential that the factors which decide whether a polymerization is ionic or pseudo-ionic be determined as soon as possible. Another important field of work is the characterization of oxonium and carboxonium ions, especially the energetics of their formation and the ranking of their stability in relation to structure. Apart from this, there is an urgent need for chemical and kinetic studies with new monomers, covering a wide range of conditions and carried out with the most rigorous techniques. Too many of Mayo and Morton’s questions still remain to be answered.

Acknowledgement I wish to thank Dr. A. Wassermann for many helpful comments and suggestions.

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Developments in the Theory of Cationoid Polymerisations

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2.

Plesch, P. H. (Ed.) Cationic Polymerisation and Related Complexes, Heffer, Cambridge, (1953).

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4.

(a) Gandini, A. and Plesch, P. H. Proc. Chem. Soc., 240 (1964); (b) Polymer Letters, 3, 127 (1965); (c) J. Chem. Soc., 4826 (1965); (d) European Polym. J., 4, 55 (1968).

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Plesch, P. H. and Gandini, A. Soc. Chem. Ind. Monograph No. 20, p.107 (London, 1966).

6.

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8.

(a) Kennedy, J. P. and Langer, A. W. Adv. Polym. Sci., 3, 508 (1964) (b) Roha, M. Adv. Polym. Sci., 4, 353 (1966) (c) Pepper, D. C. in Olah, G. A. (Ed.) Friedel-Crafts and Related Reactions Interscience, New York, (1964) (d) Kosower, E. M. Progr. Phys. Org. Chem.,3, 81 (1965) (e) Organic Reaction Mechanisms (Chem. Soc. Spec. Publ. No. 19, London, 1965). Papers by G. A. Olah and by S. Winstein (f) Kennedy, J. P. Trans. N.Y. Acad. Sci.,28, 1080 (1966).

9.

(a) Deno, N. C. Progr. Phys. Org. Chem.,2, 129 (1964) (b) Sargent, D. G. Quart. Rev. Chem. Soc.,20, 301 (1966) (c) Olah, G. A. and Pittman, C. U. Adv. Phys. Org. Chem.,4, (1966) (d) Brown, H. C. Chemistry in Britain,2,199 (1966) (e) Olah, G. A. Chem. Eng. News,7 March, p. 77 (1967).

10. Evans, A. G. et al., J. Chem. Soc.,689 (1962) and ten preceding papers. 11. Pepper, D. C. Trans. Faraday Soc.,45, 397 (1949). 12. Brown, C. P. and Mathieson, A. R. J. Chem. Soc.,3612 (1957).

150

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) 13. Metz, D. J. J. Polym. Sci.,50, 497 (1961). 14. Jordan, D. O. and Treloar, F. E. J. Chem. Soc.,734, 737 (1961). 15. Gandini, A. and Plesch, P. H. J. Chem. Soc.,4765 (1965). 16. Hanazaki, I. and Nagakura, S. Tetrahedron,21, 2441 (1965). 17. Higashimura, T., Kanoh, N. and Okamura, S. J. Macromol. Chem.,1, 109 (1966). 18. Bywater, S. and Worsfold, D. J. Can. J. Chem.,44, 1671 (1966). 19. Bertoli, V. and Plesch, P. H., (a) Chem. Comm.,625 (1966); (b) in press. 20. (a) Zlamal, Z., Ambroz, L. and Vesely, K. J. Polym. Sci.,24, 285 (1957) (b) Vesely, K., J. Polym. Sci.,30, 375 (1958) (c) Ambroz, L. and Zlamal, Z. J. Polym. Sci., 30, 381 (1958) Zlamal, Z. and Ambroz, L. J. Polym. Sci., 29, 595 (1958); Zlamal, Z. and Kazda, A. J. Polym. Sci., 53, 203 (1961); A. 1, 3199 (1963); A. 4, 367 (1966) (d) Bethell, D. and Gold, V. Carbonium Ions, Academic Press, London, (1967). 21. Plesch, P. H. J. Chem. Soc., 104 (1964). 22. Norrish, R. G. W. and Russell, K. E. Trans. Faraday Soc., 48, 91 (1952). 23. Biddulph, R. H., Plesch, P. H. and Rutherford, P. P. J. Chem. Soc., 275 (1965). 24. Wassermann, A. et al., Polymer Letters, 3, 369 (1965) and preceding papers. 25. Pac, J. and Plesch, P. H. Symp. on Macromolecules, Tokyo, (1966); Polymer, 8, 237 (1967). 26. Pepper, D. C. et al., Proc. Roy. Soc., A263, 58, 63, 75 (1961). 27. Pepper, D. C. and Reilly, P. J. (a) Proc. Chem. Soc., 200 (1961) (b) Proc. Chem. Soc., 460 (1961) (c) J. Polym. Sci., 48, 639 (1962) (d) Proc. Roy. Soc., A291, 41 (1966). 28. (a) Plesch, P. H. J. Appl Chem., 1, 269 (1951) (b) Plesch, P. H. J. Polym. Sci., 12, 481 (1954). 29. Evans, A. G. and Meadows, G. W. Trans. Faraday Soc., 46, 327 (1950).

151

Developments in the Theory of Cationoid Polymerisations 30. Plesch, P. H. Proc. Roy. Dublin Soc., 25 (N. S.), 141, 154 (1950). 31. Satchell, D. P. N. J. Chem. Soc., 1453, 3822 (1961). 32. Okamura, S., Higashimura, T. and Ogawa, Y. Chem. High Polymers (Japan), 16, 239 (1959). 33. Higashimura, T. and Okamura, S. Chem. High Polymers (Japan), 17, 57 (1960). 34. Eastham, A. M. et al., J. Chem. Soc. B, 33 (1966) and nine preceding papers. 35. Eley, D. D. and Seabrooke, A. J. Chem. Soc., 2231 (1964). 36. Colclough, R. O. and Dainton, F. S. Trans. Faraday Soc., 54, 886 (1958). 37. Overberger, C. G., Ehrig, R. J. and Marcus, R. A. J. Amer. Chem. Soc., 80, 2456 (1958). 38. Longworth, W. R., Panton, C. J. and Plesch, P. H. J. Chem. Soc., 5579 (1965). 39. Beard, J. H., Plesch, P. H. and Rutherford, P. P. J. Chem. Soc., 2566 (1964). 40. (a) Chmelir, M., Marek, M. and Wichterle, O. Symp. on Macromolecules, Prague, 1965. Preprint P 110, J. Polym. Sci. In Press (b) Marek, M. and Chmelir, M. Symp. on Macromolecules, Tokyo, 1966, Preprint 2.1.05 (c) Chmelir, M. and Marek, M. Symp. on Macromolecules, Brussels, 1967, Preprint 7/67. 41. Hunter, W. H. and Yohe, R. V. J. Amer. Chem. Soc., 55, 1248 (1933). 42. Plesch, P. H., J. Chem. Soc., 543 (1950). 43. Gantmakher, A. R. and Medvedev, S. S. Dokl. Akad. Nauk SSSR, 106, 1031 (1965). 44. Longworth, W. R., Plesch, P. H., and Rutherford, P. P. Proc. Chem. Soc., 68 (1960). 45. Lyudvig, E. B., Gantmakher, A. R. and Medvedev, S. S. Symp. on Macromolecules, Prague, 1965. Preprint P 234. 46. Longworth, W. R. and Plesch, P. H. J. Chem. Soc., 1887 (1959). 47. Pepper, D. C., Trans. Faraday Soc., 45, 404 (1949).

152

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) 48. Longworth, W. R. and Plesch, P. H. Proc. Chem. Soc., 117 (1958). 49. Bonner, T. G., Clayton, J. M. and Williams, G. J. Chem. Soc., 1705, (1958). 50. Bawn, C. E. H., Bell, R. M. and Ledwith, A. Chem. Soc. Anniversary Meeting, Cardiff, (1963); Polymer, 6, 95 (1965). 51. Bawn, C. E. H., Bell, R. M., Fitzsimmons, C. and Ledwith, A. Polymer, 6, 661 (1965). 52. Bawn, C. E. H., Fitzsimmons, C. and Ledwith, A. Proc. Chem. Soc., 391 (1964). 53. Longworth, W. R. and Mason, C. P. J. Chem. Soc. A, 1164 (1966). 54. Giusti, P. et al., (a) Symp. on. Macromolecules, Prague, 1965, Preprint P 492; Chim. Ind., 48, 435, 442 (1966) (b) Makromol. Chem., 98, 170 (1966). 55. Meerwein, H. et al., Ann., 635, 3 (1960). 56. Kennedy, J. P. and Thomas, R. M. J. Polym. Sci., 49, 189 (1961) and earlier paper. 57. Scott, H., Miller, G. A. and Labes, M. M. Tetrahedron Letters, 1073 (1963); Scott, H., Konen, T. P. and Labes, M. M. Polymer Letters, 2, 689 (1964). 58. Bawn, C. E. H., Carruthers, R. and Ledwith, A. Chem. Comm., 522 (1965). 59. Chih-Hua Wang, Chem. Ind., 751 (1964). 60. Bawn, C. E. H., Ledwith, A. and Shang Shih-Lin Chem. Ind., 769 (1965). 61. Farthing, A. C. and Reynolds, R. J. W. J. Polym. Sci., 12, 503 (1954). 62. Rose, J. B. J. Chem. Soc., 546 (1965). 63. Worsfold, D. J. and Eastham, A. M. J. Amer. Chem. Soc., 79, 900 (1957). 64. Worsfold, D. J. and Eastham, A. M. J. Amer. Chem. Soc., 79, 897 (1957). 65. Kern, W. and Jaacks, V. J. Polym. Sci., 43, 399 (1960). 66. Higashimura, T., Okamura, S. and Miki, T. Bull. Chem. Soc. Japan, 38, 2067 (1965); 39, 25, 31, 36, 41, 2480 (1966); J. Polym. Sci. A-1, 5, 95 (1967). See also Weissermel, et al., Angew. Chem. (Intern. Edn), 6, 526 (1967).

153

Developments in the Theory of Cationoid Polymerisations 67. Eley, D. D. and Johnson, A. F. J. Chem. Soc., 2238 (1964). 68. Passmann, W. and Plesch, P. H. Unpublished. 69. Coombes, J. D. and Eley, D. D. J. Chem. Soc., 3700 (1957). 70. (a) Dreyfuss, M. P., Westfahl, T. C. and Dreyfuss, P. ACS Meeting, Sept. 1966. Preprint W2 (b) Kuntz, I. J. Polym. Sci., B. 4, 427 (1966). See also Dreyfuss, M. P. and Dreyfuss, P. J. Polym. Sci., A-1, 4, 2179 (1967). 71. Plesch, P. H. Ric. Sci. Suppl. Simp. Internat. Chim. Macromol., 25, 140 (1955). 72. van Lohuizen, O. E. and de Vries, K. S. Symp. on Macromolecules, Prague, (1965), Preprint P 515. 73. Pinazzi, C. and Brossas, J. Symp. on Macromolecules, Prague, (1965), Preprint P 626; Compt. Rend. 261, 3410 (1965). 74. Kennedy, J. P. et al., Makromol. Chem., 53, 28 (1962); 64, 1 (1963); 77, 26 (1964); 79, 109 (1964); 93, 191 (1966). J. Polym. Sci. A., 2, 367, 381, 1441, 2093, 5029 (1964), C, 4, 289 (1963); Polymer Letters 2, 1159 (1964); 3, 729 (1965); Polymer, 6, 111, 133; 287 (1965); J. Macromol. Chem., 1, 243 (1966). 75. Tipper, C. F. H. and Walker, D. A. J. Chem. Soc., 1352 (1959). 76. Ketley, A. D. Polymer Letters, 1, 313 (1963). 77. Mazur, R. H. et al., J. Amer. Chem. Soc., 81, 4390 (1959). 78. Tipper, C. F. H. and Walker, D. A. J. Chem. Soc., 1199 (1957). 79. Naegele, W. and Haubenstock, H. Tetrahedron Letters, 4283 (1965). 80. Marechal, E., Basselier, J.-J. and Sigwalt, P. Bull. Soc. Chim. France, 1740 (1964). 81. Story, V. M. and. Canty, G. J. Res. Nat. Bur. Stand., Wash., 68A, 165 (1964). 82. Zharov, A. A., Berlin, A. A. and Enikolopyan, N. S. Symp. On Macromolecules, Prague, (1965), Preprint P 272; Zharov, A. A., Tatarintsev, V. V. and Yenikolopyan, N. S. Polym. Sci., USSR,2044 (1965). 83. Brown, G. R. and Pepper, D. C. Polymer, 6, 497 (1965). 84. Brown, C. P. and Mathieson, A. R. J. Chem. Soc., 3608 (1957).

154

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) 85. (a) Kennedy, J. P. and Thomas, R. M. J. Polym. Sci., 55, 311 (1961) (b) Kennedy, J. P., Kirshenbaum, I., Thomas, R. M. and Murray, D. C. J. Polym. Sci. A., 1, 331 (1963) (c) Kirshenbaum, I., Kennedy, J. P. and Thomas, R. M., J. Polym. Sci. A., 1, 789 (1963). 86. (a) Fontana, C. M. and Kidder, G. A. J. Amer. Chem. Soc., 70, 3745 (1948) (b) Fontana, C. M. Ref. 2, p.127. 87. (a) Matsushita, S., Higashimura, T. and Okamura, S. Chem. High Polymers (Japan), 17, 456 (1960) (b) Okamura, S., Kanoh, N. and Higashimura, T. Makromol. Chem., 47, 19 (1961). 88. Evans, A. G. et al., J. Chem. Soc., 2757 (1956). 89. Cherdron, H., Ohse, H., and Korte, F. Makromol. Chem., 56, 179 (1962). 90. (a) Hubmann, E., Taylor, R. B., and Williams, F. Trans. Faraday Soc., 62, 88 (1966) (b) Williams, F., Okamura, S., et al., Trans. Faraday Soc., 63, 1478, 1489, 1501 (1967). 91. Gresham, W. F., US Patent 2,394,910 (1946). 92. Plesch, P. H. and Westermann, P. H. Symp. on Macromolecules, Prague, (1965). Preprint P 506; J. Polym. Sci., In press. 93. Plesch, P. H. and Westermann, P. H. Unpublished; Westermann. Ph.D Thesis, Keele (1967). 94. Goodman, M. and Abe, A. J. Polym. Sci. A, 2, 3471 (1964). 95. Yamashita, Y., et al., Polymer Letters, 2, 549 (1964); Makromol. Chem., 82, 16 (1965); 86, 301 (1965). 96. (a) Kabanov, V. A., Zubov, V. P., Kovaleva, V. P., and Kargin, V. A. Internat. Symp. on Macromol. Chem., Paris, 1963 (b) Kargin, V. A. et al., Dokl. Akad. Nauk. SSSR, 139, 605 (1961) (c) Kabanov, V. A., Kargin, V. A., Kovaleva, V. P., and Topchiev, D. A. Vysokomol. Soed., 6, 1852 (1964); Polym. Sci. USSR, 6, 2050 (1965) and references quoted there. 97. Ellinger, L. P. Chem. Ind., 1982 (1963); Polymer, 5, 559 (1964); 6, 549 (1965).

155

Developments in the Theory of Cationoid Polymerisations 98. George, J., Wechsler, H., and Mark, M. J. Amer. Chem. Soc., 72, 3891, 3896 (1950). 99. Overberger, C. G., et al., J. Amer. Chem. Soc., 77, 2201 (1955) and subsequent papers. 100. Plesch, P. H., Ref. 2, p. 85; J. Chem. Soc., 1659 (1953). 101. Okamura, S., et al., J. Chem. Soc. (Japan), Ind. Chem. Section, 61, 1640 (1958); Chem. High Polymers (Japan), 16, 239, 441 (1959); 18, 333 (1961). 102. Vofsi, D. and Tobolsky, A. V., J. Polym. Sci. A, 3, 3261 (1965). 103. Rosenberg, B. A., Lyudvig, Y. B., Gantmakher, A. R., and Medvedev, S. S., (a) Symp on Macromolecules, Prague, (1965), Preprint P 223 (b) Vysokomol. Soed., 6, 2030 (1964); 6, 2035 (1964). 104. Sakurada, Y., Higashimura, T., and Okamura, S., J. Polym. Sci., 33, 496 (1958); J. Chem. Soc. (Japan), Ind. Chem. Section, 61, 1940 (1958). 105. Further systems falling into these categories have been described in the following papers: (a) Sobolev, V. M., Prokofyev, YA. N., and Spiridonova, G. N. Symp. on Macromolecules, Prague, 1965, Preprints P 564, 565 (b) Ref 38 of this paper. 106. Plesch, P. H., Polanyi, M., and Skinner, H. A. J. Chem. Soc., 257 (1947). 107. Tsuda, Y. Makromol. Chem., 36, 102 (1960). 108. Colclough, R. O. and Wilkinson, K. Internat. Symp. on Macromol. Chem., Paris, 1963. J. Polym. Sci., C, 4, 311 (1963). 109. Blake, G. J. and Eley, D. D. J. Chem. Soc., 7412 (1965). 110. Onyon, P. F. and Taylor, K. J. European Polym. J., 1, 133 (1965). 111. Williams, G. J. Chem. Soc., 775 (1940). 112. Kennedy, J. P. and Squires, R. G. J. Macromol. Sci. (Chem.), A-1, 805 (1967); for other important contributions concerning polymerisation of isobutene see pp.831, 847, 861. 113. Brookes, B. T. et al., (Ed.) Chemistry of Petroleum Hydrocarbons, Vol. 2, Chap. 27, Reinhold, New York, (1955).

156

Cationic Polymerisation from ‘Progress in High Polymers’ (1968) 114. Mcdowell, C. A., Lossing, F. P., Henderson, I. H. S., and Farmer, J. B. Can. J. Chem., 34, 345 (1956). 115. Lossing, F. P. and de Sousa, J. B. J. Amer. Chem. Soc., 81, 281 (1959). 116. Anosov, V. I. and Korotkov, A. A. Vysokomol. Soed., 2, 354 (1960); Polym. Sci. USSR, 2, 277 (1961). 117. Okamura, S., Higashimura, T. et al., Chem. High. Polymers (Japan), 18, 389 (1961); 20, 369 (1963); J. Polym. Sci. A, 3, 2455 (1965); Symp. on Macromolecules, Prague, (1965), Preprint P 280. 118. Kennedy, J. P. and Squires, R. G. Polymer, 6, 579 (1965). 119. Sims, D. J. Chem. Soc., 864 (1964). 120. Davies, A. G. and Baughan, E. C. J. Chem. Soc., 1711 (1961). 121. (a) Higashimura, T. and Okamura, S. Chem. High Polymers (Japan) 13, 397, (1956) (b) Higashimura, T., Yonezawa, T., Fukui, K., and Okamura, S. Chem. High Polymers (Japan), 13, 431 (1956). 122. Penfold, J. and Plesch, P. H. Proc. Chem. Soc., 311 (1961). 123. Imanishi, Y. et al., Makromol. Chem., 70, 68 (1964). 124. Higashimura, T. and Okamura, S. Chem. High Polymers (Japan), 15, 702 (1958). 125. Biddulph, R. H. and Plesch, P. H. J. Chem. Soc., 3913 (1960). 126. Imanishi, Y., Higashimura, T., and Okamura, S. Chem. High Polym. (Japan), 18, 333 (1961). 127. (a) Higashimura, T. and Kanoh, N. Chem. High Polymers (Japan), 23, 114 (1966) (b) Imanishi, Y., Nakayama, H., Higashimura, T., and Okamura, S. Chem. High Polymers (Japan), 19, 565 (1962) and earlier papers of that series. 128. Blake, G. J. and Eley, D. D. J. Chem. Soc., 7405 (1965). 129. Fontana, C. M. et al., Ind. Eng. Chem., 44, 1688, 2955 (1952).

157

Developments in the Theory of Cationoid Polymerisations 130. Beard, J. H. and Plesch, P. H., J. Chem. Soc., 3682 (1964). 131. Plesch, P. H. Chem. Ind., 739 (1955). 132. Throssell, J. J. Sood, S. P. Szwarc, M., and Stannet, V. J. Amer. Chem. Soc., 78, 1122 (1956). 133. Bhattacharyya, D. N., Lee, C. L., Smid, J., and Szwarc, M. Polymer, 5, 54 (1964). 134. Overberger, C. G. and Endres, G. F. J. Polym. Sci., 16, 283 (1955). 135. For instance: Patat, F., Symp. on Macromol. Chem., Montreal, 1961, p.333 Butterworths, London, (1962). 136. Davies, C. W. Ion Association, Butterworths, London, (1962). 137. Szwarc, M. Makromol. Chem., 89, 44 (1965). 138. Stern, K. H. and Amis, E. S. Chem. Rev., 59, 1 (1959); International Electrolyte Symposium, Ed. Pesce, B., Pergamon, London, (1962). 139. Fuoss, R. M. J. Amer. Chem. Soc., 80, 5059 (1958). 140. Gleysteen, L. F., and Kraus, C. A. J. Amer. Chem. Soc., 69, 451 (1947). 141. Okamura, S., Kanoh, N., and Higashimura, T. Makromol. Chem., 47, 35 (1961). 142. Ref. 1, p.174.

158

3.3

Some Considerations Concerning Energetics (1955) P. H. Plesch

This paper was first published in La Ricercha Scientifica, Supplemento Simposio Internazionale di Chimica Macromolecolare, 1955, No.25, 140-153.

Prologue Because this paper appeared only in the Proceedings of a large symposium in Italy, its contents remained largely unknown and some parts were subsequently rediscovered by others. This applies particularly to the heterolytic bond dissociation energy, here given the symbol θ. The importance of this quantity was understood only slowly, and it was ‘rediscovered’ most recently by H. Mayr. The main content of this paper is a further application of the ‘Manchester energetics’, which is mentioned in the Prologue to Section 4.1. It was to remain one of this author’s most effective ‘thinking tools’. The topics analysed here include reversible termination and the formation of p-tolyl endgroups on polystyrenes made in toluene. For unknown reasons, most authors have very largely ignored this Friedel-Crafts alkylation, which in a polymer context is a transfer reaction. It was unfortunately termed molecular termination by Overberger and was explored by his and Smets’ groups. There is here also support from energetic considerations for a mechanism accounting for the formation of linear polymethylene from diazomethane. This subject had become popular, despite the hazards associated with that monomer, because of the almost frantic search in the 1950s for new methods of making that polymer. The energetic argument concerning the monohydrate of BF3 is based very largely on Skinner’s thermochemical discussion given in reference [7] of this paper. It is no longer valid, as the monohydrate is now known to be not ionic. In any case, the discussion of ion-pairs in which the cation is a bare proton, is now seen to be rather pointless. In this discussion the author also explains for the first time why initiating sytems giving complex anions are more effective for polymerisations than those which yield simple anions; it is because the latter can and do terminate cationic chains by neutralisation much more effectively than the former.

159

Developments in the Theory of Cationoid Polymerisations

Summary Some of the individual processes involved in the cationic polymerisation of olefins are examined here from a thermochemical point of view. In the initiation reaction a (complex) acid reacts with the olefin to give an ion pair consisting of a carbonium ion and a (complex) anion. It is shown that in general this reaction is only exothermic if the Coulombic energy of this ion pair is sufficiently great. It is suggested that the superiority of complex acids over the hydrogen halides (excluding HF) as polymerisation catalysts may be due to the fact that the complex anions cannot form covalent bonds, so that the carbonium ion-anion pairs of which they form part are relatively stable. The formation of the red oils in hydrocarbon reactions only when these are catalysed by complex catalysts is explained similarly. Detailed discussion of the energetics of the cationic polymerisation of ethylene shows that it cannot yield linear polymethylenes, in agreement with experiment. Since the cationic polymerisation of diazomethane does yield linear polymethylenes it cannot proceed through carbonium ions, as suggested by other workers. The following equations summarise the mechanism proposed here for this reaction:

H + BF3OH – + CH2 N 2 → BF3OH – CH3 N 2+

Initiation

N 2 = CH2 + CH3 N2+ → +N2 ⋅ CH2 ⋅ CH3 + N2

Propagation

Concerning the (generally complicated) polymerisation of higher alkenes, it is shown that the transfer of CH3–, analogous to H– transfer, may play a significant part, except for isobutene. The energetic reasons for the distinctive polymerisation behaviour of isobutene are analysed, with special reference to the energetics of the transfer of protons or carbonium ions to monomer. The hypothetical termination reaction for the isobutene– BF3 polymerisation. + –CH = CMe2 ⎧ ⎫ + – –CH2 ⋅ C( Me2 ) BF3OH – → ⎨ ⎬ + H BF3OH –CH – C Me CH = ( ) 2 2⎭ ⎩

which his been postulated previously is shown to be endothermic and therefore inadmissible, though with other monomers and metal halides a similar reaction may occur. Concerning the cationic reaction of styrene in toluene to give oligomers with tolyl end groups thermochemical calculations provide a decision between the two possible mechanisms for the formation of these endgroups, in favour of the reactions:

160

Some Considerations Concerning Energetics (1955) +

+

— CH2 ⋅ C H ⋅ C6 H5 + C6 H5 ⋅ CH3 → —CH2 ⋅ CH ⋅ C6 H 5 CH3 C6H5 +

+

—CH2CH ⋅ C6 H 5 CH3 + CH2 : CH → CH2 ⋅ CH ⋅ C6 H 4 ⋅ CH3 + C H3 ⋅ C H C6 H5 C6 H5 C6 H5 C6 H5

In the earlier papers of this series [1, 2] the chemistry of the individual steps involved in the cationic polymerisation of olefins has been discussed critically. It may now be useful to consider some of these processes in terms of the energy changes involved and to reexamine, from this point of view some of the hypotheses which have been made in the past. Similar discussions of closely related topics have been given by Evans and Polanyi [3], Evans and Halpern [4], Meier [5], Greensfelder [6] and Skinner [7]. A very useful and comprehensive review of ionic polymerisations has recently been given by Pepper [8]. The arguments to be presented below are based on bond dissociation energies (D), ionisation potentials (I) and electron affinities (E). The values of these quantities, as usually determined, appertain to the molecules and radicals in the dilute gas phase, whereas the polymerisations to which we wish to apply them take place in the liquid phase. For the purpose of this discussion we shall assume that solvation effects in non-polar solvents are negligible; for reactions in polar media we shall try to estimate the solvation effects. Unless otherwise stated, the reactions discussed below are assumed to take place in nonpolar media. It is convenient in the present context to use a heterolytic bond dissociation energy θ, defined as the endothermicity of the process.

RX → R + + X – , ΔH = θ Evidently θ = D( R – X ) + I(R) – E(X) where D is the homolytic bond dissociation energy of the bond R – X, I (R) the ionisation potential of radical R, and E(X) the electron affinity of X; the ions are infinitely separated in vacuo, in accordance with the usual definitions of D, E and I. Alternatively, θ is given by

θ( R + – X – ) = ΔH f ( RX ) – ΔH f ( R + ) – ΔH f ( X – )

161

Developments in the Theory of Cationoid Polymerisations which is often more convenient to use. The proton affinity P(C = C) of an olefin is defined as the exothermicity of the reaction |

|

|

| +

|

|

|

|

H + + C = C → H – C – C , ΔH = –P(C = C) and, if the olefin is unsymmetrical, always refers to the larger P *.

The initiation It is generally agreed that cationic polymerisations are initiated by (complex) catalysts (e.g. BF3 – H2O, TiCl4 – CCl3CO2H, AlBr3 – i-C3H7Br) which can donate a proton or carbonium ion to the monomer, thus converting it into a carbonium ion. If the catalyst is a (complex) acid AH, the initiation is represented by: +

AH + R1 R2C = CR3 R4 → R1 R2 HC – C R3 R4 ⋅ A – , ΔH = ΔHi the H+ adds onto the olefin in accordance with Markownikow’s rule. The reaction product is an ion-pair, which will dissociate to a degree depending, inter alia, on the dielectric constant of the environment. ΔHi is given by

[

]

ΔHi = θ( A – – H + ) – P( R = ) – e 2 / rD

R+ A −

(1)

where P(R=) is the larger of the two proton affinities of the olefin (if asymmetrical), and the last term is the Coulombic energy of the resulting ion pair. An important consequence of equation (1) is that since ΔHi must be negative because ΔSi is negative, and since the θ (A– – H+) even for strong acids is well in excess of 200 kcal ** and the largest known value of P for an olefin is about 200 kcal [1], the very existence of this type of reaction depends upon the Coulombic energy of the ion pair resulting from it. In polar solvents the Coulombic energy is partly replaced by the solvation energy of the ions. The subsequent reactions of this system will depend on the nature of the carbonium ion, * According to the convention used here, a heat change ΔH is negative for an exothermic reaction. ** θ(A– – H+) can be found thus: AH + nH2O → A– aq + H3O+ aq, ΔH = –θ′ θ′ is the heat of solution of AH and is given by θ′ = θ(A– – H+) – ΔHy – ΔHs(H3O+) – ΔHs(A–) + L where ΔHy is the heat of hydration of the proton, the ΔHs are heats of solvation and L is a latent heat of evaporation or sublimation. The greatest value of θ′ (strongest acids) is probably not greater than 25 kcal, ΔHy + ΔHs(H3O+) = 260 kcal, L – ΔHs (A–) = –70 to –120 kcal. Thus θ(A– – H+) probably exceeds 300 kcal even for very strong acids.

162

Some Considerations Concerning Energetics (1955) the nature of A–, the dielectric constant and nature of the reaction medium, and the temperature. For instance, the ions may combine to form a neutral molecule, RA. Whether the ion pair is stable or whether such combination takes place depends essentially on the relative magnitude of [e2/rD] R+A–, the Coulombic energy of the ion pair, and θ(R+ – A–), the exothermicity of the combination, since the activation energy will be small. Even if θ > e2/rD, addition can be delayed by a polar solvent which increases the dissociation of the ion pairs, and decreases the rate of addition by increasing the activation energy for this process through the solvation of the ions. This is probably the explanation for Pepper’s observation [9] that the interaction of styrene with HBr or HCl gives the addition product in solvents of low DC but polymers if the solvent has a high DC. It has long been known that formation of polymers usually accompanies the addition of hydrogen halides to olefins at low temperatures. These polymers mostly contain halogen, and the addition of the anion to the carbonium ion to form a covalent bond is indeed one of the obvious possible termination mechanisms in these polymerisations. The curious and hitherto unexplained fact that complex acids or esters of the type of BF3•OH2 or Me+ AlBr4– are far superior as polymerisation catalysts to the simple halogen acids can also be understood in these terms, because the complex anion cannot form a covalent bond with the carbonium ion, i.e., θ(R+ – A–) = 0, whereas the simple anion, e.g., Cl–, can and does. For a fragment of the complex, e.g., the anionic moiety of the co-catalyst, to form a covalent bond with the carbonium ion might require a fairly drastic steric rearrangement of the constituents of the ion pair, and therefore an appreciable activation energy, as was shown to be the case for the system isobutene–TiCl4 with CCl3CO2H as co-catalyst [10]. Complex anions such as HSO4– or ClO4– occupy an intermediate position, because although they can form covalent bonds to carbon, these are weak. Presumably the formation of the red oils, or acid sludges in acid-catalysed reactions of hydrocarbons is also largely due to the inability of complex ions to form covalent bonds to carbon. The red oils are found when, e.g., AlCl3, H2SO4 or HF are used as catalysts, but not when the other hydrogen halides act on olefins; in the presence of HF the true catalyst is presumably HF2–H+, which also has a complex anion. The oils, consisting of carbonium ions and complex anions, are stable with respect to any esters which could be formed because of the high Coulombic energy of the ion pairs, and in some cases the resonance stabilisation of multiply charged polyeneic ions [11].

Chain propagation and transfer reactions The energetics of the propagation step are dominated by the fact that it involves a decrease in entropy. Therefore, propagation can only take place if it is exothermic and if no other

163

Developments in the Theory of Cationoid Polymerisations reactions such as transfer or isomerisation can take place which have an activation energy of comparable magnitude. It is instructive to analyse explicitly the case of ethylene from this point of view. Ethylene - There is no evidence that ethylene can be converted to high polymers by a homogeneous cationic reaction. If we assume that reaction is initiated by the addition of a proton to C2H4 and that after each subsequent monomer addition there is complete, fast isomerisation to the most stable (tertiary) ion, it is not difficult to show that after the third or fourth step the exothermicity of the propagation will have fallen to about 15 kcal, because of the increasing steric crowding of the oligomers. This value is of the same order of magnitude as the negative TΔS for propagation at ordinary temperatures, so that the oligomerisation must then cease. At this stage other reactions, such as transfer, will be energetically more favourable than propagation. It is evident that transfer of protons or other positive ions to monomer will not be included among these alternative reactions, because it would be endothermic: if we represent by Rn+ the oligomeric tertiary ion, by Rn= a corresponding olefin, we have for proton transfer

Rn+ + C2 H4 → Rn= + C2 H5+ , ΔH = –P(C2 H4 ) + P( Rn= ) Since the proton affinity P(Rn=) of the branched olefin Rn= is certainly greater than P(C2H4), the reaction would be endothermic; a similar argument applies to the transfer of carbonium ions. This may account for the low yields observed even in the heterogeneous cationic oligomerisation of ethylene. The most likely transfer reactions are hydride ion and methide ion transfers between oligomer ions and molecules (see below), leading to conjunct polymerisation [12]. This discussion is certainly an over-simplification. Unfortunately there are no detailed experimental results for this reaction under strictly homogeneous conditions, but even with heterogeneous catalysts (e.g., AlCl3 and Ni [13]) only mixtures of branched paraffins, naphthenes and polyenes of low molecular weight are obtained. If isomerisation is slower than propagation, as indicated, e.g., by the experiments of Meier [5] on the polymerisation of 3,3-dimethyl butene-1, this would modify in detail but would not invalidate the above general conclusions. Diazomethane - In view of its contrast to the behaviour of ethylene, the production of linear polymethylenes of high molecular weight from diazomethane by means of cationic catalysts is of considerable interest in the present context. Among others, Kantor and Osthoff [14] have examined the homogeneous reaction catalysed by BF3 in ether solution and suggested a mechanism. Contrary to their assumption that BF3 itself is the initiating species we prefer to assume that, in conformity with other systems, the initiator is a proton from adventitious water, acting as co-catalyst:

164

Some Considerations Concerning Energetics (1955)

BF3 ⋅ OH2 + CH2 N 2 → BF3OH − CH3 N2+ ⋅ We formulate the propagation reaction between the alkyl diazonium ion and the monomer as an SN2 reaction*:

(CH2)nCH3 δ+ δ– N2 = CH2 + C – N2+ →

R +N

2 • CH2 • CH2

+ N2

H H This also differs from the scheme of Kantor and Osthoff who postulated propagation by a carbonium ion instead of a diazonium ion. The highly crystalline nature and great molecular weight of the products obtained show that the intermediate species did not undergo either isomerisation or anion-transfer reactions, so that propagation through the unstable and reactive primary carbonium ions seems very unlikely. A very similar scheme has recently been put forward independently [15]. Even if the above suggestion is found to be valid for this particular system, it will not explain the curious behaviour of diazoalkanes with other catalysts, which remains enigmatic. Higher alkenes - Among the numerous complications occurring in the cationic polymerisation of most alkenes one of the most obvious is that some of the oligomers do not consist of an integral number of monomer units [5]. In general, intermolecular shifts of alkyl groups could take place by the transfer of positive ions to monomer or to unsaturated polymer (to be discussed below), or by the abstraction of, e.g., a methide ion (CH3–) from a neutral molecule or ion by a carbonium ion, thus producing a new, or doubly charged ion, and a neutral molecule. As this reaction is analogous to the transfer of hydride ions it may be useful to compare the energetics of these two processes in terms of the heterolytic bond dissociation energies θ (R1+ – H–) and θ (R2+ – CH3–) for various types of radical R. The θ values are calculated from the equations

θ( R1+ – H – ) = D( R1 – H ) + I( R1 ) – E(H)

θ( R2+ – CH3– ) = D( R2 – CH3 ) + I( R2 ) – E(CH3 ) The data used in these calculations and the results are listed in Table I. This shows that even allowing for the considerable uncertainty in the θ(R+ – CH3–) values, these are * I am indebted to Dr. W.C.E. Higginson for this suggestion.

165

Developments in the Theory of Cationoid Polymerisations

Table 1 Some heterolytic bond dissociation energies (all figures in kcal/mole) R(a)

I (R)

D (R–H) (b)

D (R–CH3)(d)

θ (R+ –H–)

θ (R+ – CH3–)

83

317

287

CH3

229

(b)

102

C2H5

200

(b)

97

(b)

82

281

257

R1(CH2)2

183

(c)

99

(c)

79

266

237

R1R2CH

171

(c)

94

(c)

75

249

221

R1R2R3C

159

(c)

89

(c)

74

232

208

E (H) = 16.4; E (CH3) = ~ 25 (Reference [26]); The θ for the unspecified radicals are necessarily approximate The uncertainty of the θ (R+ – H–) is probably ± 5, that of the θ (R+ – CH3–) ± 15, because of the uncertainty in E(CH3) (a) R1, R2, R3 are saturated alkyl radicals (b) Reference [24] (c) These are the figures for the n-Pr, s-Pr and t-Bu radicals given in Reference [24] (d) Reference [25]

appreciably smaller than the corresponding θ(R + – H–). It is evident that from a thermochemical point of view methide ion transfer is certainly no less likely than hydride ion transfer; whether this will be reflected in the activation energies is difficult to say, but it seems not improbable that the activation energy for methide ion transfer would be less than that for hydride ion transfer. Evidently, this reaction may take place wherever primary or secondary carbonium ions occur in the presence of secondary or tertiary methyl groups. The transfer of larger carbanions may, of course, also be found under appropriate circumstances but cannot be treated quantitatively at present. Isobutene - In contrast to the complicated picture presented by the polymerisations of most other alkenes, the polymerisation of isobutene at low temperatures is a clean reaction with apparently few complications [10, 16, 17, 18]. The propagation step seems to be a simple addition to the monomer of the tertiary carbonium ion at the growing end of the chain. This difference between the behaviour of isobutene and of most other olefins is so striking that isobutene could usefully be regarded as a standard of reference; it would thus be possible to enquire into the behaviour of other olefins by comparing them and their polymers with isobutene and polyisobutene.

166

Some Considerations Concerning Energetics (1955) One of the most important reasons for the chemically (but not necessarily kinetically) uncomplicated nature of the polymerisation of isobutene is that neither the initial tertiary butyl ion, nor the intermediate polyisobutyl ions can undergo any energetically advantageous isomerisations. Furthermore, since all the ions concerned are tertiary, all anion transfers with monomer, polymer or (most) solvents would be endothermic, and therefore unlikely. A third reason is that the transfer of cations (H+, CH3+, t-Bu+) to monomer produces polymers which are virtually indistinguishable from the simple polyisobutene. General considerations show that such transfers are likely to have greater activation energies than the propagation, which agrees with the evidence concerning the variation of molecular weight with temperature. [10a, 16] For the three processes

PIB+ → PIB= + H + , ΔH = P( PIB= ) = ~ 200 (*) kcal

PIB → PIB= + CH3+ , ΔH = AMe + ( PIB= ) = ~ 130 (*) kcal

PIB → PIB= + t − Bu + , ΔH = ABu + ( PIB= ) = ~ 15 (*) kcal where PIB+ is a polyisobutyl ion, PIB= are the corresponding most stable olefins, and the A their corresponding ion affinities. Since the structures of the PIB= and the monomer are so similar, the cation transfer, of which the above equations are the first parts, will be approximately thermally neutral. Thus it seems probable that the activation energies for these transfers have a similar gradation, though it is not possible to say anything about their absolute values. There are reasons for believing that with heterogeneous catalysts the activation energy for proton transfer may be lower than for the other transfer processes [19]. The termination - A termination reaction which has been favoured by many authors involves the transfer of a proton to the anion, with regeneration of the catalytic complex. This has been criticised qualitatively before [2, 20] but we can now give some precision to these arguments. We shall consider the system isobutene – BF3 – H2O in a non-polar solvent, involving the anion BF3OH— (discussed in detail by Skinner [7]), since we are still too ignorant of the nature and structure of the anions derived from the aluminium or Group IV halides. The reaction in question can be represented thus:

PIB+ BF3OH – → PIB= + BF3 ⋅ OH2 , ΔH = ΔH1

(2)

where PIB= is the polymer with terminal unsaturation. If we designate the Coulombic energies of the initial and final ion pairs as e2/r1 and e2/r2, ΔH1 is given by; * See Appendix.

167

Developments in the Theory of Cationoid Polymerisations

ΔH1 = e 2 /r1 – e 2 /r2 + P(PIB= ) if the complexes can be treated as purely ionic structures. The lower limit for r2 is 1 AU (e2/r2 = 330 kcal), the upper limit for r1 is about 2.5 AU (e2/r1 = 130 kcal), and P(PIB=) is about 200 kcal, so that the minimum value of ΔH1 is about zero. A more probable value is about 50 kcal, (r1 = 2.2, r2 = 1.2 AU, so that Δ(e2/r) = — 150 kcal). The entropy change is indeed positive, though at 200 °K the TΔS term is unlikely to exceed 10 kcal. Thus, for the reaction as written, ΔG° is probably of the order of 40 kcal. Resonance stabilisation in the complex might reduce this somewhat, but hardly sufficiently to make ΔG° negative. Thus, this reaction which is the reverse of the initiation can be ruled out for this particular system; in other words, the initiation ↔ termination equilibrium lies far over on the initiation side. It is also instructive to examine a different version of reaction (2), namely

PIB+ BF3OH – → PIB= + BF3 ⋅ OH2 , ΔH = ΔH2

(3)

where the reaction products are the olefin and a non-ionic co-ordination compound.

ΔH2 = e 2 /r1 + D(BF3 – OH – ) – θ(H + – OH − ) + P(PIB= ) – D(BF3 – OH2 ) ~ 150

79

380

~ 200

= 50 – D(BF3 – OH2 ) As Skinner has pointed out [7], there is no evidence for the existence of BF3·H2O in the gas phase at ordinary temperatures, and the solid monohydrate of BF3 owes its stability to the lattice energy; thus D(BF3 – OH2) must be very small. The calculation of ΔH2 shows that even if BF 3·H2O could exist in solution as isolated molecules at low temperatures, reaction (3) would not take place. We conclude therefore that proton transfer to the complex anion cannot occur in this system and that there is probably no true termination except by impurities. The only termination reactions which have been definitely established in cationic polymerisations have been described before [2, 8], and cannot at present be discussed profitably in terms of their energetics. It should be noted, however, that in systems such as styrene-SnCl4 the smaller proton affinity of the dead (unsaturated or cyclised) polymer, coupled, with the greater size of the anion and smaller size of the cation may make ΔH1 much less positive so that reaction (2) may then be possible because ΔG° ~ 0. This would mean that the equilibrium between initiation and termination is in an intermediate position.

168

Some Considerations Concerning Energetics (1955) Reaction with solvent - The solvent influences the course of cationic reactions not only through its dielectric constant, but also because many substances used as solvents are far from inert in these reactions [22, 23]. Although much more experimental material is required before a full treatment of the subject becomes possible, at least one example, the cationic polymerisation of styrene in toluene, is amenable to quantitative discussion. Experiment shows that polymerisation is rapid and complete, the molecular weight is low and the polymer contains para-substituted rings which are almost certainly tolyl endgroups [22]. Theoretically, a polystyryl carbonium ion can react with toluene in six different ways, only two of which (a.1 and b.1 below) can lead to tolyl endgroups; in the first case the tolyl group is at the end of the terminated chain, in the second it is the start of a new chain. The alternative reactions can be represented as follows

ΔH = → — CH2 • CH

H+

CH3

ΔHa

•

1

a•1

H+

ΔHa

•

2

a•2

•

1

•

2

b•1 b•2

C 6 H5 → — CH2 • CH • CH2 C 6 H5 +

—CH2 • CHC6H5 + C6H5 • CH3

→ —CH2 • CH2 • C6H5 +

CH3 • C6H4+ C6H5 • CH2+

ΔHb ΔHb

→ —CH2 • CH(CH3)C6H5 + C6H5+

ΔHc

c

→ — CH = CH – C6H5 + CH3C6H6+

ΔHd

d

The carbonium ions thus formed are assumed to react with styrene by proton transfer (a.1, a.2, d) or combination (b.1, b.2, c) to give a new carbonium ion which starts a new chain. In view of the analytical evidence for p-tolyl endgroups, only reactions a.1 and b.1 need be considered in detail. The experimental findings are supported by calculations which show all the other reactions to be endothermic. Let the growing polystyryl ion be represented by PSt+. By the usual analysis we obtain explicit expressions for the ΔH.

ΔHa•1 = I(H) – I(PSt) + D(CH3 ⋅ C6 H4 – H) – D(PSt – C6 H4 ⋅ CH3 ) 312

~ 190 (**)

105

~ 90

*

– P(PSt ⋅ C 6 H4 ⋅ CH3 ) *

= 137 – P(PSt ⋅ C 6 H4 ⋅ CH3 ) ± 10 kcal

169

Developments in the Theory of Cationoid Polymerisations *

Thus the minimum value of P(PSt· C 6H4·CH3) required to make ΔHa·1 negative is about 140 kcal which is not unreasonable.

ΔHb⋅1 = θ(CH3C6 H4+ – H – ) – θ(PSt + – H – ) = ΔH f (C7 H8 ) – ΔH f (CH3 ⋅ C6 H4+ ) – ΔH f (H – ) – D(PSt – H) – I(PSt) + E(H) – 12 (gas) = 20 ± 10 kcal

– 240 (**)

– 36

~ 70

~ 190 16

TΔS at 300 °K will be of the order of –10 kcal for reaction a.1, and about zero for b.1. In spite of the considerable uncertainties in the ΔH values, these calculations show that process (a.1) is more probable than (b.1), the only other reaction which can give a tolyl endgroup. Having decided that the first stage of the process is the formation of PSt·C6H5+ CH3, we must now enquire whether the next step +

+

PSt ⋅ C 6 H5 ⋅ CH3 + CH2 : CH ⋅ C6 H5 → PSt ⋅ C6 H4CH3 + CH3 ⋅ C H ⋅ C6 H5 ΔH = ΔHt

(4)

which is required to complete the chain transfer is energetically feasible. *

*

ΔHt = P(PSt ⋅ C 6 H4 ⋅ CH3 ) – P(C6 H5CH : C H2 ) *

P(C6 H5 ⋅ CH : C H2 ) is calculated thus : +

*

P(C6 H5 ⋅ CH : C H2 ) = ΔH f (C8 H8 )gas + ΔH f (H + ) – ΔH f (C6 H5 ⋅ C H ⋅ CH3 ) 35 = 180 kcal *

364

219(**)

Thus, if P(PSt· C 6H4·CH3) = ~ 140 kcal, as mentioned above, ΔHt is definitely negative, and reaction (4) is energetically very favourable, so that the suggested transfer mechanism (a.1) seems to be satisfactorily supported by these calculations. * The asterisk * indicates the location of the proton. ** See Appendix.

170

Some Considerations Concerning Energetics (1955)

The proton affinity of benzene The above calculations place the proton affinity of a para-di-alkyl benzene (p-R2C6H4) between the limits 140 to 180 kcal. An independent estimate of P(p-R2C6H4) can be obtained thus: Franklin and Field [27] have found the appearance potential of the cyclohexa-dienyl ion (from electron-impact studies on 1-methyl cyclohexa-2,4-diene) and hence found the heat of formation of that ion to be 234 kcal. Combining this with the heat of formation of benzene and of H+ one obtains for the proton affinity of benzene P(C6H6) = 150 kcal. Various estimates of the relative basicities of aromatic hydrocarbons indicate that P(p-R2C6H4) will be 10 to 20 kcal greater than P(C6H6), i.e., it lies well within the range indicated.

Acknowledgements I wish to thank Drs. J. L. Franklin and F. H. Field of the Humble Oil and Refining Company, and Dr. R. B. Mesrobian for letting me see, and make use of, their work before publication; and Dr. D. C. Pepper for his helpful criticism of this work.

Appendix All thermochemical data, except those given below, have been obtained from the literature (mainly References [4, 7, 25, 26]), either directly or by comparison with those of analogous compounds. 1.

P(PIB=), The proton affinity of the terminal group –CH2C(CH3) = CH2 in polyisobutene is taken as the same as that of isobutene, ~200 kcal [4].

2.

AMe+ (PIB=). Of the four isomeric olefinic groups which can be formed by removal of CH3+ from the polyisobutyl ion and subsequent isomerisation, the structure –CMe2·CMe = CH2 will have the largest AMe+ which is taken as the same as that of isobutene; this can be estimated as –70 kcal less than the proton affinity, i.e., –130 kcal.

3.

ABu+ (PIB=). This, the t-Bu+ affinity of a terminal methylene group in polyisobutene, is taken as of the same order of magnitude as the heat of polymerisation of isobutene, ~12 kcal.

4.

I(PSt). This, the ionisation potential of the –CH2·CH·C6H5 radical is taken as the same as that of the CH3·CH·C6H5 radical, 189 kcal [4].

171

Developments in the Theory of Cationoid Polymerisations 5.

ΔHf (CH3·C6H4+). This is calculated from the appearance potential of the ion from p-xylene, as 239 kcal [27].

6.

ΔHf (CH3· C H·C6H5). This is calculated from the appearance potential of the ion, as 219 kcal [27].

+

Author’s Note: All ‘kcal’ should be ‘kcal/mol’.

References 1.

Plesch, P. H., J. Applied Chem., 1, 269, (1951).

2.

Plesch, P. H., J. Polymer Sci., 12, 481, (1954).

3.

Evans, A. G. and Polanyi, M., J. Chem. Soc. London, 252 (1947).

4.

Evans, A. G. and Halpern, J., Trans. Faraday Soc., 48, 1034, (1952).

5.

Meier, R. L., J. Chem. Soc. London, 3656, (1950).

6.

Greensfelder, B. S., Advances in Chemistry, No. 5, p. 3, (1951).

7.

H. A. Skinner in Cationic Polymerisation and Related Complexes, Ed., by P. H. Plesch (Cambridge and New York, 1953); p. 28.

8.

Pepper, D. C., Quart. Rev. Chem. Soc. London, 88, (1954).

9a

D. C. Pepper and A. E. Somerfield in Cationic Polymerisation and Related Complexes, Ed., by P. H. Plesch (Cambridge and New York), 1953, p.75.

9b. Pepper, D. C. and Somerfield, A. E., Chemistry and Industry, 42 (1954). 10a. Plesch, P. H., J. Chem. Soc. London, 543, (1950). 10b. M. St. C. Flett and P. H. P. Plesch, J. Chem. Soc., London, 1952, 3355. 11. C. M. Fontana, in Cationic Polymerisation and Related Complexes, Ed., by P. H. Plesch, Cambridge and New York, (1953), p.121. 12. Schmerling, L. and Ipatieff, V. N., Advances in Catalysis, 2, 21, (1950). 13. Ipatieff, V. N. and Grosse A. V., J. Am. Chem. Soc., 1936, 58, 915. 14. Kantor, S. W. and Osthoff, R. C., J. Am. Chem. Soc., 1953, 75, 931.

172

Some Considerations Concerning Energetics (1955) 15. Feltrin, J., Restaino, A. J., and Mesrobian, B. R., J. Am. Chem. Soc., in the press. 16. Thomas, R. M., et al., J. Am. Chem. Soc., 62, 276, (1940). 17. Norrish, R. G. W. and Russel, K. E., Trans. Faraday Soc., 48, 91, (1952). 17b. Norrish, R. G. W. and Russel, K. E., Nature, London, 160, 543,(1947). 18. Russel, K. E., in Cationic Polymerisation and Related Complexes, Ed., by P. H. Plesch (Cambridge and New York), 1953, p.114. 19. Dainton, F. S., Cationic Polymerisation and Related Complexes, Ed., by P. H. Plesch (Cambridge and New York), 1953, p.137. 20. Flett, M. St. C. and Plesch, P. H., Cationic Polymerisation and Related Complexes, Ed., by P. H. Plesch (Cambridge and New York), 1953, p.120. 21. For detailed references see References [7] and [8]. 22. Plesch, P. H., J. Chem. Soc. London., 1653, (1953). 23. Overberger, C. G. and Endres, G. F., J. Am. Chem. Soc., 75, 6349, (1953), and this Symposium. 24. Stevenson, D. P., Trans. Faraday Soc., 49, 867, (1953). 25. Szwarc, M., Chem. Rev., 1950, 47, 75. 26. Pritchard, H. O., Chem. Rev., 1953, 52, 529. 27. Field, F. H. and Franklin, J. L., private communication, in the press.

173

Developments in the Theory of Cationoid Polymerisations

174

3.4

Theoretical Attempts at Improving Initiators for Cationic Polymerisation of Alkenes (1982) P. H. Plesch and S. D. Pask

Prologue This paper was first published in European Polymer Journal, 1982, 18, 839-846. Reproduced by kind permission of Elsevier, copyright 1982. It is mainly concerned with the energetics of organic cations in solution and of their reactions with alkenic double bonds, and it is a logical development from Section 3.3. The thermodynamic, and especially the thermochemical, arguments used are simple in principle, but their application is fairly sophisticated. Although the lack of some of the necessary data makes many of the conclusions rather tentative, if one uses them in the spirit in which they are offered, i.e., with optimistic caution, they do explain the relevant observations, and they contain suggestions as to the direction in which useful improvements may be found. The question ‘Why are some catalysts [metal halides in this context] better than others?’ is as old as the subject itself (14, 151) and the answers given here are a measure of the improvement in our understanding. However, this paper does not consider the energetics of the addition of a metal-based cation MtX+n-1 to an alkene (92, 112), nor any other possible mechanisms of initiation, such as electron transfer from a monomer to give a radical-cation, which are considered in other publications.

175

Developments in the Theory of Cationoid Polymerisations

Abstract The initiation of the cationic polymerisation of alkenes is examined in detail by means of simple thermodynamic concepts. From a consideration of the kinetic requirements it is shown that the ideal initiator will yield a stable, singly charged anion and a cation with a high reactivity towards the monomer by simple, well defined reactions. It must also be adequately soluble in the solvent of choice and for the experimental method to be used. The calculations are applied to carbocation salts as initiators and a method of predicting their relative solubilities is described. From established and predicted data for a variety of carbocation salts the position of their ion:molecule equilibria and their reactivity towards alkenes are examined by means of Born-Haber cycles. This treatment established the relative stabilities of a number of anions and the reason for dityl, but not trityl salts initiating the polymerisation of isobutene. The outcome of our treatment is a general method for selecting theoretically promising new initiators.

Introduction The aim of this paper is a rational approach to designing the optimum initiator for the cationic polymerisation of alkenes. Our method is based on thermodynamic calculations making use of the best available data and estimates, and it is a development of the ideas of Fairbrother [2] and Plesch [3]. Some of our conclusions have been tested experimentally and found valid. The whole complex of problems concerned with this type of initiation is treated in a very comprehensive book [4].

The specification of the ideal initiator

1 Stability and reactivity We will attempt to delineate the desirable attributes of the ideal initiator, but before doing this we need to establish clarity concerning two terms frequently used in this context: stability and reactivity. These are not antonyms: the opposite of stability is instability, that of reactivity is inertness. Both terms have little meaning unless the condition of the species to which they refer is specified; this implies that we must always be concerned with a system comprising the species, its environment and condition (pressure,

176

Theoretical Attempts at Improving Initiators for Cationic Polymerisation of Alkenes temperature, phase). For example, an ethyl radical is stable in the gas phase and an ethyl cation is stable in ‘magic acid’ because no exo-energetic reaction path is available to them and yet in an appropriate environment both are highly reactive.

2 The kinetic requirements We are concerned with the reaction (i) in which a cationic initiator fragment R+ adds to the double bond of the alkene P1:

R + + P1 → R – P1+ , ki+

(i)

the cation R - P1+ then attacks another P1 in the first propagation step (ii):

RP1+ + P1 → RP2+ , kp+

(ii)

In order to define the kinetics of any system one must know precisely what the reaction mixture contains. In particular, in order to determine kp+ the concentration of growing ends [RP+m], must be known throughout the polymerisation. Therefore, for the ideal initiator, we must know its exact state, e.g. the position of any ionisation, dissociation and solution equilibria, and how it reacts with the monomer. In the present context we will ignore enieidic systems, e.g., those comprising also paired cations or an activated ester, since, at least in principle, the requirements for their adequate specification involve only trivial extensions of our present considerations. The [RPm+] can be most easily ascertained if the initiation efficiency is unity (no sidereactions) and if the [RPm+] is constant (termination rate Vt = 0) and equal to the nominal, analytical, concentration [Int]0 of the initiator; this means (a) that the equilibrium constant of reactions such as (iii) should be effectively zero,

RPm+ + MtX n– +1 ↔ RPm X + MtX n

(iii)

and (b) that the propagating cation should not undergo isomerisation or any reaction with a component of the reaction mixture, e.g. polymer, to give inert ions. Also, kinetic analysis is greatly simplified if Vi, the rate of the reaction (i), is much greater than that of reaction (ii), Vp. The efficiency of initiation is controlled, essentially, by the reactivity of the cationic moiety of the initiator towards the monomer; and the stability of the growing ends can

177

Developments in the Theory of Cationoid Polymerisations be controlled to some extent through the nature of the anionic moiety. Therefore, in the search for an ideal initiator it is equally important to study both its cationic and anionic moieties. Finally, in order to avoid the complexities arising from heterogeneity, it is important that the initiator should have a solubility in the chosen solvent which is adequate for the experimental method to be used. Also, whatever the method, the [Int]0 in the reaction mixture must be significantly higher than that of any interfering impurities, preferably about 100 times; both the solubility of the initiator and the level of impurities depend on the solvent. In summary, a good initiator will yield a stable, singly charged anion and a cation with a high reactivity (large ki+) towards the alkenes concerned, via simple, well defined reactions. The remainder of this paper is concerned with finding, by appropriate calculations, some carbocation salts which best meet the specified requirements.

3 Solubility As far as we know, the literature contains no quantitative information on the solubility of carbocation salts and the qualitative information available indicated that such salts are relatively insoluble in the solvents of interest. Our first problem was to predict how changes in the structure of the salt would affect the solubility. Although the ideal solubility equation [Equation (1)] cannot be applied rigorously to ionic solutes, our first step was to examine its utility.

( ΔH θf / R)(1 / Tf – 1 / T ) = ln xA

(1)

where xA = mole-fraction of compound A; ΔHfθ = standard latent heat of fusion of A; Tf = temperature of fusion of A; T = temperature; R = gas constant. Despite the lack of data for carbocation salts, it is possible to use this equation by assuming that the sequence of solubilities of a series of salts is similar to that of the series of corresponding parent organic molecules (for which the relevant data are available [5]), provided that the anion remains constant (see Scheme 1). Our experimental results (Table 1) showed that this approach does work for the series of alkoyl salts but it fails to predict the considerably greater solubilities of the aroyl and aryl salts which are also shown in Table 1.

178

Theoretical Attempts at Improving Initiators for Cationic Polymerisation of Alkenes Table 1 Solubilities of carbocation salts in dichloromethane at 298 K a+

a– pm

Salt

Observed solubility*

–Δ ΔGθsol†

a+/a–

mol l-1

kJ mol-1

a+ + a–

Predicted solubility

CH3COSbF6

187

261

448

0.72

3.0 x 10-4

415

C2H5COSbF6

210

261

471

0.80

4.5 x 10-3

395

> CH3COSbF6

C2H5COPF6

210

237

447

0.89

2.3 x 10-3

407

< C2H5COSbF6 > CH3COSbF6

CF3COSbF6

218

261

479

0.84

6.0 x 10-3

389

> C2H5COSbF6

C6H5COSbF6

331

261

592

1.27

≈ 10-1

338

>> C2H5COSbF6

(C6H5)3CSbF6

490

261

751

1.88

> 10-l

263

>> C6H5COSbF6

The ionic radii a+, a– were calculated from bond lengths and covalent radii [6, 7, 8]. It should be noted that for a cation, such as CH3 – C+ = O, the C=O and C–C bonds are shorter than those of the isoelectronic neutral species * Observed solubilities are derived from as yet unpublished preparative experiments † From reference [9]

A+(g) + X–(g) ΔGθsol(A+)+

–Uc

ΔGθsol(X–)

ΔGθ

s

A+X– (c)

A+(s) + X– (s)

ΔGθs = –RTlnKθs Scheme 1 Energeties for the dissolution of an ionic crystal A second, more detailed approach was then investigated. From Scheme 1 it is clear that in order to calculate the solubility product, Ksθ, it is necessary to know both the free energy of solution, ΔGθsol(A+,X–) and the lattice energy, Uc. Abraham’s recent developments [9] of the Born Equation [10] make it possible to calculate ΔGθsol to within ± 10 kJ mol-1 from the ionic radii (a+, a–), but it is not possible to calculate Uc

179

Developments in the Theory of Cationoid Polymerisations without a knowledge of the crystal geometry. There is no simple relation between Ksθ and ΔGθsol(A+,X–). However, the available information shows that when a+/a– < 0.8, the solubility decreases as the radius of the cation increases, but when a+/a– > 0.8, as is true for most of the carbocation salts which we have considered, then the solubility is proportional to (a+ + a–) and therefore inversely proportional to |ΔGθsol| (This follows because the equations of both Born and Abraham give ΔGθsol, as inversely proportional to the ionic radii.) As can be seen from Table 1, the predicted relative solubilities are correct, and we can therefore estimate with adequate accuracy the relative solubility of any carbocation salt from its ΔGθsol, calculated by Abraham’s method.

4 The equilibria associated with carbocation salts

Introduction Carbocation salts of the type R+ MtX-n + 1 are generally involved in binary equilibria (BIE) of type (iv) [11]:

RX + MtX n ↔ R + + MtX n– +1 , K1θ

(iv)

In many systems the formation of ion-pairs is important, but because we are dealing mostly with systems of very low ionic strength the pairing of both the initiating and the propagating ions will not be considered here. As mentioned above, our considerations can be extended easily to dieidic systems where both unpaired and paired cations may initiate and propagate. The initiation (i) is of course, strictly, also an equilibrium and we will consider it as such:

R + + P1 ↔ RP1+ , K2θ

(v)

The equilibrium constants, K1θ and K2θ, which are needed to make predictions about the usefulness of the salts, are not generally available in the literature, but they could be calculated from Equation (2):

ΔG θ = – RT ln K θ

(2)

Unfortunately, most of the available data are for ΔHθ but if we assume the TΔSθ for these systems to be relatively small, we can make the approximation:

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Theoretical Attempts at Improving Initiators for Cationic Polymerisation of Alkenes

ΔH θ = ΔG θ

(3)

Despite the fact that the few studies on such systems which have been made [12 - 16] suggest that the entropy term is not unimportant for the position of the equilibrium, the lack of information on entropy obliges us to use Equation (3) in order to obtain a first approximation for these systems. However, although a major contribution to the overall ΔSθ for reactions such as those in Equations (iv) and (v) arises from the solvation of the ions [17], this is in fact incorporated in the ΔHθ calculated below by the use of a calculated ΔGθsol [9]. The equilibrium (iv). The energetics of the BIE (iv) can be described by a Born-Haber cycle (Scheme 2) which permits a detailed analysis of how changes in the alkyl halide

R+(g) + X–(g) + MtXn (g) Ax-(MtXn) I(R•)

R+(g) + MtX–n+1(g)

Ea(X•)

Ea(MtXn+1) –D(MtXn–X) + I(R•) R•(g) + X•(g) + MtXn(g) D(R–X) ΔHθsol(R+,MtX–n+1)

RX(g) + MtXn(g) ΔHθsub(MtXn)

ΔHθv(RX) RX(l) + MtXn(c)

–ΔHθs(RX, MtXn)

RX(s) + MtXn(s)

ΔHθ4

R+(s) + MtX–n+1(s)

Scheme 2 Energetics of the BIE for RX + MtXn

181

Developments in the Theory of Cationoid Polymerisations (Equation 4) and the metal halide (Equation 5) affect the overall equilibrium position characterised by ΔH4θ which is related to ΔH8θ and ΔH9θ by Equation (6).

ΔH8θ = – ΔHsθ ( RX ) + ΔHvθ ( RX ) + D( R – X ) θ + I ( R • ) + E a ( X • ) + ΔHsol (R + )

θ ΔH9θ = – ΔHsθ (MtX n ) + ΔHsub (MtX n ) θ + Ax – (MtX n ) + ΔHsol (MtX n– +1 )

ΔH4θ = ΔH8θ + ΔH9θ

(4)

(5)

(6)

The first two terms in (4) are relatively small ΔHsθ(RX) ≈ 5-10 kJ mol-1 [5, 18, 27] and ΔHvθ(RX) ≈ 20-50 kJ mol-1 [5]) and variations in these terms do not warrant discussion. Nevertheless, it should be noted that the sum of ΔHsθ(RX) and ΔHvθ(RX) can be approximated by ΔHvθ (solvent), but the use of the two terms leads to a better analysis, especially for a series of RX, since for a single solvent ΔHsθ(RX) is almost invariant and the ΔHvθ(RX) is known for many compounds. For those RX which are crystalline at the standard temperature the term required here is ΔHθsub(RX) and this is considerably larger than ΔHvθ(RX). The first of the more significant terms in (4) is the bond dissociation enthalpy (BDE) D(R - X), the variation of which for a number of methyl derivatives is shown in Figure 1 [19]. It can be seen that by changing X from fluoride to iodide with R = CH3, ΔH8θ will become less positive by approx. 240 kJ mol-1; for R = CH3CO the same change makes ΔH8θ less positive by approximately 290 kJ mol-1. Another important term in (4) is the ionisation potential I(R•) of the organic radical. Many values for this term are available but care must be taken when comparing data from different sources because some of the earlier data may be in error by as much as 15 kJ mol-1 [20]. The I(R•) values in Figure 2 show that by varying the adjacent groups (atoms) the I(R•) can be changed by up to 150 kJ mol-1. Unfortunately, there are no data available for the halogen substituted acetyl radicals; however by comparing the ionisation potentials of the acetyl and propionyl radicals and those of methylcyclohexane and trifluoromethylcyclohexane it can be suggested that the ionisation potentials of the halogen substituted acetyl radicals are greater than that of the acetyl radical and, further, that although /D(CF3CO-F) - D(CH3CO-F)/ is unlikely to be greater than 30 kJ mol-1, the difference in the ionisation potentials of the corresponding radicals could well be as much as 200 kJ mol-1. That is, by changing R from CH3CO to CF3CO, ΔH8θ will probably be made more positive by approx. 170 kJ mol-1. Of

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Theoretical Attempts at Improving Initiators for Cationic Polymerisation of Alkenes

Figure 1 Bond dissociation energies for some methyl and substituted methyl halides

the two remaining terms included in ΔH8θ the electron affinity of the halogen atom needs no discussion because it varies by only about 30 kJ mol-1 between the halogens; the second, ΔHθsol (R+) will be considered below together with the similar term for the metal halide. We can conclude that for the RX molecule, ionisation is promoted by using the iodide rather than the fluoride and by having electron donating groups adjacent to the ionogenic carbon. For the metal halide of the BIE the contribution to the overall energy change is summarised in Equation (5). The first term, ΔHsθ (MtXn) is small [21, 22, 23] and is probably relatively insensitive to changes in MtXn. Thus, the first important term for ΔH9θ is ΔHθsub (MtXn). Figure 3 shows the ΔHθsub (MtXn) for four metal halides often encountered in cationic polymerisation [8, 24, 25]. Although for the mercuric halides the variation in the ΔHθsub (MtXn) is small (46 kJ mol-1), this is not the case for the aluminium halides. The extremely high ΔHθsub of AlF3 indicates that this compound holds little promise as a possible anionogen.

183

Developments in the Theory of Cationoid Polymerisations

Figure 2 Ionisation potential of some substituted methyl radicals

For the tungsten halides the trend in ΔHθsub (MtXn) on changing from chloride to fluoride is the opposite to that shown by the aluminium halides. Thus, this is not a term with respect to which overall generalisation is possible and great care must be taken whenever numerical values for this term are not available. The next term in Equation (5) is the halide affinity of the metal halide, Ax–(MtXn). This is a very important term for the final value of ΔH4θ and a term which, were it generally available, would facilitate worthwhile conclusions as to which metal halide would be the best anionogen. However, only two halide affinities for the metals of interest are known to us, viz. the fluoride affinities of BF3 and WF5 [26, 27]. In Scheme 3 the role of the halide affinity in the Born-Haber cycle for the BIE [Equation (iv)] is emphasised and an alternative route for the same energy contribution to ΔH4θ is given. The individual BDE D(XnMt-X) is, like the halide affinity, known only for a very few examples of interest,

184

Theoretical Attempts at Improving Initiators for Cationic Polymerisation of Alkenes

Figure 3 Enthalpies of sublimation of some metal halides

ε + MtXn+1(g) –D(XnMt – X)

Ea(MtXn+1) MtXn(g) + X–(g) Ea(X)

ε + MtXn(g) + X(g)

Ax–(MtXn) MtX–n+1(g)

Scheme 3 Energetics of formation of complex anion

185

Developments in the Theory of Cationoid Polymerisations and it is preferable to look at the more reliably known average BDE, D (Mt-X). There is, however, a significant difference between D(XnMt-X) and D (Mt-X) [28]; in part this difference is due to the allowance made in the former for the reorganisation energy involved with the stepwise change in the co-ordination number of the metal, whereas the latter are derived from heats of atomisation and therefore do not take account of the relative stabilities of the various states of the metals. Generally, the difference between D(XnMt-X) and D (Mt-X) decreases with increasing atomic number down any group and, since the reorganisation energy decreases in the order F > Cl > Br > I [28], the differences shown by D (Mt-X), when used for an analysis of ΔH4θ, are exaggerations of the real situation. In addition, even by the ‘alternative route’ (Scheme 3) we require the electron affinity Ea(MtXn+1) which is known for very few metals of interest. From those

Figure 4 Average bond dissociation energies for a selection of metal halides

186

Theoretical Attempts at Improving Initiators for Cationic Polymerisation of Alkenes values which are known [27] we can only conclude that for any one Mt the electron affinity decreases in the order F > Cl > Br. Notwithstanding these considerable limitations, we can see from the data shown in Figure 4 [8, 30, 32, 37] that because D (Mt-X) becomes less positive, ΔH4θ also becomes considerably less positive as the metals are changed in the sequence As(III) → P(V) → W(VI) → B(III) and as the halide is changed in the sequence F > Cl > Br > I. Although there are obvious gaps in the values given in Figure 4 which are of particular relevance to cationic polymerisation, it has been shown [29] that from the strikingly similar pattern of changes in D (Mt-X), both with changes in the halide for any one metal and from oxidation state to oxidation state for any one metal, one can predict with a reasonable degree of accuracy those values which are required, e.g. D (Sb(V)-F) and D (As(V)-F). We can thus make several overall conclusions for all those metals of interest: although the choice of fluoride instead of iodide as the halide will increase the ΔHθsub, and therefore make ΔH9θ more positive, the sum of the differences in these terms will generally be less than the advantage gained from the other terms by using the fluoride, so that this is the halide of choice. As far as the metal is concerned (the term metal here is used to include some elements which are normally termed non-metals) considerable care must be taken before drawing any conclusions. For example, although the stability sequence of the anions SbF6– > PF6– >> SbCl6– [33] can be predicted simply on the basis of the D (Mt-X), the comparative instability of BF4– vis-à-vis SbF6– seems to present an anomaly which can only be explained in terms of the reorganisation energies and the electron affinities of the species concerned. In addition, the evidence in Figure 4 suggests that the lower oxidation state of any metal might provide ‘better’ anionogens than the higher ones, but the estimated increase in Ea for the higher oxidation state(s) probably makes the choice of the latter more favourable: for example WF5 rather than WF4 and SbF5 rather than SbF3. Thus, although the available data do not provide a precise basis for selecting a metal, there are adequate grounds to try, for example, TaF6–, WF6– and MoF6–. There remain two terms in ΔH4θ which have not been discussed: ΔHθsol(R+) and ΔHθsol(MtX–n+1). As far as we know, the recent work of Arnett [27] is the only experimental evidence relating to ΔHθsol(R+), but even these values are relative estimates and the absolute values must be calculated by means of Abraham’s equations [9]. There is an advantage to this approach, since the ΔHθsol(R+) and ΔGθsol(MtX–n+1) thus obtained contain probably the most significant contributions from entropy changes and these can be included by using the calculated ΔGθsol in any overall Born-Haber summation.

187

Developments in the Theory of Cationoid Polymerisations

MtX•n–1(g) + X•(g) + MtXn(g) Ea(X•) D(Xn–1Mt–X)

MtX•n–1(g) + X–(g) + MtXn(g) – ε AX-(MtXn)

2MtXn(g)

MtX•n–1(g) + MtX–n+1(g) – ε 2ΔHθsub(MtXn)

I(MtX•n–1) MtX+n–1(g) + MtX–n+1(g)

2MtXn(c) –2ΔHs(MtXn)

ΔHθsol(MtX–n+1)

ΔHθsol(MtX+n–1)

MtXn(s) + MtXn(s) MtX+n–1(s) + MtX–n+1(s) Scheme 4 Energetics of the BIE for self-ionisation of a metal halide

Conclusion The situation presented above is, of course, a simplification. It is well documented that metal halides can take part in a self-ionisation reaction [34] involving only the metal halide. The Born-Haber cycle for such a BIE is given in Scheme 4. – 1 2 (MtX n+1

+ MtX+n–1)

K1θ R+ + X–

RX + MtXn

R+ + MtX–n+1 1(MtX ) n y y

Scheme 5 The principal equilibria in the system RX + MtXn

188

Theoretical Attempts at Improving Initiators for Cationic Polymerisation of Alkenes If one wants to use only a metal halide as the initiator for an alkene polymerisation, an analysis similar to ours can be made for the metal halide alone. In addition, there is a 1:2 equilibrium for the organic halide [35, 36] and a molecular aggregate ↔ single molecule equilibrium associated with the metal halide. Thus, a solution of a carbocation salt is more exactly described by the series of linked equilibria summarised in Scheme 5. However, for those systems for which measurements have been made, and from a consideration of the arguments presented above, it follows that K1θ [Equation (4)] is so much greater than any of the other equilibrium constants involved, that consideration of the system can validly be restricted to the simple system described so far. However, it is essential to remember that the relative magnitudes of the equilibrium constants of Scheme 5 depend very strongly on the nature of the solvent. The errors involved in the above analysis of the Born-Haber cycle for the organic halide + metal halide are, of course, so large (of the order of 100 kJ mol-1) that to convert the derived energy change into an equilibrium constant would be meaningless, but the analysis is still worthwhile since, as has been demonstrated, it provides the basis for a comparison between systems; it permits predictions as to the effectiveness of untried systems: and it provides explanations for some of the established experimental results.

5 The initiation reaction We have shown how one can estimate which systems are promising initiators from the point of view of generating cations, but in order that an initiator will initiate a polymerisation, the generated cation must react with the chosen monomer and for that the free energy change ΔG10 of reaction (i) under the reaction conditions must be negative. As a guide to ΔG10 we use, as usual, the ΔGθ10. Before discussing the thermodynamics of Equation (i) it is worth emphasising that the arguments presented here are about equilibrium constants and are not concerned with the kinetics of the systems. However, for reactions between molecules and cations in solution it is generally found that if ΔG is negative, the reaction proceeds at a reasonable rate [37]. It is especially interesting to examine the thermodynamics of reaction (i) for the trityl and dityl (diphenylmethyl) cations as initiating salts for isobutylene because we can thus provide a theoretical explanation of the experimental fact that trityl salts do not initiate isobutylene polymerisation, but dityl salts do: Table 2 shows the relevant data. The solvation energy terms have been omitted since on the basis of a

189

Developments in the Theory of Cationoid Polymerisations

Table 2 Calculation of ΔHθ10 from Scheme 6 with CH2:CR′2 = CH2:CMe2 •

R+

I(R•)

D(RCH2CMe2)

I(RCH2CMe2)

ΔHθ10 kJ mol-1

ø3C+

658

191

66 9

+37 + ΔΔHθsol(R+)*

ø2C+H

706

223

66 9

–45 + ΔΔHθsol(R+) •

β for isobutylene = 217.6 kJ mol-1. It has been assumed that I of RCH2CMe2 is the same as that of t-C4H•9 * This is the difference in ΔHθsol for R+ and RCH2C+Me2 and is probably relatively small

‘tumbling’ radius the two ions concerned are of the same size, but it is probable that the ΔGθsol(trityl +) is less negative than ΔGθsol(dityl+). This conclusion is tentative because, whilst the greater effective size of the trityl cation would give a less negative solvation energy, the inhibition of resonance in it due to its non-planarity would make the charge less diffuse than in the dityl ion and therefore increase ΔGθsol(dityl+). Further, it is difficult to know what value to use for the ionic size of the isobutylene adducts of the two ions, but it is probable, on the grounds that the charge is more concentrated and the effective ionic size smaller, that the ΔG θsol(RP1+) will be more negative than ΔG θsol(trityl+) or ΔG θsol(dityl+). Thus, although no absolute value of the difference in the solution enthalpies (ΔΔH θsol) is included in Table 2, it is probable that the difference in ΔH θ10 for trityl and dityl additions to isobutylene is smaller, and that both values are probably less positive, than those shown. Despite these limitations the results in Table 2 predict correctly that dityl salts will initiate the polymerisation of isobutylene but that trityl salts will not, provided that under the reaction conditions ΔH10 has the same sign as ΔH θ10 and that the ΔH θsol(R+) and the TΔS terms are such that the ΔG10 have the same sign as the corresponding ΔH θ10, all of which seems to be probable. For any given monomer the terms in Scheme 6 which show the greatest variation are I(R•) for the initiator and the BDE of the bond formed between the initiator and the monomer. The minimum required value of I(R•), such that the corresponding R + will add exergonically to any given olefin, can be estimated in many instances because ˙ .C–R) usually vary symbatically. From the available data we can I(R•) and D(R′2 C estimate this limiting I(R•) for isobutylene as approximately 690 kJ mol-1. For styrene the limiting I(R •) is probably closer to 660 kJ mol-1 and we can see thence an

190

Theoretical Attempts at Improving Initiators for Cationic Polymerisation of Alkenes

+ R•CH2CR2′(g) •

•

•

CH2 – CR′2(g) + R•(g)

I(R•CH2CR′2) –D(C–C)

+β

–I(R•)

•

R•CH2•CR′2(g)

CH2:CR′2(g) + R+(g) + ΔHθsol(R•CH2•CR′2)

ΔHθv(CH2:CR′2) CH2:CR′2(l) + R+(g) –ΔHθsol(CH2:CR′2) CH2:CR′2(s) + R+(s)

–ΔHθsol(R+) ΔHθ10 + R•CH2CR′2(s)

Scheme 6 Energetics of the addition of a cation to an alkene explanation of why the trityl cation does initiate the polymerisation of styrene but not of isobutylene. On the basis of this argument it is probable that the tris-p-halogen substituted trityl salts will be useful initiators for the polymerisation of isobutylene since their ionisation potentials probably exceed 690 kJ mol-1 [38], and the p-substitution would inhibit the back-biting reactions which make both trityl and dityl salts unstable [39].

Conclusion The foregoing analysis shows how a new potential carbenium salt initiator can be rapidly assessed in terms of its relative solubility, the relative position of its ion:molecule

191

Developments in the Theory of Cationoid Polymerisations equilibrium and its reactivity with a chosen monomer. We have shown that by increasing the size of the cation the solubility of the salt will be increased and the ionisation equilibrium will be pushed to the ion side. However, as the charge density on the ionogenic carbon is reduced the reactivity of the initiator with respect to nucleophilic attack by an alkene is reduced. By estimating the limiting I(R•) of the initiator for the chosen monomer it is possible to make structural changes to the initiator such that the maximum solubility and ionisation are achieved whilst retaining the possibility for initiation. An example of such a process is the use of tris-p-chloro trityl salts rather than trityl salts to initiate the polymerisation of isobutene. From our analysis we have rationalised the order of stabilities of the anions: SbF6– > PF6– >> SbCl6– and, more important, we can suggest that some untried anions, such as TaF6–, WF6– and MoF6–, are worth studying. Finally, the above discussion has pointed to a number of gaps in the thermodynamic literature and the studies of BIE. Although the work of Arnett [21, 22, 40] has provided a sound basis for the comparative reactivity of carbocations, there are certain questions (such as the final state of the cations) which need to be clarified before these results can be applied more widely. Until these gaps in our experimental knowledge are filled, we are left with the theoretical approach described in this paper, if we wish to make a systematic choice of the optimum initiator for a chosen alkene polymerisation.

Acknowledgements S.D.P. thanks the Keele Polymer Group Alumni Fund for a grant.

References 1.

P. H. Plesch, (a) Part VI, Makromolek. Chem. 175, 1065 (1974); (b) Part V, Macromolecular Chemistry-8, p.305. IUPAC Helsinki, 1972, Butterworths, London (1973).

2.

F. Fairbrother, J. Chem. Soc. 503 (1945).

3.

(a) P. H. Plesch, La Ricerca Scientifica, Supplemento Simposio Internat. Chim. Macromol. 25, 140 (1955); (b) P. H. Plesch, Progress in High Polymers Vol. II (Edited by Robb and Peaker), p. 137. Iliffe Books, London (1968).

4.

A. Gandini and H. Cheradame, Adv. Polym. Sci. 34/35 (1980).

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Theoretical Attempts at Improving Initiators for Cationic Polymerisation of Alkenes 5.

D. R. Stull, E. F. Westrum and G. C. Sinke, The Chemical Thermodynamics of Organic Compounds, J. Wiley, New York (1969).

6.

F. B. Boer, J. Am. Chem. Soc. 88, 1572 (1966).

7.

G. J. Kruger, C. W. F. T. Pisterius and A. M. Heyns, Acta. Cryst. B32, 2916 (1976).

8.

G. H. Aylward and T. J. V. Findlay, S.I. Chemical Data, J. Wiley, New York (1974).

9.

M. H. Abraham and J. Liszi, (a) J. Chem. Soc. Faraday Trans. I 7, 1604 (1978); (b) J. Chem. Phys. 70 (5), 2491 (1979).

10. M. Born, Z. Physik. 1, 45 (1920). 11. (a) P. H. Plesch and O. Nuyken, Chem. Ind. 379 (1973); (b) D. W. Grattan and P. H. Plesch, J. Electroanalyt. Chem. 103, 81 (1978). 12. J. W. Bayles, A. G. Evans and J. R. Jones, J. Chem. Soc. 206 (1955). 13. W. Gogolczyk, S. Slomkowsky and S. Penczek, J. Chem. Soc., Perkin II 1729 (1977). 14. N. Kalfoglou and M. Szwarc, J. Phys. Chem. 72, 2233 (1968). 15. P. M. Bowyer, A. Ledwith and D. C. Sherrington, J. Chem. Soc. B, 1511 (1971). 16. S. Kipnich, Ph.D. Thesis, Technische Universitat, Munich (1978). 17. A. Ledwith, S. Al-Kass, D. C. Sherrington and P. Bonner, Polymer 22, 143 (1981). 18. P. P. S. Saliya, T. M. Young, R. F. Rodewald, F. M. Fuchs, D. Kohli and R. Fuchs, J. Am. Chem. Soc. 99. 2949 (1977). 19. J. A. Kerr, Chem. Rev. 66, 465 (1966). 20. F. P. Lossing and G. P. Semeluk, Can. J. Chem., 48, 955 (1970). 21. E. M. Arnett and N. J. Pienta, J. Am. Chem. Soc., 102 (10), 3329 (1980). 22. E. M. Arnett and C. Petro, J. Am. Chem. Soc., 100 (17), 5408 (1978). 23. N. P. Galkin, L. E. Bertina, V. T. Oreklov and E. A. Paklenkov, Zh. Fiz. khim. 49 (9), 2454 (1975).

193

Developments in the Theory of Cationoid Polymerisations 24. U.S. National Bureau of Standards, Washington, DC, JANAF Thermochemical Tables, 2nd Ed., NSRDS-NBS 37 (1975). 25. U.S. Dept. of Commerce, U.S. Govt. Printing Office, Washington, DC, NBS Technical Note, 270-1 (1965). 26. J. Burgess and R. D. Peacock, J. Fluorine Chem. 10 (1977). 27. J. Burgess, S. J. Cartwright, I. Haigh, R. D. Peacock, P. Taylor, H. D. B. Jenkins and K. E. Pratt, J. Chem. Soc., Dalton 1143 (1979). 28. F. A. Cotton and J. R. Leto, J. Chem. Phys. 30 (4), 993 (1959). 29. J. A. Conner, Topics Curr. Chem. 71, 71 (1977). 30. T. L. Cottrell, Strengths of Chemical Bonds. Butterworths, London (1954). 31. V. I. Vedenyev, L. V. Gurvich, V. N. Kondraty’ev, V., A. Medvedev and Y. L. Frankevitch, Bond Energies, Ionisation Potentials and Electron Affinities. Edward Arnold, London (1962). 32. I. Preckel and P. Selwood, J. Am. Chem. Soc. 63, 3397 (1941). 33. P. Dreyfuss and J. P. Kennedy, J. Polymer Sci. C, Polymer Symp. 56, 129 (1976). 34. D. W. Grattan and P. H. Plesch, J. Chem. Soc., Dalton 1734 (1977). 35. A. Bentley, A. G. Evans and J. Halpern, Trans. Faraday Soc. 47, 711 (1951). 36. A. G. Evans, A. Price and J. H. Thomas, Trans Faraday Soc. 52, 332 (1956). 37. Ying Wang and L. M. Dorfman, Macromolecules 13, 63 (1980). 38. A. A. Khan, S. D. Pask and P. H. Plesch, to be submitted for publication. 39. R. Filler, Chen-Shu Wang, M. A. McKinney and F. N. Miller, J. Am. Chem. Soc. 89, 1026 (1967). 40. E. M. Arnett, C. Petro and P. von R. Schleyer, J. Am. Chem. Soc. 101 (3) 523 (1979).

194

3.5

Thermochemical Aspects of the Initiation of Cationic Polymerisations by Organic Cations. Conflation of Two Unpublished Conference Contributions (1999)

Prologue This paper was conflated from the main lectures at two Symposia in 1978 with the following titles: 3.5A Thermochemical Aspects of Cationic Initiation Summary published in the Preprints of the First European Discussion Meeting on Polymer Science: New Developments in Ionic Polymerization, Strasbourg, 27.2-2.3.1978 - Full paper unpublished. 3.5B Electrical Properties and Reactivity of some Organic Cations Summary published in the Preprints of the European Symposium on Electrical Phenomena in Polymer Science, Pisa, Italy, 29-31 March 1978 - Full paper unpublished. The Abstracts were published in the Preprints of the Symposia, but because neither of the lectures was published in full, and because their themes are closely related, they were conflated into a single paper which incorporates the main points from both. Although it was not published at the time, it is presented here because it is a direct development of the thermochemical argument which is the main theme of this Section.

Reactivity and stability The terms ‘reactivity’ and ‘stability’ are amongst the most used words in chemistry. In relation to organic cations, they are evidently determined to a large extent by the electrical properties of these species, by which we mean, amongst other features, the chargedistribution and the reduction potential of the ion-in-solution.

195

Developments in the Theory of Cationoid Polymerisations We note first that ‘reactivity’ and ‘stability’ can be used in a thermodynamic and a kinetic context and - more important still - that it is meaningless to use either term without specifying the reaction and the reagents with which it is being used. Most chemists, when talking about stability or reactivity, have in mind a set of conditions, of reagents or of reactions, to which they form their ideas, but often one does not realise just how limited and limiting such a frame of reference can be. For example a preparative organic chemist working with a tetrafluoroborate salt on a large scale would not be worried if a few percent of it decomposed during an operation and would consider it ‘stable’, whereas a physical chemist making conductivity measurements may get a totally false impression of the prevailing reaction from a small (and probably irreproducible) quantity of BF3 formed by such a decomposition, and he would not regard the salt as ‘stable’ (1). Therefore, in order to limit our considerations in a useful manner, we must specify the circumstances with respect to which we will consider stability and reactivity. In the context of cationic polymerisations it is convenient to take stability and reactivity not to be antonyms. We will take stability as a measure of the ‘survival capacity’ of an ion in a particular environment, which could be measured by its halflife; its antonyms are instability and lability. The reactivity, which can be measured by a rate-constant, has the antonym inertness; both nouns can be qualified by the adjectives ‘high’ or ‘low’. Within the present framework we are interested in the stability and the reactivity of organic cations from several points of view: 1. We wish to generate cations for the purpose of initiating a chain-reaction in such a way that we can control the total number of ions generated and the rate of their generation. 2. Once a propagating cation has been generated, we wish to control, preferably suppress, the reactions which can compete with propagation, and which may thus lead to transfer and termination. 3. We may wish to control whether most of the cations are unpaired with an anion, or paired, or unpaired but complexed, or paired with an anion which is held in the surface of a crystal, as in a heterogeneous polymerisation. In order to think constructively about these problems we need some scale on which we can measure that intrinsic property of the ions which determines (in part) both stability and reactivity. In practice, we have to content ourselves, as far as carbenium ions are concerned, with the gas-phase standard enthalpy of formation, ΔHfθ, of a series of ions, and make estimates of the effects of solvation energies. In this way we can go quite a long way towards rationalising the reactivity of initiating ions with various monomers.

196

Thermochemical Aspects of the Initiation of Cationic Polymerisations by Organic Cations

Reactivity In order to assess reactivity in this context we need first to recognise that the chemical initiation of cationic polymerizations can occur in different ways. Disregarding the rarer initiations involving electron abstraction or hydride abstraction from a monomer, the most common are 1. the transfer of a cation from a convenient ‘store’ to the monomer P1, and 2. the addition of an existing ion to the monomer. 1. Covalent acids, AH, co-initiators ROR′, and -onium ions, e.g., Et3O+, are three types of ‘ion store’:

AH + P1 → HP1+ + A – or ( AH)2 + P1 → HP1+ + A 2 H –

(I)

ROR ′ + MtX n + P1 → RP1+ + R ′OMtX n–

(II)

Et 3O + + P1 → EtP1+ + Et 2 O

(III)

2. The initiation by the cation of a salt, e.g., ArCO+, is exemplified by reaction (IV): +

R + + CH 2 : CR ′′R ′′′ → R – CH 2 C R ′′R ′′′

(IV)

For each of these reactions the ΔH can be estimated in the conventional manner, and one can then predict: ‘If ΔH is large and negative, the initiation will go, if it is large and positive, initiation is unlikely.’ The basis of this statement is the Polanyi Principle, which correlates enthalpies of reaction ΔH with activation enthalpies ΔH*:

ΔH* = a.ΔH + b where a and b are constants. The less negative ΔH, the greater is ΔH*. Strictly, it should be a relation between ΔG* and ΔG, but not ΔHθ or ΔGθ, because what matters is the enthalpy or free energy change under the reaction conditions, not the standard conditions. Caution: One must compare strictly like with like, and only linear transition states.

197

Developments in the Theory of Cationoid Polymerisations Whilst it is rather hazardous to make any absolute conclusions on this basis, the method is useful for making comparative estimates, taking into account the effects of changes in conditions such as the polarity of the solvent. For example, by means of the thermochemical analysis corresponding to reaction (III) we can find an explanation of the well-known fact that Et3O+ does not initiate the polymerisation of alkenes. The thermochemical analysis for reaction (III), written for the general tertiary oxonium ion R3O+, gives us:

ΔH3 = ΔHs ( R 3O + ) + C( R + – OR 2 ) – C( R + – P1 ) – ΔHs ( RP1+ )

(1)

The ΔHs are the solvation enthalpies of the ions, C(R+–OR2) = – (the carbenium ion affinity of R2O), i.e., it is the enthalpy of the reaction (V):

R 3O + (g) → R 2 O(g) + R + (g)

(V)

where C(R+– P1) = –(R+ affinity of P1) and P1 = CH2:CHR′, so that •

•

C( R + – P1 ) = – [ I ( R + ) – β + D( R – CH 2 C⋅ HR ′) – I ( R – CH 2 C⋅ HR ′)] and the solvation energies ΔHs(P1) and ΔHs(Et2O), being relatively small, have been neglected. The fact is that Et3O+ neither alkylates olefinic hydrocarbons nor initiates their polymerisation. Can equation (1) tell us why? Because of the similarity in shape and size the difference ΔHs(R3O+) – ΔHs(RP1+) is likely to be small (probably < 10 kJ mol-1). Although we do not know the C terms, we may suppose that C(R+–OR2) – C(R+–P1) is equal to P(R2O) – P(P1), [P = proton affinity]. Since P(Et2O) = 858 and P(i–C4H8) = 816 kJ mol-1, therefore ΔP = 42 kJ mol-1 and thus the proton transfer, and by hypothesis the Et+ transfer, from Et2O to i-C4H8 would be considerably endothermic and therefore unlikely; qualitatively, it has long been known that ‘most oxygen compounds are more basic than most olefins’. However, since P(Me2O) is only 795 kJ mol-1,

ΔH3 = ΔΔHs + 795 – 816 = ΔΔHs – 21 kJ mol –1 and therefore, if our ideas are right, Me3O+ may well be an initiator for isobutene if ⏐ΔHs (- - PnCH2CMe2+)⏐ > ⏐ΔHs(Me3O+)⏐. The differences in ion size and charge density are too small for any confident predictions to be made about this inequality, and the matter will have to be decided by experiment and the outcome may well depend on the solvent. We note also that we lack the D and I values required to find out whether thermochemistry can shed light on why Et3O+ initiates the polymerisation of alkyl vinyl ethers, but not of Nvinylcarbazole (NVC) (2). 198

Thermochemical Aspects of the Initiation of Cationic Polymerisations by Organic Cations

Since some carbenium and carboxonium salts are useful initiators, it is appropriate to analyse the ΔH4 of reaction (IV):

ΔH4 = ΔHs ( R + ) – ΔHs ( RP1+ ) – C( P1 – R + ) •

(2) •

•

C( P1 – R + ) = – D( R – CH 2 C R ′′R ′′′) + β – I ( R ) + I ( RCH 2 C R ′′R ′′′)

(3)

where β is the ‘second half’ of the double bond, D is the BDE and the I are ionisation potentials. Some useful values of these quantities are listed in Table 1. We can test equation (3) for the trityl ion which initiates the polymerisation of styrene, but not of isobutene. On the basis of equation (3) we find that C is less negative for styrene than for isobutene so that the (Ph)3C+ should add to isobutene if it adds to styrene. However, we have neglected the solvation energies. The experimental result becomes compatible with the observations if one remembers that the alkylated 1-phenylethyl (polystyryl) ion, being secondary, is smaller at the site of the charge than the alkylated t-butyl (polyisobutyl) ion, so that the resulting more negative [ΔHs(R+) – ΔHs(RP1+)] may be what makes the initiation by Ph3C+ feasible for styrene. The heuristic value of equation (3) is that we can see what is required for a good initiator: D and I(R•) must be as large a possible, and ΔHs(R+) should be small compared to ΔHs(RP1+); in other words, as an efficient initiator we need a large cation whose parent radical has a high ionisation potential, and which forms a strong bond to monomer. On the last two counts the trityl cation must be one of the least suitable. These considerations indicate that the first four ions listed in Table 1 should merit detailed study as initiators for vinyl polymerisations. From the point of view of the monomer what matters most is that the radical RCH2C•R″R″′ derivable from it should have a low ionisation potential. It may be that this is the reason for the eminent polymerisability of alkyl vinyl ethers and NVC.

Stability Having analysed to some extent the factors relevant to efficient initiation, i.e., the reactivity of initiating ions in forming propagating ions, we now consider the factors which Table 1 MeCO+

Ph2CH+

NO+

NO2+

Ph3C+

C7H7+

I(R•)/kJ mol-1

778

619

89 1

950

600

608

D(R-C2H5)/kJ mol-1

314

234

-

172

201

272

R+

199

Developments in the Theory of Cationoid Polymerisations determine the stability of the ions formed. We need to ask: stability with respect to what? There are two types of instability: 1. Inherent instability, which can manifest itself by a unimolecular rearrangement to a form which has a more negative free energy of formation, e.g., the isomerisation of a secondary to a tertiary cation or to an allylic cation. 2. The inactivation of an ion (a) by its transformation into a less reactive ion by reaction with a neutral base, e.g., water, which thus gives a primary oxonium ion; or (b) by reaction with an anion to give one or more neutral molecules. Here we consider only the inactivation 2(b) of a carbenium ion by neutralisation. In the present context neutralisation can occur in two ways. The first and simplest is a combination of the carbenium ion with the anion to form an ester, i.e., a compound in which the two previously charged species become linked by a covalent bond: R+ + A– ↔ RA

(N1)

The enthalpy ΔHN1 for ester formation is given by

ΔHN1 = ΔHs ( R + ) + ΔHs ( A – ) – ΔHs ( RA ) – I ( R • ) + E( A • ) – D( R – A ) As before (Section 3.3) we define D + I - E = θ, the heterolytic BDE of the ester RA. Since the reverse of the reaction N1 is the ionisation of the ester, the equilibrium position for any one system depends critically on the nature, especially the polarity, of the solvent, which determines the ΔHs terms. The accumulation of the necessary thermochemical data is essential to a rationalisation of the relation between cationic and pseudocationic polymerisations; but the prevalence of the former at low temperatures and of the latter at high temperatures is surely related to the fact that the dielectric constant, and with it solvation energies, increases as the temperature of a polar solvent is reduced, so that decreasing temperature favours ionisation. The second form of neutralisation involves the fragmentation of the anion, or the detachment of an ionic component from it, as shown in the reaction (N2); if that fragment is a halide ion the resulting polymer-halide can be regarded as an ester of the hydrohalidic acid.

R + + MtX −n +1 ↔ RX + MtX n The enthalpy ΔHN2 for ester (halide) formation is given by

200

(N2)

Thermochemical Aspects of the Initiation of Cationic Polymerisations by Organic Cations

ΔHN 2 = ΔHs ( R + ) + ΔHs (MtX −n +1 ) – ΔHs ( RX ) – ΔHs (MtX n ) – ΔHs ( RX ) + D(MtX n – X – ) – θ( R – X ) To promote the heterolytic dissociation of the ester we need large ΔHs (ions), large D(MtXn –X¯), and small θ. We can now use the insight provided by the equation for ΔHN2 to investigate the effect on ΔHN2 of changes of reagent. If the small ΔHs of neutral molecules are neglected, we obtain:

ΔHN 2 = ΔHs ( R + ) + ΔHs (MtX −n +1 ) + D(MtX n – X – ) – θ( R – X ) For two different polymers R:

ΔΔHN 2 = – ΔD( R – X ) – ΔI ( R • ) + ΔΔHs ( R + ) Two different metals Mt:

ΔΔHN 2 = ΔD(MtX n – X – ) + ΔΔHs (MtX n +1– ) Two different X:

ΔΔHN 2 = – ΔD( R – X ) + ΔE( X • ) + ΔD(MtX n – X – ) + ΔΔHs (MtX n−+1 ) We see that the enthalpy of neutralisation in the gas phase for the fluoride is more positive by 19 kJ/mol than for the chloride. In solution, because the BF4¯ ion is smaller than the BCl4¯ ion, its enthalpy of solution is greater, so that ΔΔHs(MtX¯n+1) is also positive, which makes the enthalpy of neutralisation even more positive. Thus even without having numerical values for the ΔHs, we can account for the greater stability (with regard to neutralisation) of the pair of ions in which the anion is BF4¯. Put differently, these considerations show the advantages of small MtX¯n+1 ions and strong C–X bonds.

Table 2 Estimation of ΔΔHN2 for two boron halides F

Cl

Δ

D(Me-X)

493

334

159

E(X)

347

368

–21

D(BX3 -X¯)

359

160

199

X

201

Developments in the Theory of Cationoid Polymerisations From the data in Table 2 we obtain:

ΔΔHN 2 = –159 + (–21) + 199 + ΔΔHs (MtX n−+1 ) = 19 + ΔΔHs (MtX n−+1 ) The manner in which this method of selecting new initiators has been developed is shown in Section 3.4.

References 1.

F. R. Jones and P. H. Plesch, Journal of the Chemical Society, Dalton Transactions, 1979, 927.

2.

G. Turchi, F. Matera and P. Magagnini, Makromolekulare Chemie, 1973, 170, 75.

202

3.6

The Relation Between Reduction Potential and Solvation Energy for some Aryl Methylium Ions (1989) P. H. Plesch

This paper was first published in the Journal of the Chemical Society, Perkin Transactions II, 1989, 1139.

Prologue Starting in the late 1950s I had tangled with the very difficult subject of the UV-vis spectra of aryl cations and we had resolved the then confused problem of the spectrum of the α-phenylethyl (styryl) cation at least as far as the then available methods permitted (1-4). UV-vis spectroscopy and NMR spectroscopy were the only commonly used methods for studying such species and for what I had in mind neither was useful. I wanted to monitor the concentration of the organic cations involved in polymerisation at concentrations well below 1 mmolar, and for that NMR spectroscopy was useless and the utility, if any, of UV-vis spectroscopy was limited to aromatic ions. Thinking about electrical methods I ruled out conductivity and EMF measurements because they are non-specific, but decided to investigate polarography which was by far the most sensitive analytical method available. At Cambridge in the late 1930s I had encountered the beginnings of this technique in the Colloid Science Department. The equipment and indeed the ideas had been primitive, but having once struggled with both, I had kept an interest in that technique, and in the late 1950s I had introduced an experiment on polarography into the Physical Chemistry practical course at Keele with equipment which I had scrounged from a local foundry. What was involved there was, of course, conventional aqueous polarography. What I wanted to do was polarography in nonaqueous solutions, which at that time had received little attention. I adapted the equipment for use with methylene chloride solvent and tried to record the polarogram of the tryphenylmethylium ion in that solvent. The signals I got were so encouraging that I then got a research student and better equipment, and thus was started a research line which I carried on with a series of post-doctoral workers which continued until 1982; and that line of research acquired a life of its own (5). For various reasons we did not achieve my aim of doing polarography on polymerising solutions. However, in the course of these studies we accumulated data which provided new insights into the energetics of ions-in-

203

Developments in the Theory of Cationoid Polymerisations solution (3). That is why the present paper is included here, although it does not deal directly with any other aspects of cationic polymerisation. The paper contains several innovations in the interpretation of polarographic reduction potentials, E1/2. One is the recognition that the E1/2 obtained in the presence of baseelectrolytes is not that of an isolated, solvent-solvated cation, but of one which is part of an ion-pair or of a higher aggregate. A practically useful innovation is to use the E1/2 of the triphenylmethylium ion as the zero of the potential scale in all solvents. By means of this device one can compare a wide range of E1/2 differences in different solvents, and it is especially useful because that ion is stable in strongly acidic media in which the commonly used marker ferrocene decomposes.

References 1.

V. Bertoli and P. H. Plesch, Journal of the Chemical Society, (B), 1968, 1500.

2.

V. Bertoli and P. H. Plesch, Spectrochimica Acta, 1969, 25A, 447-465.

3.

Kabir-ud-Din and P. H. Plesch, Journal of the Chemical Society, Perkin II, 1978, 892. This paper also contains spectroscopic data on the same carbenium ions.

4.

S. D. Pask and P. H. Plesch, European Polymer Journal, 1982, 18, 939.

5.

See References 1 - 11 of the paper.

204

Relation Between Reduction Potential and Solvation Energy for some Aryl Methylium Ions

Abstract The polarographic half-wave potentials, E1/2, of arylmethylium ions in MeSO3H range from -0.275 V for Ph2HC+ to -0.955 V for (4-MeOC6H4)3C+, against the Hg/ HgSO 4/98% H2SO4 electrode. The narrowness of this span, equivalent to approximately 70 kJ mol-1, is explained in terms of the ionization potentials Ei of the corresponding radicals and the solvation enthalpies ΔHsθ of the ions. Since the factors which increase Ei also diminish ΔHsθ, the sum of Ei and ΔHsθ which determines E1/2, does not change much from one extreme of the array of ions to the other, although both terms may vary over a much greater range. A comparison of E1/2 for the three triarylmethylium ions in MeSO3H and CH2Cl2 shows that (a) as the charge becomes more diffuse, the difference between E1/2 for any one ion in the two solvents I and II, I-IIΔE1/2(R+), becomes smaller; and (b) the difference in E1/2 between two ions, A-BΔ E1/2 becomes smaller for a given solvent, the more polar that solvent. The value of E1/2 obtained in different solvents can be correlated by a new kind of diagram in which the origin of the axes represents the E1/2 of Ph3C+. For each of three very different ions the E1/2 values are almost identical in CH2Cl2 and MeCN; this can be attributed to the fact that E1/2 is not that of a free cation, but of a cation which is part of an ion pair or a higher aggregate, formed from the abundant supporting electrolyte. In the course of our polarographic studies on organic cations we determined the half-wave potentials, E1/2, for various arylmethylium ions [1-11]. The aim of the present work is to extract from these values some new information concerning the relative magnitude of their solvation enthalpies in three very different solvents. A comparison of our results [obtained in methanesulphonic acid (MSA) and dichloromethane (DCM)] with those of Volz and Lotsch [12] [obtained in cyanomethane (CM) solutions] yields some useful conclusions.

Results and Discussion E1/2 in MSA In MSA the ions listed in Table 1 give a single reduction signal (wave or peak, depending on the apparatus used), and as the corresponding E1/2 value depends slightly on the concentration of the precursor from which the ion is generated, all potentials are given for 10-3 mol dm-3 solutions [3]. This signal corresponds to reduction of the carbenium ion to the radical [2]:

R1 R 2 R 3 C + + e → R1 R 2 R 3 C •

(1)

205

Developments in the Theory of Cationoid Polymerisations The fate of the radical does not concern us here. The appropriate tests showed that the reductions are diffusion controlled, and the nα values in Table 1 show that most of the reductions are reversible or nearly so. The ranking of the ions in Table 1 is as expected, but the difference between E1/2 for the most reactive ion (No. 1) and the most inert ion (No. 12), amounts to only approximately 70 kJ mol-1. This first part of the discussion attempts to explain why this span is so unexpectedly small. We start with the well-known approximate identification of E1/2 with Eθ (the standard reduction potential of the ion measured against some arbitrary standard in the first instance (see the Appendix); and we relate E θ to ΔG θ for the reduction process (1), so that we obtain:

– FE1 / 2 ≈ – FE θ = ΔG θ

(2)

Further,

ΔG θ = ΔH θ – TΔS θ

(3)

Table 1 E1/2 values of carbenium ions in MeSO3H at approximately 295 K. [Ion] = 10-3 mol dm-3. Reference electrode: Hg/HgSO4/98% H2SO4 Ion number

Cation

-E1/2/V

nα

1

Ph2HC+

0.275

0.88

2

Ph2MeC+

0.565

0.92

3

Ph2(n-C3H7)C+

0.575

0.88

4

3-Methyl-l-phenylindan-l-yl

0.585

0.85

5

(4-ClC6H4)3C+

0.61

-

6

(4-MeOC6H7)2HC+

0.62

-

7

Ph3C+

0.635

1.0

8

(2-EtC6H4)PhMeC+

0.66

-

9

(2,4-Me2C6H3)3C+

0.70

0.69

10

(2-MeC6H4)3C+

0.745

0.80

11

(4-MeC6H4)3C+

0.745

1.0

12

(4-MeOC6H4)Ph2C+

0.82

-

13

(4-MeOC6H4)3C+

0.955

-

206

Relation Between Reduction Potential and Solvation Energy for some Aryl Methylium Ions

and

ΔH θ = ΔHsθ ( R + ) – Ei ( R • ) – ΔHsθ ( R • ) + Z ′

(4)

Here R+ is the carbenium ion from equation (1), ΔHsθ are solvation enthalpies, Ei(R•) is the ionization potential of radical R•, and Z′ includes all electro-energetic terms which do not depend upon the nature of R. If, to a first approximation, TΔSθ and ΔHs(R•) are taken to be independent of the nature of R and are incorporated into Z, then:

Z = Z ′ – ΔHsθ ( R • ) – TΔS θ

(5)

– FE1 / 2 ≈ ΔH θ = ΔHsθ ( R + ) – Ei ( R • ) + Z

(6)

and

This type of analysis is not new (see below) but, unlike some previous authors, we will refrain from attempting an absolute evaluation of Z and instead investigate what information can be extracted from a differential approach. If one writes equation (6) for two ions, A and B, in the same solvent and subtracts one from the other, one obtains for A-BΔE1/2, the difference between the half-wave potentials of the two ions, Equation (7):

– F A – B ΔE1 / 2 = ΔHsθ ( A + ) – Ei ( A • ) – ΔHsθ ( B) + Ei ( B• )

(7)

This equation helps us to understand why ΔE1/2 of the ions at the extremes of Table 1 is so relatively small: the reason is that those factors which reduce Ei, such as increasing

Table 2 E1/2 values for three ions in two solvents CH2Cl2 Ion

E1/2

(4–ClC6H4)3C+

0.6

Ph3C+ (4–MeOC6H4)3C+

} } 0.00

MeSO3H ΔE1/2/V

A-B

0.135

ΔE1/2/V

I-II

1.2 1 1.10

0.465

0.465

0.955

E1/2/V

} } –0.955 –0.61

ΔE1/2/V

A-B

0.025

–0.635

0.320

207

Developments in the Theory of Cationoid Polymerisations

Figure 1 The correlation between ET1/2 in MeSO3H and in CH2Cl2 (O) and MeCN (Δ) substitution by Me or MeO groups, do so by reducing the charge density at the central C-atom and therefore they also produce a reduction in the enthalpy of solvation, ΔHsθ(R+). Therefore, although both ΔHsθ and Ei for different ions can vary over a wide range, their difference changes only slightly. It is of course evident that if one could obtain the Ei values for any two radicals R•, the corresponding ΔΔHsθ could be calculated. It is curious that although most of the radicals of interest here could probably be generated simply by introducing the corresponding dimers into a mass spectrometer where they would dissociate into the required radicals, their ionization potentials do not appear to have been measured. A useful practical result of our work is that E1/2 of the triphenylmethylium ion was found to be a convenient reference potential for strongly acidic solutions as the ion is very stable under such conditions, for which, in fact, there is no other convenient standard.

Comparison of E1/2 in MSA and DCM Polarography in pure liquid acids such as MSA is relatively simple because the ions resulting from the self-ionization of the acid provide the conductivity needed, and the

208

Relation Between Reduction Potential and Solvation Energy for some Aryl Methylium Ions

main operating precautions required are the exclusion of oxygen (for electrical reasons) and of water (for chemical reasons). In solvents which do not self-ionise, (which means effectively all organic liquids which are not acids) polarography is more difficult because a supporting electrolyte is needed to provide adequate conductivity. The use of a supporting electrolyte, e.g., tetrabutyl ammonium perchlorate, introduces three complications: unless it is very rigorously dried, it will carry with it an important quantity of water; its nature and concentration influence the E1/2 (slightly); and, because its concentration is usually in the 10-1 mol dm-3 range, the polarographic reduction is no longer that of an isolated ion, but that of an ion which is part of an ion-pair or a higher aggregate. It should be possible to obtain E1/2 for unpaired ions either by Fleischmann’s technique [13] (which was published too late for the Keele Research Group, now dispersed, to make use of it), or by extrapolating E 1/2 obtained conventionally with varying concentrations of supporting electrolyte, to zero ionic strength. Table 2 contains E1/2 values for three ions in the two solvents MSA and DCM. Two effects are evident: (a) the minor effect is that I-IIΔE1/2 (difference between two solvents) becomes smaller as the charge becomes more diffuse; (b) a much stronger effect is that A-B ΔE1/2 (difference between two ions) is much smaller for the more polar solvent. As before, one can seek an explanation in terms of the energetics of the processes involved. The formulation of Equation (4) for ion A+ and the two solvents I and II yields equation (8) for the difference between the E1/2 values obtained for the same ion in the two solvents:

– FI – II ΔE1 / 2 ( A + ) = ΔHsθ ( A + )I – ΔHsθ ( A + )II + Z ′I – Z ′II – T [ ΔS θ ( A + )I – ΔS θ ( A + )II ](8) As before, the Z′ terms are independent of the nature of A + . The first, minor, effect, interpreted by equation (8), means that as the charge on the ions becomes more diffuse, the differences between the ΔHθs terms, i.e., between ΔHθs(A+)I ΔHθs(B+)I and ΔHθs(A+)II - ΔHθs(B+)II, becomes smaller, and so does the difference in the ΔSθ terms, which seems very plausible. The second, and major, effect means that in the more polar solvent, in which the ΔSθ values are relatively large, the change in ΔHθs accompanying the change of chargedensity from one ion to another is a relatively small change in a large quantity. By contrast, in the less polar solvent we are dealing with a relatively large change in a much smaller quantity.

209

Developments in the Theory of Cationoid Polymerisations

Normalization of E1/2 values In view of the useful interpretations which can be given to the differences in E1/2 values, an obvious step is to select the E1/2 of one convenient ion as a zero or reference point. We follow Taft [14] and Breslow [15] in selecting E1/2 for the triphenylmethylium (trityl) cation, as this ion is easy to procure and is stable under acidic conditions. It seems useful T to define a quantity E1/2 which is E1/2 of the species in question minus E1/2 of the triphenylmethylium ion measured under the same conditions of concentration, temperature, solvent, and nature and concentration of base electrolyte, and against the same reference electrode:

E1T/ 2 ≡ E1 / 2 ( R + ) – E1 / 2 ( Ph 3C + )

(9)

The advantage of this procedure is that one can make useful comparisons between sets of measurements obtained under a variety of conditions. An informative example of the method is presented in the next section. In practice, it is often convenient to add trityl cations to a solution of an ‘unknown’ as a marker; one must, however, beware of offering to the trityl cation a substrate from which it can abstract a hydride or other ion, with formation of a more stable cation [8].

Correlation of E1/2 obtained in different solvents Results obtained by ourselves on the ions 5, 7, 11 and 13 (see Table 1) in MSA and DCM, and by Volz and Lotsch [12] in CM, are listed in Table 3 and plotted in the Figure 1, normalised against E1/2 of the trityl ion, as suggested in the previous section. A T remarkable feature which emerges from this representation of the results is that E1/2 in

Table 3 E1/2 Values for three triarylmethyl ions in two solvents I (CH2Cl2) E1/2 (4-ClC6H4)3C+ Ph3C+ (4-MeOC6H4)3C+

210

II(MeCN) T 1/2

E

E1/2

T 1/2

E

T Δ E1/2

I-II

+0.60

-

+0.38

-

-

-

+0.14

-

+0.11

+0.03

+0.46

-

+0.27

-

-

-

–0.46

-

–0.47

–0.01

0.00

-

–0.20

-

-

Relation Between Reduction Potential and Solvation Energy for some Aryl Methylium Ions

DCM and CM seems to be independent of the solvent, despite the great difference in the dielectric constants, ε, of these solvents (DCM, ε = 9; CM, ε = 37), from which differences in ΔHθs and hence E1/2 would be expected. The reason is that the measured E1/2 value is not that of an isolated ion, but of one which is at least paired because of the high concentration of supporting electrolyte. If the free energy of the cation in solution is reduced by the Coulombic interaction resulting from ion-pairing, any further reduction by solvation of the resulting ionpair is a relatively minor effect in which the dielectric constant of the solvent is not a dominant factor. Nonetheless, the very fact that there is a correlation between the reduction potentials of the paired and unpaired ions indicates clearly that the near-neutralization of the cation by pairing does not obliterate, let alone reverse, the energetic differences between the cations.

Relation to earlier work The direct access to the electrical-energetic properties of an ion-in-solution which polarography and related electro-analytical techniques seem to offer, has invited many attempts to interpret the results in terms of fundamental energetic quantities, such as ionization potentials and solvation enthalpies. An early and seminal analysis by Case et al., [16] was followed up by an extension of the theory to various aromatic cations by Kothe et al. [17]. They attempted the absolute calculation of the solvation enthalpies of cations, molecules, and anions of the triphenylmethyl series, and our Equations (4) and (6) are derived by implicit arguments closely related to theirs, but we have preferred not to follow their attempts at absolute calculations. Such calculations are inevitably beset by a lack of data (in this instance especially the ionization energies of the radicals) and by the need for approximations of various kinds. For example, Kothe et al., attempted to calculate the electrical contribution to the solvation enthalpy by Born’s equation, applicable to an isolated spherical ion, uninhibited by the fact that they then combined it with half-wave potentials obtained for planar ions at high ionic strength. The relative stabilities of various carbenium ions in sulphuric acid were studied by Feldman and Flythe and discussed in terms of the energetics of ion formation [18]. However, their arguments are obscure, because they do not appear to define adequately the various energetic terms and seem to ignore solvation energies; moreover, they appear to be unaware of the near contemporary British [16] and German [17] work. These studies are also ignored by Wasielewski and Breslow [19] who used thermodynamic arguments to derive the basicity of various cyclopropenyl anions and the bond-dissociation energies of cyclopropenols from electrochemical measurements; they also included measurements on the trityl and tropylium cations. It appears therefore that although the fundamental basis of our considerations is not new, the use which we have made of the energetic analysis provides a better insight into the factors determining the electrochemical properties of organic cations; in other words it is heuristically more useful.

211

Developments in the Theory of Cationoid Polymerisations

Experimental The polarographic apparatus, reference electrodes, supporting electrolytes, solvent preparation, and preparation of the carbenium-ion solutions have been described in references 1-11 and 20. It is noteworthy that the reference electrode [9] described in 1978 maintained its EMF of -0.130 versus SCE until accidentally broken in 1983.

Appendix In view of the range of conclusions which will be derived from the ‘approximate identification of E1/2 with Eθ’ it is appropriate to clarify what is involved. We mean here that E1/2 = Eθ + x; the term x is omitted in the subsequent treatment because, as we will show below, it is both small and approximately constant under the relevant conditions. From the theory of polarography it follows that for reversible, one-electron systems

E1 / 2 = E θ ′ + ( RT / 2 F )ln( DR / DO )

(10)

where DR and DO are the diffusion coefficients of the reduced and oxidised forms of the electroactive species, and

E θ ′ = E θ + ( RT / 2 F )ln( γ O / γ R )

(11)

where γO and γR are the mean ionic activity coefficients of the reduced and oxidised electroactive species, respectively [21]. The shape and size of the tetrahedral triarylmethyl radical and of the propeller-shaped corresponding cation, even assuming that it carries one firmly attached solvent molecule, are very similar. For the present purposes, it is not necessary to assume that they are equal; we need only make the plausible assumption that their ratio is fairly constant, both when comparing a range of ions in one solvent and for one ion in several solvents. If we denote DR/DO by Q and combine Equations (10) and (11), we obtain: E1/2 − E θ = ( RT / F )lnQ1 / 2 γ O / γ R = x

(12)

Since Q is independent of the nature of the solvent and of the ion, lnQ1/2 is a constant, and probably very small, term for the reasons given above. The reduced species is the radical R• the activity coefficient of which, γOx, is close to unity. The oxidised species, at any rate in the organic solvents, is not the lone carbenium ion R+, but one that is part of an ion-pair because of the relatively high ionic strength

212

Relation Between Reduction Potential and Solvation Energy for some Aryl Methylium Ions

and the low polarity of the solvents. Therefore γR is also close to unity and probably does not vary much from one solvent to another. Therefore our initial assumption, that x is both small and constant, is seen to be justified.

Acknowledgements Thanks are due to all the collaborators cited in References 1-11 and to Dr. C. C. Corke for contributing to the stock of data used in this work; to the Harrison Memorial Fund of this University for the support of C. C. C.; to the Leverhulme Trust for help with the production of this paper; and especially to the SERC for the support of I.S., A.S., K.-ud-D., A.A.K., and G.E.H., and for providing much of the equipment.

References 1.

M. I. James and P. H. Plesch, J. Chem. Soc., Chem. Commun., 1967, 508.

2.

P. H. Plesch and I. Sestakova, J. Chem. Soc. B, 1970, 87.

3.

P. H. Plesch and I. Sestakova, J. Chem. Soc. B, 1971, 1337.

4.

P. H. Plesch, A. Stasko, and D. Robson, J. Chem. Soc. B, 1971,1634.

5.

P. H. Plesch and A. Stasko, J. Chem. Soc. B, 1971, 2052.

6.

P. H. Plesch and F. G. Thomas, J. Chem. Soc., Perkin Trans. II, 1975, 1532.

7.

Kabir-ud-Din and P. H. Plesch, J. Chem. Soc., Perkin Trans. II,1978, 892.

8.

Kabir-ud-Din and P. H. Plesch, J. Chem. Soc., Perkin Trans. II,1978, 937.

9.

Kabir-ud-Din and P. H. Plesch, J. Electroanal. Chem. Interfacial Electrochem., 1978, 93, 29.

10. G. E. Holdcroft, Kabir-ud-Din, and P. H. Plesch, J. Chem. Res. (S), 1980, 390. 11. G. E. Holdcroft, Kabir-ud-Din, A. A. Khan, and P. H. Plesch, J. Electroanal. Chem. Interfacial Electrochem., 1982, 139, 157. 12. H. Volz and W. Lotsch, Tetrahedron Lett., 1969, 27, 2275. 13. A. M. Bond, M. Fleischmann, and J. Robinson, J. Electroanal. Chem. Interfacial Electrochem., 1984, 168, 299.

213

Developments in the Theory of Cationoid Polymerisations 14. E. D. Jenson and R. W. Taft, J. Am. Chem. Soc., 1964, 86, 116. 15. R. Breslow and W. Chu, J. Am. Chem. Soc., 1970, 92, 2165. 16. B. Case, N. S. Hush, R. Parsons, and M. E. Peover, J. Electroanal. Chem. Interfacial Electrochem., 1965, 10, 360. 17. G. Kothe, A. Stuewe, and H. Baumgaertel, Tetrahedron, 1972, 28, 5957. 18. M. R. Feldman and W. C. Flythe, J. Org. Chem., 1978, 43, 2596. 19. M. R. Wasielewski and R. Breslow, J. Am. Chem. Soc., 1976, 98, 4222. 20. P. H. Plesch, High Vaccuum Techniques for Chemical Syntheses and Measurements, Cambridge University Press, Cambridge, 1989. 21. See, for example, A. J. Bard and L. R. Faulkner, Electrochemical Methods, Wiley, Chichester, 1980.

214

4

Theorising about Reaction Mechanisms

215

Developments in the Theory of Cationoid Polymerisations

216

4.1

Suggestions Concerning the Ionic Polymerisation of Vinyl Ethers (1950) S. D. Hamann, P. H. Plesch and H. A. Skinner

This paper was first published in the Scientific Proceedings of the Royal Dublin Society, 1950, 25, 131-164. Reproduced with permission of the Royal Dublin Society, copyright 1950.

Prologue This publication is the record of the papers given and of the discussions at a meeting convened in May 1950 at Trinity College, Dublin by D.C. Pepper which is usually referred to as the First International Cationic (occasionally just Ionic) Symposium (A). It is important in the history of polymer science because many important new ideas were discussed there, some for the first time. These included Dainton and Ivin’s theory of equilibrium polymerisations, co-catalysis (Plesch, Polanyi and Skinner), and the energetics of polymerisations. The present author made several contributions to that discussion, the most substantial of which was a joint theoretical paper which is reproduced here: This was his first venture into theorising about unexplained facts. Its central point is an extension of the new idea of co-catalysis and the application of a thermochemical argument to decide which of two reactions is the more likely. This type of argument, which goes back to M. Polanyi and M.G. Evans, was the ‘small change’ of the tea-room discussions in the Chemistry Department at the University of Manchester, where H.A. Skinner, a thermochemist, was the writer’s research supervisor and S.D. Hamann was a fellow research student working under A.G. Evans.

Reference A

Actually, this was the second public discussion on this subject. The first one was convened by M. Polanyi on 15th September 1945 at the University of Manchester. The Proceedings of that meeting were eventually published by the present writer (151). Polanyi, M. and Plesch, P.H., Symposium on Friedel-Crafts Catalysts and Polymerization (The Zeroth Ionic Polymerization Symposium) Notes and Records of the Royal Society, London, 1999, 53, 135-141.

217

Developments in the Theory of Cationoid Polymerisations Eley and Pepper [1] and Eley and Richards [2] have recently studied the kinetics of the catalysed polymerisation of vinyl ethers. The very simple formal scheme which accounts adequately for the kinetics of these reactions does not provide a definite picture of the mechanism of the reaction. Nor does the oxonium theory of Shostakovskii [3] appear adequate to explain the observations. Our suggested explanation of the observed facts arises from the following considerations. It is difficult to see how the presence of two double bonds in each polymer molecule (reported by Eley and Richards for the polymerisation of 2-ethyl hexyl vinyl ether) can be explained without assuming that the chain is started by an unsaturated entity, and that the second double bond is formed in the termination process. Since the chain growth is almost certainly a carbonium ion process the initiating entity must be a positive ion of some sort. We assume therefore that the ether is split into two ions under the influence of the catalyst. This may obviously occur in two different ways, but energetic considerations can show which of these will in fact take place.

Process I

R – OCH = CH 2 → R + + CH 2 = CHO –

This requires an amount of energy given by

E1 = D( R – OCH = CH 2 ) + I ( R ) – A(OCH = CH 2 ) Process II

RO – CH = CH 2 → RO – + CH 2 = CH +

requires

E2 = D( RO – CH = CH 2 ) + I (CH = CH 2 ) – A(OR )

where R represents the 2-ethyl hexyl radical, D is the bond dissociation energy, I the ionisation potential and A the electron affinity of the entity in brackets after the symbol. We now make the plausible assumption that the difference between the two electron affinities concerned is negligible compared with the differences in D and I. Writing V for the vinyl radical, we put

ΔD = D( R – OV) – D( RO – V) Therefore

E1 – E2 = I ( R ) – I (V) + ΔD If this is negative, i.e., if more energy is required for Process II than for Process I, the latter will be more likely.

218

Suggestions Concerning the Ionic Polymerisation of Vinyl Ethers (1950) We can estimate ΔD as follows: The two bond dissociation energies are given by

D( R – OV) = D1 (O – C) – R( R ) – R(OV) D( RO – V) = D2 (O – C) – R(OR ) – R(V) where D1(O – C) and D2(O – C) are standard or normal bond energies and are assumed to be equal to a first degree of approximation. The R terms are the resonance energies of the radicals indicated in brackets. Therefore

ΔD = R(OR ) – R(OV) + R(V) – R( R ) R(V), R(R), and R(OR) are probably small, but R(OV) is likely to be relatively large, since the O – CH=CH2 radical is similar electronically to the allyl radical. Because of the dissymmetry of the resonance structures A and B •

O = CH – C H 2 A

•

O – CH = CH 2 B

the resonance energy may not be as large as in the allyl radical itself, and we may estimate it at about half of this. If we take the resonance energy of the allyl radical as about 20 kcal/mole we get for R(OV) about 10 kcal/mole. R(OR) – R(R) will certainly not be large enough to offset this if it is positive, or to increase it appreciably if it is negative. We thus arrive at an estimate of –10 kcal/mole for ΔD. I(V) is known to be 228 kcal/mole [4]. The ionisation potential of the 2-ethyl hexyl radical is not known, but we may estimate that it is unlikely to differ materially from that of the npropyl radical, which is 180 kcal/mole [5]. Therefore El – E2 = 180 – 228 – 10, i.e., approximately –60 kcal/mole. This difference is so large that we consider the results of our argument to be unaffected by any possible differences in the heats of coordination of the alternative oxygen-containing fragments with the catalyst, and by possible differences in the heats of solution of the alternative ions. These considerations therefore indicate strongly that Process I will actually take place. That vinyl allyl ethers do, in fact, split in the manner postulated above is suggested by the occurrence of butyl benzene in the products of reaction of vinyl butyl ether and benzene in presence of AlCl3 [6]. No styrene is formed. The whole reaction by which the initiating ion is formed may be pictured as taking place as in Figure 1.

219

Developments in the Theory of Cationoid Polymerisations

(I) CH = CH2

(II) CH = CH2

SnCl4 + O

SnCl4

O R′

CH2•CH•C4H9 C2H5 (CH2 = CHO•SnCl4)-

+ C4H9CH•CH2

+

(III)

C2H5

(IV)

+ C4H9•C•CH3 (V) C2H5

O – SnCl-4

SnCl4 + R•CH2•CHO

R•CH2•C+

+ CH2 = CH•O•R′

H

(VII)

(VI)

SnCl-4 O

O•R′

R•CH2•C•CH2•C+

(VIII)

H

H

O•R′ R•CH2•CH=•CH•C+ H

H Figure 1

220

HO•SnCl-4

(IX)

Suggestions Concerning the Ionic Polymerisation of Vinyl Ethers (1950) The ether-catalyst complex (II) splits into a complex anion (III) and a carbonium ion (IV), which rearranges to the configuration of maximum stability (V). This carbonium ion (V) could itself initiate polymerisation, but it is more likely that it attacks the double bond of the closely associated anion (III), giving the double ion (VI) in equilibrium with the aldehyde (VII). Rearrangements of the type (I)–(VII) have been observed for vinyl ethers [7], and a closely parallel isomerisation is that of isobutyl phenyl ether into paratertiary butyl phenol under the influence of AlCl3 [8]. It is unlikely that the steps from (II) to (VI) take place in a well defined succession. The process probably proceeds by a single intramolecular transformation. It is considered that the rate determining step in the initiation process is the attack of the positively charged carbon atom of (VI) upon a monomer molecule to give (VIII). This double ion must then, or at an early stage in the polymerisation, rearrange to the associated ions (IX), if the charge separation is not to become too great. The configuration of the growing polymer chain is therefore:

OR′

OR′

OR′

R•CH2—CH = CH—CH—[—CH2—CH—]n CH2—CH+ HOSnCl4The termination takes place by the loss of a proton from the polymer chain, leaving a double bond and forming the catalyst monohydrate, thus:

R ⋅ CH 2 ⋅ CH = CH KKKKKCH = CHOR ′ + SnCl 4 ⋅ H 2 O

(X)

Aldehydes of the type (VII) are effective reagents in Friedel-Crafts condensations, and it has been reported that in some conditions diolefines are formed from aldehydes and olefines in the presence of BF3 and water [9]. This latter process is analogous to the reaction (VII) → (X). This scheme gives a rate of initiation which is of the first order in monomer if the concentration of (VII) depends only on the SnCl4 concentration (monomer in great excess). It also accounts for the observed unimolecular termination, because in a hydrocarbon solvent the ions cannot be separated, and it explains the presence of two double bonds per polymer molecule. According to the suggested mechanism the monomer itself acts as cocatalyst, so that this reaction can now be regarded as a special case of the ionic hydrocarbon polymerisations. The indifference of the initial reaction rate to the presence of water (2) also becomes intelligible in terms of the suggested reaction scheme. Moreover, the slow increase in the reaction rate observed with the n-butyl vinyl ether (but not with the 2-ethyl hexyl ether) which was ascribed to a slow increase in the number of growing polymer chains (I) may find a more detailed explanation in the following terms. The initial formation of the carbonium ions analogous to (V) will probably be much slower for the n-butyl vinyl ether than for the 2-ethyl hexyl vinyl ether, so that the

221

Developments in the Theory of Cationoid Polymerisations formation of the chain-initiating species will be slow and possibly rate-determining. This condition has been shown by Plesch [10] to account for the S-shaped reaction curves found in other ionic polymerisations.

References 1.

D. D. Eley and D. C. Pepper, Transactions of the Faraday Society, 1947, 43, 112.

2.

D. D. Eley and A. W. Richards, Transactions of the Faraday Society, 1940, 45, 425.

3.

M. F. Shostakovskii, Doklady Akad. Nauk SSSR, 1943, 41, 120.

4.

D. P. Stevenson, JACS, 1943, 65, 209.

5.

A. G. Evans, Transactions of the Faraday Society, 1946, 42, 719.

6.

V. V. Korshak, K. K. Samplavskaya and A. I. Gershanovich, Journal Gen. Chemistry, 1946, 16, 1065, Chemical Abstracts, 41, 2715.

7.

C. D. Hurd, and M. A. Pollak, Journal of Organic Chemistry, 1938, 3, 550.

8.

C. Hartmann and L. Gattermann, Ber., 1892, 25, 3531.

9.

R. Rosen and E. Arundale, US Patent 2368494, (1945). Chemical Abstracts, 39, 4529.

10. P. H. Plesch, J.C.S., in the press.

222

4.2

Developments in the Theory of Cationic Polymerization, Part I (1951) P. H. Plesch

This paper was first published in Journal of Applied Chemistry, 1951, 1, 269-272. reproduced with permission from John Wiley and Sons, copyright 1951.

Prologue This paper was presented at the Symposium on ‘Polymer Chemistry as Applied to Plastics’ on the 22nd of September 1950. In it the author recognises the possible types of reaction by which a co-catalyst may initiate polymerisation in a mixture of an alkene and a metal halide. It is stated, probably not for the first time, that the hydrogen halides, HX, do not form protonic acids with metal halides, but nonetheless these ghosts kept on spooking around the literature for decades, and they have still not been exorcised completely. The suggestion that alkyl halides can act as co-catalysts is recognised as stemming from D. C. Pepper, but it goes back to the work of F. Fairbrother on the ionisation of trityl halides by metal halides. An incorrect statement to the effect that there is no evidence for the complexing of double bonds with hydrogen halides must be corrected. This writer himself has quoted several times the demonstration by O. Maas and his collaborators that the HX (X = Cl, Br) do form complexes with alkenes [A, B].

References A. O. Maas, Journal of the American Chemical Society, 1924, 46, 2664. B. O. Maas, Journal of the American Chemical Society, 1925, 47, 283.

223

Developments in the Theory of Cationoid Polymerisations

Abstract The polymerization of olefins by metal halides is discussed with special emphasis on the role of the co-catalyst in these reactions. A new extension of the existing theory is proposed to account for some hitherto inexplicable observations, especially those relating to the effect of hydrogen halides on various polymerization systems. It is suggested that the carbonium ion which starts the polymerization may be formed by either of two essentially different reactions, depending on the nature of the catalyst, co-catalyst and monomer. In one class of reactions the monomer reacts with a catalyst/co-catalyst complex, in the other the co-catalyst reacts with a monomer/catalyst complex. In both cases a carbonium ion and a complex anion are formed. In recent years appreciable progress has been made in the investigation of ionic polymerizations, and the cationic or carbonium-ion polymerizations of olefins are now clear in their fundamentals, though certainly not in all their very varied detail. In this discussion we shall be concerned mainly with olefin polymerizations catalysed by metal halides of the Friedel-Crafts type. Following the ideas of Whitmore [l] these can be interpreted in terms of the reactions and properties of carbonium ions. (The first approach to this concept in aliphatic chemistry must probably be ascribed to Prins [2].) That the reaction chains are propagated by carbonium ions is now universally agreed, though the exact mechanism in individual instances is still a matter for controversy [3]. For the termination of the reaction chains, which is closely related to the phenomena of inhibition and poisoning [4-7], there are at least three different mechanisms which have been discussed recently [810]. The whole subject has been reviewed by several authors [11-16]. In the present paper we are concerned principally with the initiation step. The new observations and suggestions regarding this step put forward by Polanyi and his collaborators [17-21] marked the first real practical and theoretical advance since the work of Whitmore. They found that in the polymerization of isobutene by TiCl4 or BF3, both at room temperature and at very low temperatures, the metal halide alone was inactive, and that a third component, the co-catalyst, was required to initiate the polymerization. The word ‘co-catalyst’ was chosen for the substances concerned, by analogy with ‘co-enzyme’. It is to be preferred to the term ‘promoter’, often used by American workers, as this indicates a substance which speeds up a reaction which would also take place in its absence, and since the characteristic of co-catalysts is that they are essential to the reaction. The first co-catalyst to be discovered was water, but shortly afterwards certain alcohols and acids were found to act in a similar manner. An analogous phenomenon is of course familiar to organic chemists in the Friedel-Crafts reaction, and it had also been observed in metal halide-catalysed polymerizations on at

224

Developments in the Theory of Cationic Polymerization, Part I (1951) least two previous occasions [22, 23b] (discussed by Plesch [12]) but was not followed up. It has since been confirmed for other polymerization systems [6, 24] and the same phenomenon was found in the closely related alkylations and isomerizations catalysed by metal halides [25, 26]. The available data are collected in Table 1. It is important to note that there is no single instance on record where it has been shown unequivocally that an olefin has been polymerised by a metal halide alone, i.e., in the absence of a third substance which is potentially ionogenic under the conditions of the reaction. According to the current theory, the metal halide reacts with the co-catalyst to give a complex acid, e.g.

TiCl 4 + CCl 3 ⋅ CO 2 H → TiCl 4 ⋅ O 2 C ⋅ CCl 3– H + Table 1 Monomer

Catalyst

Temperature °C

Solvent, etc.

Proved co-catalysts

1. Ethylene

AlCl3

10–50

50 atm.

H2O, HCl [22]

2. Propene

AlBr3

–78

n-Butane

HBr, EtBr [24]

3. isoButene

BF3

Room

Gas-phase*

H2O [18], tert.-BuOH [18] Et2O [9a], CH3 COOH [21b]

4. isoButene

B F3

–100

No solvent

H2O [9b]

5. isoButene

TiCl4

–100 - +20

Hexane

H2O [19], di- and trichloroacetic acids [10], H2SO4 [20]

6. isoButene

SnCl4

–80

EtCl

H2O [6], HCl [39]

BF3

Room

Gas-phase*

H2O [21c], CH3•CO2H [21d]

8. Styrene

SnCl4

25

CC l 4

H2O (?) [23b]

9. Styrene

SnCl4

25

EtCl

H2O, HCl [38]

10. Styrene

SnCl4

25

(CH2Cl)2

Solvent (?) [29]

11. Styrene

TiCl4

–60 - +20

Hexane, toluene

CCl3•CO2H, (CH2Cl)2 [30]

12. Styrene

TiCl4

–30 - +30

(CH2Cl)2

Solvent (?) [30]

7. Diisobutene

* The polymerization of the gaseous monomer actually takes place in the polymer droplets, not in the gas phase

225

Developments in the Theory of Cationoid Polymerisations which donates a proton to the olefin, converting it into a carbonium ion:

R1 | H + CH 2 : CR1R 2 → CH 3 ⋅ ⋅ C + |

R2 This carbonium ion adds on to the double bond of the next monomer molecule, regenerating the carbonium ion, and thus the chain grows:

R1 R1 R1 | | | CH 3 ⋅ C ⋅ C H 2 ⋅ CKKKKKCH 2 ⋅ C + | | | R2 R2 R2 Chain propagation may stop either through the loss of a proton to the complex anion, which for energetic reasons must remain close to the carbonium ion [9, 10], or to a monomer molecule, leaving the chain with a terminal double bond. Or the ion-pair at the growing end of the chain may rearrange itself to a neutral molecule with regeneration of the metal halide. The rates of chain initiation and termination and the occurrence and rate of chain transfer may be profoundly affected by the nature of the co-catalyst. The co-catalysts may be divided into several groups: a) The first co-catalysts to be discovered were those which form a complex strong acid by co-ordinating on to the metal halide, e.g., TiCl4 and trichloroacetic acid [10], BF3 and tert.-butyl alcohol [18], SnCl4 and water [6].

AH + MX n → MX n A – H + The complex acids thus formed are closely similar to sulphuric, hydrofluoric and aluminosilicic acid, all of which will catalyse olefinic polymerizations. b) Alkyl halides RX in the presence of metal halides MXn form esters of the hypothetical acids HMXn+1, and these esters are partially ionised [27], R+MX-n+1. The co-catalytic activity of alkyl halides is presumably due to the initiation of polymerization by the R+ ions. This type of reaction may be regarded as a special case of alkylation. It is closely analogous to the polymerization of vinyl ethers by triphenylmethyl chloride alone [28]. The polymerization of styrene by SnCl4 in CH2Cl•CH2Cl was found to proceed in the absence of water, and was tentatively explained on the basis of cocatalysis by the solvent [29]. This suggestion is now supported by recent experiments with the system styrene–TiCl4–CH2Cl•CH2Cl [30]. The residual reactivity which was

226

Developments in the Theory of Cationic Polymerization, Part I (1951) found in the system isobutene–EtCl–SnCl4 in the absence of deliberately added cocatalyst even after intensive purification [6] might possibly be due to the small but finite concentration of Et+ ions to be expected in this system, and not to adventitious impurities. This supposition is supported by the S-shape of the reaction curve under these conditions, since it has been shown [10] that S-curves may be due to slow initiation and a gradual build-up of the concentration of growing chains as the initiating species is formed by the slow shifting of an equilibrium. With respect to the co-catalytic activity of alkyl halides, BF3 occupies a special position, since these (other than fluorides) cannot form complexes with BF3 for steric reasons. It has indeed been found [31a] that in MeCl solution the n-butenes are not polymerised by BF3. MeCl cannot act as co-catalyst in this system and some other (e.g., SO2) was required. The mode of action of SO2 is still obscure, but it is possible that H2SO3 was the real co-catalyst. c) The hydrogen halides present certain unusual and interesting features as co-catalysts. In some systems they do act whereas in others they are inactive, or may even inhibit the reaction (Table 2). Furthermore, whereas all the other co-catalysts considered above form complexes with the metal halides, it is known that the acids HBF4, HBF3Cl, HAlBr4 do not exist as independent species [32, 33], and there is no evidence that the halides of tin and titanium behave differently in this respect [34, 35].

Table 2 Monomer

Catalyst

Temperature °C

Solvent

Effect of HX

22

Ethylene

AlCl3

10–50

50 atm.

HCl: co-catalyst

24

Propene

AlBr3

–78

n-Butane

HBr: co-catalyst

39

isoButene

SnCl4

–80

EtCl

HCl: co-catalyst

19

isoButene

TiCl4

–70

Hexane

HCl has no cocatalytic effect

21c

Diisobutene

BF3

Room

Gas-phase*

HCl has no cocatalytic effect

7

Styrene

SnCl4

25

CCl4

HCl at high concn. reduces mol. wt.

38

Styrene

SnCl4

25

EtCl

HCl: accelerates polymerization

Reference

* See footnote to Table 1

227

Developments in the Theory of Cationoid Polymerisations Since the initiation reaction is hardly likely to be termolecular, and since in hydrocarbon solution at least, the metal halide and the HX do not interact, we are driven to the conclusion that either the metal halide or the HX form a complex with the monomer, and that the reaction of this complex with the third component starts the polymerization chain. There is much circumstantial evidence that aluminium halides can form complexes with double bonds, but unfortunately a rigorous investigation of this interesting phenomenon does not appear to have been made. On the other hand, there is some evidence against, and no evidence for the formation of such complexes by BF3 [9, 31b]. One would expect that in this respect the tin and titanium halides would resemble BF3 rather than AlX3, but here is no evidence on this point. The fact that the aluminium halides alone are dimeric fits well into this picture. The high residual affinity of the AlX3 molecule makes the complex formation with electron-donor groups very plausible, and suggestions to this effect are to be found in the older literature [36]. For the formation of complexes between double bonds and hydrogen halides there is no satisfactory experimental evidence. Thus we propose to divide the polymerizations of olefins by metal halides into two classes: I) Those systems in which the catalyst forms a complex with the co-catalyst (B, Ti, Sn halides acting on alkenes). II) Those systems in which the catalyst forms a complex with the monomer (Al halides with olefins in general; B, Ti, Sn and some other halides with arylenes). Class I is covered by the current theory. The Class II reactions can be explained on the assumption that although the acids HMXn+1 have no independent existence, HX can react with the olefin–MX complex to give a carbonium ion and MXn+1. Since the halides of B, Ti and Sn form complexes neither with a double bond nor with the hydrogen halide, the latter cannot be expected to act as co-catalyst in the polymerization of alkenes. The polymerization of aromatic olefins belongs to Class II for both types of metal halide if the co-catalyst is HX, but in this case the metal halide will probably be complexed not with the double bond but with the aromatic part of the molecule. Such complexes have been shown to exist in many different systems [37]. Provided that the aromatic ring is sufficiently close to the double bond the HX can react simultaneously with the metal halide complexed on to the aromatic ring and with the adjacent double bond to form the MX–n+1 and carbonium ions. For co-catalysts other than HX, polymerization might proceed by either or both mechanisms. Since the polymerization of arylenes is sensitive to HCl [23, 38], the study of these monomers is technically more difficult than that of the alkenes, because of the extremely dry conditions required. The difficulty of obtaining reproducible results for the styrene–

228

Developments in the Theory of Cationic Polymerization, Part I (1951) SnCl4 system in hydrocarbons [29, 30] or CCl4 [23] can probably be directly ascribed to the presence of variable amounts of moisture and, in CCl4 of co-catalytic alkyl halides. Finally it is necessary to account for the co-catalytic activity of HCl in the system isobuteneSnCl4–EtCl [39], which is in contrast with its inactivity in the system isobutene-TiCl4– hexane [19]. The fact that the reaction

MX n + HX → H + MX n– +1 does not proceed in the absence of a proton acceptor indicates that the halogen atoms bound to a metal are apparently unable to ‘solvate’ the proton sufficiently for this highly endothermic reaction to become energetically favourable. But in a polar medium such as EtCl the proton could be solvated by the solvent, so that ion-formation, and thus polymerization, could take place.

References 1.

F. C. Whitmore, Industr. Engng. Chem. 1934, 26, 94.

2.

H. J. Prins, Rec. Trav. Chim. Pays-Bas 1932, 51, 1065.

3.

F. R. Mayo and C. Walling, J. Amer. Chem. Soc., 1949, 71, 3845.

4.

R. M. Thomas, W. J. Sparks, P. K. Frolich, M. Otto and M. Mueller-Cunradi, J. Amer. Chem. Soc., 1940, 62, 276.

5.

C. Horrex and F. T. Perkins, Nature, Lond., 1949, 163, 486.

6.

R. G. W. Norrish and K. E. Russell, ibid. 1947, 160, 543.

7.

G. Williams and H. Thomas, J. Chem. Soc. 1948, 1867.

8.

F. S. Dainton and G. B. B. M. Sutherland, J. Polymer Sci. 1949, 4, 37.

9.

a. A. G. Evans and G. W. Meadows, ibid. 1949, 4, 359. b. A. G. Evans and G. W. Meadows, Trans. Faraday Soc., 1950, 46, 327.

10. P. H. Plesch, J. Chem. Soc., 1950, 543. 11. R. G. Heiligmann, J. Polymer Sci. 1949, 4, 183. 12. P. H. Plesch, Research 1949, 2, 267. 13. Symposium on Friedel-Crafts Polymerization, Proc. Roy. Dublin Soc., 1950, 25, 131.

229

Developments in the Theory of Cationoid Polymerisations 14. L. Schmerling and V. N. Ipatieff, Advances in Catalysis, 1950, Vol. II, Chapter 2 (New York: Academic Press). 15. C. Walling, E. R. Briggs, W. Cummings and F. R. Mayo, J. Amer. Chem. Soc., 1950, 72, 48. 16. F. R. Mayo and C. Walling, Chem. Rev., 1950, 46, 191. 17. A. G. Evans, D. Holden, P. Plesch, M. Polanyi, H. A. Skinner and M. A. Weinberger, Nature, Lond., 1946, 157, 102. 18. A. G. Evans and M. Polanyi, J. Chem. Soc., 1947, 252. 19. P. H. Plesch, M. Polanyi and H. A. Skinner, ibid., 257. 20. P. H. Plesch, Nature, Lond., 1947, 160, 868. 21. a. A. G. Evans, G. W. Meadows and M. Polanyi, Nature, Lond., 1946, 158, 94. b. A. G. Evans, G. W. Meadows and M. Polanyi, Nature, Lond., 1947, 160,869. c. A. G. Evans and M. A.Weinberger, Nature, Lond., 1947, 159, 437. d. M. A. Weinberger, Ph.D. Thesis, Manchester 1947. 22. V. N. Ipatieff and A. V. Grosse, J. Amer. Chem. Soc., 1936, 58, 915. 23. a. G. Williams, J. Chem. Soc., 1938, 246. b. G. Williams, ibid., 1046. c. G. Williams, ibid, 1940, 775. 24. C. M. Fontana and G. A. Kidder, J. Amer. Chem. Soc., 1948, 70, 3745. 25

a. H. Pines and R. C. Wakher, J. Amer. Chem. Soc., 1946, 68, 595. b. H. Pines and R. C. Wakher, J. Amer. Chem. Soc., 1946, 68, 599.

26. O. Grummitt, E. E. Sensel, W. R. Smith, R. E. Burk and H. P. Lankelma, ibid. 1945, 67, 910. 27. F. Fairbrother, J. Chem. Soc., 1941, 253. 28. D. D. Eley and A. W. Richards, Trans. Faraday Soc., 1949, 45, 425. 29. D. C. Pepper, ibid. 1949, 45, 397. 30. P. H. Plesch, unpublished.

230

Developments in the Theory of Cationic Polymerization, Part I (1951) 31. a. R. L. Meier, Private Communication. b. R. L. Meier, J. Chem. Soc., 1950, 3656. 32. H. S. Booth and D. R. Martin, ‘Boron Trifluoride and its Derivatives’ 1949 (New York: J. Wiley and Sons Inc.; London: Chapman and Hall). 33. C. M. Fontana and R. Herold, J. Amer. Chem. Soc., 1948, 70, 2881. 34. a. R. E. Engel, C.R. Acad. Sci., Paris 1886, 103, 213. b. K. Seubert and E. Schürmann, Ber. Dtsch. Chem. Ges. 1887, 20, 793. 35. T. O. Konig and O. F. v. d. Pforten, ibid. 1888, 21, 1711; 1889, 22, 1485. 36. W. H. Hunter and R. V. Yohe, J. Amer. Chem. Soc., 1933, 55, 1248. 37. a. e.g. H. V. Euler and H. Willstadt, Arkiv Kemi Mineral. Geol. 1929 [B], 10, (9), I ; Chem. Abs. 23, 4465. b. J. F. Norris and D. Rubinstein, J. Amer. Chem. Soc. 1939, 61, 1163. c. Tadatomo Asaoka, J. Chem. Soc. Japan 1943, 64, 541 ; Chem. Abs., 41, 3742. d. M. H. Dilke, D. D. Eley and M. J. Perry, Research, 1949, 2, 538. e. R. E. van Dyke, J. Amer. Chem. Soc. 1950, 72, 3619. 38. S. S. Medvedev and A. R. Gantmakher, Zhur. Fiz. Khim., 1949, 23, 516. Chemical Abstracts, 43, 7295. 39. K. E. Russell, Ph.D. Thesis, Cambridge 1947, Private Communication.

231

Developments in the Theory of Cationoid Polymerisations

232

4.3

Developments in the Theory of Cationic Polymerization. Part II (1954) P. H. Plesch

This paper was first published in the Journal of Polymer Science, 1954, 12, 481-487. Reproduced with permission from John Wiley & Sons, NY, USA. Copyright 1954.

Prologue The main subject treated is the various types of chain-breaking (although this collective term is not used yet). Very clear distinctions are made between termination, which is the irreversible destruction of the growing end of the polymer chain and transfer reactions in which the physical chain is broken, but the kinetic chain persists. Both types of reaction can occur in several ways. These terms and definitions originated from the radical polymerisations. Unfortunately, they were not adopted consistently by all practitioners, and Overberger’s group at Brooklyn Polytechnic muddied the water further by using the term ‘molecular termination’ for the alkylation of (mostly) aromatic compounds by growing polymer chains, which actually involves the transfer of a proton from the alkylated molecule to a monomer molecule, thus starting a new physical chain and preserving the kinetic chain. Various reversible chain-breaking reactions between the growing cations and the various kinds of complex anions are discussed for the first time in some detail. It is also emphasized that terminations, i.e., irreversible chain-breaking, may be rather rare.

Introduction The experimental evidence which has accumulated in recent years shows that in every system which has been rigorously investigated the polymerization of olefins by metal halides depends upon the presence of some third substance, the co-catalyst [2-8]. The function of the cocatalyst is to provide the ions which start the polymerization proper, by forming an ionogenic complex with the metal halide. In most systems the metal halide is not consumed in the course of the reaction, so that the term ‘catalyst’ in its classical sense may be retained in this respect. Exceptions to this are some polymerizations involving aluminum halides: in the polymerization of propene [9], and possibly of styrene and α-methyl styrene [10], these catalysts may be inactivated by the formation of stable complexes. In other cases, such as the

233

Developments in the Theory of Cationoid Polymerisations commercial process for the production of butyl rubber, the AlCl3 is apparently consumed by being occluded in the flocs of polymer which are precipitated during the reaction. On the other hand, the very nature of the co-catalytic function implies that at least a part of the co-catalyst molecule is consumed in the course of the reaction. In other words, of the ions formed by interaction of catalyst and co-catalyst, the cation must, and the anion may be incorporated in the polymer, e.g., whenever an acid is the co-catalyst, the proton is transferred during the initiation reaction to a monomer molecule which then forms the first link in the chain. The anion may or may not become attached to the end of a polymer molecule in a termination reaction. Similarly, when an alkyl halide acts as co-catalyst [6, 11], the alkyl cation necessarily forms the start of a chain, and a halide ion may be incorporated in a termination reaction. Thus, our present picture of the initiation process in these cationic polymerizations is based upon the reaction of catalyst and co-catalyst to form an ionizable complex. In media of low DC the ions must remain together as an ion pair [5, 12]. In solvents of high DC the ions may separate and form distinct kinetic entities [13, 14]. The cation then adds on to the first monomer molecule forming a new ion, this adds on to the next monomer molecule, regenerating the ion, and thus propagation proceeds. Although this synoptic picture of the propagation is generally agreed, the details of the mechanism are by no means clear for all systems. In contrast to the initiation and propagation steps, the termination and transfer reactions are still rather obscure. This is due as much to the great variety of reactions which can take place in ionic systems as to the very considerable experimental difficulties.

The termination step In the present context the word ‘termination’ is applied not to the breaking-off of a physical chain, i.e., the cessation of growth of a particular molecule, but to the complete destruction of a kinetic unit, which means the irreversible annihilation of one ion pair. This kinetic termination, which is a well-understood feature of radical polymerizations, is a comparatively rare event in cationic polymerizations; it may occur in several different ways and in some systems not at all. The mutual termination of growing chains which prevails in radical polymerizations must be ruled out for all ionic systems in which the opposite ions form separate kinetic units because of the electrostatic repulsion between like ions. However, in solvents of low DC in which the growing end of the polymer chain consists of an ion pair, a mutual termination by interaction of two such ion pairs is at least conceivable.

234

Developments in the Theory of Cationic Polymerization. Part II (1954) The reaction which was suggested in earlier papers as a probable termination mechanism involves the removal of a proton from the growing chain:

CH3 ...CH2 — C+

TiCl4OH– →

CH3

...CH2 • C = CH2 + TiCl4OH–H+

(I)

CH3

This is the reverse of the initiation reaction. Although several authors have favoured it, it has recently been shown to be very improbable, at any rate in media of low DC, for energetic reasons [15]. Even if it did take place it would not be a termination reaction in the present sense, since the catalytic species is regenerated. An alternative reaction for the same system leads to the formation of:

CH2 ...CH2 — C — OH → TiCl4

(II)

CH3 The metal halide will stay bound to the oxygen atom, and since tert-butanol does not act as co-catalyst in the system TiCl4–isobutene [16], the complex (II) will not be catalytically active. This, therefore, would be a true termination. With BF3 and isobutene, however, tert-butanol does act as co-catalyst [2], so that the analogous complex would be catalytically active. This presumably means that the equilibrium:

CH3 ...CH2 — C — OH → BF3 CH3

CH3

↔ ...CH2 — C+ BF3OH-

(III)

CH3

does not lie very far to the left. It was found, in fact, that in this system there does not appear to be a kinetic termination. Thus the same reaction which represents a termination with TiCl4 does not do so with BF3. Another possible reaction in these systems, which is a variant of reactions (II) and (III), can be represented thus:

235

Developments in the Theory of Cationoid Polymerisations

RC + MX n OH − ↔ RCX + MX n −1OH

(IV)

Whether in any particular case it represents a termination depends upon the position of the equilibrium. It is probably responsible for the small quantities of halogen which are always found in polymers produced under conditions where the only halogen compound present was the catalyst [17]. If an acid is used as co-catalyst instead of water, the analogue of reaction (II) is the formation of an ester. For the system isobutene–TiCl4-CCl3COOH in hexane solution it has been shown that reaction may cease through exhaustion of the co-catalyst [12] and that the termination reaction implicit in this phenomenon involves the formation of polyisobutyl trichloroacetate [18]. In other words, the ion pair at the growing end of the chain isomerizes to give an ester. An analogous termination reaction involving the monomer is also possible [12]:

K(CH 3 )2 C + TiCl 4 ⋅ O 2 CCCl 3– + CH 2 = C(CH 3 )2 →

TiCl 4 ↑ K(CH 3 ) ⋅ C = CH 2 + (CH 3 )3 ⋅ C ⋅ O 2 ⋅ CCl 3

(V)

Whether and under what conditions this takes place, remains to be seen. An entirely different type of termination mechanism has been proposed to account for the cessation of polymerization in the system propene–AlBr3–HBr through exhaustion of the catalyst [9]. It is suggested that by the transfer of a hydride ion, and then of a proton, an allylic ion:

CH3 CH3 R — C . . . . CH . . . . C — H AlCl4- δ+ δ+ is formed, which is too stable to propagate the reaction, and thus inactivates one equivalent of AlCl4-. This type of termination should be possible for all 1-olefins [19], and it may explain the observation that in the polymerization of styrene by AlCl3 the reaction may cease through consumption of the catalyst [10]. This fact and its present interpretation provide additional support for the contention [1] that there is a fundamental difference between the mode of action of the aluminum halides and of the group IV halides, since there is no evidence that the polymerization of styrene consumes the catalyst when this is

236

Developments in the Theory of Cationic Polymerization. Part II (1954) SnCl4 or TiCl4 [11, 13, 20, 21]. On the contrary, the experiments show that in the system styrene–TiCl4-(CH2Cl)2 there is no termination at all, since successive portions of styrene added to the same solution of TiCl4 in (CH2Cl)2 polymerized at the same rate [11]. This means that the concentration of the catalytic species remained constant. There is evidence to show that in this system polymerization is initiated by Cl•CH2•CH2+ ions. The same phenomenon was found in the polymerization (to dimers and trimers) of transstilbene by TiCl4–CCl3COOH in benzene [8]. In this case chain initiation is presumably by protons, and there appears to be no kinetic termination at all. The foregoing discussion has shown that termination reactions in cationic polymerization may be of many different kinds, that they may differ for apparently closely related systems, and that they may even be entirely absent. However, the polymers produced in many of these reactions are of low molecular weight and this means that transfer reactions are dominant. They may take on an even greater variety of forms than the termination reactions and their classification and discussion are still in an early stage of development.

Transfer reactions The existence of chain transfer in ionic polymerizations was first found in the system isobutene-BF3 at room temperature when it was discovered that very small traces of water, tert-butanol, or acetic acid would, as co-catalysts, cause the transformation of large quantities of monomer to very low unsaturated polymers [2, 5]. It was assumed that the process involved proton transfer, and there is no cause to change this view:

K(CH 3 )2 C + BF3OH – + CH 2 = C(CH 3 )2 → K(CH 3 )C = CH 2 + (CH 3 )3 C + BF3OH –

(VI)

The high proportion of unsaturated terminal groups found in polyisobutenes prepared in solution at low temperature [18] makes it appear likely that a similar process operates there, although the reaction (V) above might also account for at least some of these under certain conditions. For isobutene polymerized in ethyl chloride by SnCl4 and H2O a transfer mechanism involving the catalytic complex has been suggested on kinetic grounds [4]:

K(CH 3 )2 C + + CH 2 = C(CH 3 )2 + SnCl 4 OH 2 → K(CH 3 )C = CH 2 + (CH 3 )3 C + + SnCl 4 OH 2

(VII)

237

Developments in the Theory of Cationoid Polymerisations The existence of chain transfer in the polymerization of the n-butenes and of propene has also been shown [19], and for the last named a hydride ion transfer mechanism has been proposed, which yields branched chains [9]. The cationic polymerization of arylenes differs in some respects from that of alkenes. The most notable features are that the degree of polymerization is generally lower and that the proportion of unsaturated end groups is always small [21, 22] and often very variable [10]. In the system styrene–TiCl4–CCl3COOH–toluene low polymers are formed which have tolyl end groups [11]. It is not possible to decide at present whether the transfer reaction involved in this is (VIII) or (IX):

RC + + S → RCS+ and RCS+ + M → RCS + HM +

(VIII)

RC + + S → RCH + S+ and S+ + M → SM +

(IX)

where RC+ is the growing chain, HM+ and SM+ the first links of a new chain, S is the solvent (toluene), and M is monomer; RCS and RCH are saturated, dead polymer. In (VIII) the tolyl group is attached to the chain that has stopped growing: in (IX) it is the beginning of the new chain. In alkyl halide solvents (RX) there is the possibility of a transfer reaction analogous to the initiation reaction with RX as co-catalyst: +

KCH 2 ⋅ C⋅ C 6 H 5 + RX → KCH 2 ⋅ CH(C 6 H 5 )X + R + +

+

(X)

R + CH 2 : CHC 6 H 5 → R ⋅ CH 2 ⋅ C H ⋅ C 6 H 5 This reaction may be the origin of at least some of the halogen found in polymers produced in alkyl halide solvents. However, one of the most common mechanisms is undoubtedly proton transfer; but whereas in alkene polymerizations this reaction leaves a terminal double bond, in arylene polymerizations these are generally not found. Instead the terminal group is usually a substituted indane formed by an internal Friedel-Crafts alkylation [8, 21, 23], e.g., for α-methyl styrene:

238

Developments in the Theory of Cationic Polymerization. Part II (1954)

CH3

CH3

..CH2 — C — CH2 — C+ C6H5

C6H5

+ CH2 = C(CH3)C6H5 → CH3 ...CH2 — C — CH2

+ + (CH3)2 • C • C6H5

(XI)

C — CH3 C6H5

Conclusion The list of termination and transfer reactions given here is certainly not exhaustive. Furthermore, it must be remembered that hydrocarbons under the influence of metal halides may undergo alkylation and isomerization reactions, and conjunct polymerizations [24], especially if the temperature is much above 0°. It is therefore of the greatest importance that in future the simplest systems should be selected for investigation, and that the nature of the reaction products be examined with particular care. It is in many ways unfortunate that the study of cationic polymerization has, from its very start, been so intimately linked with the very complicated and ill-understood chemistry of the metal halides. This connection is largely fortuitous and there is the promise of much progress in this field when these two problems can be attacked independently. On the one hand, we need to know much more about the complex acids and esters which are formed when water, alcohols, carboxylic acids, and alkyl halides react with metal halides; on the other hand, a study of olefin polymerizations catalysed by simple acids such as HBr [14], HClO4 [25], and H2SO4 [26] should be rewarding, because they would presumably be unobscured by the complications and uncertainties accompanying the formation of the initiating species when this involves a metal halide.

239

Developments in the Theory of Cationoid Polymerisations

References 1.

Part I: P. H. Plesch, J. Appl. Chem. (London), 1, 269 (1951).

2.

A. G. Evans and M. Polanyi, J. Chem. Soc., 1947, 252.

3.

P. H. Plesch, M. Polanyi, and H. A. Skinner, J. Chem. Soc., 1947, 257.

4.

R. G. W. Norrish and K. E. Russell, Nature, 160, 543 (1947); Trans. Faraday Soc., 48, 91 (1952).

5.

A. G. Evans and G. W. Meadows, J. Polymer Sci., 4, 359 (1949); Trans. Faraday Soc., 46, 327 (1950).

6.

C. M. Fontana and G. A. Kidder, J. Am. Chem. Soc., 70, 3745 (1948).

7.

Cationic Polymerisation and Related Complexes, Ed., by P. H. Plesch, Heffers, Cambridge, and Academic Press, New York, 1953; D. Clark, p. 99.

8.

D. S. Brackman and P. H. Plesch, ref. 7, pp. 19, 103; J. Chem. Soc., 1953, 1289.

9.

C. M. Fontana, ref. 7, p. 122. C. M. Fontana et al., Ind. Eng. Chem., 44, 1688 (1952).

10. D. O. Jordan and A. R. Mathieson, ref. 7, p. 90; J. Clem. Soc., 1952, 611, 2354. 11. P. H. Plesch, J. Chem. Soc., 1953, 1653; ref. 7, p. 85. 12. P. H. PIesch, J. Chem. Soc., 1950, 543. 13. D. C. Pepper, Trans. Faraday Soc., 45, 397 (1949). 14. D. C. Pepper, ref. 7, p. 75. 15. P. H. Plesch, ref., 7, p. 120. 16. P. H. Plesch, Nature, 160, 868 (1947). 17. P. H. Plesch, ref. 7, p. 102. 18. M. St. C. Flett and P. H. Plesch, J. Chem. Soc., 1952, 3355. 19. R. L. Meier, ibid., 1950, 3656.

240

Developments in the Theory of Cationic Polymerization. Part II (1954) 20. G. Williams, et al., ibid., 1938, 246, 1046; 1940, 775; 1948, 1867; 1952, 1707. 21. F. S. Dainton, R. H. Tomlinson, and T. L. Batke, ref. 7, p. 80. 22. F. S. Dainton and G. B. B. M. Sutherland, J. Polymer Sci., 4, 37 (1949). 23. G. S. Schoepfle and J. D. Ryan, J. Am. Chem. Soc., 52, 4021 (1930). 24. L. Schmerling and V. N. Ipatieff, in Advances in Catalysis, Vol. 2, Academic Press, New York, 1950, p. 21. 25. H. S. Lilley, ref. 7, p. 111. 26. R. G. Heiligmann, J. Polymer Sci., 6, 155 (1951).

Synopsis Olefins can only be polymerized by metal halides if a third substance, the co-catalyst, is present. The function of this is to provide the cation which starts the carbonium ion chain reaction. In most systems the catalyst is not used up, but at any rate part of the cocatalyst molecule is necessarily incorporated in the polymer. Whereas the initiation and propagation of cationic polymerizations are now fairly well understood, termination and transfer reactions are still obscure. A distinction is made between true kinetic termination reactions in which the propagating ion is destroyed, and transfer reactions in which only the molecular chain is broken off. It is shown that the kinetic termination may take place by several different types of reaction, and that in some systems there is no termination at all. Since the molecular weight is generally quite low, transfer must be dominant. According to the circumstances many different types of transfer are possible, including proton transfer, hydride ion transfer, and transfer reactions involving monomer, catalyst, or solvent.

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242

4.4

The Mechanism of Cationic Polymerisations Catalysed by Metal Halides (1959) W. R. Longworth, P. H. Plesch and P. P. Rutherford

Prologue This paper was published only in Russian in Doklady Akad. Nauk, USSR, 1959, 127, 97 and therefore did not become well known. It was provoked by a theoretical proposal, which was disproved by our experiments, details of which are given here. S. S. Medvedev, the doyen of Russian polymer chemists, with his long-time collaborator A. R. Gantmakher, had proposed a theory of a certain group of cationic polymerisations, which was a variant of that proposed much earlier by Hunter and Yohé. It also involved a ‘complex’ (product) formed from isobutene and the catalysts. The purpose of our paper was to show that the Russian theory was incompatible with evidence in the literature, and to put before the public some experiments, which we had designed to test the Russians’ theory. That the complex of isobutene with AlCl3 or with AlBr3 does not initiate the polymerisation of isobutene was shown clearly approximately 20 years later (see Section 4.3), and many other examples of analogous behaviour can be found in the older literature. This paper also contains the first mention that more than one mechanism of initiation might be operating in the same reaction mixture. The senior author had met Professor Medvedev at a conference in the mid-1950s and he asked him to communicate this paper to the Doklady. When, at a later conference, he thanked Professor Medvedev for having done this although that paper contained a refutation of his views, Medvedev replied: ‘But that was the natural thing to do. It is what one scientist owes to another.’

The cationic polymerisation of olefins by metal halides has been interpreted in two ways. The first theory, proposed by Hunter and Yohé [1], ascribed the catalysis to the formation of a polarised complex between the metal halide and the olefin:

243

Commercial rubbers

Developments in the Theory of Cationoid Polymerisations |

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PX n + C = C → PX n – C – C + and supposed that the carbonium ion thus formed started the chain reaction. Subsequently it was found that in solvents of low dielectric constant (hydrocarbons and carbon tetrachloride) neither polymerisations [2] nor alkylations [3] and isomerisations [4] could be effected by a metal halide alone, but that a third substance, called the co-catalyst, is required. The most common, and indeed ubiquitous co-catalyst is water; other substances proved to act in this capacity are alcohols [5], organic acids [6] and nitro-compounds [7]. In each case the catalysis can be ascribed to a complex protonic acid PXnA-H+: X n + AH → PX n A – H + PX n A – H + + M → HM + PX n A –

A carbonium ion is formed by proton-transfer from the complex acid to the olefin. The polymerisation is initiated by the carbonium ion, and the growing end of the polymer consists of an ion-pair. For reactions in alkyl halide solvents the situation was less clear. Early experiments [8] suggested that the addition of water had little or no effect. This prompted Pepper [8] to suggest that the alkyl halide solvent itself was acting as co-catalyst: PX n + RX → R + PX n– +1 R + PX n– +1 + M → RM + PX −n +1

Experiments by one of us [9] appeared to confirm this for certain alkyl halides, but also showed that - at any rate in the system styrene - TiCl4–(CH2Cl)2 the addition of water accelerated the reactions. Further, and much more cogent evidence for the co-catalytic effect of some alkyl halides was produced by Colclough and Dainton [10]. They showed that for the system styrene –SnCl4 both (CH2Cl)2 and t–C4H9Cl acted as co-catalysts - but only in solvents of dielectric constant greater than about 7. Before the publication of Colclough and Dainton’s work, Gantmakher and Medvedev [11] had revived Hunter and Yohé’s theory of direct initiation, but restricted it to solvents of moderately high dielectric constant. They maintained that in such solvents neither a protonic acid nor an alkyl halide co-catalyst is required. The experiments of Colclough and Dainton make this appear highly unlikely, although they do not disprove it completely. It is important to realise that several types of initiation could co-exist in the same system: even if in certain systems co-catalysis by alkyl halides were proved, this does not exclude the existence of a concurrent direct initiation by the Hunter-Yohé, Gantmakher-Medvedev mechanism.

244

The Mechanism of Cationic Polymerisations Catalysed by Metal Halides (1959) However, our own experiments now provide unambiguous proof that Gantmakher and Medvedev’s modification of Hunter and Yohé’s theory is not applicable to the system CH2Cl2–TiCl4 –H2O with styrene or isobutene. We have developed an apparatus [12] in which the amount of residual water per reaction mixture (100 ml) can be reduced to less than 10-5 moles. With CH2Cl2 as solvent and TiCl4 as catalyst, we found that isobutene polymerises to an extent which is strictly proportional to the amount of water present up to a certain limiting water concentration giving 100% yield. The yield at a given water concentration increases with decreasing temperature. A polymerisation which has stopped for lack of water can be restarted by the addition of more water, but not by the addition of more TiCl4. For styrene, the behaviour pattern is quite different: however low the concentration of water may be, the reaction always goes to 100% yield. Thus, our experiments with isobutene show that for this monomer the Gantmakher and Medvedev theory is not applicable; they also show that for isobutene CH2Cl2 is not a cocatalyst to TiCl4. However, it was still possible that the polymerisation of styrene at the lowest water concentration was due not to residual water, but either to co-catalysis by the solvent or to direct initiation by the Gantmakher and Medvedev mechanism. However, since we found the molecular weight to be independent of both the water and the TiCl4 concentration and the rate at low water concentration to be independent of the TiCl4 concentration, these alternatives appeared unlikely. We finally settled the matter in the following way: In a series of experiments under conditions of extreme dryness isobutene was polymerised by TiCl4. Only a small fraction of the isobutene polymerised, consuming the residual water, and the reaction then stopped. Dry styrene was then added. A further slight reaction occurred which stopped after a few seconds. This was presumably caused by a trace of water in the styrene. When it was quite certain that the polymerisation had ceased, enough water was added to the system to give 100% polymerisation. There ensued a fast polymerisation at the end of which a 100% yield of a co-polymer of styrene and isobutene was obtained. Some typical results are shown in Table 1. They prove conclusively that in the solvent CH2Cl2 neither isobutene nor styrene can be polymerised by TiCl4 alone, and therefore in this system, at any rate, there is neither co-catalysis by the solvent nor direct initiation by the TiCl4 alone, as was postulated by Gantmakher and Medvedev. The kinetic arguments which these authors adduce to support their theory are not decisive - they are based on the ‘steady state’ hypothesis which is by no means always valid for cationic polymerisations. There is no independent evidence for the various types of initiation which they give, and they are too general to be useful. Without going into a detailed discussion we would merely point out that under identical conditions (CH2Cl2 – TiCl4 –

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Developments in the Theory of Cationoid Polymerisations

Table 1 Concentration of TiCl4 mol/l

Isobutene concentration mol/l

% yield

Styrene concentration mol/l

% yield

% yield on addition of water

–14.3°

0.00220

0.0893

6.4

0.0685

8.5

85

–29.1°

0.00225

0.0912

15.5

0.0560

15.1

69.4

Temperature

1. The % yield is calculated with respect to the total number of gram-molecules of both monomers added 2. The intervals between the start of the isobutene polymerisation and the addition of the styrene were about 3 minutes, those between the addition of styrene and the addition of water about 5 minutes

H2O, temperature –30 °C to –95 °C) the initial rate of polymerisation of isobutene is proportional to the concentration of monomer, that of styrene proportional to the square of the monomer concentration [13], so that the same mechanism cannot apply to both monomers. Further, in the very system in which the Gantmakher and Medvedev mechanism would be most plausible: styrene + SnCl4 + nitrobenzene [10] - the polymerisation is found to be of first order in monomer and not, as Gantmakher and Medvedev predict, of second order, and moreover depended on the presence of water. Details of our own results will be published shortly elsewhere. We thank Polymer Corporation of Canada and Esso Research Ltd., for funds which made this work possible, and Mr. J. Forsyth for translating this paper.

References 1.

W. H. Hunter and R. V. Yohé, J. Am. Chem. Soc., 1933, 55, 1248.

2.

a. P. H. Plesch, M. Polanyi and H. A. Skinner, J. Chem. Soc., 1947, 257. b. A. G. Evans and G. W. Meadors, Trans. Faraday Soc., 1950, 46, 327. c. D. Clarke in Cationic Polymerisation and Related Complexes, Ed., P. H. Plesch, Heffer and Sons, Cambridge, 1953, p.99. d. D. S. Brackman and P. H. Plesch, J. Chem. Soc., 1952, 2188.

3.

L. Schmerling, J. Am. Chem. Soc., 1945, 67, 1778.

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The Mechanism of Cationic Polymerisations Catalysed by Metal Halides (1959) 4.

H. Pines and R. C. Walker, J. Am. Chem. Soc.,1946, 68, 595. H. S. Bloch, H. Pines and L. Schmerling, J. Am. Chem. Soc., 1946, 68, 153. O. Grummitt et al., J. Am. Chem. Soc., 1945, 67, 910.

5.

A. G. Evans and M. Polanyi, J. Am. Chem. Soc., (1947) 252. A. G. Evans and G. W. Meadows, J. Pol. Sci., (1949) 4, 359.

6.

P. H. Plesch, J. Chem. Soc., 543 (1950).

7.

K. E. Russell, Reference 2c, p.114.

8.

D. C. Pepper, Trans. Farad. Soc., (1949) 45, 404.

9.

P. H. Plesch, J. Chem. Soc., 1953, 1653.

10. R. C. Colclough and F. S. Dainton, Trans. Farad. Soc., (1958) 54, 886. 11. S. S. Medvedev and A. R. Gantmakher, Doklady Akad. Nauk., SSSR, (1956) 106, 1031. 12. R. H. Biddulph and P. H. Plesch, Chemistry and Ind., (London), in the press. 13. R. H. Biddulph, W. R. Longworth, P. H. Plesch and P. P. Rutherford, contributions to International Symposium on Macromolecules, Wiesbaden, October, 1959.

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248

4.5

A New Theory of Initiation by Aluminium Halides (1972) P. H. Plesch

This paper was first published in Macromolecular Chemistry – 8, 1973, 305-318. Reproduced with permission from IUPAC, copyright 1973. (International Symposium, Helsinki, Finland, 1972.)

Prologue This is the author’s first publication of his theory explaining one of the oldest and certainly the best known of cationic polymerisations. It contains three separate ideas which together explain the hitherto unexplained phenomena encountered when AlX3 (X = Cl or Br) is used to polymerise isobutene. In subsequent papers the experiments were described which provided the evidence [104, 112]. The first supposition is that the AlX3 ionises to give AlX2+ ions and that these create a propagating carbenium ion by cationating the monomer, giving, for example, the X2AlCH2CMe2+ ion. This author missed that a similar idea seems to have been published by Korshak [A], but he acknowledged that it was favoured at one time by the Prague workers (Wichterle, Marek, et al.). However, their idea remained entirely hypothetical until it was proved experimentally by this author’s group at Keele. An essential precursor to these studies was the thorough exploration of the ionisation of AlX3 in alkyl halide solutions, which opened up a new field of ionic solution chemistry [4], the Binary Ionogenic Equilibria (BIE) [(138) and papers quoted there]. The second supposition of the theory is an innovation in reaction kinetics. It is that when a solution of a reagent, in which an equilibrium is established, is introduced into another solution containing a reagent that can react rapidly with one of the participants in the first equilibrium, that equilibrium is quasi frozen and can make at best only a slow contribution to the subsequent events occurring in the mixed solutions. The studies of the BIE in the AlX3 solutions had shown that only a very small fraction of the AlX3 molecules is ionised to AlX2+. Therefore when such a solution is introduced into a solution of monomer, the then existing AlX2+ ions initiate polymerisation and, as this is a fast reaction, the subsequent formation of more AlX2+, which is slow (the rate-constants were measured during the BIE studies), is irrelevant. This picture explained the ancient mystery that the quantity of AlX3 consumed during the polymerisations was found to be almost immeasurably small. Further, it was proved that the un-ionised AlX3 forms a

249

Developments in the Theory of Cationoid Polymerisations complex with the monomer which is always present in great excess. Such complexation had been suspected by analogy with a large number of similar systems, and it makes the replacement of the consumed AlX2+ ions even slower. The frozen equilibrium idea subsequently proved useful in explaining the very low initiation efficiency of protonic acids [B]. The idea that a metal-centred cation, arising from a BIE, can cationate an alkene and thus be an initiator could have been propounded by this author when he discovered the BIE of titanium tetrachloride [30]: 2TiCl4 = TiCl3+ + TiCl5¯ He did not think of it then, and when he did, he showed that apparently the formation of a metal-carbon bond was unlikely on thermochemical grounds [68]; in other words, he was taken in by his own propaganda; but in a “Note added in Proof” in that same work he indicated that electrochemical factors (solvation and Coulombic energies) could make this initiation exo-energetic. However, at that time, 1960-1970, such a suggestion would have been no more plausible than when it was made by others. It was only the painstaking and detailed exploration of the nature of the solutions of AlX3 in alkyl halides [104, 112] that provided the basis of fact which was required to make the theory plausible.

References A.

V. Korshak and N.N. Lebedev, J. Gen. Chem., U.S.S.R., 1948, 18, 1766.

B.

See paragraph 4.3.2 of Section 5.7.

250

A New Theory of Initiation by Aluminium Halides (1972)

Abstract In the field of cationic polymerisation a notoriously intractable problem is the mechanism of initiation by aluminium halides. Despite much work on the polymerisation itself, there are few studies of the initiation mechanism. Existing theories are shown to be inadequate to explain the most characteristic features of the reactions: when a solution of an aluminium halide in an alkyl halide is introduced into a solution of isobutene, there ensues a fast polymerisation which generally stops at incomplete conversion, and the number of moles of polymer formed is much smaller than the number of moles of initiator; these features are found over a very wide range of conditions. A new theory is proposed which is based partly on well-known facts and makes use of some older ideas. The theory contains three essential Suppositions. i) The solutions of initiators contain cations derived from the aluminium halide by self-ionisation (AlX+2, and/or Al2X+5) and in all but the very purest systems also other ions derived from impurities, the solvent, or both; the concentration of ions is very much less than that of AlX3. ii) When the initiator solution enters the monomer solution, the cations initiate the polymerisation by adding to the monomer to give the propagating species, e.g., AlX2CH2•CMe+2, and the reaction thus started is terminated more or less rapidly according to the exact circumstances (temperature, purity, etc.). iii) The un-ionised AlX3 becomes inactivated by complexing with monomer, and the regeneration of ions from the very small concentration of free AlX3 is so slow as to be irrelevant. Thus, only the aluminium atoms which are in the form of ions at the instant of mixing can be effective, and the low efficiency and variable yield of the reactions are explained. The literature evidence for the three suppositions is reviewed and some implications and criticisms of the theory are discussed. In particular, it is demonstrated that certain other reaction mechanisms which are currently under discussion, are inadequate.

Introduction The polymerisation of isobutene by aluminium chloride is certainly the most widely known example of a cationic polymerisation: it has been studied for nearly forty years, and until recently it was the only cationic polymerisation which, in the form of the Butyl process, was of major economic significance. However, despite its antiquity and industrial importance the number of fundamental studies devoted to its exploration, and indeed the number of

251

Developments in the Theory of Cationoid Polymerisations research groups interested in such studies, is minute compared with the multitude of patents and the host of industrial scientists who have been concerned with improvements in the homo- and co-polymerisation of isobutene by aluminium halides and some more or less closely related compounds, and with the general properties of these initiators. Of the relatively few fundamental mechanistic studies, only a small proportion were in any way concerned with the problem of initiation, and they went only a small way towards its solution. In 1968 J. P. Kennedy, the acknowledged master of this field since the retirement of the great R. M. Thomas, could write with full justification [2]: The details of initiation in the isobutene-aluminium chloride system are still obscure, and after 30 years of intensive study we still do not know the exact nature of the actual catalytic species. Most disturbing is the fact that the ‘true’ catalyst concentration is for some reason much less than what one would expect from the measured catalyst concentration. The number of chains produced from one mole of AlCl3 is much less than one. Since that time the situation has changed only in so far as a number of papers have appeared which, though relevant, were inconclusive by themselves, but helped to generate the synthetic train of thought which culminated in the theory which I will expound here. It is a curiosity which should be of interest to historians of chemistry and philosophers of science, that the most important ideas comprised in this theory have been known for several years, and yet the catalytic event required for their synthesis did not occur until now. It may be that since the Butyl plants were working satisfactorily, the theoretical problem was not of sufficiently urgent concern to a sufficient number of sufficiently intelligent workers, or the whole nexus of complicated and to some extent contradictory facts was written off as ‘too difficult’ and inadequately rewarding of effort. The ‘catalytic event’ mentioned above was our observation that under some conditions the formation of ions from aluminium bromide in methyl bromide is a comparatively slow reaction’. The ‘slowness’ of this reaction is not now an essential feature of my theory, but it set off the train of thought which resulted in the theory.

The facts In the first instance we are concerned here with the polymerisation of isobutene by aluminium chloride or bromide. Most of the most relevant published observations stem from the Esso group and from the Macromolecular Institutes at Brno and Prague and they have been expertly summarised by Kennedy [2a]. In assessing these observations it is important to remember that the materials used in the earlier work were very impure by the standards of today, so that many discrepancies between the results of two or more

252

A New Theory of Initiation by Aluminium Halides (1972) groups of workers, or between results obtained by one group over a span of several years, can find a natural explanation through differences in the nature and amount of impurities present in any or all of the monomer, solvent or initiator solutions; some of these effects have been explored in detail [1, 2b]. It must also be remembered that the phenomena observed depend critically upon the details of experimental procedure. Most work originating in industrial laboratories was done by injecting a solution of metal halide in alkyl halide or hydrocarbon into a solution of monomer in alkyl halide or hydrocarbon. This mode of operation is essentially similar to that used on the (Butyl) plant and was used for this reason; we will refer to it for brevity as the ‘Esso technique’. On the other hand, an investigator interested in the fundamental chemistry rather than in the optimisation of the reaction conditions (from the commercial point of view) would naturally refrain from preparing, and then using after a variable storage-time, a solution of aluminium halide in alkyl halide, because the rapid reactions which can occur in such systems at all but the lowest temperatures would obscure largely the true nature of the initiator. For such studies it is necessary to introduce the monomer into a freshly prepared initiator solution, or to introduce into a solution of the monomer the solid initiator or a freshly prepared solution of initiator in a very pure and inert solvent. It so happens, however, that the most interesting problem was presented by the much more abundant experimental material obtained by the ‘Esso technique’, the addition of an initiator solution to the monomer solution. All reports agree that with this mode of operation a very fast polymerisation is achieved, which can give a product of very high molecular weight, and which stops generally at incomplete conversion. Such stopped reactions can be restarted by the addition of more initiator solution, but not by the addition of putative co-initiators, such as water [2b]. Moreover, the efficiency of the initiator, in terms of the number of polymer molecules per atom of aluminium, is always very small. These three features: fast reaction, incomplete conversion, and low efficiency, are found over a very wide range of concentrations, temperatures, and solvents, irrespective of whether the polymer remains in solution or is precipitated, and it is these which have so far defied explanation. This task is made even more difficult by the findings that in a reaction which has stopped at incomplete conversion, aluminium halide is still present, and so is alkyl halide, either as main solvent or introduced as vehicle for the initiator.

Current theories It is worth recalling that the phenomenon of co-catalysis (now more consistently renamed ‘co-initiation’) was found first with boron trifluoride and with the tetrahalides of titanium and tin. It is well known that it can be interpreted by the reaction scheme (1)

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Developments in the Theory of Cationoid Polymerisations

MtX n + H 2 O → MtX n ⋅ H 2 O MtX n ⋅ H 2 O + P1 → HP1+ MtX n OH –

( P1 = monomer )

(1)

for co-initiation by water, and this scheme can be adapted easily to co-initiation by other protonogenic reagents, such as carboxylic acids or phenols. This theory of the phenomenon had an immediate appeal because it was simple and because initiation by a complex acid such as BF3•H2O was seen to be but a special case of initiation by conventional protonic acids. It was quite natural that one would try to apply an interpretation along the same lines to reactions initiated by other metal halides, including of course those of aluminium. However, in the very few instances where the effect of added water on polymerisations initiated by aluminium halides has been investigated rigorously, the water was found to have either no effect on the rate, or to diminish it. Further, since the most stringent drying techniques failed to stop polymerisation in these systems, one came to the conclusion that whatever else was initiating the reactions, it could not be a product formed from water. It would be inappropriate, and indeed superfluous, to review here the whole of this very complicated field, since this has been done adequately by several authors [2, 4-7]. For our present purposes we need to pick out only one other aspect, that of co-initiation by alkyl halides. It was proved that with certain olefins and metal halides the addition of an alkyl halide to a mixture of metal halide and olefin would initiate polymerisation [8], and this was interpreted by an extension of the theory of co-initiation, in terms of the reaction scheme (2):

MtX n + P1 → MtX n ⋅ P MtX n ⋅ P1 + RX → RP1+ MtX n– +1

(2)

The distinction between systems in which a complex of initiator and co-initiator reacts with the olefin (scheme (1)) and those in which the coinitiator reacts with a complex of monomer and metal halide (scheme (2)) was made very early in the history of this subject [9]. When we tried to interpret our experiments on the polymerisation of isobutene by aluminium chloride in methylene dichloride [10], in which the irrelevance of water had been demonstrated, we rejected (for good reasons) the theory of co-initiation by an impurity R´X (more reactive than the solvent RX) according to scheme (2), and put up for consideration the following three reaction schemes: ‘Direct’ initiation (i.e. without the intervention of a co-initiator), either according to the Hunter-Yohé mechanism (3):

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A New Theory of Initiation by Aluminium Halides (1972)

i – C 4 H 8 + AlCl 3 → – AlCl 3 ⋅ CH 2 ⋅ CMe 2+

(3)

or by an ion derived from the initiator by self-ionisation:

i – C 4 H 8 + 2 AlCl 3 → AlCl 2 ⋅ CH 2 ⋅ CMe 2+ + AlCl 4–

(4)

and co-initiation by the solvent, according to scheme (2) which takes the form:

i – C 4 H 8 + AlCl 3 + CH 2 Cl 2 → CH 2 Cl ⋅ CH 2 ⋅ CMe 2+ AlCl 4–

(5)

For reasons which still seem adequate, scheme (3) was rejected and we concluded that scheme (5) was the most likely, overlooking the fact that it was incompatible with the results obtained by the ‘Esso technique’ (in particular the incomplete yields). The scheme (4) was rejected for reasons which now seem inadequate (and which will be discussed below), its implications were not understood, and it is in fact a succinct statement of the ‘new’ theory which will be set out in the following section. However, whilst our observations merely make an initiation without co-initiator appear probable for aluminium chloride in methylene dichloride, the experiments of Chmelir, Marek, and Wichterle subsequently proved this point fairly conclusively for aluminium bromide in heptane [11]. The Czech workers interpreted their findings by a scheme which is equivalent to reaction (4) or, more explicitly, to a combination of reactions (7) and (8) below. Their results occupy a central position in this field of enquiry, because they made it necessary to reassess old results and to re-examine the then current views, and therefore they were prominent among the stimuli which led to the evolution of the new theory. The latest addition to the theories of cationic polymerisation is the ‘self-initiation theory’ of Kennedy [12]. According to this theory, initiation can take place in certain systems by a reaction between the metal halide and the olefin in which a hydride ion is abstracted by the metal halide from an allylic position in the monomer: |

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C : C⋅ C — H + MtX n ↔ C : C⋅ C + + MtX n H – |

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(6)

The allylic cation thus formed is said to be the initiating species. This is not the place for a detailed critique of this ingenious theory; suffice it to say that even if it is valid in some systems, it cannot explain the limited yield of polymer and the low efficiency of the initiator with which we are concerned here. The reason is that when reaction ceases, both metal halide and olefin are still present in the reaction mixture, and there is no apparent reason why reaction (6) should not go to completion. 255

Developments in the Theory of Cationoid Polymerisations

The new theory My theory is based essentially on two suppositions (suppositions 1 and 3) which are extremely plausible extrapolations from well-established facts, and one (supposition 2) which is at present still somewhat speculative. In its simplest form the new theory can be formulated as follows: Supposition 1. The initiator solutions of aluminium chloride in alkyl chloride contain ions formed by self-ionisation of the aluminium chloride

2 AlCl 3 ↔ AlCl 2+ + AlCl 4– and/or

(7)

4 AlCl 3 ↔ Al 2 Cl 5+ + Al 2 Cl 7– The equilibrium constants for both these reactions are very small, so that only a very small fraction of the aluminium chloride is ionised. Supposition 2. When the initiator solution is introduced into that of isobutene, the cations react additively with the monomer to give the ‘active species’, which is a substituted t-Bu cation (I) containing a C–Al bond:

AlCl 2+ or Al 2 Cl 5+ + i − C 4 H 8 → AlCl 2 ⋅ CH 2 ⋅ CMe 2+ ( + AlCl 3 )

(8)

(I) The ion (I) propagates the polymerisation. Supposition 3. Most of the unionised aluminium chloride becomes bound to isobutene (reaction (2), first stage); the resulting complex has no initiating capability; and the equilibrium concentration of free aluminium chloride is so small, that the rate of the ionogenic reaction (7) becomes negligible and there is thus no further initiation. In other words, only those aluminium atoms which are present in the initiator solution as cations at the moment when it enters the monomer solution are effective in starting polymer chains, the rest of the aluminium chloride becomes inactivated by complexing with the monomer:

AlX 3 + i − C 4 H 8 → AlX 3 ⋅ C 4 H 8 Since the degree of ionisation in the initiator solution, although generally not known precisely, is certainly very small, we have a simple explanation of the notoriously low

256

A New Theory of Initiation by Aluminium Halides (1972) efficiency of the reaction in terms of moles of polymer formed per atom of aluminium, which was mentioned earlier. The theory also implies in a fairly obvious manner that the whole pattern of the reactions (kinetic order, yield, etc.) will be highly sensitive to the purity of all reagents and the exact circumstances of the experiments. Under most conditions the chain-growth is terminated more or less rapidly by one or more of several possible termination reactions, the relative importance of which depends on purity, nature of solvent, temperature, etc. The practice (on the plant) of ‘maturing’ the catalyst solution, and of adding various compounds to it to increase the efficiency can now be rationalised, because in the presence of almost any compound containing more than one carbon atom, and especially at relatively high temperatures (say, above approximately –50 °C), aluminium chloride reacts to give a ‘soup’ containing much higher concentrations of ions (of many different kinds) than are to be found in stable binary systems, e.g., MeCl + AlCl3, at low temperatures. Further, the practice of chilling the initiator solution to a temperature equal to or less than that of the monomer solution, may find a rational explanation because in alkyl halide solvents many ionogenic equilibria become displaced towards more abundant formation of ions as the temperature is reduced. From the conditions prevailing in the initiator solutions-high polarity of solvent and low total concentrations of ions - it is easy to estimate that most of the ions present in those solutions will be free, and that questions concerning the relative speed of initiation by free and paired cations do not in fact arise. Once the initiator solution has entered the monomer solution, however, the situation may be different as regards propagation. The dilution effect will certainly displace any ion-pair-free-ion equilibria even further towards the free ions, but if the reaction mixture is of low polarity, (e.g., if the solvent is a hydrocarbon) this effect may outweigh the dilution effect, and then under some conditions paired cations may be in excess over free ions. Beyond such rather trite statements no useful generalisations can be made, and each system must be analysed individually to clarify the electrochemical situation prevailing in it.

Evidence for the suppositions Two of the suppositions on which the theory is based-self-ionisation of aluminium chloride, and complexing between aluminium chloride and isobutene-are made by analogy with the facts established for closely related systems. Unfortunately we have here a prime example of the well known fact that the less one knows about a situation, the more one needs to say about it. If reliable measurements on the conductivity of solutions of aluminium chloride in methyl chloride were available, and if we had direct evidence for

257

Developments in the Theory of Cationoid Polymerisations the formation of a complex between isobutene and aluminium chloride, a large part of what follows would be superfluous. As it is, we will present here a summary of the evidence from which our suppositions 1 and 3 can be deduced as reasonable extrapolations. (See, Note added in proof). Supposition 1. In the paper in which we first described the self-ionisation of titanium tetrachloride in methylene dichloride or ethyl chloride, we also showed that the conductivity measurements on aluminium bromide solutions available at that time could be explained by a self-ionisation of the type

4 AlBr3 ↔ Al 2 Br5+ + Al 2 Br7–

(9)

and that this interpretation fitted the facts better than those given by the original authors [13]. Current work in our laboratory [3] indicates that in methyl bromide solution the ionogenic reaction is of second order with respect to [AlBr3], and the same has been found [14] for the ionisation of AlI3, GaI3, and InI3 in EtI. Since it is known that the aluminium halides are monomeric in these solutions, it follows that the rate-determining step for the selfionisation is the reaction (10):

2 AlBr3 → AlBr2+ + AlBr4–

(10)

and that this is followed by the formation of the Al2 species. Our data also indicate that as we purify our methyl bromide more and more, and as its conductivity is thus progressively reduced, the conductivity behaviour of the aluminium bromide solutions in it approaches that which corresponds to a binary ionisation equilibrium: K

2AlBr3 → AlBr2+ + AlBr4–

(11)

namely a direct proportionality between the specific conductance and the total solute concentration, [AlBr3]0. The actual relation is

κ = 10 –3 K 1 / 2 Λ T [AlBr3 ]0 /(1 + 2 K 1 / 2 ) where ΛT = 103κ/[AlBr+2] and is (almost) invariant with [AlBr3]0 because of the low ionic strength of the solutions. The same linear relation was found by Halpern and Polaczek for solutions of AlI3 in EtI, but was not interpreted by them [14]. Their plot of κ against [AlI3]0 goes through the origin (like ours for AlBr3 in MeBr) which shows that their solvent must have been very pure.

258

A New Theory of Initiation by Aluminium Halides (1972) The fact that the results of some earlier studies can be explained better in terms of equilibrium (9) than equilibrium (11) is undoubtedly related to the relatively high level of impurities prevalent in the earlier experiments, but it has not yet been explained in detail. This matter is, however, not as irrelevant as it may seem, because (as mentioned above) in the actual solutions of aluminium halides which have been, or are likely to be, used in most polymerisation experiments, an important fraction of the ions present probably arises from reactions of the initiator with impurities, solvent or both, and the case discussed here in detail - ions arising only from reaction of the initiator molecules with their own kind - is surely an idealisation. The self-ionisation of aluminium chloride and bromide in nitrobenzene has been studied in great detail [15], and the rates of the forward and back reactions have been determined so that all the relevant equilibrium constants are known. The whole body of evidence available shows that self-ionisation of the initiator, with or without other ionogenic reactions in the initiator solutions, can be regarded as well established for all aluminium halides and as highly probable for the alkyl aluminium halides. Moreover, the ionogenic reactions are relatively slow and - except under the ‘dirtiest’ conditions - the concentration of ions in the initiator solution will be very much less than [AlX3]0. Supposition 3, concerning complex formation between isobutene and aluminium chloride, is derived from one piece of direct evidence and is also a reasonable extrapolation from the behaviour of many closely related systems. It has been reported that when a solution of aluminium chloride in methyl chloride is poured into pure pentane, the aluminium chloride is precipitated, but when such a solution is introduced into a solution of isobutene in pentane, the resulting mixture remains optically clear [16]. The prevention of precipitation by the isobutene can be interpreted most simply in terms of a ‘solubilisation’ of the aluminium chloride by its forming a complex with the isobutene. This is a plausible interpretation because on the one hand other, less-reactive olefins interact reversibly with aluminium bromide, e.g., pent-2-ene [17], and because on the other hand isobutene is known to form at least one (possibly two) complexes reversibly with another, less reactive metal halide, namely titanium tetrachloride. Our study of the system i-C4H8-TiCl4 by means of its freezingpoint phase diagram shows complex formation quite unambiguously [18]. Thus, the supposition 3, that in a reaction mixture the unionised aluminium halide is inactivated by complex formation with monomer, appears to be reasonable. It now remains for us to discuss our Supposition 2 (see, note added in proof). At this stage it is useful to distinguish two separate features of this supposition. The first is that the true initiating species are cations derived from the initiator, which may be formed by selfionisation, reaction with the solvent or impurities, or by a combination of these ways.

259

Developments in the Theory of Cationoid Polymerisations The second is that the initiation consists of the addition to the monomer of some or all of the cationic species thus formed to give the growing carbenium ion (I) (reaction (8)). Even if the first part is proved, the second part must be tested separately, for it is possible, though at present it seems unlikely, that the cations in the initiator solution could generate cations from the monomer by reactions other than the addition reaction (8). For instance, they could generate an allylic cation (II) by abstracting H (reaction (12)), or they could form a radical-cation (III) by abstracting an electron (reaction (13)), from the monomer:

AlX2H

Me

or + CH2•C•CH2 +

RH

(12)

(II)

AlX+2 or R+ + C4H8 AlX 2 or + CH 2CMe+2 (III) R•

(13)

(R + is an organic or metal-organic cation originating from side reactions in the initiator solution.) If the reactivity of the cations (II) and (III) towards the monomer is sufficiently great, these reactions represent initiation without formation of an Al–C bond, but if these ions are too stable to add to monomer, their formation represents a wastage of the cations originating from the initiator. It is a fundamentally important point that the reaction (12) involving abstraction of a hydride ion from the monomer by a cation is essentially different from Kennedy’s reaction (6) in which the neutral metal halide molecule acts as a hydride ion abstractor [12]. For our idea that initiation is due to the cations present in the initiator solution, there is some very relevant evidence, and once again it has been available for many years although its import was not appreciated. This evidence is the ‘ZAV effect’ [4], i.e., the antibatic correlation between the conductivity of an initiator solution (containing aluminium chloride and an oxygen compound, e.g., ethanol) and the molecular weight of the polymer resulting from its addition to an isobutene solution [19]. The now evident conclusion

260

A New Theory of Initiation by Aluminium Halides (1972) from these experiments is the very simple one, that the higher the concentration of ions in the initiator solution, the larger is the number of chains started by it, and - for a given set of conditions - the lower will be the molecular weight of the resulting polymer. Unfortunately, the exact mechanism whereby the various oxygen-containing additives used in that work enhance the extent of ionisation in the initiator solution is far from clear at present, and it seems to merit further study. As far as the second part of the supposition 2 is concerned, namely that initiation is by addition of an AlX2 ion to the monomer (reaction (8)), there is as yet no direct evidence for it; moreover, such evidence is very difficult to obtain. The problem is that of identifying a C–Al bond in concentrations which are likely to be in the micro-molar range. An approximate order-of-magnitude calculation may illustrate the difficulty of the task. Consider a polymerisation in an alkyl halide solvent where kp≈105 l mol-1 s-1 and which has a half-life t1/2 of 7 s and which is internally of first order (rate-constant k1):

– dm / dt = k1m = kp [ Pn+ ]m

([ P1 ] ≡ m)

and therefore, since k1 = ln 2/t1/2 ,

[ Pn+ ] = ln 2 / kpt1 / 2 = 0.7 / 7 × 10 5 = 10 –6 mol l –1 Thus, if m = 10-2 mol l-1, and if all the monomer is polymerised, and if all kinetic chains are started by addition of AlX+2 to monomer, there will be 10-4 mole of Al–C bonds per base-mole of monomer. For reactions in a hydrocarbon solvent, where kp is of the order of 108 l mol-1 s-1, and t1/2 appreciably greater, [Pn+] is correspondingly smaller and the whole task much harder. Further, before the C–Al bonds can be identified, they must be converted into a stable, analysable species by unambiguous reactions and these must be such that the products formed from the unreacted AlBr3 during the conversion do not interfere with the subsequent analysis. It is evident that radioactive tracer methods offer the best hope of solving this problem. A scheme equivalent to our supposition 2 was put forward by Chmelir, Marek and Wichterle to explain the polymerisations initiated by aluminium bromide in heptane [11]. The fact that these reactions were of second order with respect to the initiator demanded an explanation in terms of a pre-initiation reaction between two molecules of initiator. Subsequently, Marek and Chmelir used a closely related set of ideas to explain their findings concerning two-component initiator systems, the most typical of which consists of aluminium bromide and titanium tetrachloride. In the presence of both these compounds the polymerisation of isobutene in heptane is much faster than when either of them is

261

Developments in the Theory of Cationoid Polymerisations used alone [20-23]. They explained their observations very plausibly in terms of an enhancement of the concentration of reactive cations by an ionogenic reaction between the two metal halides: [21, 22]

AlBr3 + TiCl 4 ↔ TiCl 3+ + AlBr3Cl –

(14)

and a subsequent initiation by addition of TiCl+3 to the monomer. The possibility that the analogous reaction

AlBr3 + TiCl 4 ↔ AlBr2+ + TiCl 4 Br –

(15)

may take place simultaneously (with consequent initiation by AlBr+2) was not considered, probably because the polyisobutene resulting from these reactions was found to contain titanium [21]. Unfortunately, the presence of titanium in a polymer after it has been repeatedly treated with aqueous sulphuric acid, cannot be taken as evidence for the existence of Ti–C bonds, so that their results do not in fact provide any relevant evidence, and both reactions (14) and (15) remain serious possibilities which need to be investigated. The most important point, however, is that these views were an earlier expression of our supposition 2, but unfortunately the authors did not see their wider implications. It is relevant to note here that the findings of Marek’s group concerning two-component initiator systems appear to provide a plausible explanation for the phenomenon, well known to the operators of Butyl plants and related processes, that the efficiency of commercial aluminium halides can be very variable from batch to batch. We can now see that this is most probably due to variations in the content of traces of other metal halides, Ti, Fe, etc., which would have a disproportionately great effect on the characteristics of the initiator solution.

Some critical considerations There are several distinct lines of argument along which the new theory may be criticised. i) It might be asked in what way the present theory is superior, i.e., more plausible and more useful, to that which ascribed the initiation to reactions represented by the scheme (2). This type of reaction has been discussed in great detail [7], so it may suffice here to say that although it appears to exist in some systems (and indeed could co-exist with other concurrent initiation reactions) it cannot be of great importance in the systems considered here, because the limited yields and the ZAV effect cannot be explained on this basis. Moreover, once the existence of reactive cations in the

262

A New Theory of Initiation by Aluminium Halides (1972) initiator solutions is admitted, it becomes obvious that the reaction of these cations with an olefin is likely to be much faster than the possibly competitive reaction in the second step of (2). The reason is that the former will at worst involve a very small activation energy arising from the displacement of solvating solvent molecules from the cation during the formation of the linear transition state complex from cation and olefin, whereas the latter occurs by way of a four-centred transition state involving the co-ordination complex of MtXn with olefin and the alkyl halide, and thus necessarily requires a relatively large activation energy. ii) The reactions in (2) do not exhaust the possible reactions in systems containing an olefin, an alkyl halide and an aluminium halide. It is now well established that solutions of aluminium halides in alkyl halides contain weak complexes RX•AlX3 [24-27], and it is at least possible that for some systems the initiation reactions (16) and (17) could occur:

RX ⋅ AlX 3 + P1 → RP1+ + AlX 4–

(16)

RX ⋅ AlX 3 + P1 ⋅ AlX 3 → RP1+ + Al 2 X 7–

(17)

It is evident, however, that this cannot explain any of the important features of the polymerisations and that therefore even if they do occur, they can only be of minor importance. iii) As mentioned earlier, the reaction (4), which is a summary of the new theory, was dismissed by us some years ago as unlikely on thermochemical grounds [10]. Whilst this opinion is still valid, it is not really relevant, because one of the essential points of the new theory is that the ‘initial state’ for the initiation reaction does not consist of AlCl3 molecules plus monomer, but of AlCl+2 (and possibly other) ions plus monomer. Once the endothermic ionisation reaction, by which the Al-ions are formed, is thus removed from the thermochemical balance, the resulting reaction (8) is at worst thermally neutral and probably exothermic. iv) The generation of metal-containing cations from the initiator, and initiation by addition of such a cation to the monomer, are ideas which were put forward by the Prague group in order to explain the functioning of their two-component initiators, but which were later abandoned by them [23]. Since this change of opinion is equivalent to a criticism of our own application of the same ideas, it will be useful to examine how Marek and his co-workers arrived at their rather resigned and uninformative conclusion: In contrast to the earlier views concerning the reaction of the components of the bimetallic catalysts (ZK) of the type AlX3/MtYn, we reach the conclusion that the initiating process with these ZK is in general very

263

Developments in the Theory of Cationoid Polymerisations complicated, because a whole series of mixed aluminium halides and catalytically active complexes of different concentrations and different efficiencies may be concerned therein [28]. Summarised briefly, the reason for their agnosticism appears to be that the authors were unable to see any pattern in the multitude of qualitative and semi-quantitative results which they obtained with a large number of binary initiator systems (ZK). However, it appears to us that there is nothing in these results which could not be explained in terms of ionisation equilibria of the type suggested by these authors earlier (reaction (14) and its analogues). In fact no evidence for or against our (and their earlier) views is derivable from the experiments with ZK until the electrochemical aspects of these two-component systems have been explored. In the latest paper from Marek’s group [29] they once again introduce the self-ionisation of titanium tetrachloride in order to explain their photo-initiation results. Unfortunately, their reaction scheme is very obscure, but evidently it does not involve addition of a metal-containing cation to the monomer.

Conclusions The usefulness of a new theory can be assessed by two criteria: (a) How widely applicable is it? and (b) What testable predictions follow from it? It is evidently not feasible to enumerate all possible explanatory applications of the theory to presently known facts, nor is it practicable to cite here more than a very few testable predictions. There is in the literature a very large number of systems in which extreme drying and purification reduced the rate of polymerisation in the presence of a metal halide initiator to very low values, but not to zero; a comprehensive list of these has been compiled by Kennedy [12]. Hitherto most of these slow, unsuppressible reactions have been explained in terms of co-initiation by unknown and irremovable impurities, (e.g., adsorbed water) or by solvent (reaction (2)), or by Kennedy’s ‘allylic hydride’ theory [12]. It is evident now that these reactions could be explained by the theory presented here, and the matter is open to testing in at least three ways: the kinetics, the correlation (if any) between conductivity of initiator solution and polymerisation rate, and the existence of metalcarbon bonds in the polymers. It is known that different related metal- or organometallichalides, e.g., AlBr3, AlCl3, EtAlCl2, in appropriate solvents, MeBr, MeCl, EtCl, etc., have different degrees of ionisation, and it therefore follows from the present theory that for the same initiator concentration, such different initiators should give different reaction rates. Although the literature contains no strictly comparable sets of rate measurements of this kind, it is generally known that there are considerable differences between the

264

A New Theory of Initiation by Aluminium Halides (1972) initiating efficiencies of the various aluminium halides and alkyl aluminium halides under identical conditions, and it should be possible to rationalise these observations in terms of the conductivity of the corresponding initiator solutions. It also follows that a screening of new initiator systems (initiator plus solvent) without or with ‘promoters’ could perhaps be done more rapidly and easily by conductivity measurements than by conventional polymerisation experiments. The term ‘promoter’ here covers all those many compounds which have been mentioned in the literature and in patents as enhancing rate, yield, or both, but for which one cannot easily envisage a conventional co-initiation reaction such as (1) or (2) or co-initiation by halogen exchange [30]. Fairly simple, and heuristically valuable, explanations for the activity of many of these compounds may be found in terms of their increasing the degree of ionisation in the initiator system by complexing with the anions, cations, or both.

Acknowledgements I wish to thank the many friends who have discussed and criticised my ideas with patience and benevolence, especially Professor J. P. Kennedy and Professors Giusti and Magagnini and their colleagues at the University of Pisa; and I am indebted to Mr. D. W. Grattan of my Research Group for much help in the preparation of this Lecture. Note added in proof (March 1973). Researches carried out since this Lecture was delivered have given results which are directly relevant to the problems discussed here. They have provided an experimental foundation for several ideas which were somewhat speculative up till now, and in particular our supposition 2. 1. At concentrations less than approximately 10-3M, AlBr3 in MeBr, and AlCl3 in CH2Cl2 or EtCl ionise to AlX+2 and AlX–4. The kinetics of the ionisation are as expected and reproducible, provided that the solvent is sufficiently pure. 2. The K = [AlX+2] [AlX–4]/[AlX3]2 increases with decreasing temperature. 3. When isobutene is added to a solution of AlBr3 in MeBr or of AlCl3 in alkylchloride at –20 °C to –80 °C, the rate of increase of conductivity is of second order with respect to the Al compound, which supports our suggested initiation mechanism. 4. When the reaction is then killed with tritiated water, the polymer contains tritium which is not exchangeable, and the tritium content is correlated with the conductivity of the polymerising solution. These findings support the suggested reaction sequence:

265

Developments in the Theory of Cationoid Polymerisations AlX+2 + CH2 : CMe2 → AlX2•CH2•CMe+2 → AlX2•CH2-polymer TO

2 TCH2—polymer + Al-hydrol. products AlX2•CH2—polymer—→

Check experiments with pre-formed terminally-unsaturated polyisobutenes of low and high DP, and with saturated hydrocarbons, gave results supporting our conclusions that the AlX+2 reacts only with double bonds to give Al–C bonds. Thus the supposition 2 is now supported at least qualitatively by direct experimental results, but the exact quantitative correlations remain to be established. A Short Communication on this subject will be submitted shortly to Makromolecular Chemistry.

References 1.

P. H. Plesch, Part IV, J. Chem. Soc., 104 (1964).

2.

a. J. P. Kennedy, In Polymer Chemistry of Synthetic Elastomers, Part I, p. 291, (ed. J. P. Kennedy and E. G. M. Törnquist) Interscience, N.Y. (1968). b. J. P. Kennedy and R. G. Squires, J. Macromol. Sci.-Chem., A1, 805 (1967).

3.

D. W. Grattan and P. H. Plesch, unpublished.

4.

P. H. Plesch, in The Chemistry of Cationic Polymerisation, Chapter 4 (ed. P. H. Plesch) Pergamon Press, London (1963).

5.

J. P. Kennedy and A. W. Langer, Adv. In Polymer Sci., 3, 508 (1964).

6.

A. M. Eastham, in Encyclopaedia of Polymer Science, 3, 35, John Wiley Inc., New York (1964).

7.

P. H. Plesch, in Progress in High Polymers, Vol. 2, p. 137, (ed. J. C. Robb and F. W. Peaker) Illiffe Books, London (1968).

8.

See for example: C. M. Fontana, in Cationic Polymerisation and Related Complexes, pp. 126, 129, (ed. P. H. Plesch) W. Heffer and Sons, Cambridge (1953); R. O. Colclough and F. S. Dainton, Trans. Faraday Soc., 54, 894, 898 (1958).

9.

P. H. Plesch, J. Applied Chem., 1, 269 (1951).

10. J. H. Beard, P. H. Plesch and P. P. Rutherford, J. Chem. Soc., 2566 (1964). 11. M. Chmelir, M. Marek and O. Wichterle, J. Polymer Sci., C16, 833 (1967).

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A New Theory of Initiation by Aluminium Halides (1972) 12. J. P. Kennedy, J. Macromol. Sci.-Chem., A6, 329 (1972). 13. W. R. Longworth and P. H. Plesch, J. Chem. Soc., 1887 (1959). 14. A. Halpern and A. Polaczek, Inst. of Nuclear Research Report, No. 491/V, Warsaw (1963). The authors did not analyse their data and D. W. Gratton found the second-order nature of the reactions by an order-analysis of their conductivity-time curves. 15. H. Wendt, Ber. Bunsenges., 68, 29 (1964). 16. J. P. Kennedy and R. M. Thomas, J. Polymer Sci., 46, 233 (1960). 17. F. Fairbrother and J. F. Nixon, J. Chem. Soc., 3224 (1958). 18. W. R. Longworth, P. H. Plesch and P. P. Rutherford, Chem. Soc. Special Publ., 13, 115 (1959); P. H. Plesch, J. Macromol. Sci. Chem., A6, 979 (1972). 19. The relevant results are those of Vesely’s group and they are cited fully and discussed in detail in Ref. 4. (ZAV for Zlamal, Ambroz and Vesely). 20. M. Chmelir and M. Marek, Coll. Czech. Chem. Commun., 32, 3047 (1967). 21. M. Chmelir and M. Marek, J. Polymer Sci., C23, 223 (1968). 22. M. Chmelir and M. Marek, J. Polymer Sci., C22, 177 (1968). 23. P. Lopour and M. Marek, Makromol. Chem., 134, 23 (1970). 24. R. E. Van Dyke, J. Am. Chem. Soc., 72, 3619 (1950). 25. Z. A. Sheka and I. A. Sheka, Doklady Akad. Nauk USSR, 63, 739 (1950). 26. H. C. Brown and W. J. Wallace, J. Phys. Chem., 75, 6279 (1953). 27. D. G. Walker, J. Phys. Chem., 64, 939 (1960). 28. The author’s translation of the last sentence of Ref. 22. 29. M. Marek and L. Toman, IUPAC Symposium on Macromolecules, Preprint I-97 Helsinki (1972). 30. P. Lopour, J. Pecka and M. Marek, Makromol. Chem., 151, 139 (1971).

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Developments in the Theory of Cationoid Polymerisations

268

4.6

Approaches Towards a Comprehensive Theory of the Cationic Polymerisation of Olefins (1974) P. H. Plesch

This paper was first published in Die Makromolekulare Chemie, 1974, 175, 4, 10651076. Reprinted with permission from Wiley-VCH, copyright 1974.

Prologue In this paper the relevance of Binary Ionogenic Equilibria (BIE) to various aspects of cationic polymerisations is explained and explored for the first time. There is mention that the kp+ values of Bawn, Ledwith et al. may be faulty because of their neglect of the BIE involved in both initiation and propagation; actually, much later, most of their results were found to be entirely wrong (see paragraph 4.2.1 of Section 5.7). Further, the complexing of the MtXn initiator with the monomer is considered here for the first time, and a rate-equation is derived which takes account of this and also of the BIE. It shows how the freeing of complexed MtXn as the monomer is consumed during a polymerisation can account for the low kinetic orders, which were often found for these polymerisations. There is also an attempt to account for the puzzlingly varied behaviour of TiCl4 in terms of the BIE and of its complexation with alkenes.

Summary Some of the factors which influence, or must be contained in, a Comprehensive Theory of the cationic polymerisation of olefins are discussed from new points of view, starting from the author’s new theory concerning initiation by metal halides. Alleged determinations of the rate constant kp+ are criticised because they ignored two equilibria which make the concentration of growing polymer chains [Pn+] in general less than the nominal concentration, c0, of initiator. One of them is a binary ionogenic equilibrium involving metal halide MtXn and polymer halide PnX. The other is between metal halide and olefin. An equation relating [Pn+] to c0 is deduced which takes account of these equilibria. The importance of the second equilibrium is illustrated by the way in which it provides simple explanations of hitherto obscure phenomena. Some of these arise during the interaction of aluminium halides with olefins in different circumstances, others concern

269

Developments in the Theory of Cationoid Polymerisations the different interactions which can take place between titanium tetrachloride and 1,1diphenylethylene. The fact that titanium tetrachloride appears to be able to initiate without co-initiator in some systems, but requires one in others is explained by the self-ionisation of the metal halide and the effects of impurities.

Introduction At the IUPAC Polymer Symposium in Helsinki in 1972, I put forward a new theory concerning the initiation of cationic polymerisations by metal halides [1]. This comprised three principal ideas: (a) Initiating metal halides undergo self-ionisation in solution. (b) Metal halide cations formed in this way can be the principal initiators in certain circumstances, and act by combining additively with the monomer to give a metalated carbenium ion. (c) The metal halides form complexes with the monomers. The usefulness of these ideas in clearing up some old mysteries and puzzles made me think that we are now reaching a clarification of ideas which is bringing a comprehensive theory of cationic polymerisations at last within sight, if not yet within our grasp. A further reason for believing this is that advances in the fields of anionic polymerisation, of radiation chemistry, of electrochemistry, of donor-acceptor complexes, and others, have helped to define the limits within which the comprehensive theory must be constructed. It may be useful to show here just what some of these limits are.

Some aspects of propagation Without doubt the kinetic aspect is amongst the most important which determine the nature of the Comprehensive Theory which we are seeking. Starting from the fact that in hydrocarbon medium (dielectric constant DC ≈ 2) the kp+ values are in the range 106 to 109 l mol-1 s-1, conventional rate-theory enables one to calculate that in solvents of greater DC the kp+ will be smaller, and in particular that if the DC is ca. 10, the kp+ will be in the region of 102 to 104 l mol-1 s-1. The kp+ values obtained by Bawn, Ledwith et al. [2] for the polymerisation of isobutyl vinyl ether in methylene dichloride and by Pepper [3] for the Stage I polymerisation of styrene by perchloric acid in methylene dichloride, are indeed of this order of magnitude. Conventional kinetics and electrochemistry then tell us to what extent free and paired cations will be important in different circumstances and from different points of view (rate, yield, degree of polymerisation, tacticity) and this is one of the strands of the Comprehensive Theory [4].

270

Approaches Towards a Comprehensive Theory of the Cationic Polymerisation of Olefins As far as the kp+ for the isobutyl vinyl ether are concerned, the critical examination below will reveal another line of reasoning which must form part of the Comprehensive Theory. In our opinion the kp+ values calculated are wrong -but not very wrong; probably they are too small by a factor of between 2 and 10. The reason is that in evaluating the kp+ by means of the defining equation with m = monomer concentration

– dm / dt = kp+ [ Pn+ ]m

(1)

it was assumed that the concentration of growing chains [Pn+] was equal to the nominal concentration c0 of the initiating trityl or tropylium salt. It now appears as a consequence of our electrochemical study of acetylium hexafluoroantimonate that this is unlikely to be so in general and in particular for the anions used in the kinetic study (BF–4 and SbCl–6)[5]. Our investigation showed that in solution CH3CO+SbF–6 is in equilibrium with CH3COF and SbF5. It follows that analogous equilibria must be expected in polymerising solutions, so that the concentration of propagating cations (irrespective of whether they are free or paired) is determined by an ionogenic equilibrium involving two molecules. Suppose that we have an initiator which is an organic salt R+MtX–n+1, and that its nominal (analytical) concentration is c0; suppose further that it yields polymer Pn, which will be present in the form of growing ions Pn+ and dormant molecules PnX (dead molecules formed by transfer are irrelevant to the present discussion). These two species are involved in an equilibrium which, although largely neglected hitherto, was in fact discussed by me twenty years ago [6]. This is the equilibrium (i) which determines [Pn+] directly: Kp

Pn X + MtX n ↔ Pn+ + MtX n– +1

(i)

However, this is not the only relevant equilibrium. The halide MtXn is necessarily one of the class of electron-deficient compounds which form complexes with monomers: Kc

MtX n + P1 ↔ MtX n ⋅ P1

(ii)

If one takes into account the charge-balance [Pn+] = [MtX–n+1] and the mass-balances for Mt:

c O = [MtX n ] + [MtX n– +1 ] + [MtX n ⋅ P1 ], and for the ‘extra’ halogen atom X:

c O = [MtX n– +1 ] + [ Pn X] one obtains the following equation for [Pn+]:

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Developments in the Theory of Cationoid Polymerisations

[ Pn+ ] = K p1 / 2 cO /( K p1 / 2 + [1 + Kc m]1 / 2 )

(2)

where m = [P1]. Equation (2) shows quantitatively what is intuitively obvious, namely that as the monomer is consumed and thus more of the MtXn is set free, equilibrium (i) is shifted and [Pn+] increases. In other words the deceleration expected in a reaction due to consumption of monomer may be compensated - more or less, according to circumstances - by a concurrent increase in the concentration of growing chains; this effect may well account for the low internal order found in many polymerisations. The point can be seen more clearly from Equation (3) which is obtained by substituting Equation (2) into Equation (1):

– dm / dt = kp+ K p1 / 2 cO m /( K p1 / 2 + [1 + Kc m]1 / 2 )

(3)

In order to obtain kp+ one can follow several different procedures. One could use the inverted form (4) of Equation (3):

cO m /(– dm / dt) = 1 / kp+ + (1 + Kc m)1 / 2 /( Kp1 / 2 kp+ )

(4)

and from sufficiently accurate rate measurements obtain kp+ by computer; this method, however, is unlikely to give very accurate values. Another, more indirect but perhaps more efficient method, would be to determine Kp for a number of typical systems, perhaps by use of model compounds, and then to select for kinetic experiments initiator systems for which Kp is so great that [Pn+] is effectively equal to c0, so that then the simple Equation (1) with [Pn+] = c0 is applicable. The trouble is that this method will probably only work for fairly polar solvents, because it is to be expected that Kp will be smaller, the less polar the solvent. This effect is probably one of the factors responsible for the improbably low kp+ value obtained by Higashimura for styrene in benzene solution [7]. In any case, for solvents of low polarity the participation of paired cations must be taken into account, which makes the relevant equations rather more complicated, but does not alter the relevance and importance of equilibrium (i).

Some aspects of initiation 1 Aluminium halides One reason why the Comprehensive Theory which I have in mind has been so elusive is that it has proved to be enormously difficult to obtain a body of facts which could be

272

Approaches Towards a Comprehensive Theory of the Cationic Polymerisation of Olefins regarded as well established and well understood, and on whose interpretation and meaning the majority of workers would agree. It is instructive to examine briefly the logical chain which is the origin of this situation; it may be expressed in the form of a series of propositions, thus: 1. Carbenium ions are generally so reactive that the rate of their addition reactions with monomer or with a basic scavenger can be very close to the collision rate. 2. For this reason carbenium ion polymerisations with conveniently observable halflives involve concentrations of carbenium ions in the range 10-9 to 10-6 mol l-1. 3. Since the reactive carbenium ions can react with many compounds to give less reactive or unreactive products, very low concentrations of such carbenium ion scavengers (poisons, inhibitors) can exert great influence on the rate and pattern of the polymerisations. 4. In many systems the initiating species are formed from compounds, such as metal halides, which can generate ions by reacting in different ways with several types of compounds. For this reason traces of such co-initiators will alter the rate of formation and the nature of the ions and thus the pattern of the ensuing polymerisations. These simplified propositions do not exhaust the subject, but serve to show up some of the fundamental reasons why it has proved so difficult to agree on what the facts really are. The experimentation required to prove that any observed phenomenon is not an artefact due to impurities is always extremely lengthy and tedious. The question of purity becomes of paramount importance when one studies the details of initiation by metal halides. A study of aluminium halide solutions in alkyl halide solvents shows that provided the impurity level is less than about 10-7 mol l-1, the halides ionise simply by binary disproportionation: K′

2 AlBr3 ⋅ CH 3Br ↔ AlBr2+ (CH 3Br )2 + AlBr4_

(iiia)

and for the chloride probably K

2 Al 2 Cl 6 ↔ Al 2 Cl 5+ + Al 2 Cl 7–

(iiib)

For the sake of simplicity we will argue in terms of (iiia) since there is no difference in principle between the two alternative versions. The details of these equilibria have now been explored very thoroughly [8]. It needs to be emphasised that the cation is not to be regarded as ‘bare’. It is most probably solvated

273

Developments in the Theory of Cationoid Polymerisations specifically by one or two solvent molecules RX, especially if it is a simple ion AlX+2 rather than a double ion Al2X+5. Thus one should think of the initiation reaction as a transfer of AlX+2 or of RX·AlX+2 from RX to the more basic monomer P1:

( RX )2 ⋅ AlX 2+ + P1 → RX ⋅ X 2 AlP1+ + RX

(iv)

At this point we are really at the closest approach to a Comprehensive Theory, because the initiation by AlX+2, expressed by Equation (iv), has now been proved for isobutene and made very probable for styrene and norbornadiene by a radio-tracer technique which leaves little room for any alternative explanation [8]. We can now begin to see some of the implications of the theory and in which directions its applicability can be tested. In the course of these considerations one must always keep in mind that the rate of the ionogenic reaction (iii) (‘left to right’ rate-constant kf) is very small in comparison with the rates of polymerisation and of complex formation (reaction (ii)) and that the equilibrium concentration of ions is very small (see Table 1).

Table 1 Experimental values of the equilibrium constants, K and K', for self-ionisation (Eq. (iii)) and of the rate-constant, kf, of ion formation, the 'left to right' process of Eq. (iii); kf may be a composite quantity for some systems, especially at low temperatures Types of metal halide

Solvent

Temperature in °C

108•K′′ or 108•Ka

106•kf mol l-1 s-1

Notes b

AlBr3

CH3Br

0

1.1

4.5 ± 1

I

AlBr3

CH3Br

–78

24

600 ± 260

I

AlCl3

C2H5Cl

0

970a

840

I

a

C2H5Cl

–78

120 0

600

I

AlI3

CH3I

22

0. 7

0.4

II

InI3

C2H5I

22

0. 4

1

II

Al(C2H5)2Cl

CH3Cl

–40

3

40

II I

AlCl3

a Calculated for double ions, i.e., by Equation (iiib) b Notes: I D. W. Grattan and P. H. Plesch, unpublished data [8] II A. Halpern and A. Polaczek, Institute of Nuclear Research (Poland), Report No. 491/V (1963), interpreted by D. W. Grattan and P. H. Plesch III P. Giusti, P. L. Magagnini and P. Narducci, unpublished data interpreted by D. W. Grattan and P. H. Plesch

274

Approaches Towards a Comprehensive Theory of the Cationic Polymerisation of Olefins Having commented briefly on the first two parts of my new theory (the self-ionisation and the initiation by AlX+2), it is appropriate to consider the complex formation between monomer and metal halide, expressed by Equation (ii), which we have mentioned in the previous section. This complex formation actually provides an easy and plausible explanation for some of the hitherto rather obscure phenomenological differences which are observable when monomer and aluminium halide solutions are brought together in different ways; we can distinguish three such techniques which give very different results. 1. When the aluminium halide solution is added to a solution of monomer, only the aluminium present as cations can initiate (disregarding any active cations that may have been formed by reaction of the initiator with impurities in the solvent) and the unionised aluminium halide becomes complexed with monomer and thus formation of further ions from it stops or becomes at best a very slow process. This is what was called the ‘Esso technique’ [1] and it was the commonest method of experimentation. If the system is sufficiently free from terminating impurities and if the propagating ions are not occluded in precipitated polymer, all the monomer should be consumed eventually, and so the bound aluminium halide should in the end become free by the shifting of equilibrium (ii). However, these conditions are generally unfavourable for the reaction going to completion, and it comes virtually to a stop at incomplete conversion. 2. A quite different situation prevails when the monomer is run into a solution of the aluminium halide. The polymerisation initiated by the AlX+2 ions in solution is very fast so that there is never sufficient monomer to complex an appreciable fraction of the aluminium halide; thus there is no obstacle to the continuous formation of AlX+2 ions by reaction (iii), and the polymerisation therefore goes to completion. Such polymerisations are always accompanied by a rapid and large increase in conductivity. 3. However, if isobutene is distilled very slowly into a solution of aluminium bromide in methyl bromide, or of aluminium chloride in methylene dichloride, one sees a very different and strange behaviour (Figure 1). There is no polymerisation, the conductivity drops to a low, nearly constant level, and even relatively large amounts of isobutene added rapidly at this stage do not polymerise. The drop in conductivity is in striking contrast to the spectacular increase which occurs when there is polymerisation. After the reaction mixture has been killed with water or ethanol, virtually all the isobutene is still present as monomer; but sometimes traces of oligomers are found. This is a new phenomenon and nothing like it appears to have been reported. It can be interpreted as follows: Since the extent of self-ionisation of aluminium chloride and bromide in the alkyl halide solvent is very small (Table 1) ([AlX+2]/[AlX3] approximately 10-4) the isobutene whose concentration is always kept very low, reacts preferentially with the much more abundant AlX3 to form the complex, and if any isobutene does react with AlX+2, the resulting 275

Developments in the Theory of Cationoid Polymerisations

Figure 1 The change of specific conductivity when isobutene was distilled slowly into 36 ml of a 1.4 x 10-4 mol/l solution of aluminium bromide in methyl bromide at –74.5 °C. No polymer or oligomer was formed. The isobutene was added continuously over a period of 2 h 40 min carbenium ion does not find any free monomer with which to react further. By consumption of AlX3 the equilibrium (iii) is shifted completely to the left; the residual conductivity is due to ions which cannot initiate polymerisation and these probably include oxonium ions derived from water and other impurities. By this complex formation with monomer the AlX3 is effectively deactivated. It is important to realise that these experiments not only provide convincing evidence for the initiation by ions derived from the initiator, but also an almost insuperable obstacle to Kennedy’s ‘allylic hydride’ theory [9] and any other theory which involves a reaction of monomer with AlX3 molecules as the initiation step.

2 Titanium tetrachloride The formation of complexes between olefins and metal halides is particularly well documented for titanium tetrachloride [10, 11, 12]; thus my theory can be applied with some confidence to systems which involve this metal halide. I will show that it provides a simple qualitative explanation for observations which have so far remained obscure and affords also a quantitative interpretation which is open to testing once the necessary 276

Approaches Towards a Comprehensive Theory of the Cationic Polymerisation of Olefins observations are available. Sigwalt [13] reported that when TiCl4 and 1,1-diphenylethylene were mixed in methylene dichloride in the molar ratio, 1:100, there was no dimerisation and the UV-visible spectrum showed some weak and ill-characterised absorption; but if the ratio was less than about 10, then the spectrum of RCH2C+(C6H5)2 appeared and dimer was formed. The simple qualitative explanation is that in the presence of a large excess of olefin all the metal halide is complexed, but when the [olefin]/[TiCl4] ratio is small, there is sufficient free metal halide to form TiCl+3 ions by the analogue of reaction (iii) [14], and these ions then react with the olefin in a manner analogous to reaction (iv), thus generating the observed carbenium ions. We have here essentially five linked equilibria:

2 TiCl 4 ↔ TiCl 3+ + TiCl 5–

(v)

TiCl 4 + P1 ↔ TiCl 4 ⋅ P1

(vi)

TiCl 3+ + P1 ↔ TiCl 3 P1+

(vii)

TiCl 3 P1+ + P1 ↔ TiCl 3 P2+

(viii)

TiCl 3+ + P2 ↔ TiCl 3 P2+

(ix)

and two non-equilibrium reactions

YP2+ + P1 → YP2 + HP1+

(x)

where Y = TiCl3 or H, and

YP2+ + B → Yind + HB+

(xi)

where ind is the indane dimer and B is P1 or some other proton-acceptor. The initiation reaction (vii) and reaction (ix) are written as equilibria because of the very low strength of the Ti–C bond. This complicated system of equations is not amenable to a general analytical solution, but it is not quite as intractable as it may seem, because there is an unusually large number of observable variables: the total concentration of cations by UV-visible spectroscopy, the total concentration of Ti–C bonds by quenching with tritiated water, the concentration of monomer and of unsaturated and cyclised dimer-all as functions of reaction time! Further, the system can be simplified by the use of extreme conditions, as was done by the original investigators. 277

Developments in the Theory of Cationoid Polymerisations Thus this system could provide a very instructive testbed to examine the performance of my new theory of initiation. This brings us to the complicated and difficult question concerning the mechanism of initiation by titanium tetrachloride. There is extensive evidence, obtained with many different systems, that under certain circumstances titanium tetrachloride will only act as initiator in the presence of a co-initiator. There is also good evidence from different laboratories that in other circumstances a co-initiator is apparently not required, and in at least one system both types of initiation go on simultaneously [15]. It seems to me that we can understand these apparent contradictions by means of the ideas which are implicit in my earlier arguments. If the monomer concentration is not so high that all the titanium tetrachloride is complexed, and if the solvent is of suitable polarity, and if the system is sufficiently pure, then a rate of formation of TiCl+3 adequate for initiation by it can be expected. If, however, these conditions are not fulfilled, for instance if the solution contains such a high level of basic impurities that they compete effectively with the monomer for the TiCI+3 then there will be no polymerisation until the concentration of impurities has been reduced sufficiently. It seems most likely now that it is these circumstances which produce the ‘quiescent’ mixtures of monomer and initiator. In order to induce a polymerisation in such quiescent systems it is necessary to produce a sufficient quantity of reactive ions. This can happen either if one waits long enough for the self-ionisation to produce sufficient initiating TiCl+3 ions, or if one adds a co-initiator which reacts with the titanium tetrachloride to generate ions in a different manner and in greater numbers. In other words, if the conditions of the experiment are such that insufficient ions are formed by self-ionisation then a co-initiator is required to help generate the ions which are needed for the initiation of polymerisation. It should be clear now that the basic ideas involved here are very simple, but to the experienced investigator it is also clear that their testing and application are not easy.

Conclusion The topics which I have discussed were selected not so much because they could be considered more important than others, but because they had become ripe and ready to be placed before my colleagues and because they contained new ideas which I thought would help us in our understanding of the complicated phenomena which interest us all.

278

Approaches Towards a Comprehensive Theory of the Cationic Polymerisation of Olefins Michael Polanyi once said to me: ‘The laws of Chemistry must be simple, otherwise there would be no Chemistry’. This is a feeling which I share and you will no doubt have observed that the ideas and arguments which I favour are fundamentally very simple ones. However, it is an unfortunate fact of the scientific life that the simple ideas are by no means always the obvious ones, and we all are concerned with looking beyond the obvious and the trivial and finding the simple and the significant. I hope that I have made a useful contribution to this quest. I thank Professor Giusti for permission to quote the unpublished conductivity data in Table 1, and Dr. D. W. Grattan for help in the preparation of this paper.

References 1.

P. H. Plesch, IUPAC Symposium on Macromolecules, Helsinki 1972, Macromolecular Chem. - 8 (Supplement to Pure and Applied Chem.) Butterworths, London 1973, p.305.

2.

C. E. H. Bawn, C. Fitzsimmons, A. Ledwith, J. Penfold, D. C. Sherrington and J. A. Weightman, Polymer 1971, 12, 119.

3.

M. de Sorgo, D. C. Pepper, M. Szwarc, Chem. Comm. 1973, 419; J. P. Lorimer, D. C. Pepper, Int. Symp. on Cationic Polymerisation, Rouen 1973, Comm. no. 23.

4.

P. H. Plesch, Brit. Polym. J., 1973, 5, 1, 1.

5.

O. Nuyken and P. H. Plesch, Chem. and Ind., 1973, 8, 379.

6.

P. H. Plesch, J. Polym. Sci., 1954, 12, 481.

7.

T. Higashimura, H. Kusano, T. Masuda and S. Okamura, J. Polym. Sci. B9, 463 1971.

8.

D. W. Grattan and P. H. Plesch, unpublished; Thesis, University of Keele, 1973.

9.

J. P. Kennedy, J. Macromol. Sci., 1972, A6, 2, 329.

10. H. L. Krauss and J. Nickl, Z. Naturforsch. 1965, 630, 20b. 11. T. Saegusa, J. Macromol. Sci., 1972, A6, 6, 979. 12. D. S. Brackman and P. H. Plesch, J. Chem. Soc. 1953, 1289.

279

Developments in the Theory of Cationoid Polymerisations 13. G. Sauvet, J. P. Vairon and P. Sigwalt, Bull. Soc. Chim., France, 1970, 4031. 14. W. R. Longworth and P. H. Plesch, J. Chem. Soc. 1959, 1887. 15. W. R. Longworth, C. J. Panton and P. H. Plesch, J. Chem. Soc. 1965, October, 5579.

280

4.7

The Initiation of Polymerisations by Aluminium Halides (1980) D. W. Grattan and P. H. Plesch

This paper was first published in Die Makromoleculare Chemistry, 1980, 181, 751-755. Reproduced with permission by Wiley-VCH, copyright 1980.

Prologue This paper marks the end of the quest upon which the present writer set out in 1944 when he joined M. Polanyi’s Department of Physical Chemistry at the University of Manchester. The first entry in his notebook under the date 7.11.1944 reads as follows: “The polymerization of isobutene is so far a repeatable but not a reproducible reaction. [A] Following on from the work of Seymour et al. in this department and work at I.C.I. and in America, we are attempting to elucidate the reaction mechanism of this polymerization. In particular, we want to find out how it is that a decrease in temperature increases reaction rate and within what limits that holds. It is also of considerable interest to discover why it is that under certain conditions catalyst and monomer can coexist without reaction taking place.” It so happened that 30 years later to the day I gave a research colloquium at Manchester University in which I could report that this job had now been completed, and we have in this paper the experimental details and the results concerning the title reaction which form the basis for the theory expounded in Section 4.5. The central point is the experimental proof that in very pure systems the principal initiating species is the AlX2+ ion (X = Cl or Br). Whilst this idea was quite old as a theoretical suggestion, its experimental verification had not been attempted previously. It is evident that this work could not have been done without the Keele group’s previous very thorough investigation of Binary Ionogenic Equilibria (BIE) (30, 89, 104, 111, 122, 127, 138), especially, of course, those of the aluminium halides in alkyl halide solutions (104). That work also finally clarified an area of inorganic chemistry which had been exceedingly confused, largely because previous workers had used impure systems and inadequately rigorous methods.

281

Developments in the Theory of Cationoid Polymerisations However, in addition to these advances, the paper contains two further innovations which are important outside the domain of polymer chemistry. One is the demonstration that in adequately pure systems aliphatic carbenium tetrahaloaluminates, R3C+AlX4¯ in solution are stable electrolytes. The other is the direct demonstration that AlX3 and isobutene form a stable, reversible, complex. The paper under review also contains the first application of a new kinetic idea to explain the very old mystery why in polymerisations, especially of isobutene, only an infinitesimally small amount of AlCl3 is consumed and the remainder seems to co-exist with unreacted monomer. Subsequently, the same idea served to explain another puzzle, namely why in the polymerisations by protonic acids only a very small fraction of the acid is consumed by the initiation (144). The very demanding work recorded here and its exhaustive exploitation yielding the sought-for results and also many quite unexpected insights are an instructive example of this worker’s style which he explained in the General Introduction. It is all the more curious that this entire work has been effectively ignored in a recent text-book which thereby was out-of-date and inadequate even as it appeared [B]. The scant recognition which the findings recorded here have found amongst polymer chemists are only partly explicable by their general unfamiliarity with electrical, especially conductimetric, evidence. Even so experienced an all-round chemist as the Nobel laureate George Ola′h, in a lengthy discussion refused to see that the formation of halonium ions, RX2+, in the systems involved in this work, which was favoured by him, is incompatible with the conductimetric evidence (104), a matter which is actually taken up explicitly in that paper.

References A.

The distinction between repeatable and reproducible was clarified much later by the present author (152).

B.

“Cationic Polymerizations”, Ed. K. Matyaszewski. Marcel Dekker, Inc. (N.Y. 1996).

282

The Initiation of Polymerisations by Aluminium Halides (1980)

Summary The polymerisation of isobutylene by aluminium chloride and bromide in corresponding alkyl halide solution was studied by conductivity measurements and radio-tracer techniques in high-vacuum apparatus. Some of the reaction mixtures were killed with tritiated water. The conductivity changes during and after polymerisation and the unexchangeable tritium in the polymers support the theory that initiation is by addition of AlX2+ to the double bond of the monomer with consequent formation of a carbenium ion which then propagates. Subsidiary experiments with styrene and 2,5-norbornadiene and with a saturated hydrocarbon confirmed our conclusions. Contrary to accepted views, we found tertiary carbenium tetrahaloaluminates to be stable electrolytes in our very pure alkyl halide solvents. The very slow addition of isobutylene to solutions of aluminium halide in alkyl halide reduced their conductivity markedly and produced nonreacting mixtures from which the monomer but no polymer could be recovered. This is shown to prove the long suspected complexing of isobutylene with aluminium halide and rules out all theories of initiation based on interaction of initiator molecules with monomer. It is shown that our theories can explain most features of the polymerisations; our results are compared with those of others.

Introduction The mechanism of initiation of cationic polymerisations by metal halides was clarified and systematized to some extent by the discovery of the phenomenon of co-catalysis or co-initiation. But, whereas there was, by the mid-1960s, good evidence that at any rate in many systems the halides of boron, titanium, and tin required a co-initiator, the position with regard to the best-known and most popular initiator, and the one which was of greatest economic significance, aluminium chloride, remained obscure. Of the vast number of published experiments on the system, aluminium chloride + isobutylene, hardly any could provide evidence concerning the initiation reaction, because they were almost exclusively concerned with measurements of yields and degree of polymerisation (DP). The work of the Brno group which for the first time included conductivity measurements on the same system, provided quite different insights and showed the way which we eventually followed; but that too did not give any clear leads as to the initiation mechanism. Nor did any of the very few studies done with other monomers and aluminium halides provide any clear evidence on the mode of action of the initiators [1]. In the middle 1960s the situation changed because it was shown that for the system, aluminium chloride + isobutylene + methylene chloride, water is not a co-initiator and that its only effect is to depress yield and DP [2]. About the same time it was shown that

283

Developments in the Theory of Cationoid Polymerisations aluminium bromide would initiate the polymerisation of isobutylene in heptane under conditions so dry that neither boron trifluoride nor titanium tetrachloride would initiate without the addition of water [3]. Moreover, the rate of polymerisation was of second order with respect to the initiator concentration. This work was of great importance because the absence of any ionogenic compound from the reaction mixture (in contrast to our experiments [2] with the potentially ionizable solvent methylene chloride) pointed to the conclusion that this reaction would go without a co-initiator. (A useful compilation by Kennedy showed subsequently that it may not be unique in this respect [4]). In order to account for the observations and the kinetics, it was suggested [3] that initiation was by the AlBr2+ ion, formed by the self-ionisation of the halide according to Equation (i):

2 AlBr3 ↔ AlBr2+ AlBr4–

(i)

The Prague workers generalised this theory in order to explain the action of the syncatalytic systems consisting of halides of two metals [5], but later they apparently abandoned it [6]. What they did not see was that if their idea were supplemented and extended as will be shown below, it could explain most of the important features of the polymerisation of isobutylene by aluminium chloride which had defied explanation until then. They also did not test their theory in any detail. The senior author of the present paper took up the suggestion of Chmelir, Marek, and Wichterle and developed from it a detailed theory which he presented in the form of three suppositions, accompanied by an account of the origin of the theory and a critical assessment of it [7]. Some further discussions of the theory and an ‘interim report’ on the evidence for it were presented subsequently [8]. The present paper contains a full account of the theory, its testing, and its application. For the sake of clarity the original three suppositions are now presented as propositions: Proposition 1: The initiator solutions of aluminium halide, AlX3, in alkyl halide RX contain ions formed by the self-ionization of the aluminium halide: K2

2 AlX 3 ↔ AlX 2+ + AlX 4–

(ii)

The equilibrium constant (K2) for reaction (ii) under various conditions has been measured; it is very small, so that only a very small fraction of the aluminium halide is ionized [9]. If the system is insufficiently pure, the concentration of ions derived from impurities may exceed that of the AlX2+. The AlX2+ is certainly solvated by one or two molecules of RX, but this is unimportant in the present context.

284

The Initiation of Polymerisations by Aluminium Halides (1980) Proposition 2: When the initiator solution is introduced into a monomer solution, the cations react with the double bond to give ‘the active species’ which is an aluminated carbenium ion containing an Al–C covalent bond, as shown in Equation (iii): +

AlX 2+ + H 2 C = C(CH 3 )2 → X 2 Al – CH 2 – C(CH 3 )2

(iii)

1 The cation 1 then starts the polymerisation. Cations derived from some impurities may also act as initiators. The ensuing polymerizations are terminated fairly rapidly. Since the concentration of cations of all kinds in the initiator solutions is much smaller than that of aluminium halide, the notoriously low efficiency (mol polymer/mol AlX3) can be explained on this basis. Proposition 3: Most of the un-ionized aluminium halide becomes complexed with unreacted monomer; the resulting complex is not an initiator. The concentration of free aluminium halide is thereby reduced so much, that the rate of the ionogenic reaction (ii) (the formation of AlX2+) becomes negligibly small, and there is thus no further initiation. This accounts for the limited yields which are generally found in this type of polymerisation, and which had defied plausible explanation. Our work which was aimed at testing the proposition 1 has been reported [9]; the testing of the propositions 2 and 3 forms the subject of the present paper. Our main objective was the identification and determination of the Al–C bonds. This we did by killing the reaction mixtures with tritiated water and then counting the tritium content of the polymers. In our systems this killing reaction forms one tritium-carbon bond (Equation (iv)).

X 2 Al – CH 2 – C(CH 3 )2 – K + T2 O → X 2 AlOT + TCH 2 – C(CH 3 )2 – K (iv) Tritium in the C–O–T groups, resulting from neutralisation of the carbenium ions, is removed by exchange during work-up of the polymers. We also obtained evidence for the formation of complexes between isobutylene and the bromide and chloride of aluminium; and we found that in sufficiently pure alkyl halides, polyisobutylium and tert-butylium tetrahaloaluminates are stable electrolytes. At about the time that the present work was done, there appeared a group of papers in which a very comprehensive and original attack upon the same set of problems was reported. As far as these results are relevant, they support our theory, and none of them are incompatible with it [10-16].

285

Developments in the Theory of Cationoid Polymerisations For our method of monitoring the ion population in the reaction mixtures, we chose electrical conductivity because the concentrations of ions involved were far too low for any kind of spectroscopic facility available to us at the time, and it was desirable to keep the reaction vessel attached to the vacuum line so that solvent and monomer could be added to or distilled out of it. In order to place our results in relation to those of others, we emphasise that in all this work we used the ‘reverse addition’ technique, i.e., we added monomer, or a monomer solution, to a solution of the initiator. Most other workers have used the ‘direct addition’ in which a solution of initiator is injected into a solution of monomer. However, some of the Italian work was done by the ‘reverse addition’ method [12, 13]. The reasons for the very different results obtained by both techniques will be explained.

Experimental part Materials: The methods used for the purification of aluminium bromide and chloride and for preparing phials of these catalysts, and the purification of methyl bromide, methylene chloride, and ethyl chloride, have been described [9]. The solvents were stored in a vessel coated with a sodium mirror and attached to the vacuum line, and they were metered into the observation cell by distillation from a hanging burette. NB It is extremely dangerous to contact alkyl halides with sodium unless they have been dried very well, e.g., with calcium hydride, and are free of oxygen!! Isobutylene (Philips Research Grade) was purified as described [17] by distillation on a vacuum line through a trap containing sodium at 350 °C. It was stored as liquid on a sodium mirror. Solutions in methyl bromide were made up by distilling the required quantities of solvent and isobutylene from hanging burettes along a vacuum line into a reservoir with Teflon tap, which was subsequently cut from the vacuum line and fused to a burette with Teflon tap which was then fused to the main vacuum manifold as shown in Figure 1. Styrene was purified from stabiliser and rough-dried conventionally, then it was distilled i. vac. and a 60 vol% middle fraction was stored over calcium hydride at 0 °C in the dark in a reservoir attached to the vacuum line. It was dosed into the observation vessel from a burette which was filled freshly for each experiment by distillation from the reservoir. 2,5-Norbornadiene (from Koch-Light Ltd.) of purity greater than 99% was purified by distillation through a Normatron automatic still at a reflux ratio of 25:1. The fraction (60 vol%) boiling at 89.3 °C/998 mbar was collected [18]: bp 89.5 °C/1013 mbar). Analysis by gas liquid chromatography (GLC) (Pye Unicam - with OVO-1 columns), showed one

286

The Initiation of Polymerisations by Aluminium Halides (1980)

Figure 1 Apparatus for polymerisations. For details see Grattan [9]. The polymerisations and other experiments are done in the conductivity cell E fitted with electrodes, stirrer, thermocouple, phial retainer, and phial breaker. TF1 to TF10 are ‘Rotaflo’ Teflon taps; TF5 goes to the vacuum line, TF6 to the solvent supply line. B1, B2, B3 are burettes of 1 cm3, 2 cm3 and 20 cm3 capacity, respectively. A is a 50 cm3 flask containing tritiated water, C contains monomer solution, and D contains toluene

minor peak (volume ratio 1:5000). The monomer was dried over freshly ground calcium hydride under its own vapour pressure, and was then distilled onto a fresh sodium mirror where it was stored over night. A methyl bromide solution of the monomer was prepared as described for isobutylene and it was dosed from a similar apparatus. Polyisobutylene and nonadecane, used in control experiments, were dissolved in ethyl bromide and the solutions were dried over calcium hydride before use.

287

Developments in the Theory of Cationoid Polymerisations Tritiated water (from the Radiochemical Centre, Amersham) was diluted to an activity of 5•10 -2 mCi•ml -1(1 curie = 3.7 x 1010 s -1. 2-Propanol, labelled with 14C (from Radiochemical Centre, Amersham), was diluted to 12.5 mCi•ml-1) with AnalaR 2propanol, in a vacuum apparatus. Analytical procedures: The molecular weights of the polyisobutylenes (Systematic name: poly(1,1-dimethylethylene) and of the polynorbornadienes (Systematic name: poly(3,5tricyclo[2.2.1.02, b]heptylene) were determined by membrane osmometry in toluene solution and those of the polystyrenes were determined by vapour-pressure osmometry in chloroform. The radiochemical assays were done as follows: At the end of a polymerisation experiment, when the conductivity had become constant, a ten-fold excess of tritiated water was added from a burette (see Figure 1), the cell was warmed rapidly to room temperature, and any polymer which had been precipitated during the polymerisation was allowed to re-dissolve. It was always noted that no hydrolysis occurred until the solutions reached 0 °C. This could be seen from a rapid drop of conductivity to a very low value. The solvent and most of the tritiated water were then distilled out, within about 15 minutes. The polymer was then dissolved in toluene, also run from a burette into the reaction vessel, which was then cut from the vacuum line. The polymer was precipitated in methanol and prepared for the determinations of radioactivity and DP. For the radiochemical assay the polymers were dissolved in toluene, re-precipitated in methanol, dried, weighed, re-dissolved in toluene, and the activity determined. The processes of precipitation and dissolution were repeated until the activity of the polymer became constant, (up to 7 repetitions). It was assumed that when the activity had become constant, all the excess of tritium had been removed. The activity of the polymers was determined in toluene solution with Koch-Light KL.356 xylene-based scintillator in 4 ml glass vials, at an efficiency of 24% for tritium and 75% for 14C by means of an IDL liquid scintillation counter type 6012. Apparatus: The polymerisation experiments were done in a conductivity cell of the type described [9], which was attached to a vacuum manifold as shown in Figure 1. The measurement of conductivity and the temperature control were done as described [9]. Procedure: The cell, charged with a phial of the aluminium halide, was fused to the vacuum line at X (Figure 1) and then flamed and pumped for about 24 h before each experiment. Then the solvent was distilled into the cell and brought to the required temperature, its conductivity was checked, and then the phial of aluminium halide was broken. When the conductivity had become constant, the required volume of monomer solution was run in rapidly from its burette. In most experiments several additions of monomer were made into the same reaction mixture. 288

The Initiation of Polymerisations by Aluminium Halides (1980) A very rapid polymerisation accompanied each addition of monomer, and sometimes polymer precipitated out. The amount was exceedingly hard to judge, but with isobutylene and aluminium bromide it was normally very little. At −78 °C more polymer was seen to come out of solution than at −63 °C. Throughout the whole process the solutions always remained colourless, except in experiments with styrene, in which the solution and the precipitated polymer became yellow. Since most of our observations on the reacting systems were made by means of conductivity measurements it is necessary to remember that in these systems the only factor which increases conductivity is an increase in the concentration of ions, but that a decrease of conductivity could be due to any or all of the following effects: increase of size of cation by polymerisation, increase of viscosity of solvent due to polymer, occlusion of ions in precipitated polymer, trapping of polymer between the electrodes. A similar list was given by Matyska in one of the earliest applications of conductivity measurements to a cationic polymerisation, that of isoprene by aluminium bromide in toluene solvent [19].

Results Isobutylene polymerisation

Conductivity changes In order to study the changes of conductivity which accompany the polymerisations, a wide range of experimental conditions was explored with aluminium bromide in methyl bromide and with aluminium chloride in ethyl chloride; these will be described separately. The polymerisations with ‘bromides’ were carried out at 0, –23, –63, and –78 °C. In each experiment approximately six similarly sized doses of a methyl bromide solution of isobutylene were added at approximately 15 minute intervals to a solution of aluminium bromide in methyl bromide. The details of each experiment are shown in the legend to Figure 2. On each occasion when the monomer was added there was a large and rapid increase of conductivity. This is illustrated in Figure 2 for polymerisations at 0, –23, and –63 °C (R1, R2 and R3). These plots show that the conductivity during polymerisation was several orders of magnitude greater than the conductivity of the initiator solution and that the shapes of the conductivity-time curves were similar at all temperatures. Observation of the reaction mixtures showed us that the polymerisations were completed in a few seconds (temperature surge, precipitation of polymer, changes of flow-pattern due to increase of viscosity, etc.). However, the conductivity traces, such as those shown in Figure 2, showed a protracted increase in conductivity. This, however, did not continue indefinitely, and in all experiments which were left sufficiently long the conductivity 289

Developments in the Theory of Cationoid Polymerisations

Figure 2 The change in conductivity (κ) during the polymerisation of isobutylene by a solution of aluminium bromide in methyl bromide. In each experiment the isobutylene was added in several similar doses, as a solution in methyl bromide (3.3 mol•dm-3). The polymerisations were finally stopped with a large excess of tritiated water; conditions are given in the following Table

290

The Initiation of Polymerisations by Aluminium Halides (1980) 2 Expt. Temp. 10 •[AlBr] no. in °C mol dm-3

R1 R2 R3

a

Vol. of AlBr3 sol. in ml

Amount of isobutylene added in mmol I

II

III

IV

V

0

3.6

56

2.39

2.05

2.21

3.1

2.65

–23

2.0

56

2.39

2.39

2.39

2.39

4.78

–63

4.8

56

3.32

3.32

3.32

3.32

3.32

a The DP was ca. 100 and the yield 95%; DP and yield for R1 and R2 are not available

reached a final value which was then stable for hours or days. This feature will be described in detail and discussed below. In Figure 3 the dependence of conductivity on the concentration of added isobutylene is shown for six experiments. This shows that the final equilibrium conductivity after polymerisation was repeatable from experiment to experiment. The results obtained at –63 and –78 °C were very similar. The conductivities of the initiator solutions before addition of the isobutylene were so low, in comparison with those of the solutions containing growing polymer, that the plots in Figure 3 appear to pass through the origin. With increasing number of monomer additions the increase of conductivity for a given dose of added isobutylene, decreased. This could have been caused by one or more of the effects which reduce the conductivity, which were mentioned in the Experimental Part. The polymerisations with ‘chlorides’ were carried out at –78 and 0 °C, and the results are shown in Figure 4, the legend to which contains the experimental details. The concentration of aluminium chloride was about one-tenth of that of aluminium bromide in the polymerisations described above. At –78 °C much more of the polymer came out of solution during polymerisation than in the polymerisations by aluminium bromide. There was no noticeable difference in the polymerisation rates with the two halides. The behaviour of the conductivity was similar to that described for initiation with aluminium bromide (compare Figure 2 with Figure 4). At –78 °C there was a big increase of conductivity for the first dose of isobutylene, but with further additions the changes in conductivity became less pronounced and the overall tendency was a decrease in conductivity. The latter effect could also have been caused by the factors mentioned in the Experimental Part. Figure 4 is remarkably similar to Figure 3 of Reference [19], which shows the conductivity changes when doses of isoprene are added to AlBr3 in toluene. Several experiments were done at −63 and −78 °C with the bromide or the chloride as initiator, in which one large dose of isobutylene was added rapidly to the initiator solution. Most of the polymer was precipitated and the products had the relatively high DP of ca. 4.5 •103. The conductivity showed little change in these experiments, (in one it actually decreased), presumably for the reasons which have been mentioned before.

291

Developments in the Theory of Cationoid Polymerisations

Figure 3 The final, equilibrium conductivity of polymerised mixtures of isobutylene and AlBr3 in methyl bromide as a function of the isobutylene concentration [IB]. Each point represents the conductivity resulting from an addition of isobutylene; conditions see following Table

Exp. no. 2

-3

10 •[AlBr3]/(mol•dm ) Temperature in °C Symbol

R1

C10

R2

R3

R8

R11

3.5

2.0

2.0

4.8

1. 3

0.6

0

0

–23

–63

–63

–78

❑

Δ

●

▲

■

O

Yield in %-

-

-

-

95

98

97

DP

-

-

-

ca. 100

45 0

400

292

The Initiation of Polymerisations by Aluminium Halides (1980)

Figure 4 Experiment D6: The change in conductivity during the polymerisation of isobutylene by 53 ml of a solution of aluminium chloride (1.0 mmol•dm-3) in ethyl chloride at –78 °C. The isobutylene was added as a solution (3.3 mol•dm-3) in methyl bromide, in six doses of 2 mmol each

Radiochemical assays A representative selection of the polymerisations described above were terminated with tritiated water, and one of them with 14C-labelled 2-propanol, and the polymers were worked up and assayed as described in the Experimental Part; the number of tritium atoms per polymer molecule is shown in Table 1. The polymers from Experiments R8, R15 and R9 contained ca. 1 tritium atom, and therefore originally 1 aluminium–carbon bond, per molecule. For those experiments in which the polymer remained in solution, the final value of the conductivity suggested a minimum of 1 mol of ions for 1 mol of polymer. When aluminium chloride was used as initiator, the results obtained resembled closely those obtained with the bromide. In experiment R11 the reaction mixture was treated with 14C-labelled 2-propanol, and the resulting polymer contained negligible activity. It follows that the reaction of the end-groups with the alcohol does not produce a detectable concentration of isopropyl ether end-groups. When the alcohol was added to the reaction mixture, the conductivity fell to zero within half a minute, which indicated a rapid removal of ions from the organic phase.

293

294

IBa

IB

IB

IB

NBD

St

St

IB

R3

R8

R15

R9

R10

R12

R14

R11b

1.4

2.4

2.9

6.8

3.3

4.34

3.25

1.1

mol•dm-3

10•[P1]

Br

Br

Br

Br

Cl

Br

Br

Br

X in AlX3

6. 1

2.6

7.2

9. 4

2.0

21.4

12.8

48

mol•dm-3

10•[AlX3]

–125

CH3Br/ C2H5Br

CH3Br

CH3Br –63

–78

–63

–78

C2H5Cl

CH3Br

–78

–63

–63

Temp. in °C

CH3Br

CH3Br

CH3Br

Solvent

a IB = Isobutylene, NBD = 2,5-norbornadiene, St = styrene b This polymer was killed with 14C-labelled 2-propanol

Monomer (P1)

Expt. no.

74

37

33

50

30

25

110

80

Polymer reaction time in min

97

99

76

20

96

99

98

95

Yield in %

400

44

44

460

430

3900

450

≈100

DP

No. of 14C incorp. <0.01

0.05

0.04

42

1.0

0.66

1.5

≈(4)

Amount of T in mol per mol polymer

Most of the polymer in solution during polymerisation

Little polymer In solution

Most of the polymer in solution during polymerisation

Notes

Table 1 Details of polymerisations killed with tritiated water or 14C-labelled 2-propanol

Developments in the Theory of Cationoid Polymerisations

The Initiation of Polymerisations by Aluminium Halides (1980)

The polymerisation of styrene and norbornadiene Once it had been established that aluminium-carbon bonds are involved in the polymerisation of isobutylene, other monomers were tested, namely styrene and norbornadiene (2,5bicyclo[2.2.1]heptadiene). The results are included in Table 1. The polymerisations were carried out as described for isobutylene. Styrene was dosed from a burette, then diluted with methyl bromide, and the resulting solution was added to the initiator solution; norbornadiene was added in methyl bromide solution in the same way as isobutylene. Neither monomer behaves quite like isobutylene during polymerisation because both give polymers which are precipitated to a greater extent than polyisobutylene. The styrene gave a gel which adhered to the walls of the vessel, whereas norborndiene gave a white crusty precipitate. In Experiment No. R14 at −78 °C the styrene solution was added in small amounts at ca. 5 minute intervals. Both the precipitated polymer and the reaction mixture in the cell became yellow, but this colour disappeared rapidly on hydrolysis; the conductivity changes are shown in Figure 5. In this experiment the polymer was allowed to dissolve by raising the temperature, and the conductivity of the solution increased as the dissolution proceeded. The final value of the conductivity indicates a concentration of ions which is of the same order as the concentration of carbon-aluminium bonds determined by the tritium method. The number of chains containing tritium is much smaller than for polyisobutylene. In another polymerisation, at −63 °C and with the styrene added undiluted, there was only a very small increase of conductivity during and after the polymerisation.

Figure 5 Experiment R14: The change in conductivity during the polymerisation of styrene by 70 ml of a solution of aluminium bromide (36 mmol•dm-3) in methyl bromide at –78 °C. Styrene was added as a 5 mol•dm-3 solution in methyl bromide, in six doses of 1.7 mmol each. There was a 99% yield of polymer of DP = 44

295

Developments in the Theory of Cationoid Polymerisations The conductivity changes accompanying and following the polymerisation of five portions of norbornadiene added to an aluminium bromide solution at −63 °C are shown in Figure 6 (Experiment No. R4). The polymer, which was precipitated during the reaction, was subsequently found to be insoluble and therefore presumably crosslinked. Since this polymer was, therefore, unsuitable for radiochemical assay, another experiment (R10) was done with norbornadiene in a mixture of methyl and ethyl bromide at −125 °C to prevent cross-linking. The polymer was soluble and the number of tritium atoms per molecule of polymer was much greater than for polyisobutylene.

Check and blank experiments To ascertain whether tritium could have entered the polyisobutylenes by a process other than the hydrolysis of a carbon-aluminium bond, we tested the reaction of suitable polymers with aluminium bromide. The polyisobutylenes were dissolved in ethyl bromide, and phials of aluminium bromide were crushed into these solutions, which were subsequently kept at 0 °C for ca. 15 minutes, and then hydrolysed in the usual way with tritiated water. The three substances examined in this way were polyisobutylenes of high and low DP, and nonadecane. The polyisobutylenes contain approximately one double bond per molecule. The results in

Figure 6 Experiment R4: The change in conductivity for the polymerisation of five doses of 5.5 mmol each of norbornadiene added to 56 ml of a solution of aluminium bromide in methyl bromide (18 mmol•dm-3) at –63 °C. The norbornadiene was added as a solution (2.5 mol•dm-3) in methyl bromide

296

The Initiation of Polymerisations by Aluminium Halides (1980) Table 2 show that ca. one molecule of tritium per polymer molecule was incorporated. In the experiment with nonadecane, no tritium was incorporated into the hydrocarbon. It therefore seems established that Al–C bonds are formed only from double bonds.

Preparation of non-polymerising mixtures of isobutylene and aluminium halides In some experiments with the same apparatus isobutylene was not added to the solution of aluminium halide as a solution, but it was distilled in very slowly through a capillary from a thermostatted hanging burette. The unprecedented result of these experiments was that no polymerisation occurred and that the isobutylene could be distilled out of the mixture and was recovered almost quantitatively. A brief preliminary account of these experiments has been given [8]; because of the novelty of this phenomenon, the experiments will be described in detail. The particulars are summarised in Table 3 and the conductivity changes during the experiments are shown in Figure 7. In Experiment C7 (triangular points in Figure 7), 50 mmol of isobutylene was added at –70 °C over ca. 2 h to 0.14 mmol of aluminium bromide in 40 ml of methyl bromide. According to the ratio (κe - κi)/κi, which was 0.25, the initiator solution was rather impure. No polymer was formed. The GLC of the solution after addition of iso-butylene (Figure 8) shows that some dimerisation had occurred, but that most of the isobutylene was unchanged. On warming this solution to 0 °C, the conductivity decreased to nearly zero, but there was no polymerisation and almost all the isobutylene was recovered unchanged by distilling it out of the conductivity cell. (As explained in Ref.[9], κi is the conductivity due to ions formed from impurities. κe is the final equilibrium conductivity, and κe – κi is, therefore, the conductivity due to the

Table 2 Check and blank experiments showing levels of incorporation of tritium into preformed polyisobutylenes (PIB) and a saturated hydrocarbon (nonadecane) Polymer

DPa

Amount of T in mol per mol of polymer

R5

PIB

1 30 0

1.3

R6

PIB

3 60 0

1.8

R7

Nonadecane

-b

0

Expt. no.

a Viscosimetrically determined b Molecular weight: 268.5

297

Developments in the Theory of Cationoid Polymerisations

Table 3 Details of the formation of non-polymerising mixtures of isobutylene and aluminium halides C7

C9

D2

C8

–70

–80

–78

–78

Br

Br

Cl

Br

CH3Br

CH3Br

C2H5Cl

CH3Br

102•[AlX3]/(mol•dm-3)

0.37

1.0

1.06

0.5

(κe - κi)/κi

0.25

≈103

>104

0.05

Final [IB]/(mol•dm-3)

1.38

5.0

0.37

2.0

Time for addition in min

160

105

40

1

None

None

100% of polymer

Temperature in °C X in AlX3 Solvent

Product

Trace of DIB

a

a Dimers of isobutylene

Figure 7 The change of conductivity when isobutylene is added very slowly to solutions of aluminium halide in alkyl halide at ca. –78 °C. No polymerisation occurred in any of these experiments. The experimental conditions are specified in Table 3. The point ▲ marks the conductivity of mixture C7 when it was warmed to 0 °C 298

The Initiation of Polymerisations by Aluminium Halides (1980) ions formed by the self-ionisation of the aluminium halide. Thus, (κe – κi)/κi is a measure of the purity of the solvent.) In Experiment C9 (circular points in Figure 7) 0.75 mol of isobutylene was added at –80 °C to 3.3 mmol of aluminium bromide in 40 ml of methyl bromide over ca. 1.5 h. According to the ratio (κe – κi)/κi, which was ca. 103, the initiator solution was very pure. No polymerisation took place; the isobutylene was shown by GLC analysis to be unchanged and this showed no dimers. In both experiments the conductivity decreased considerably as the isobutylene was added; this behaviour contrasts strongly with the large increases of conductivity that occur during polymerisation. Even though subsequently large quantities of isobutylene ([IB]/[AlBr3] ≈ 102) were added rapidly, no polymerisation took place; it seems, therefore, that once the non-polymerisation of isobutylene had been established, it mattered not whether further isobutylene was added slowly or rapidly: no polymerisation took place. In Experiments C7 and C9, the initiator solutions remained clear and colourless throughout the addition of isobutylene. At the end of the experiments the solutions were hydrolysed, and immediately the cloudy precipitate of Al(OH)3 was observed. This showed that under the conditions of the Experiment the initiator solution had not been hydrolysed and that the aluminium was still there, i.e., it had not been distilled out of the conductivity cell as a volatile organo-aluminium compound.

Figure 8 GLC trace of the solution from Experiment C7. See Table 3 and Figure 7

299

Developments in the Theory of Cationoid Polymerisations In Experiment C8, in which conditions were similar to Experiments C7 and C9, the isobutylene was added rapidly in ca. 1 minute, and a polymer of high molecular weight was formed immediately. The same behaviour was found for the addition of isobutylene to solutions of aluminium chloride in ethyl chloride. In Experiment D2, 29 mmol of isobutylene was added over 40 minutes to 8.3•10-2 mmole of aluminium chloride in 78 ml of ethyl chloride at –78 °C. The ratio (κe - κi)/κi was found to be >104. During the isobutylene addition the conductivity dropped steadily to about half the initial value and no polymerisation took place.

The formation of stable ionic solutions It was mentioned above that when a portion of monomer had polymerised, the conductivity rose and then became constant in many experiments and in some it subsequently fell slowly. This was an entirely unexpected feature because most investigators had found that the conductivity of solutions containing aluminium halide together with olefin and alkyl halide generally rose continuously and that there were signs, such as evolution of hydrogen halide and the formation of halogenated hydrocarbons, which pointed to extensive degradation reactions. For this reason we investigated this phenomenon by several experiments, the most extensive of which is described here. It was done by admitting 3.4 mmol of isobutylene in 1.0 cm3 of methylene chloride fairly rapidly to 62 cm3 of a solution of aluminium chloride (1.25 mmol⋅dm-3) in methylene chloride at 0 °C. The polymerisation went to completion in a few seconds, the polymer, subsequently found to have DP = 17, remained in solution, and the conductivity rose from 2 • 10-6 to 12.5 • 10-6 S⋅cm-1. As usual, the time required to reach a constant conductivity was considerably greater than that required for the polymerisation to be complete. The dependence of the conductivity of this solution on the concentration and the temperature were studied during three days. The concentration was varied by distilling solvent out of the solution into a hanging burette, or into it from the burette. The resulting plots are shown in Figure 9. They are straight lines converging to a common intercept which represents the impurity contribution to the total conductivity. On Day 1 the solution was diluted at 0 °C so that the concentration of aluminium chloride was reduced from more than 10 mmol•dm-3 to 5 mmol dm-3. On Day 2 it was concentrated, still at 0 °C, to about 8 mmol • dm-3, then it was brought to −63 °C, diluted to 5 mmol•dm-3, warmed to −23 °C, concentrated at that temperature to 8 mmol•dm-3 and left there over night. On Day 3 it was first warmed to 0 °C and then cooled to −63 °C. The remarkable stability of this electrolyte solution is evident from the Figure.

300

The Initiation of Polymerisations by Aluminium Halides (1980)

Figure 9 Experiment D4: The dependence of the conductivity on concentration and on temperature, for a polymerised solution of isobutylene in methylene dichloride. The polymerisation was carried out at 0 °C with 3.4 mmol of isobutylene and 62 ml of a solution of aluminium chloride (1.25 mmol • dm-3). For sequence of concentration and temperature variations see text. (O): Day 1 at 0 °C; (●): day 2 at 0 °C; ( ∇ ): day 2 at –23 °C; (▲): day 2 at –63 °C; (■): day 3 at –63 °C; (❑): day 3 at 0 °C Since we believed that the cations of this electrolyte include the polyisobutylium ion, it was an obvious next step to test whether the corresponding tert-butylium salt is also stable under these conditions. The question was tested by breaking a phial of carefully purified tert-butyl bromide into a solution of AlBr3 in methyl bromide at –78 °C; the mole ratio of the reagents was 1. The introduction of the tertiary halide produced a rapid increase in conductivity which became stable after approximately 10 minutes and remained thus; the solution was colourless throughout. Its concentration was varied as described above and the resultant conductivity change is shown in Figure 10. In view of the reports of the instability of solutions in which the formation of tert-butyl cations had been attempted and of the formation of allylic ions from cyclic condensation

301

Developments in the Theory of Cationoid Polymerisations

Figure 10 The dependence of conductivity on concentration for a mixture of aluminium bromide and tert-butyl bromide (mole ratio 1:1) in methyl bromide solution at –78 °C products [20-24] under conditions not too dissimilar from ours, the stable conductivity could have been due to such cations. Therefore, the reaction mixtures were hydrolysed and analysed by GLC-mass spectroscopy. The recovered organic material (other than solvent) was equivalent to more then 90% of the tert-butyl bromide introduced and its analysis showed it to be a mixture of tert-butyl alcohol and tert-butyl bromide; this proves that ions other than the tert-butyl cation, if present at all, could only have constituted a very small part of the electrolyte. There was no involatile residue, which shows that no oligomers or polymers had been formed.

Discussion

The tritiation experiments with isobutylene The most unexpected features of our results are the slow increase of conductivity after the polymerisations of isobutylene to a definite, stable maximum and the finding of approximately one tritium atom, i.e., one C–Al bond, per polymer molecule. These observations are puzzling because at first thought it appears that only those polymer molecules which had been started by initiation (and not those started by proton transfer)

302

The Initiation of Polymerisations by Aluminium Halides (1980) should have had Al–C bonds; and there appeared no evident reason for a slow increase in conductivity (after polymerisation) to a stable and reproducible value, at a reproducible rate (these features exclude degradation reactions). Our results obtained with the nonadecane and with the preformed polyisobutylenes provide the clue to that puzzle. They show that under our conditions of extreme dryness and purity the saturated hydrocarbon does not form C–Al bonds with aluminium bromide, but that the terminally unsaturated polyisobutylene takes up one Al atom per double bond; this is indeed the analogue of the initiation reaction (iii). If we now recall that in the polymerisation of isobutylene the most common chain-breaking reaction is proton transfer from the growing end to monomer, which leaves terminal unsaturation (Equation (v)),

CH3 ... —CH2—C = CH2 + (CH3)3C+ CH3 —CH2—C+

CH3 + H2C = C

CH3

CH3 CH3

2

+(CH3)3C+

... —CH = C CH3

(v)

and if we note that all these double bonds have been formed during the very short polymerisation time, we see that the subsequent slow rise in conductivity is due to their alumination [reaction (vi)] and to the consequent slow increase in the concentration of ions by the shifting of the ionisation equilibrium (ii), which is known to have a very small rate constant [9].

... —CH2—C = CH2 + AlX+2

+ ...—CH2—C—CH2AlX2•

CH3

CH3 3

CH3 + AlX+2

... —CH = C CH3

+ ...—CH—C

CH3 (vi)

CH3

AlX2 4

303

Developments in the Theory of Cationoid Polymerisations The kinetics of reaction (vi) will be discussed below; its stoichiometric aspect explains why we found one C–Al bond for every polyisobutylene molecule: if we disregard any initiation and chain-breaking by impurities we see that all those chains which were initiated by AlX2+ and which then underwent proton transfer will have a C–AlX2 group at both ends, one from initiation and one from alumination of the terminal double bond. Those that started by proton transfer and ended in the same way will have one C–AlX2 group at the end from alumination of the terminal double bond, and those that started by proton transfer and were still live when the reaction was killed will have a tritiumoxy group (...–CH2C(CH3)2OT) from the reaction of the carbenium ion with the tritiated water; this category will include those molecules having a halogeno group (…–CH2C(CH3)2X) through participation in the equilibrium (vii) [25, 26]. +

K – CH 2 C(CH 3 )2 + AlX 4– ↔ K – CH 2 C(CH 3 )2 X + AlX 3

(vii)

The tritiumoxy group will of course disappear by exchange during the work-up of the polymers. If there is no termination, then the number of molecules in the third category (containing no C–AlX2 group) must equal that in the first category (containing two C–AlX2 groups per molecule) so that for the polymer as a whole we have one C–AlX2, i.e., one tritium atom, per molecule.

The kinetics of the alumination (reaction (vi)) The formation of the aluminated cations is the second of two successive reactions, the first being the self-ionisation in reaction (ii). We know that the rate-constants, kf, for selfionisations in alkyl halides are relatively small, ranging from 1.8•10-6 dm3•mol-1•s-1 for AlBr3 in methyl bromide at 0 °C to 1.4 •10-1 dm3 mol-1 • s-1 for AlCl3 in methylene chloride at –78 °C [9]. On the other hand, the rate-constants for reactions of aromatic cations with olefins in methylene chloride at ambient temperature are of the order of 106 to 108 dm3 • mol-1•s-1 [27]. Thus, it seems most likely that the self-ionisation is rate-determining. Unfortunately, kinetic analysis of our curves gives no clear-cut evidence on this matter, or reliable rate-constants, mainly because they were not designed to provide these.

The tritiation experiments with styrene and norbornadiene In the polystyrenes produced by cationic initiators most of the chain-ends are terminal indanyl groups, and olefinic groups are rare. As this terminal indanyl group cannot be aluminated like a double bond, the amount of tritium incorporated comes only from the initial AlBr2CH2CHPh-groups and the few residual terminal double bonds and it, therefore, represents (approximately) the total number of initiated chains.

304

The Initiation of Polymerisations by Aluminium Halides (1980) The structure of polynorbornadiene [poly(3,5-tricyclo(2.2.1.02, 6]heptylene] (5) [28] and the high level of incorporation suggest that the three-membered rings in the polymer behave like double bonds and have been aluminated.

Conclusion on alumination The conductimetric, kinetic, and radiochemical experiments lead to the conclusion that alkenes, but not strainless alkanes, are aluminated by AlX2+. This and the balance of the number of C–Al bonds in our polyisobutylenes support Proposition 2 that initiation is by reaction (iii).

The non-polymerisations Certainly the most startling of our experiments are those in which the very slow addition of isobutylene to a solution of an aluminium halide did not result in polymerisation. Our explanation is as follows: our earlier studies [9] showed that in the relevant solutions the degree of ionization is extremely small and that the concentration of AlX3 is 103 to 105 times greater than the concentration of ions. Therefore, when the isobutylene is introduced very slowly the chances of one such molecule meeting an AlX3 molecule is vastly greater than that of its meeting an ion. Thus, the olefin and AlX3 can start complex formation which is accelerated by further but slow supply of olefin to the solution. The complexing of the AlX3 shifts the equilibrium (ii) towards removal of ions, and the concurrently decreasing dielectric constant also favours that reaction; both these factors also reduce the conductivity. Once (almost) all the AlX3 has been complexed and the AlX2+ ions have been removed, even the rapid introduction of large amounts of isobutylene cannot induce the formation of polymer. The residual conductivity is probably due to ions derived from impurities, which may include oxonium ions, e.g., AlX2OH2+ which, like Et3O+ cannot initiate the polymerisation of isobutylene. These experiments provide the most direct evidence so far for the formation of complexes between AlX3 and isobutylene. The formation of such complexes was of course to be expected on the basis of the complex formation between aluminium halides and other olefins [29-33] and between titanium tetrachloride and isobutylene [34], and numerous other examples of complexes formed by an olefin and a metal halide: it can be objected 305

Developments in the Theory of Cationoid Polymerisations that the formation constants of complexes between olefins and metal halides are generally small so that an almost complete sequestration of the AlX3 seems unlikely; however, all those known are for aromatic olefins and it is very likely that for aliphatic ones they would be larger. An order-of-magnitude calculation shows that even if the formation constant is as low as 5 dm3 • mol-1, 83% of the AlX3 would be complexed under typical conditions*). This means that the rate of formation of ions would be reduced to 3% (since (AlX3]2 is involved) of what it would be for the same [AlX3] if there were no complexing. It must be emphasised that this is by no means the only evidence for this complexation: It was reported a long time ago that aluminium chloride is much more soluble in a mixture of pentane and isobutylene than in pentane alone [35], and Magagnini et al. [16] have shown that the complexation of isobutylene and aluminium chloride is so firm that addition of the normally very efficient co-initiators chlorine and tert-butyl chloride will not initiate polymerisation in such a system where the AlCl3 has been sequestered. This evidence for formation of a stable complex between isobutylene and AlX3 also finally disposes of all theories of initiation by aluminium halides which are based on a reaction of the halide itself with the olefin, such as that put forward by Kennedy [4]. We conclude therefore that all the available evidence supports our Proposition 3.

The stable electrolyte solutions The assumption that tertiary alkyl cations are not stable in solvents other than super-acids is widespread and was apparently well founded on many experiments by different workers over many years [20, 24]. For this reason the stability of our polymerised solutions was astonishing and it seemed at first unlikely that the cation of the electrolyte could be a simple tertiary ion: the tert-butyl cation in the experiment with tert-butyl bromide and the ions 2-4 in the polymerised solutions. This was because we did not know then that Cesca,

*

The equilibrium is

C4H8 + AlX3 ↔ C, Kc = [C]/[B][A] B A If [B]0 >>[A]0, [A] = [A]0/(Kc[B]0 + 1). If we take from Table 3 average values [B]0 = 1, [A]0 = 10-2 mol • dm3, then we find for different assumed values of Kc the concentration and percentage of uncomplexed AlX3 shown in the following Table.

Kc/(dm3 • mol-1) 5 10

3

•

[A]/mol • dm )

100 [A]/[A]0

306

-3

10

100

1.67

1

0.1

17

10

1

The Initiation of Polymerisations by Aluminium Halides (1980) Priola, and Ferraris [36] had done what was considered impossible, namely to prepare a stable crystalline product from tert-butyl chloride and AlCl3, and that they had used it to initiate polymerisation. From our own experiments we concluded independently that stable tert. aliphatic cations can be prepared and our discussion has been based on this view throughout. Our conclusion is derived from the following argument: Our experiments, such as those shown in Figures 9 and 10, showed that the conductivity is concentration- and temperature-reversible, i.e., that the systems are in equilibrium. Since for both the tert-butyl and the polymer solutions the conductivity depends rectilinearly on the concentration, the electrolyte must be involved in an equilibrium in which n molecules generate n ions [26, 37], in these systems most probably n = 2, and the equilibrium is, therefore, of the type K11

RX + AlX 3 ↔ R + + AlX 4–

(viii)

where the nature of R+ remains to be determined. In order to find out what R+ is, we consider first the common experience that when a tert-butyl halide is treated with an aluminium halide under ordinary conditions, there is a brisk evolution of hydrogen halide and a coloured solution containing oligo-isobutylenes and condensed allylic ions is formed. In the present experiments the solutions were colourless, no hydrogen halide was evolved, and the conductivity was stable and behaved reversibly. Further, the rectilinearity of the κ-[AlX3] plots in Figures 9 and 10, and the smallness of the intercepts on the κ-axis, showed that ions generated by reactions other than those of type (viii) must have been very scarce, and for the experiment with tertbutyl bromide this was borne out by the absence of any byproducts. We concluded, therefore, that in sufficiently pure alkyl halide solvents the tert-alkyl tetrahaloaluminates are stable electrolytes and that previous failures to produce them, and the consequent legend of the instability of tert-alkyl carbenium ions, arose from the use of inappropriate and insufficiently rigorous experimental techniques. On this basis it seems highly probable that in the polymerised solutions the cations R+ partaking in reaction (viii) were also ‘original’ ions, i.e., 2 at the end of a live chain and 3 and 4 formed by alumination of a terminal double bond, and not ‘derived’ ions formed by degradative reactions of monomer or polymer. We think that our findings may have useful applications in polymer chemistry. The most obvious of these, the synthesis of block copolymers by cationic polymerisation from the stable ions 2–4, we were prevented from exploring through unfortunate circumstances beyond our control.

307

Developments in the Theory of Cationoid Polymerisations The importance of equilibria of the type (viii) for polymerisations has been discussed [16, 25, 26] but the present experiments provide the first direct evidence for their existence. We can also now make preliminary estimates of the equilibrium constants. For the experiment with tert-butyl bromide we use the method of Nuyken and Plesch [26], with the data of Figure 10 and we take Λ0[(CH3)3C+AlBr4-] = 50 S cm2 • mol-1, in CH3Br at –78 °C, based on Λ0(AlBr4-) = 28 S • cm2 • mol-1 for the same solvent and temperature. This gives K11 = 2.5 • 10-5, which means that the degree of ionisation of tert-butyl bromide under these conditions is only ca. 5%. A similar calculation can be made for the ‘polyisobutylium tetrachloroaluminate’, a mixed electrolyte containing the three cations 2– 4 derived from the three corresponding chlorides, by means of the equation appropriate for unequal concentrations of the ionogenic molecules [37].

K11 = a0 b0 Λ2i / κ 2 – ( a0 + b0 )Λ i / κ + 1 where a0 = [AlCl3]0, b0 = [Polymer], Λi = molar conductivity of the electrolyte. This gives K11 = 5.6•10-4 at 0 °C and K11 = 5.1 •10-4 at –63 °C; these are of course weighted averages for the mixed electrolyte, and are afflicted by the errors involved in calculating Λi values from crystallographic radii [9]; however, they are probably correct as to order of magnitude, and where previously there was no information, even approximate values are useful. Finally, we need to consider another aspect of the cations occurring in our systems, namely whether they are carbenium or halonium ions. There is no doubt, as was stated in the introduction, that the AlX2+ ion in an alkyl halide solvent is closely solvated by at least one RX molecule and one could regard the (RXAlX2)+ species as a form of halonium ion. Similarly, carbenium ions R1+ can form (R1XR)+ with an alkyl halide, as was shown a long time ago by Davies and Baughan [38]. However, whether these ‘halonium’ ions are to be regarded as a species sui generis or merely as the solvate of the carbenium ion depends on the particular system and on the aspect of its chemistry which is under consideration [39]. When R1 is tertiary and R primary (as in our systems) the charge distribution, the strengths of the two C–X bonds, and consequently the reactions (such as hydrolysis), are such that the solvated tert-carbenium ion is probably the most realistic model; however, when R1 and R are more similar, the halonium ion concept may be more fruitful.

The scope of the initiation theory As the result of our work the three propositions specified in the introduction now appear plausible and in accord with the experimental evidence. It is, therefore, appropriate to show how they form a coherent theory which will explain adequately the known phenomena.

308

The Initiation of Polymerisations by Aluminium Halides (1980) We recall first that the most prominent feature of the polymerisation of isobutylene by aluminium halides, as carried out by most investigators, is that almost irrespective of solvent, temperature, and concentrations, the injection of a catalyst solution into a monomer solution produces a fast polymerisation which stops at incomplete conversion. At this stage aluminium halide is still present in the solution and so is monomer, and the polymer (or some of it) might have been precipitated. Thus, nonreacting (quiescent) mixtures of isobutylene and aluminium chloride have in fact been produced very frequently before our experiments reported here, with the difference that they always contained much polymer. The addition of water, HCl, tert-butyl chloride, or chlorine to such a quiescent mixture does not restart the reaction, but the addition of more aluminium chloride solution will do so; however, the polymerization again does not go to completion unless the second dose of AlCl3 is very great. The most efficient way of restarting the reaction is by addition of Et 2AlCl or Et 3Al, which leads to fast and complete polymerisation. Generally the number of polymer molecules formed is very much smaller than the number of aluminium halide molecules added. On the other hand, when the monomer is added to the initiator solutions, in a normal, rapid manner, the conversions are always complete. These differences can be explained by our theory as follows: when a solution of AlX3 is run into a monomer solution, the ions present in the initiator solution start chains and the lengths to which these grow is governed by the many factors which affect the DP. These factors include the nature of the solvent, the temperature, the nature and concentration of impurities, and occlusion of growing ions in precipitated polymer; however the most important termination, which has been identified and placed in proper perspective by the Italian workers is the reaction (from left to right) of equilibrium (vii). They made the important point that this reaction (vii) becomes irreversible, and therefore a termination, if the AlCl3 liberated is sequestered by unreacted monomer [16]. This picture is also applicable when these polymerisations are done under conditions much less rigorous than ours, including those prevailing on the production plants, because the ‘impurity’ cations which may be partly or largely responsible for initiation of the polymerisations under such conditions are also consumed rapidly and after that the further supply of initiating ions is restricted in the same way as in experiments under very pure conditions. We now consider the ‘reverse addition’ procedure used by us, involving a fast addition of monomer to the initiator solution, and contrast if both with the ‘direct addition’ just described and with the very slow ‘reverse addition’ described earlier which produces the quiescent mixtures. When the monomer is added fast to an AlX3 solution, it encounters both AlX2+ ions and AlX3 molecules. In contrast to the slow addition experiments, the monomer is consumed by the very fast polymerisation before it can complex with the

309

Developments in the Theory of Cationoid Polymerisations aluminium halide molecules, there is no (or little) termination so that there is an appreciable stock of polymer molecules with cationic end-groups (live polymers), as shown by the rapid polymerisation of many successive portions of monomer and the high conductivity. After the completion of each polymerisation all the molecules whose growth had been stopped by proton transfer from the growing end to monomer acquired terminal cations by their double bonds becoming aluminated by AlX2+. However, for steric reasons it is doubtful whether the ions formed by reaction (vi) can propagate; this is a matter which needs to be clarified experimentally.

Comparisons with results of other workers Our radiochemical work at first sight invites comparison with that of Ghanem and Marek [40] who used tritiated water to find out whether tritium is incorporated by initiation into polyisobutylenes made with aluminium bromide, boron trifluoride, or titanium tetrachloride. However, the conditions and methods used by these workers were so different from ours that a detailed comparison is not appropriate. The most important differences are that they worked with heptane solutions and that their quantities of water were (roughly) between 0.3 • 10-3 and 5 • 10-3 of the quantity of metal halide; whereas all our work was with polar alkyl halide solvents and with quantities of tritiated water greatly in excess of the aluminium halides. In interpreting their results they failed to take account of the reaction of water with any metal-carbon bonds, despite the fact that from their results they deduced that one function of the water was to facilitate initiation by the TiCl+3 and analogous ions, by our reaction (iii), which forms such a metal-carbon bond; the argument and the alleged chemistry of this hypothetical action of the water are obscure and implausible. A further comparison which should be made is with all those results which appear to involve initiation by a metal halide without co-initiator which were compiled by Kennedy [4]. Whilst a detailed discussion of these would be out of place here, it is appropriate to consider our own results obtained with titanium tetrachloride initiator for isobutylene [41] and styrene [42] in methylene chloride. For both systems it was found that at temperatures below ca. –50 °C a contribution to the reaction rate became prominent which was independent of the concentration of water and that it became more important as the temperature was reduced. It is curious that although our discovery of the self-ionisation of titanium tetrachloride coincided with the early part of those polymerisation studies, we did not take the logical step of attributing the water-independent initiation to the TiCl3+ ion. The reason was a ‘thermochemical inhibition’ which resulted from a calculation of the enthalpy of the addition of the ion to the monomer, which has been given in detail and which made that type of initiation appear rather unlikely [43]. It appears worthwhile to reexamine these systems by our improved methods. Just how much techniques have improved

310

The Initiation of Polymerisations by Aluminium Halides (1980) over the period is shown by the work of Plesch and Turner [44] who, in what is now conventional all-glass high vacuum apparatus, obtained methylene dichloride with a κ = 4.3 •10-11 S •cm-1 at 20 °C, which is very close to the best literature values [45, 46]. With that solvent we checked the conductivity of titanium tetrachloride solutions. This went through a maximum of about 2 •10-10 S • cm-1 near [TiCl4] = 3 mol • dm-3. Whilst the exact shape of this curve remains to be determined and does not matter in the present context, the fact that the κ is 1/400 of that recorded in our earlier work on the same subject [47] is a vivid demonstration of the improvement in techniques and also an indication of how difficult a study with titanium tetrachloride, analogous to ours with the aluminium halides, will be because of the much smaller degree of ionisation.

Conclusion Starting with the idea, originating from Wichterle’s group, that the polymerisation of isobutylene, ostensibly by AlX3, is initiated by AlX2+, we developed a detailed theory of the processes involved. With the help of evidence collected by the Giusti and Cesca groups and Kennedy’s group, but mainly through our own experiments which were designed specifically for testing the various parts of our theory, we have arrived at explanations of all the essential features of one of the oldest, most studied, and most puzzling of cationic polymerisations, that of isobutylene by aluminium chloride. The theory is in no way restricted to this one alkene and to aluminium halides, but its detailed application to other systems remains to be worked out.

Acknowlegements We thank Prof. J. C. Bevington for providing facilities for D.W.G. to learn radio-tracer techniques, Prof. E. J. Goethals for helpful comments. and the Science Research Council for equipment. Note added in proof: Recently, the tert-butylium ion has been identified in alkyl bromide solutions by 1H NMR (P. Brueggeler, E. Mayer, Z. Naturforsch. Teil B, 34, 891 (1979)), and some dimethylhalonium ions have been identified in alkyl halide solvents by the same method (P. Brueggeler, E. Mayer, Z. Naturforsch. Teil B, 34, 896 (1979)).

References 1.

The most comprehensive recent literature compilation is in J. P. Kennedy, ‘Cationic Polymerisation of Olefins’, Wiley, New York 1975. 311

Developments in the Theory of Cationoid Polymerisations 2.

J. H. Beard, P. H. Plesch, P. P. Rutherford, J. Chem. Soc. 1964, 2566.

3.

M. Chmelir, M. Marek, O. Wichterle, IUPAC Symposium on Macromolecules, Prague 1965, Preprint P110; J. Polym. Sci. 16, 833 (1967).

4.

J. P. Kennedy, J. Macromol. Sci., Chem. 6, 329 (1972).

5.

M. Chmelir, M. Marek, J. Polym. Sci., Part C, 23, 223 (1968), ibid. 22, 177 (1968).

6.

P. Lopour, M. Marek, Makromol. Chem. 134, 23 (1970).

7.

P. H. Plesch, IUPAC Symposium on Macromolecules, Helsinki 1972, Macromolecular Chem. - 8 (Supplement to Pure and Applied Chem.) Butterworth, London 1973, p. 305.

8.

P. H. Plesch, Makromol. Chem. 175, 1065 (1974).

9.

D. W. Grattan, P. H. Plesch, J. Chem. Soc., Perkin Trans. II, 1977, 1734.

10. A. Priola, G. Ferraris, M. di Maina, P. Giusti, Makromol. Chem. 176, 2271 (1975). 11. A. Priola, S. Cesca, G. Ferraris, M. di Maina, Makromol. Chem. 176, 2289 (1975). 12. P. Giusti, A. Priola, P. L. Magagnini, P. Narducci, Makromol. Chem. 176, 2303 (1975). 13. S. Cesca, P. Giusti, P. L. Magagnini, A. Priola, Makromol. Chem. 176, 2319 (1975). 14. S. Cesca, A. Priola, M. Bruzzone, G. Ferraris, P. Giusti, Makromol. Chem. 176, 2339 (1975). 15. M. di Maina, S. Cesca, P. Giusti, G. Ferraris, P. L. Magagnini, Makromol. Chem. 178, 2223 (1977). 16. P. L. Magagnini, S. Cesca, P. Giusti, A. Priola, M. di Maina, Makromol. Chem. 178, 2235 (1977). 17. R. H. Biddulph, P. H. Plesch, J. Chem. Soc. 1960, 3913. 18. J. Hine, J. A. Brown, L. H. Zalkow, W. E. Gardner, M. Hine, J. Am. Chem. Soc. 77, 594 (1955).

312

The Initiation of Polymerisations by Aluminium Halides (1980) 19. B. Matyska, M. Svestka, K. Mach, Collect. Czech. Chem. Commun. 31, 659 (1966). 20. N. C. Deno, ‘Progress in Physical Organic Chemistry’, Vol. 2, Wiley, Interscience, New York 1964, p. 129. 21. N. C. Deno, D. B. Boyd, J. D. Hodge, C. U. Pittman, J. O. Turner, J. Am. Chem. Soc. 86, 1745 (1964). 22. G. A. Olah, C. U. Pittman, Adv. Phys. Org. Chem. 4, 305 (1966). 23. H. C. Brown, W. J. Wallace. J. Am. Chem. Soc. 75, 6279 (1953). 24. H. C. Brown, L. P. Eddy, R. Wong, J. Am. Chem. Soc. 75, 6275 (1953). 25. P. H. Plesch, J. Polym. Sci. 12, 48 (1954). 26. O. Nuyken, P. H. Plesch, Chem. Ind. (London) 1973, 379. 27. Y. Wang, L. M. Dorfman, Macromolecules, in the press. 28. J. P. Kennedy, J. A. Hinlicky, Polymer 6, 133 (1965). 29. F. Fairbrother, K. Field, J. Chem. Soc. 1956, 2014. 30. F. Fairbrother, J. F. Nixon, J. Chem. Soc. 1958, 3224. 31. D. G. Walker, J. Phys. Chem. 64, 939 (1960). 32. H. H. Perkampus, W. Weiss, Ber. Bunsenges. Phys. Chem. 75, 446 (1971). 33. H. H. Perkampus, G. Orth, Z. Phys. Chem. 73, 155 (1970). 34. W. R. Longworth, P. H. Plesch, P. P. Rutherford, Internatl. Conf. on Coordination Chem. 1959, Chem. Soc. Special Publ. No. 13, p. 115; P. H. Plesch, J. Macromol. Sci., Chem. 6, 980 (1972). 35. J. P. Kennedy, R. M. Thomas, J. Polym. Sci. 46, 233 (1960). 36. S. Cesca, A. Priola, G. Ferraris, Makromol. Chem. 156, 325 (1972). 37. D. W. Grattan, Ph. D - Thesis, Keele, 1973; D. W. Grattan, P. H. Plesch, J. Electroanal. Chem. 103, 81 (1979).

313

Developments in the Theory of Cationoid Polymerisations 38. A. G. Davies, E. C. Baughan, J. Chem. Soc. 1961, 1711. 39. G. A. Olah, Halonium Ions, J. Wiley and Sons, New York 1975 40. N. A. Ghanem, M. Marek, Eur. Polym. J. 8, 999 (1972). 41. R. H. Biddulph, P. H. Plesch, P. P. Rutherford, J. Chem. Soc. 1965, 275. 42. W. R. Longworth, C. J. Panton, P. H. Plesch, J. Chem. Soc. 1965, 6019. 43. P. H. Plesch, p. 137, in Progress in High Polymers Vol. II, Ed. J. C. Robb and F. W. Peaker, Heywood Books, London 1968. 44. P. H. Plesch, P. J. Turner, unpublished. 45. M. Rabinowitsch, Z. Phys. Chem. 119, 59, 70 (1926). 46. S. O. Morgan, H. H. Lowry, J. Phys. Chem. 34, 2413 (1930). 47. W. R. Longworth, P. H. Plesch, J. Chem. Soc. 1959, 1887.

314

4.8

Some Effects of the Complex Formation Between Cations and Monomers P. H. Plesch

This paper was first published in Die Makromolekulare Chemie, Macromolecular Symposia, 1990, 32, 299-306. Reprinted with permission from Wiley-VCH, copyright 1990. This is Part IX of the series Developments in the Theory of Cationic Polymerisation.

Prologue An analysis is presented in this paper of the influence exerted on polymerisation kinetics by the complexing of carbocations with monomers. This had been brewing in the author’s mind for a long time and had been mentioned in earlier works, and most other workers were aware of it to some extent. Curiously, few if any others had drawn the electrochemical conclusion that such a process would make meaningless the estimates of the population of paired cations in the reaction mixtures, because of the increase in the size of the cations resulting from such an association. The fundamental problem, why such a complexation can occur instead of the monomer reacting with the cation when it meets it in solution, is merely reformulated here in terms of potential energy minima, but not addressed clearly. The solution of that mystery did not come to this author until he started grappling with the problems presented by the polymerisations initiated by ionising radiations (Section 4.9). The last sentence of the paper under consideration here turned out to be illusory, because, as shown in Section 5.6, the rate-constants measured in nitrobenzene solution turned out to be not those for the attack of a carbenium ion on the double-bond of the monomer, but hybrids. The paper concludes that in order to get at the “true” kp+ for an ion which is solvated only by the solvent, extrapolations to zero monomer concentration would be required. The author then did not draw the conclusion that all these would most likely be (nearly) the same and close to those for binary collisions - which now seems likely. This theme is elaborated and used to resolve a notorious kinetic discrepancy in [154].

Abstract The formation of complexes Pn+M between a propagating carbenium ion Pn+ and the monomer, M, is considered from several points of view:

315

Commercial rubbers

Developments in the Theory of Cationoid Polymerisations i) Under the most usual conditions the formation of the Pn+M reduces the population of ion-pairs, Pn+A–, drastically. This can account for the frequently found nil-effect of common ion salts on the rate of attack of carbenium ions on alkenes in initiation, model reactions, and polymerisations. ii) The formation of Pn+M increases the degree of dissociation α of Pn+A–, so that all the estimates of α on which kinetic schemes have been based, are too low. iii) The very high polymerisation rates found for n-donor monomers, say 4-MeOstyrene or N-vinylcarbazole compared to styrene, may be attributable not, primarily, to a difference in rate-constants, but to a difference in ionic population. This is because the fast Pn+M is in greater excess over the slow Pn+A– for the more strongly complexing n-donors than for the π-donors. iv) Since the nature of the Pn+M is different for every monomer, a comparison of their propagation rate-constants kp+M is hardly meaningful and valid comparisons can only be made between the kp+ of the Pn+. The measurement of these requires extreme conditions, either extrapolations to [Pn+] = 0 and [M] = 0, or the use of highly polar solvents in which neither M nor the anion can compete with the solvent for the solvation of the Pn+.

1 Introduction and phenomenology The present paper is an attempt to unravel a rather confused aspect of cationoid polymerisations. This concerns the phenomenon comprised in the term ‘monomer complexation of the growing cation’. The idea seems to have occurred for the first time in the work of Fontana and Kidder on the polymerisation of propene by AlBr3 and HBr in n-butane [3]. The kinetics indicated a reaction of zero order with respect to monomer, M; to explain this, it was assumed that the growing end of the chain, written as a carbenium ion, Pn+, is complexed with M and that the rate-determining growth step is an isomerisation of this complex:

Pn+ + M ↔ Pn+ M,

KM

(1)

Pn+ M

k p1

(2)

→ Pn++1 ,

The usual analysis gives for the rate of monomer consumption

– dm / dt = R = k p1K M [ Pn+ M]m /(1 + K M m )

316

(3)

Some Effects of the Complex Formation Between Cations and Monomers This well-known kinetic expression for a ‘drained equilibrium’ implies that at high values of m the reaction is of zero order, at low values of first order, with respect to m. Few other examples of this type have been reported. However, orders of reaction less than unity with respect to m may also be due to the sequestration of a metal halide initiator by complexation with the monomer [4]. Which, if any, of these two causes is responsible in any particular case for a low or varying kinetic order with respect to m may be determined by suitable experiments, and there seems no reason why both may not occur in the same system. In contrast to the previous work, high reaction orders of up to approximately 3 with respect to m, which had been found in several early kinetic studies on the cationic polymerisation of styrene and related monomers, were also attributed to ‘solvation’ of the growing cation by the monomer. The idea was that in an apolar solvent the monomer, being polarisable, e.g., styrene, or polar, e.g., a vinyl ether, solvates the cation strongly, thus increasing the degree of dissociation of ion-pairs and accelerating the polymerisation. The rate of propagation was written as of first order with respect to m [5, 6]. The solvation of carbenium ions by 4-MeO-styrene and by alkyl vinyl ethers and their polymers has been cited more recently as an explanation for multi-modal DPD curves [7], but again the propagation is seen as of first order with respect to m. Therefore, it appears that in some systems the unimolecular isomerisation of the Pn+M complex is rate-determining, whereas in others it requires the participation of a second monomer molecule to effect propagation, i.e., the addition of the carbenium ion to one of the monomer molecules. It may be that in the first type the potential well in which the M is held is sufficiently shallow for the isomerisation to occur at an observable rate, whereas in the second (more common) type the well is so deep that an attenuation of the charge-density of the cation by the second M is needed before the rearrangement resulting in propagation can take place.

2 Different types of complexes The resolution of the above-mentioned conflicts is not yet clear, but this author thinks that a profitable approach can be made by investigating the nature of the different complexes that may be involved. This line of thought was catalysed partly by the papers from the Jena school concerning the formation of a variety of complexes between cations and molecules [8, 9]. Unfortunately, this extensive work is less valuable than it might be and difficult to use because no account was taken of the intervention of binary ionogenic equilibria (BIE) in the systems studied. These mostly comprise trityl and tropylium ions and a variety of composite anions of the MtX–n+1, type, i.e., typical components of BIE [10]. In respect of the systems of interest to us, one needs to distinguish at least three types of complexes:

317

Developments in the Theory of Cationoid Polymerisations 1. The π-complex (I) formed between a cation and a double bond:

C P+n + CH2:CHR

P+n (I)

C

R

There is a great amount of literature on this subject. 2. The complex formed with an aromatic ring which may carry a double bond:

P+n + PhCH:CH2

P+n

O

(II)

P+n (III)

Ph

The complexes of type (II) have been known for several decades. 3. The formation of n-donor complexes (IV). This involves stronger forces than the previous two types because the lone pair of the hetero-atom is involved. It is clear that the polymerisations of some of the favourite monomers, such as the alkyl vinyl ethers, 4-MeO-styrene, and N-vinylcarbazole may be dominated by this phenomenon. A corollary of the complexation by an n-donor monomer is that the hetero-atoms in the corresponding polymers will also interact with the growing carbenium ions. The authors who have proposed this include Stannett (alkyl vinyl ethers) [11], Boelke (dimethoxyethene) [12], and Sauvet (4-MeO-St) [7]. The details of which type of complex (π- or n-) has what kinetic and other effects, e.g., on termination and transfer constants, copolymerisation ratios, tacticity, etc., need to be worked out on the basis of published results and well-aimed new experiments. Having established some essential distinctions, it must be emphasised that the kinetic relevance of these complexations, i.e., their importance as phenomenological determinants, depends essentially on+the experimental circumstances; these comprise mainly the nature + of the cation (e.g. – C R ′R ′′ or R – O – C H ⋅ CH 2 − Pn ), the solvent, the temperature, and the nature of the anion; and for some systems the sequence of mixing of the reagents. A detailed analysis of the literature data from this point of view remains to be done.

3 The effects of complexing on ion populations Mechanistic considerations indicate that the complexing monomer molecule must displace at least one solvent molecule from the solvation shell. Since the charge-density is reduced

318

Some Effects of the Complex Formation Between Cations and Monomers by the complexation, this may release more than one solvent molecule, so that the complexation may actually involve an increase in entropy. It is therefore to be expected that the importance of complexation varies with the solvating power of the solvent. The effects of solvents on equilibria involving cations were studied cursorily by various authors, and in some detail by the Jena group, but for the reasons given the results are at best qualitatively indicative [13]. One of the effects of equilibrium (1) can be determined by regarding the coefficient of [Pn+M]m in equation (3) as a composite rate-constant kp*:

R / m[ Pn+ M] = k *p = k p1K M /(1 + K M m ) The kp* evidently decreases with increasing m, and both constants can be found from a suitable plot. The monomer is but one of several competitors, whose interactions with the carbenium ion serves to lower the free energy of the system. The second important competitor is the anion, A–. It forms the ion-pair Pn+A– which has an even lower charge density than the Pn+M and is a strong dipole. For these reasons the formation of the doubly complexed species Pn+MA– and Pn+A–M seems unlikely to be of kinetic importance. However, the formation of Pn+M does have some interesting electrochemical, and therefore also kinetic, consequences. One such effect is that the presence of the complexing monomer must enhance the dissociation of the Pn+A–. In terms of the association constant KA = KD-1 and the equilibrium

Pn+ + A – ↔ Pn+ A – and equations (4), (5), and (6):

K A = [ Pn+ A – ]/[Pn+ ][A – ]

(4)

[ Pn+ ] = [A – ]

(5)

[ Pn* ] = [ Pn+ ] + [ Pn+ A – ]

(6)

one obtains the familiar equation (7):

K A [A – ] = –1 / 2 + (1 / 4 + [ Pn* ]K A )1 / 2

(7)

319

Developments in the Theory of Cationoid Polymerisations If we introduce the monomer-complexation by means of equation (1) and write the new charge and mass balances as

[A – ]M = [ Pn+ ] + [ Pn+ M]

(8)

[ Pn* ]M = [ Pn+ ] + [ Pn+ M] + [ Pn+ A – ]

(9)

and

one obtains

[A – ]M /[A – ] = 1 + K M m

(10)

Therefore, if [A–] and [A–]M can be measured as a function of m, either directly or via [Pn+] and [Pn+M] + [Pn+] by spectrophotometry or some other method, the KM can be found. The only relevant measurements known to us are in an amazing little paper by Bos and Treloar [14] which contains more, and more useful, information than many related and much more extensive researches. The authors studied the equilibria

Ph 3CCl + HgCl 2 ↔ Ph 3C + HgCl 3– ↔ Ph 3C + + HgCl 3– K F 11

KD

spectrophotometrically, determining the constants by the method of Evans [15], i.e., they used the BIE theory later formalised by Grattan and Plesch [16],whose nomenclature for the constants is used here. They then recorded the effect of increasing quantities of styrene on KF11, and KD, and on the ratio p/y given by equation (11): [paired ions]/[unpaired ions] = p / y = –1 / 2 + (1 / 4 + [ Pn ]/ K D ) *

(11)

Unfortunately, their data are insufficient for determining KM by our equation (10), but the increase of the dissociation with increasing m is very clear. There is great need for more studies along the same lines. (The equation (11) is the reciprocal of Plesch’s much more cumbersome equation for y/p [17]). The complexing of alkenes with cations is likely to be the more important, the less polar the solvent, the lower the temperature and, with respect to the competing pairing of ions, the larger the anion. It follows from these considerations that the ignoring of this complexing reduces the validity of all estimates of the degree of dissociation α of ion-pairs [see equation (10)]. In fact, such estimates have addressed the wrong question, because what is really of interest is the fraction of all cations which is unpaired, i.e., ([Pn+] + [Pn+M])/([A–] + [Pn+A–]).

320

Some Effects of the Complex Formation Between Cations and Monomers The general effect is that the fraction of unpaired ions is underestimated. Two examples from many: The calculations of the present author [17a, 18] for styrene and HClO4 in CH2Cl2 and those of Sauvet [7] for 4-MeO-styrene; the latter are likely to be more strongly affected because of the n-donor nature of this monomer, which implies greater values of KM and therefore a smaller population of Pn+A–. The complex formation with monomer also provides a simple and logical explanation for the decrease of the rate-constant for the attack of a cation, R+, such as a trityl ion from an initiator, on a monomer, with increasing m; this can be shown thus:

[R * ] = [R + ] + [R + M] if

K M = [ R + M]/[R + ]m R i = k i+ A [ R * ]m = ( k i+ [ R + ] + k i+ M [ R + M])m

then the apparent rate-constant, ki+A, is given by equation (12):

k i+ A = R /[ R * ]m = ( k i+ + k i+ M K M m ) /(1 + K M m )

(12)

and this decreases as m increases, as found, e.g., by Sauvet [7] and Sawamoto [19] and other investigators. An analogous argument can account for the decrease of second-order propagation rate-constants with increasing m, which has been found by many investigators. The formation of Pn+M is likely to compete successfully with ion-pairing under most conditions. This is because, although KA may be considerably greater than KM, the massaction effect, with [A-]/m usually of the order of 10-3, will make the Pn+A– the scarcest species in the solution, especially if A– is large, e.g., BCl4–. We thus find a plausible explanation for the nil-effect of a common-ion salt on the apparent rate-constant of ion-molecule reactions. For example, Mayr’s finding [20] that the rate-constant for the addition of a diarylmethylium ion to alkenes is unaffected by a common-ion salt is most likely due to this effect, rather than to k+ and k± being equal. The rate of the reaction is given by

– dm / dt = ( k + [ R + ] + k ± [ R + A – ] + k + M [ R + M])m

(13)

and [R+M] >> [R+] > [R+A–], so that the reaction pattern is dominated by the last term. When the same considerations are applied to the propagation rate-constant, kp, one can find the reason for the nil-effect of a common-ion salt in terms of the apparent propagation rate-constant kp+A, defined in analogy with equation [13]. It must mean that ion-pair formation is negligible because either the KA is very small (highly polar solvent) or for 321

Developments in the Theory of Cationoid Polymerisations the ‘normal’ solvents, such as CH2Cl2, that there is a more successful competitor, the monomer, for the Pn+. Conversely, if there is a noticeable common-ion effect, it means that complexing by monomer is of minor importance [21]. Further, if we follow these ideas through, we may find at least one reason why the monomers containing hetero-atoms appear to polymerise so much more rapidly than the hydrocarbons under the most common conditions. The reason may well be that because for these n-donor monomers the KM is much greater than for the π-donors, the fraction of the Pn+M chain-carriers is much greater than that of the much more slowly growing Pn+A–. In other words, it is a question of the composition of the ionic population rather than of rate-constants, although these may, of course, contribute to the effect. This idea is open to test by measurements of KM and kp+, kp+M, and kp±. These considerations lead us directly to the problem of propagation rate-constants. Perhaps the most profound kinetic consequence of the multiplicity of propagating species and of different types of monomer complexes is that there must be corresponding doubts about the significance of any alleged measurements of a propagation rate-constant. Even if one leaves out all systems in which the conversion curves are not of first order throughout, one is still left with an unsatisfactory situation. The reason is that in most of these systems the monomer-complexed cation is probably the dominant species, and the nature of this species will be different for every monomer: for example, a carboxonium ion from a vinyl ether, complexed with its monomer, is in some essential respects different from a styryl cation complexed with styrene. This means that even for almost monoeidic systems in which the Pn+M is the dominant species, it is not meaningful to compare the corresponding rate-constants kp+M of different monomers. To obtain data for comparing like with like, the apparent kp+A must be extrapolated to m = 0 and [Pn+] = 0 so that they refer to a situation where the only propagating species is the unpaired, uncomplexed cation, Pn+. These considerations apply especially to the popular solvents of moderate polarity. The kp+A values which may not need such extrapolations are those obtained at extremely low m, e.g., possibly some of those obtained from stopped-flow experiments, and, more likely, those obtained in highly polar solvents, because in these neither the anion nor the monomer can compete successfully with the solvent for a place in the solvation shell of the cation, so that the kp+A is the real kp+. This author’s choice of nitrobenzene as the solvent for kp+ measurements, which was made for kinetic and electrochemical reasons, now seems to have been also the best one for the purpose of avoiding complexation by monomer. It is likely that the rate-constants obtained in that solvent really are genuine kp+ and comparable one with another (2). Author’s Note (2001): The last sentence is not true.

322

Some Effects of the Complex Formation Between Cations and Monomers

4 Conclusion The short lesson from this long sermon is that for meaningful quantitative results to be extracted from cationic polymerisations several requirements need to be fulfilled henceforth: 1. Choice of a suitable solvent, preferably of high polarity, such as PhNO2 or sulpholane and for low temperatures SO2 or eutectic mixtures of PhNO2 with 1,2-dinitrobenzene or nitrotoluenes. [Author’s note (2002): Disregard this bad advice!) 2. Choice of a very rapidly initiating cation, e.g., an aroyl or diarylmethylium salt, to avoid the complication from slow initiation. 3. A very large, stable anion, from amongst those recommended by Pask and Plesch [1]. 4. Use of a marker reagent to react with the growing ends of all kinds so that they may be counted. 5. Check on any dependence of kp+A on m and other parameters. 6. Concurrent measurements of conversion and conductivity, and measurements of the DPD, throughout the reaction. Far too much effort has been wasted hitherto with unsuitable initiators and kinetically and electrochemically obscure systems.

5 Acknowledgement I thank the contributors to the Keele Polymer Group Alumni Fund which helped me with the production of this paper.

References 1.

Part VII. S. D. Pask and P. H. Plesch, European Polymer Journal, 1982, 18, 11, 839.

2.

Part VIII. P. H. Plesch in Cationic Polymerization and Related Processes, Ed., E. J. Goethals, Academic Press, 1984, p.1.

3.

C. M. Fontana and G. A. Kidder, Journal of the American Chemical Society, 1948, 70, 3745; C. M. Fontana, G. A. Kidder and R. J. Herold, Ind. Eng. Chem., 1952, 44, 1688; C. M. Fontana in Cationic Polymerisation and Related Complexes, Ed., P. H. Plesch, W. Heffer and Sons, Cambridge, 1953, p.121.

323

Developments in the Theory of Cationoid Polymerisations 4.

P. H. Plesch, Die Makromolekular Chemie, 1974, 175, 1065.

5.

For example C. G. Overberger and A. G. Kamath, J. Amer. Chem. Soc., 1963, 85, 446; S. Okamura and T. Higashimura, J. Polym. Sci., 1956, 21, 289. The subject is discussed in some detail by A. R. Mathieson in The Chemistry of Cationic Polymerisation, Ed., P. H. Plesch, Pergamon, 1963, Ch. 6, p.235.

6.

S. Spange, R. Dreier, G. Opitz and G. Heublein, Acta Polymerica, 1989, 40, 55.

7.

G. Sauvet, M. Moreau and P. Sigwalt, Die Makromolekulare Chemie, Macromolecular Symposia, 1986, 3, 33.

8.

G. Heublein, J. Macromol. Sci. Chem., A16, 563 (1981).

9.

For example G. Heublein and C. Grimmer, J. Prakt. Chem., 1982, 324, 973.

10. S. D. Pask and O. Nuyken, European Polymer Journal, 1983, 19, 159. 11. V. Stannett and A. Deffieux in Cationic Polymerization and Related Processes, Ed., E. J. Goethals, Academic Press, 1984, p.306. 12. M. Boelke, P. Hallpap, G. Heublein, V. V. Stepanov, S. S. Skorochodov, D. Heidrich and C. Weiss, Die Makromolekulare Chemie, Rapid Communication, 1985, 6, 485. 13. G. Heublein and S. Spange, J. Prakt. Chem., 1982, 324, 187. 14. S. S. Bos and F. E. Treloar, Aust. J. Chem., 1978, 31, 2445. 15. The numerous refs. to this work are given in Ref.14. 16. D. W. Grattan and P. H. Plesch, J. Electroanal. Chem., 103, 81 (1979). 17. a. P. H. Plesch, Brit. Polym. J., 5, 1 (1973); b. J. Polym. Sci., Polymer Symp., 56, 373 (1976). The Bos-Treloar equation, which has priority (S. S. Bos., Ph.D. Thesis, Melbourne, 1971), is much simpler to use. 18. P. H. Plesch, Adv. Polym. Sci., 8, 137 (1971). 19. M. Sawamoto, T. Higashimura, A. Enokida and T. Okubo, Polym. Bull., 2, 309 (1980). 20. R. Schneider, U. Grabis and H. Mayr., Angew. Chem., 98, 94 (1986). 21. J. P. Lorimer and D. C. Pepper, Proc. R. Soc. London, A351, 551 (1976).

324

4.9

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) P. H. Plesch

This paper was first published in the Philosophical Transactions of the Royal Society of London A, 1993, 342, 469-504. Reproduced with permission from The Royal Society, copyright 1993. This is Part XI of Developments in the Theory of Cationic Polymerisations.

Prologue When around 1990 this writer was working on a critical review of rate-constants of cationic polymerisations, kp+ (Section 5.7), he thought that the reactions initiated by various kinds of ionising radiations would be easy to deal with because the field seemed fairly mature and had been created by experienced scientists; and because the (alleged) kp+ obtained from this type of reaction had been quoted so often as the ‘benchmark’ for these quantities. Instead, when he had scutinised the major papers, he found that the field was a mess, but it was a mess of a very interesting kind of messiness. Because there are certain internal checks as to the purity of reagents and cleanliness of operations which were well known and generally agreed, most of the experimental results were sound, internally consistent and reproducible, in fact they were of far better quality than most of the kinetic results obtained with conventional chemical initiation. However, the interpretation of the results was astonishingly inadequate. Not only did each one of the (very few) groups of workers ignore the results of the others, but they did not explain plausibly even their own results; the reason for this situation was the absence of an adequately detailed general theory of this kind of polymerisation; evidently no-one had endeavoured to create one. Because the experimental results were so good and therefore promised to provide new insights if properly exploited, this writer interrupted the writing of his review on the kp+ to attempt the devising of a general theory of the polymerisations by ionising radiations. This took over two years and resulted in the paper under discussion now, after which he went back to the Review, which finally took nearly five years to complete. As he had hoped and suspected, some careful analytical thinking, based on a new, but very simple, model, led this writer to the explanations he had sought and also explained

325

Developments in the Theory of Cationoid Polymerisations several hitherto un-explained phenomena, quite unconnected with polymerisations by ionising radiations. In the present paper this author did essentially the same as he had done in the work on the DP variations (Section 4.10), namely to develop a simple new theory to explain coherently a mass of disparate, apparently unconnected and unexplained observations. The new view was formed by thinking through the physico-chemical consequences of the characteristics of the growing carbenium ions along the following lines: 1. The C+ carry a positive charge. 2. They are trigonal and more or less planar, depending on the size of the groups attached to the central C atom. 3. Features 1 and 2 imply that each ion has two principal co-ordination or solvation sites, or positions of closest approach or of minimum potential energy. All this is fairly obvious and has been noted in various ways by a few other workers (A). 4. What appears to be new in the theory developed here is that the strength of the electrical field on each side depends on the nature of what is occupying the other site on the opposite side. This explains the marked differences between the reactions in polar and non-polar solvents. 5. An unexpected consequence of this new view of the carbenium ion was that an explanation for the complexing of the C+ with the monomer emerged almost spontaneously. That this complexing is an important feature of cationic polymerisations had been known for a long time (see for example Section 4.8 here), but no-one had produced a theory explaining under what conditions a C+ could encounter a monomer molecule and, instead of reacting with it, form a complex. Such an explanation is now available. When this complexing is important, i.e. extensive, the bulk of the propagation steps are unimolecular isomerisations whereby the complexed monomer molecule is incorporated in the chain. The new theory also explained why the rate of this unimolecular reaction depends on the nature of the solvent - which is apparently a contradiction. The reason is that the rate depends on the nature of the species attached to the other side of the C+, which in many systems is the solvent. 6. A further innovation in this work is the recognition that monomers with more than one electron-donor site, e.g. an aromatic ring or an oxygen atom in addition to the double bond, can form two kinds of complex with the C+, only one of which can isomerise with incorporation of the monomer into the chain. Therefore there are then

326

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) two kinds of cation: one which can and one which cannot propagate. Therefore it was not valid to assume for the monomers with two complexing sites that the number of propagators is equal to the number of cations, however measured, and therefore the fundamental assumption on the basis of which the much-quoted kp+ had been calculated, was wrong, except for isobutene; and even the kp+ of that is wrong - but for another reason. 7. All the kp+ calculated by the original workers for bulk polymerisations and those obtained at high monomer concentrations are wrong because they are second-order rate-constants, calculated on the assumption that the polymerisations are secondorder reactions. This is a considerable curiosity because all the kinetic curves published showed clearly that the polymerisations were of zero order with respect to the monomer concentration (m). A new set of kp+ values is given here. 8. By means of the new theory it became possible to derive equations for the rate and the DP as functions of m only, which covered the whole range of m from bulk to low values. These equations contain the change of order from zero at high to unity at low m; or rather they show why even at the lowest m the order is always somewhat greater than unity - as had been observed frequently, but had not been explained adequately. 9. The information on the DP of the polymers had not been evaluated effectively by the original authors because they suspected that the degradation of the polymers by the radiation would make it unreliable. Nevertheless, in the present work it is shown that the DP evidence supports this writer’s fundamental theoretical views regarding the reaction mechanism. In short, this paper contains a completely new and functionally effective theory of the polymerisations by ionising radiations.

Reference A.

For example, Litt in his discussion of donor-acceptor complexes notes the existence of two principal sites on any one ion. M.H. Litt and J. Wellinghoff, J. Physical Chem., 1977, 81, 2644.

327

Developments in the Theory of Cationoid Polymerisations This paper is about a reinterpretation of the cationic polymerizations of hydrocarbons (HC) and of alkyl vinyl ethers (VE) by ionizing radiations in bulk and in solution. It is shown first that for both classes of monomer, M, in bulk ([M] = mB) the propagation is unimolecular and not bimolecular as was believed previously. This view is in accord with the fact that for many systems the conversion, Y, depends rectilinearly on the reaction time up to high Y. The growth reaction is an isomerization of a π-complex, Pn+M, between the growing cation Pn+ and the double bond of M. Therefore the polymerizations are of zero order with respect to m, with first-order rate constant kp1+ . The previously reported second-order rate constants kp+ are related to these by the equation

kp+1 = kp+ mB If the monomer contains a group, other than the double bond, that can complex with the carbenium ion, such as an aromatic ring or a hetero-atom, the resulting complexes, Pn+G, are not propagators; in such systems the concentration of the propagators, [Pn+M], is less than the total concentration, c, of cations. This newly recognized effect makes the + of most monomers calculated from c too small; it may be at least partly responsible kp1 for the rate of polymerization of styrene being significantly less than that of isobutene, and for the rate of polymerization of the VE being much less than that of the HC. The behaviour patterns ensuing when bulk monomers are diluted by solvents are very varied. The most detailed information concerns the VE. My re-examination of the results shows that, contrary to current belief, no one kinetic scheme will fit all the systems over the whole range of m. My interpretations were facilitated considerably by the availability of the dependence of c on m, which for most systems can be expressed by a linear equation of the form c = Am + B, where in some systems A is positive, in others negative. By making this substitution in the kinetic equations it becomes obvious why for most systems the external kinetic order with respect to m is greater than unity, an effect noted, but hitherto not explained convincingly. Both for ethyl vinyl ether (EVE) and isopropyl vinyl ether (IPVE) in benzene the unimolecular character of the propagation persists down to m ≈ 7 mol dm-3. Below that, a bimolecular propagation becomes dominant, of first order in m. The behaviour of EVE in Et2O and in diglyme [bis(2-ethoxyethyl)ether] is apparently similar, but detailed examination shows marked differences. In Et2O the propagation is of second order over most of the range of m. The rate of polymerization in diglyme goes through a sharp maximum near m = 8.5 mol dm-3, which requires a more complicated explanation. For EVE and 4-methoxystyrene in CH2Cl2 the addition of the solvent produces a dramatic fall in rate. This is explained by a change from unimolecular to bimolecular propagation at high m, near mB. The rate of polymerization of styrene in toluene and in CH2Cl2 from

328

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) m ≈ 2 mol dm-3 up to m = mB shows a marked discontinuity, and the rate for isobutene in four very different solvents goes through a maximum near m = 5 mol dm-3. Many of these phenomena point to the solvent affecting the rate of the unimolecular propagation at high m, which seems paradoxical. The following new theory of what is essentially a new type of unimolecular reaction accounts for the phenomena. My new idea is this: The k+p1 through its free energy of activation, depends upon the strength of the π-bond between the carbenium ion and the double bond of the monomer. But this depends on the ‘electrostatic environment’ of the complex, which in the present context means primarily the strength of the dipole at the ‘back-side’ of the near-planar carbenium ion. The stronger that dipole is, the weaker is the π-bond, and consequently the greater is the kp1+ . The dependence of the degree of polymerization (DP) on m is available only for EVE and isobutene in CH2Cl2 and for styrene in toluene. For all three systems, the discontinuities in the dependence of the DP on m betray changes in reaction mechanism corresponding to the indications from the kinetics. The dependences can be interpreted by the conventional Mayo equation for the low-m region where bimolecular propagation prevails, and by the corresponding, new, equation for unimolecular propagation at high m. The new rate-constants resulting from my analysis are listed. The lessons from these theoretical investigations will also be useful in the context of chemically initiated cationic polymerizations, especially for those in which propagation by unpaired ions is dominant.

1 Preamble In the present context the term ‘cationic polymerization’ refers to reactions in which compounds with C=C bonds are added to carbenium ions, R′R′′R′′′C +, with the reformation of the carbenium ion after each addition, and the eventual formation of polymers in this way. The polymerizations via oxonium ions are excluded, as are pseudo-cationic polymerizations (Plesch 1988). In the course of reviewing the propagation rate-constants of cationic polymerizations in general (Plesch 1993), I came to suspect certain inconsistencies in the interpretations of the rates of the cationic polymerizations initiated by ionizing radiations. I found that there was no general theory covering the polymerizations in bulk and in various solvents. Therefore I examined in detail the primary data and scrutinized the existing theories, and this paper is the result of what turned out to be a very lengthy enquiry. I would not have attempted to develop a comprehensive theory, if the experimental work had not been of such very high quality and recorded in such an accessible manner. Because the theory presented here is mainly concerned with accounting for the changes in the rate of polymerization brought about by some change in the chemical circumstances, it is useful to clarify just what is involved.

329

Developments in the Theory of Cationoid Polymerisations Generally, the rate of a polymerization depends on several factors, which include the nature of the monomer, the presence and nature of any solvent, the nature and number of the propagating species, and the concentration of each of these, which together is called the population of propagators. If there is but one species, the system is monoeidic, if there is more than one, it is enieidic (these terms were introduced by Biddulph et al. (1965) and Plesch (1973)). The system as a whole is characterized by the reactivity of each species, measured by its rate constant for attack on the monomer. This is determined by the chemical nature of the propagator and of the monomer, the solvent, the temperature, pressure and the population of other compounds in solution. Rate constants can be of two kinds: simple, e.g., the second-order rate constant of a bimolecular reaction, or composite, containing several simple rate constants and one or more equilibrium constants and/or concentrations. In all polymerizing systems the rate depends on the concentration of one or more reagents which may, but need not, include the monomer. The purpose of this Preamble is to remind the reader that when we attempt to explain a change of rate brought about, for example, by dilution with a solvent that may be more or less polar than the monomer, we are attempting to visualize and rationalize the resulting changes in the physico-chemical circumstances and the consequent changes in the population of the propagators, and in the equilibrium constants and rate constants involved. That is what this paper is about. (In this work the term ‘population’ is shorthand for ‘nature and concentration’.)

2 Introduction Ever since 1962, when Williams, Okamura, and their associates started to publish propagation rate-constants k+p for the cationic bulk polymerization of cyclo-pentadiene, isobutene, styrene, α-methylstyrene and isopropylvinyl ether by ionizing radiations, these constants have been accepted as the best, most likely, values for the k+p of unpaired cations in a medium of low-polarity, and those obtained subsequently by Stannett and his collaborators, using similar methods, enjoyed the same status, (The loci classici are Bates et al. (1962), Bonin et al. (1964), Taylor & Williams (1969) and the three papers by Ueno et al. (1967), Hayashi et al. (1967) and Williams et al. (1967).) The fundamental chemistry of the events leading to polymerizations initiated by ionizing radiations are largely agreed to be as follows. The reactive species formed in hydrocarbons by the ionizing radiation, which survive the very fast geminate recombinations in what might be called a ‘Coulombic cage’, are organic cations and anions. The cations are those normally generated by the removal of an electron, i.e., radical cations and, in unsaturated hydrocarbons, conventional carbenium ions are formed in times that are short on the timescale of the subsequent reactions caused by these carbenium ions, in particular, cationic polymerizations (Williams 1968, 1972). For isobutene (IB) the initiation is represented as (Aquilanti 1967; Hayashi 1969):

330

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993)

CH 2 = CMe 2 + e – → • CH 2 – C + Me 2 + 2e – •

+

•

+

CH 2 – C Me + CH 2 = CMe 2 → Me 3C + CH 2 = C( Me)C H 2

}

(2.I)

According to the traditional view, the Me3C+ adds to the monomer in a bimolecular reaction of second order, generating a new carbenium ion, and repetitions of this process produce the growing polymer of chain length n, P+n; we shall show below that this simple view needs to be refined. The anions originate from the attachment of an electron to whatever electron acceptors are available in the system; in bulk hydrocarbon monomer this results in the formation of radical anions. Because the electron affinities of alkenes are much lower than the ionization potentials of hydrocarbon radicals, the neutralization reaction between the cations and the anions, one possible version of which is •

R – CH 2 – CMe 2+ + CH 2 CMe 2– → R – CH 2 – C M e 2 + CH 2 CMe 2

(2.II)

is highly exo-energetic. However, not all hydrocarbons are the same in this respect, and for α-methylstyrene, which forms a more stable cation and radical anion than isobutene, the rate constant, kt, of reaction (2.II) is smaller than for isobutene (Taylor & Williams 1969). The rate, Rt, of the termination reaction is therefore

Rt = kt c 2

(2.1)

where c is the total concentration of either species of ion, and kt can be calculated by the simple diffusion equation (see below). Equation (2.1) implies that kt is the same, whatever the nature of the anion, and that it is also independent of the state of the cation, i.e., whether, and if so by what, it is complexed or solvated. In view of the fact that such neutralizations involve large, negative ΔH and a positive ΔS because of the release of the ion-solvating molecules, this is probably a sound approximation. The theory of polymerizations by ionizing radiations gives the rate of initiation Ri (ions cm-3 s-1) as

Ri = IGi /100

(2.2)

where I(eV cm-3 s-1) is the dose-rate and Gi(ions (100 eV)-1) is the yield of free ions. In the steady state

Ri = Rt

(2.3)

331

Developments in the Theory of Cationoid Polymerisations and therefore c = (10 Gi / kt ) –2

1/ 2

(2.4)

The traditional equation for the rate of polymerization is given in our symbols as

R = kp+ [ Pn+ Sv]m

(2.5)

where Sv is a molecule of solvent. In bulk monomer, where m = mB, M replaces Sv. If, according to the traditional view,

c = [ Pn+ Sv]

(2.6)

it follows from (2.4) and (2.5) that

R = kp+ (10 –2 G i I )1 / 2 m / kt1 / 2

(2.7)

The dependence of R on I1/2 became a corner-stone of the theory of the polymerizations by ionising radiations. If an experiment gave an exponent of I greater than 0.5, it was concluded that chain-breakers other than the anions, e.g., impurities such as water, were intervening. It was common practice to continue purification of apparatus, monomer and solvent until the exponent approached 0.5. Conversely, it was concluded that if the exponent was 0.5, then the propagation must be by unpaired ions; but the question whether other types of termination might give the same dependence of R on I1/2 has not been examined explicitly, probably because there was no obvious need. However, since the time when this theoretical framework was established by Williams and his collaborators our understanding of the mechanisms of ionic reactions in organic media has developed, especially with regard to the kinetic importance of ion pairs. It is therefore useful to examine briefly the hypothetical termination reactions (2.III) and (2.IV) with rate Rt in which ion pairs react with free ions or with their own kind to give a non-ionic product Nt:

Q + R – + Q + → Nt + Q +

(2.IIIa)

Q + R – + R – → Nt + R –

(2.IIIb)

2Q + R – → 2 Nt

(2.IV)

If, as before, we designate the total concentration of either positive or negative ions by c, we find that reactions (2.IIIa) and (2.IIIb) give Rt = f(c , c1/2) and reaction (2.IV) gives R t = f(c2, c , c1/2).

332

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) Only the reaction

Q + + R – → Nt

(2.V)

gives Rt = f(c2) and hence RP = f(I1/2). Departures from the latter behaviour have traditionally been attributed to termination by impurities or solvent, or by the products formed by electron capture fragmentation of monomer, polymer, or solvent. To this list must now be added the possible intervention of ion pairs. However, this brief analysis has established that only if the half-power dependence of R on the dose-rate prevails, the only propagating species that needs to be considered is the unpaired cation. In polymerizations by ionizing radiations in the presence of strong electron acceptors which reduce the reactivity of the electrons, the termination reaction is inhibited, the concentration of ions grows and under these conditions the participation of paired cations becomes relevant (Hayashi et al. 1977; Yamamoto et al. 1977). The propagation rate-constants mentioned in the first paragraph of this section were calculated by Williams and his successors in the following manner on the assumption that there is only one kind of cation, and that this is the propagator. The Gi in (2.7) for different compounds is known from independent experiments. The kt can be obtained by two independent methods. a) The Einstein-Smoluchowski equation for the rate of encounter of two ions gives –

kt = 4 πe 2 D / ε k T

(2.8)

where e is the electronic charge, D is the average diffusion coefficient of the two ions, ε _ is the dielectric constant of the medium, and k is Boltzmann’s constant. Substitution of (2.8) into (2.7) gives –

R = kp+ m(Gi IεT/D)1 / 2 ( k/ π)1 / 2 / 20e

(2.9)

The greatest sources of uncertainties are Gi, what value should be given to ε, and the size of the ions, which is implicit in D. b) The second method involves measuring the electrical conductivity, κ, of the polymerizing system, and using Langevin’s equation (2.10) to obtain kt in terms of κ:

kt = 4πeΛ / ε

(2.10)

333

Developments in the Theory of Cationoid Polymerisations where Λ is the ionic conductivity which can be calculated from Stokes’ equation. Since

Λ = κ / ec

(2.11)

kt = 4πκ / ec

(2.12)

we substitute for c from (2.4) and obtain

kt1 / 2 = 4 πκ / ε(10 –2 Gi I )1 / 2

(2.13)

Substitution of this into (2.7) gives

R = kp+ mGi Iε / 400 πκ

(2.14)

To summarize: m, I and ε are given by the materials and the experimental conditions; R and κ are the measured variables, but Gi is assumed by analogy with similar systems; the weakness of this procedure is acknowledged. The two methods have generally given reasonably concordant results (see, for example, Deffieux et al. 1981). We shall see that there are good reasons for supposing that not all cations are propagators, and that there may be more than one kind of non-propagating cation and more than one kind of propagator. If the propagators are designated as before by P+n and the nonpropagators by R+n:

c = Σ[ Pn+ ] + Σ[ R n+ ]

(2.15)

These ideas are new, since traditionally non-propagating cations have not been considered; and the polymerizations by ionizing radiations have been thought of as monoeidic, the sole propagator being the cation P+n, solvated of course, but otherwise unencumbered. To clarify what is implied, it must be understood that the propagators considered below include cations complexed by the solvent (solvated) P+nSv, and cations complexed by the monomer through its double bond, P+nM; and that the principal non-propagators are cations complexed by an aromatic ring or a hetero-atom in the monomer, P+nG. It is possible that polar or polarizable side-groups of polymers, e.g., RO from VE, can complex with the growing cations, but for the reasons explained (Plesch 1993) this effect will not be considered in detail (see also Section 3a).

334

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) The theory developed for the hydrocarbons was transferred virtually without change to the polymerization of alkyl vinyl ethers (Ueno et al. 1967), and it was not realized that these monomers might behave rather differently, for several reasons. 1. The ionization of the alkyl vinyl ethers generates radical cations which break up into radicals and cations. The question how an alkyl vinyl ether would split into a cation and an anion was considered by Hamann et al. (1949), and following their arguments it seems likely that the split would produce an alkyl cation R+ and a vinyloxy radical, ViO•, thus: e−

R − O − Vi

R – O – Vi → R + + Vi – O• + 2 e − → RCH 2 C + HOR

(2.VI)

The difference from the hydrocarbons is that the oxocarbenium ion resulting from the addition of R+ to the monomer becomes solvated by the strong dipoles of the monomer (for EVE μ = 1.14 Debye units (Taskinen et al. 1978)). 2. The irradiation of alkyl vinyl ethers leads to dissociative electron capture. Yoshida et al. (1972) showed that dimethyl ether decomposes according to

Me 2 O + e – → Me• + MeO –

(2.VII)

The calculations of Hamann et al. quoted above indicate that an alkyl vinyl ether would fragment according to

ROCH = CH 2 + e – → R • + CH 2 = CHO –

(2.VIII)

The vinyloxy anion formed in this way is much less reactive than hydrocarbon anions and it might be expected that therefore the termination reaction with the propagating cation would be slower. 3. The vinyl ethers, being polar, are much better solvating agents than alkenes, so that both cations and anions have a stabilizing solvation shell. (Hayashi et al. 1971). 4. The dielectric constants, ε, of the vinyl ethers are around 3.5, whereas for alkenes it is ca. 2, for styrene 2.4 and for α-methylstyrene 2.6. It seems that these essential differences between alkenes and vinyl ethers were ignored when the kinetic interpretation of the polymerizations of alkenes by ionizing radiations were extended to the vinyl ethers, but any or all of them may help us to understand the behavioural differences between hydrocarbons and hetero-atomic monomers (see Section 4c).

335

Developments in the Theory of Cationoid Polymerisations

3 The kinetics of bulk polymerization

a) Theory Fontana et al. (1948, 1952) showed that the kinetics of the cationic polymerization of C3H 6 by AlBr3 and HBr in an hydrocarbon solvent can be explained on the assumption that the alkene forms complexes with the growing cations, which might be unpaired or paired:

Pn+ + M ↔ Pn+ M, equilibrium cons tan t KM+

(3.I)

A – Pn+ + M ↔ A – Pn+ M, equilibrium constant KM±

(3.II)

and this idea has been used since then by so many authors that it has become part of the general theory of cationic polymerizations, and it is hardly possible to give adequate references. These complexes are not ad hoc inventions, but are closely related to those formed by alkenes with Ag+ (Dewar 1951; Salomon 1953) and other cations. If the monomers are hydrocarbons, these complexes are π-complexes; but for aryl alkenes (styrene, etc.), both the aromatic ring and the double bond can be co-ordinated to the carbenium ion, and only the latter type of complex can rearrange to the lengthened chain; in other words, the former complex is not a propagator. Other monomers that can form two types of complexes with the carbenium ion are those containing heteroatoms, such as 4-methoxystyrene and the alkyl vinyl ethers. The two kinds of complex are the π-complex with the double-bond and the n-complex involving the hetero-atom. (The interaction of both the double bond and the O-atom with the carbenium ion seems to have been suggested first by Higashimura et al. (1969).) These features have been discussed in some detail (Plesch 1989, 1990). The complexing with the hetero-atom of the monomer to give a non-propagating complex, P+nG, will be considered further in a later section. Evidently, any polymers containing hetero-atoms can also complex through these with the cations, but I shall show that this is probably relatively unimportant, except possibly at high conversions. However, Stannett and his co-workers, the most prolific workers with alkyl vinyl ethers, accorded great importance to the complexing of the growing carbenium ion with the polymer, but disregarded its complexing with the monomer, and they stated explicitly at the end of the first paper on solvent effects (Deffieux et al. 1981): ‘These results appear to indicate that there is little or no solvation by the monomer’. In the light of other evidence, their arguments seem rather less convincing. We now consider the polymerizations in bulk, i.e., without a solvent, of hydrocarbon monomers by ionizing radiations in the light of the monomer complexing of cations which has been noted for polymerizations in solution. If in a solvent of low polarity this

336

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) complexing is kinetically important, then it follows a fortiori that in bulk monomer it is likely to be dominant. In the absence of a solvent, and especially at low conversion, the solvation shell consists entirely of monomer molecules, one of which is in the special position of being the electron donor to the carbenium ion. A mono-alkene can form such a complex only through its double bond, giving P+nM, but an aryl alkene can form this or it can complex through its aromatic ring, giving one form of P+nG; and a vinyl ether can form the π-complex through the double bond and an n-complex through the Oatom, which is another variety of the non-propagating P+nG. The first part of the following discussion concentrates on monomers which can only form the π-complex with their double bond. According to Fontana’s theory, the rate-determining step in a polymerization involving a monomer-complexed cation is a unimolecular isomerization of the complex, which is kinetically of first order:

R = kp+1[ Pn+ M]

(3.1)

This means that the rate constants derived from ionizing radiation experiments with bulk monomers are not the second-order k+p given by (2.5), but first-order rate constants, + kp1 , given by (3.1). A comparison of these equations shows that the putative k+p reported in the literature are related to the kp1+ by (3.2),

kp+1 = kp+ mB

(3.2)

where mB is the concentration of bulk monomer. Because for all the usual monomers the mB lie in the range of 9 ± 2 mol dm-3, the kp1+ are numerically about one order of magnitude greater than the ‘k+p’, which henceforth shall be put between inverted commas. Since the + kp1 have the dimension of a first-order rate constant (time-1), they cannot be compared with any second-order k+p. Because of this misidentification, the numerous attempts at comparing the putative second-order rate constants ‘k+p’ with the genuine second-order k+p obtained in dilute solutions by chemical initiation, have been futile. This is not the first time that the kinetics of bulk polymerizations has been analysed critically. Szwarc (1978) has made the same objection to the identification of the rate constant for the chemically initiated bulk polymerization of tetrahydrofuran as a secondorder rate constant, k±p, and he related the correct, unimolecular, rate constant to the reported k±p by an equation identical to (3.2). Strangely, this fundamental revaluation of kinetic data was dismissed in three lines in a major review (Penczek et al. 1980). Evidently, it is likely to be relevant to all rate constants for cationic bulk polymerizations, e.g., those of trioxan, lactams, epoxides, etc. Because of its general importance I will refer to this insight as ‘Szwarc’s correction’ and to (3.2) as ‘Szwarc’s equation’.

337

Developments in the Theory of Cationoid Polymerisations It is necessary now to find out whether my theoretical conclusion is supported by experimental evidence; in fact, there are many results for bulk polymerizations that indicate a first-order growth reaction. The experimental support that I seek would be found in the shape of the curves relating the conversion, Y, to the total received dose of radiation or to the time at a constant dose-rate. If the polymerizations are of zero order with respect to m, the conversion curves will be rectilinear instead of concave to the dose (or time) axis. Rectilinear conversion curves are actually much more common than ‘firstorder type’ curves, and some instances of this behaviour are listed in Table 1. In example 8 of Table 1 the experimental points are actually on a straight line, but a curve has been drawn past them. The plots in the figures quoted in Table 1 all show such a small scatter from a straight line up to conversions of 20% or more, that they are incompatible with a first-order curve. (For a first-order reaction, the rate R at Y = 20%, is 20% less than the initial rate R0, and therefore also 20% less than the rate which the reaction would have at that stage if it were of zero

Table 1 Examples of systems in which Y increases rectilinearly with dose or with time Dose-rate, Y* (%) I/(rad s-1) a

Figure number in reference

Monomer

T,°C

1 isobutene

–78

5.6

22

1

Stannett et al. (1964)

2 cyclopentadiene

–78

7.2 to 75

2

1

Bonin et al. (1965)

3 β-pinene

25

66

60

1

Bates et al. (1962)

4 α-methylstyrene

30

67

c

2-4

Best et al. (1962)

5 α-methylstyrene

30

96

30

1, 2

Hubman et al. (1966)

6 EVE

0

9.1

16

4

Suzuki et al. (1977)

7 EVE

30

70.6

60

1

Hsie et al. (1980)

8 IPVE

26

71

27

1

Deffieux et al. (1983)

9 IPVE

30

70.6

28

3

Ma et al. (1979)

0, 30 and 60

Various

60

Tables I and II

10 IBVE

b

References

Bonin et al. (1964)

a Converted from the original authors’ units at the rate of 1 rad = 6.242 x 1013 eV g-1 b Y* is the yield (% conversion) up to which the rate of polymerization is constant c Some of the curves show slight acceleration

338

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) order. Such a deviation would be easily detectable, as it is well outside the scatter of the experimental points.) I therefore conclude that the experimental evidence supports amply the theoretical conclusion, and can but wonder why this was ignored by so many workers. Can my new view explain why alkenes, e.g., isobutene, polymerize so much more rapidly than aryl alkenes, e.g., styrene? (See Table 2). I think that since the activation enthalpies for both types of monomer are very small, and the activation entropies are probably very similar, the effect arises from the difference in the concentrations of the propagating πcomplexes. As mentioned above, the simple alkenes can interact with the carbenium ion only through their double bond, whereas the aryl alkenes can also be held by their aromatic ring, and for the fraction thus held a considerable rearrangement would be required before the new bond can be formed. This means that there are actually two types of complexed cations, those π-bonded to the double bond, P+nM, which can propagate, and those π-bonded to the aromatic ring, P+nG, which cannot. The same considerations can be applied to a comparison of the vinyl ethers (VE) with the hydrocarbon monomers, thus: the VE form complexes with the carbenium ions mainly through the O-atom; this view leads to the same conclusion as in the comparison of alkenes with arylalkenes, namely that this is the principal reason why the VE polymerize more slowly than the alkenes. It can be put differently. The VE polymerize more slowly than the alkenes mainly because the concentration of propagators, [P+nM], is smaller, even when the total concentration of cations, [P+nM] + [P+nG], is the same. The fact that IPVE polymerizes more rapidly than EVE is likely to be at least partly due to the fact that for stereochemical and polarity reasons [P+nM]/[P+nG] is greater for the IPVE. These matters will be discussed further in the section on the alkyl vinyl ethers. Stannett and his co-workers suggested that the differences between the hydrocarbons and the vinyl ethers and between the various vinyl ethers are due to the following effect. One of the O-atoms in the polymer chain, probably from the penultimate unit, was believed by them to be complexed with the carbenium ion, so that in comparison to the hydrocarbon monomers the access of monomer to the reaction site is impeded; and with increasing bulk of the alkyl group this obstruction by the polymer diminishes, so that the rate constant increases. It seems unlikely to me that the complexing of polymer can play an important part in the bulk polymerization of the vinyl ethers, for the following reason. Let the cation complexed by a hetero-atom of its own or of some other polymer chain be represented by P+nP. The reaction pattern then depends on the ratio [P+nP]/[P+nM]. The only way in which a cation complexed by a hetero-atom pendent from a chain, or indeed by any species other than the monomer, can propagate is bimolecularly. Therefore if this ratio is large, i.e., if [P+nP] is dominant, we must have a second-order polymerization, the rate of which is given by

R = kp+ [ Pn+ P ]m

(3.4)

339

Developments in the Theory of Cationoid Polymerisations

Table 2 Alleged rate constant kp2+B for bulk polymerizations and first order calculated from them Result number

mB/(mol dm -3 )

kp+/(dm3 mol-1 s-1)

–78

13.6

5.8 x 108±1

7.9 x 109

Bonin et al. (1965)

0

11.0

1.5 x 108

1.6 x 109

Taylor & Williams (1969)

–78

12.6

1.5 x 10

8

9

1.9 x 10

Taylor & Williams (1969)

15

8.75

(2 ± 0.5) x 106

1.8 x 107

Williams et al. (1967)

8.54

(2.9 ± 1) x 10

8.66

(2.4 ± 0.9) x10

7.75 7.58

T,°C

a

kp1+B/s-1

b

References

Cyclopentadiene 1 Isobutene 2 3 Styrene 4 5 6

40 25

6

7

Hayashi et al. (1973)

7

2.1 x 10

Hayashi et al. (1973)

4.4 x 106

3.4 x 107

Williams et al. (1967)

6.5 x 10

5

6

Chawla & Huang (1975)

9.9 x 10

5

6

Chawla & Huang (1975)

7

Chawla & Huang (1975)

6

9.5 x 10

Chawla & Huang (1975)

6

2.5 x 10

α-methylstyrene 7 8 9 10 11

0 35 20 0 –20

7.71

3.0 x 10 7.6 x 10

1.30 x 10

6

8.05

1.18 x 10

6

7.45

3 x 106

2.2 x 107

Deffieux et al. (1980)

10.3

9.4 x 104

9.7 x 105

Hsieh et al. (1980)

10.5

3.5 x 10

4

5

Hsieh et al. (1980)

2.9 x 10

4

5

Deffieux et al. (1981)

7.2 x 10

3

4

Goineau et al. (1977)

8.3 x 10

3

4

9.0 x 10

Suzuki et al. (1977)

Hsieh et al. (1980)

7.75

1.0 x 10

4-methoxystyrene 12

20

Ethyl vinyl ether 13 14 15 16 17

30 23 20 0 0

10.54 10.8 10.8

3.7 x 10 3.1 x 10 7.8 x 10

Isopropyl vinyl ether 18 19 20 21

340

30 26 0 0

8.65

1.3 x 104

1.1 x 107

8.72

1.2 x 10

6

7

Deffieux et al. (1983)

9.0 x 10

5

6

Goineau et al. (1977)

9.2 x 10

5

6

Hsieh et al. (1980)

9.0 9.0

1.0 x 10 8.1 x 10 8.3 x 10

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993)

Table 2 Continued Result number

T,°C

mB/(mol dm-3)

kp+/(dm3 mol-1 s-1)

a

kp1+B/s-1 b

References

4.4 x 106

Hayashi et al. (1971)

Isobutyl vinyl ether 22

50

23

6 x 10 5

7.3

42.5

7.4

1.1 x 10

6 5

6

Ueno et al. (1968)

6

2.6 x 10

Williams et al. (1967)

8.1 x 10

24

30

7.6

3.4 x 10

25

25

7.6

1.2 x 105

6.2 x 105

Hayashi et al. (1971)

26

0

7.9

3.8 x 104

3.0 x 105

Hayashi et al. (1971)

27

0

7.9

3.8 x 104

3.0 x 105

Goineau et al. (1977)

5 x 104

4 x 104

Goineau et al. (1977)

Tert-butyl vinyl ether 28

0

ca. 8.0

+

a The kp are the constants calculated by the original authors b The kp1+B are the unimolecular rate-constants calculated by (3.2). As explained in the text, they are probably minimum values for all systems except 1, 2 and 3

a conclusion which is in conflict with the observations. However, in solution the participation of the species P+nP is probable, especially with polar monomers in non-polar solvents, but because of the difficulty of diagnosing when this occurs, I will ignore it during most of the subsequent discussions.

C

C

Y–Z

C+

1

H

C

M

Pn – CH2

OR

Pn – CH2 C+

M

OR C+

X

M

C 2

H

3

H

It is useful to anticipate here that my analysis of the kinetics of the polymerizations in solution indicates the prevalence of unimolecular propagation in some systems down to quite low m. Moreover, we will see that the corresponding first-order rate constant is influenced by the nature of the diluent. Such an effect seems paradoxical, and as it appears to be a newly recognized phenomenon, I will present here my explanation of it which is as follows. The kp1+ characterizes a unimolecular transformation of the π-complex between the cation and the double-bond of the monomer, to the newly formed cation, which now has the

341

Developments in the Theory of Cationoid Polymerisations previously complexed monomer molecule added to the chain. The rate of this process, or rather the activation energy, is determined by the strength of the π-bond, and this must depend to some extent on the electrical environment of the complex. What I have in mind is this: If there is a dipole Y-Z at the side of the near-planar trigonal carbenium ion opposite to where the complexed monomer is held, the π-bond will be weakened and the reaction accelerated. This idea is represented schematically by 1. This model will help us to account for the apparently paradoxical fact that the rate of the unimolecular growth reaction is evidently influenced by the polarity of the solvent. If we pursue the idea that R depends on what is attached to the ‘backside’ of the carbenium ion, it follows that if there is present a compound other than the monomer, e.g., a solvent, the rate R is composite, consisting of at least two components, one representing the more reactive species having the stronger dipole at the backside, and one having the weaker; and one of these usually is the monomer, so that we have species 2 and 3 propagating with rate constants k+Mp1 and k+Xp1. It follows that (3.1) should be written as

R = kp+1M [MPn+ M] + kp+1X [ XPn+ M]

(3.5)

The relative magnitude of the two concentrations evidently depends on the magnitude of the equilibrium constants and of the concentrations of M and X. Two further points need to be made. (i) It is likely that the formation of 3 from 2 will be favoured, i.e., the equilibrium constant will be enhanced, by a statistical factor akin to an entropy of mixing. (ii) For the species 2 there is no ‘front’ and ‘back’, the MP+nM is symmetrical, and therefore the probability of the propagation, i.e., the kp1+ , is twice as great as it would be for XP+nM, even if the free energy of complexing is the same for X and M. I have refrained from introducing these refinements explicitly into the algebra, but the ideas will explain at least qualitatively some otherwise puzzling and hitherto unexplained phenomena to be discussed in Section 4. My idea that in bulk monomer and in some solutions the propagation is a unimolecular reaction is supported strongly by the way in which the DP depends on the monomer concentration. At low m, 1/DP increases rectilinearly with 1/m, as demanded by the conventional Mayo equation for bimolecular propagation; but at high m, 1/DP increases rectilinearly with m, as is required for unimolecular propagation (see Section 5).

b) New rate-constants for bulk polymerizations In Table 2 we present the new unimolecular propagation rate-constants k+Bp1 for bulk polymerizations, calculated from the published bimolecular ‘ kp1+ ’ by Szwarc’s

342

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) equation (3.2). The bulk concentrations mB of the monomers are from standard sources. These rate-constants fall into three groups. 1. Cyclo-pentadiene and isobutene, for which the k+Bp1 are of the order of 109 s-1. These monomers have but one ‘attachment point’ to the carbenium ion, but there is no means of ascertaining what fraction of these is complexed; it is likely to be high. The ‘ kp1+ ’ were originally calculated on the assumption that the concentration of propagators, which is [P+n] on the traditional view, equals c, and by implication therefore also our [P+nM] = c. This means that if indeed [P+nM] = c, my k+Bp1 for these monomers are the true values, but if that equality does not hold, then they are ‘apparent’ and minimum values. Over the whole range of conditions for which the conversion curves are rectilinear any bimolecular propagation by whatever species of propagator must be kinetically unimportant. This means that whenever the polymerizations are of zero order with respect to m, our assumption that effectively only one reaction, namely complexing, results directly from the encounter of the P+n with M, is vindicated. 2. The results for styrene and its two derivatives are all of the order of 107 s-1. Because for these monomers the c comprises not only [P+nM], but also [P+nG], so that [P+nM] is a fraction of c, these apparent k+Bp1 are necessarily minimum values. The same holds for the VE, and it is easy to show from our equations that if R = k+Bp1[P+nM] and the minimum value (k+Bp1) is calculated from R = (k+Bp1)c, the true k+Bp1 is given by

kp+1B = ( kp+1B )( KG + KM ) / KM

(3.6)

where KM and KG are defined by (4.2) and (4.3) below. Therefore further progress in this area depends on the measurement of equilibrium constants. At this stage I simply cannot say how much of the difference of two powers of 10 between the k+Bp1 of the alkenes and the styrenes is to be attributed to an intrinsic difference in reactivity and how much to the existence of the P+nG complexes. The negative temperature coefficient of the rate constant for α-methyl styrene found by Chawla & Huang (1975) is a strong indication in favour of my view that the propagation is not a simple bimolecular reaction. 3. The k+Bp1 of the VE cover the range from 104 to 107 s-1 and it is not obvious what determines the differences between them, and in particular why IPVE appears to be so outstandingly reactive. Evidently, for these monomers too, the k+Bp1 are minimum values, but it is not obvious which are the main factors depressing these ‘apparent’ k+Bp1 below the true value given by R/[P+nM]; in particular, what is the origin of the great differences between the k+Bp1 of the various VE; this problem will be encountered again in the context of the kp1+ for the polymerizations in solution. In seeking a solution

343

Developments in the Theory of Cationoid Polymerisations it must be remembered that the VE differ not only in terms of their stereochemistry and polarity, factors which affect their complexing with the carbenium ion and the rate of the subsequent isomerization, but they also differ with respect to the dissociative electron capture of both the monomers and their polymers and the production of inhibiting species (Suzuki et al. 1977). It is because of such effects that MeVE does not polymerize cationically under ionizing radiations, although it does so with typical cationic initiators (Desai et al. 1977).

4 The kinetics of polymerizations in solution

a) Development of the general kinetic equations When considering the polymerizations by ionizing radiations in solution, I adopt a point of view opposite to that customary in conventional reaction kinetics. In these it is normal practice to progress from dilute to more concentrated solutions, usually up to no more than ca. 2 mol dm-3. In the present context, the actual experimental practice determines that we think in terms of a gradual dilution of the bulk monomer; this also happens to be heuristically fruitful. To develop the required kinetic equations, we start from the proposition that it is unlikely that the same species, namely the monomer-complexed cation, P+nM, can propagate both unimolecularly and bimolecularly. However, unimolecular and bimolecular propagation by different species can be going on simultaneously. This is my interpretation of the fact that all the R against m plots (except possibly that for 4-MeO-styrene) and the DP against m plots have a more or less prominent inflection. This is the region of dieidic propagation in which P+nM and P+nSv coexist in kinetically significant concentrations. The m at which the R against m plot from m = 0 begins to curve upwards we denote by mC, the critical m at which the previously monoeidic second-order propagation begins to be dieidic. The rate R of such a dieidic polymerization, consisting of a bimolecular component R2 and a unimolecular component R1 is given by

R = R2 + R1 = kp+ [ Pn+ Sv]m + kp+1[ Pn+ M]

(4.1)

on the assumption that the concentration of the bare cation, [P+n] is kinetically insignificant. This means that all the P+n-species are involved in competitive equilibria. The complexing of the monomer with P+n through its double bond is therefore represented as

Pn+ Sv + M ↔ Pn+ M + Sv 344

(4.I)

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) which gives the equilibrium equation

KM+ = [ Pn+ M][Sv]/[Pn+ Sv]m

(4.2)

The non-propagating species P+nG, in which the monomer is complexed with P+n through a hetero-atom or a phenyl ring is involved in the equilibrium

Pn+ Sv + M ↔ Pn+ G + Sv

(4.II)

described by

KG+ = [ Pn+ G][Sv]/[Pn+ Sv]m

(4.3)

As before, we define c as the total concentration of positively charged species, which is the same as what Stannett’s group designate as [C+], the total concentration of cations which have escaped geminate recombination, so that

c = [C + ]

(4.4)

and therefore

c = [ Pn+ M] + [ Pn+ G] + [ Pn+ Sv]

(4.5)

From (4.2), (4.3) and (4.5) we obtain + [ Pn+ M] = [ KM+ mc /( m[K M + K G+ ] + [Sv])

(4.6)

[ Pn+ Sv] = c[Sv]/( m[ KM+ + KG+ ] + [Sv])

(4.7)

and

and by means of the simplification + KGM = KG+ + KM+

(4.8)

and (4.1) we arrive at the general rate-equation which has two useful forms: + R = mc( kp+1 KM+ + kp+ [Sv]) /( KGM m + [Sv])

(4.9a)

345

Developments in the Theory of Cationoid Polymerisations and + + R = kp+1 KM+ c/( KGM + [Sv]/ m) + kp+ cm /(1 + KGM m /[Sv])

(4.9b)

The [Sv] can be expressed as a function of m in terms of the molar volumes of monomer, vM, and solvent, vS, by

[Sv] = (1 – mvm ) / vs

(4.10)

If (4.10) is introduced into (4.9) we obtain + + R = [kp+ mc(vs–1 – mvm vs–1 ) + kp+1KM mc]/[m( KGM – vm vs–1 ) + vs–1 ]

(4.11)

The somewhat clumsy (4.11) is a necessary stage in the development of the complete rateequation with m as the single independent variable. The c can be eliminated by taking advantage of the fact that the comprehensive results from Stannett’s group enable us to express c as a function of m for their systems. I introduce this innovation because of the self-consistency of the c values and their trends, and despite the warning of the original authors, that they are afflicted with some uncertainties. For most of the systems these variables are related over a considerable range of concentrations by an equation of the form

c = Am + B

(4.12)

where A can be positive or negative. The fact that c is itself a function of m is sufficient to account for the fact, repeatedly noted by Stannett’s group, that the external order of the polymerizations with respect to monomer is consistently greater than unity. The introduction of (4.12) into (4.11) gives the general rate-equation (4.13), whereby we obtain R as the ratio of two polynominals in m: + [m(vm vs–1 – KGM ) – vs–1 ]R

= m3 Akp+ vm vs–1 – m 2 ( Akp+1Km+ + Akp+ vs–1 – Bkp+ vm vs–1 ) – mB(kp+1Km+ + kp+ vs–1 )

(4.13)

The form of (4.13) offers a ready explanation for the fact that the formal order of the polymerizations, d(ln R)/d(ln m), as shown by the bilogarithmic plots of Stannett et al., varies with m. Equation (4.13) is such that both the first derivative dR/dm and the second derivative d2R/dm2 can be zero; the former applies to the polymerization of isobutene for which the R against m curves have a maximum (Figures 9 and 10), the latter to the VE and styrene, the R against m curves for which all show inflections. The pursuit of this

346

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) line of enquiry, though possibly rewarding, would take us too far from the main theme of this paper. The development of the equations for analysing the kinetic results now proceeds as follows. Note that to make an analysis of the data feasible, it is essential to assume that the equilibrium constants do not vary with m, i.e., with the changing polarity of the medium. Since none of the equilibria involve a change of charge, this is reasonable. The same is not true of both the rate constants k+p and kp1+ . The variation of the second-order rate constant k+p with the polarity of the medium, usually expressed in terms of its dielectric constant, is well known and needs no comment at this stage. As noted in Section 3, the + does depend on the solvent, but the effect is different in kind from that on k+p. The kp1 reason is that for the unimolecular propagation there are at most three species to be considered: MP+nM, SvP+nM, and PP+nM, the relative concentrations of which change throughout the reaction, but the kp1+ of each of these species is probably not influenced strongly by the composition of the solvation shell, in contrast to k+p. However, having made this warning signal, I will not attempt to include solvent effects formally in my considerations. So far I have conducted my kinetic analysis on the basis of a ‘worst case scenario’ applicable for the whole range of m, and the resultant (4.13) is not suitable for the calculation of the rate constants and equilibrium constants. Therefore, since c and therefore A and B, are given at least for the systems studied by Stannett’s group, we go back to (4.9b), and we will use the first term to analyse the region of high m, near mB, where [Sv]/m is small, so that + R1 = kp+1 KM+ c/KGM = kp+1W ( Am + B)

(4.14)

where W = K+M/K+GM. From appropriate plots we can determine k+p1W. However, for most systems the kp1+ increases strongly with m, so that the kp1+ W cannot be used to calculate W. At low m, we use the approximation

R2 = kp+ cm

(4.15)

since m/[Sv] is small. The calculation of k+p from (4.15) is the method used by the original authors, so that we obtain essentially similar results for low m. These, however differ from those that they calculated by the best line for the whole bilogarithmic plots and which therefore generally differ from my values.

347

Developments in the Theory of Cationoid Polymerisations A guide to the behaviour of all the systems is the shape of the R against m plots, and the DP against m plots, shown in Figures 1-15. The detailed information for all the figures in this paper is compiled in Table 3.

b) The alkyl vinyl ethers The VE are discussed first because very detailed information is available for them from Stannett’s group. Then we will investigate whether the ideas evolved concerning the VE are useful for interpreting the rather scantier results for other monomers. During these studies it became clear that if the original authors had plotted simply R against m for all their systems instead of making bi-logarithmic plots, the very different shapes of the various curves and their inflections might have caused them some misgiving about applying to all systems the simple second-order kinetics according to (2.5) and (4.15), in their symbols.

Rp = kp [C + ][M]

(4.16)

Table 3 Particulars of the systems, the results for which are plotted in Figures 1-15 T,°C

mB/(mol dm-3)

Diluent

EV E

20

10.54

C6H6

71

Deffieux et al. (1981)

2

IPVE

26

8.72

C6H6

71

Deffieux et al. (1983)

3

EVE

23

10.54

Et2O

71

Hsieh et al. (1982)

4

EV E

23

10.54

Me(OC2H4)2OMe

71

Hsieh et al. (1982)

5,12

EVE

22

10.54

CH2Cl2

71

Deffieux et al. (1982)

6,13

Styrene

10

8.5

Toluene

9.7

Ueno et al. (1966c)

7,14

Styrene

23

8.5

Toluene

53

Ueno et al. (1966c)

8

Styrene

10

8.5

CH2Cl2

9.7

Ueno et al. (1966c)

9

Isobutene

–78

12.6

CS2, CHCl3

7.5

Ueno et al. (1966b)

10,15

Isobutene

–78

12.6

CH2Cl2, C6H14

7.5

Ueno et al. (1966b)

11

4-MeOstyrene

0

7.4

CH2Cl2

70.5

Deffieux et al. (1980)

Figure

M

1

348

I/(rad Reference s-1)

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) A synoptic view of the rate-curves shown in Figures 1-5 shows that they all consist of several regions. Figures 1-3 and 5 show a sharp drop in R from m = mB to the first dilution point; Figure 4 shows R rising to a maximum. All five figures show an inflection

Figure 1 The dependence of R (O) and of c (❑) on m for EVE in C6H6.

Figure 2 The dependence of R (O) and of c (❑) on m for IPVE in C6H6

349

Developments in the Theory of Cationoid Polymerisations

Figure 3 The dependence of R (O) and of c (❑) on m for EVE in Et2O

Figure 4 The dependence of R (O) and of c (❑) on m for EVE in diglyme

350

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993)

Figure 5 The dependence of R (O) and of c (❑) on m for EVE in CH2Cl2

near the middle of the concentration range. If an inflection had occurred only once and if it had been feeble, as that in Figure 1, I might have ignored it, but I prefer to draw curves through the experimental points, especially when they are as well documented by duplication as in Figure 1, rather than to draw a curve born of prejudice past the experimental points. Finally, at lowest m all the plots are rectilinear. These different regions are the symptoms of different kinetic regimes, i.e., ranges of m over which the different propagating species dominate the kinetics. My interpretations are not complete; in particular, I have not attempted to introduce into my picture the species P+nP, which is very likely to play a part and which may eventually help in a more detailed comprehension of the facts. What does seem clear and common to all these systems is (a) that the statistical factor explained at the end of Section 3 a must produce a reduction in R at or near to the first dilution step, and (b) that in the low m region the principal propagating species is P+nSv with an indeterminable contribution from P+nP, which will be larger or smaller, according to the outcome of the competition between Sv and the pendent OR groups. For the following detailed analysis I now divide the systems into three groups. 1. Solutions in benzene, for which at higher monomer concentrations the complexing of P+n by the solvent is assumed to be negligible compared to its complexing by the much more polar monomer, and therefore R2 of (4.1) is assumed to be negligible over that part of the concentration range.

351

Developments in the Theory of Cationoid Polymerisations 2. Solutions in diethyl ether and diglyme, whose behaviour, despite their chemical similarity, is different and rather more difficult to understand. 3. Solutions in CH2Cl2, for which the complexing by the solvent is so strong, that the monomer is effectively excluded from the solvation shell of the cation, and therefore the propagation becomes predominantly a bimolecular reaction, i.e., the R1 of (4.1) is negligible after a very small degree of dilution.

i) EVE and IPVE in benzene The R against m plots together with the c against m plots are shown in Figures 1 and 2, and it is clear that the kinetic patterns are not simple. Both systems show a drop in rate upon the first dilution which is much greater for IPVE, and at the m = 0 end a threshold value of m = mi ≈ 0.5 mol dm-3, below which the rate is negligibly small. I will not attempt to account for the apparent thresholds, as it is probable that they arise from impurity effects that are always more important at low concentrations of the reagents. For the kinetic analysis of the reactions at high m we use (4.14). From this point it is more useful to discuss the two systems separately. EVE in benzene. From Figure 1 we find that the slope S1, of the line from the first dilution point below mB down to ca. 8.5 mol dm-3 is

S1 = ( 45.2 – 27.6) × 10 –6 /(10.17 – 8.55) = 9.17 × 10 −6 dm 6 mol −2s −1 Because A = (1.65 - 0.84) x 10-10/ 10 = 8. 1 x 10-12, k+p1 W = S1/A = 1.1 x 106 s-1. Because by definition K+GM > K+M, this gives a maximum value of kp1+ . A second value of + W can be obtained thus. When m= 10.17 mol dm-3, R = 4.52 x 10-5 mol dm-3 s-1, kp1 therefore kp1 W = 4.52 x 10-5/(10.17A + B), and since B = 8.6 x 10-11, kp1 W = (4.52/ 16.84) x 106 = 2.7 x 105 s-1, which gives another, rather lower, maximum value for kp1+ . In view of the considerable uncertainties, especially in the A and B values, the disagreement in the kp1+ W values by a factor of ca. 4 is not astonishing; the mean value of kp1+ W = 7 x 105 s-1. As we do not know the magnitude of K+M and K+GM, there is no means of estimating + at present. Figure 1 shows that the slope R/m increases strongly as m → mB. This kp1 means that kp1+ W increases and since, as discussed above, the equilibrium constants, and a fortiori their ratio, are likely to be insensitive to the concurrent change of medium, we attribute this mainly to the change in the kp1+ which is caused by the change in the population of propagators, the [MP+nM] increasing at the expense of the [SvP+nM] as m → mB (see (3.5) in which the X is Sv in the present application). It is because of this

352

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) increase of kp1+ with m that we cannot use the value of kp1+ to calculate W for this and similar systems. At m ≤ 7 mol dm-3 a different polymerization mechanism appears to gain prominence, so that we then have a dieidic reaction, which is followed by a monoeidic regime below m ≈ 3 mol dm-3. For this region we calculate k+p, as the original authors did, from (4.15). If the result at the lowest m is neglected, their ‘kp’ values give for m = 1.32 to 3.10 mol dm-3 a k+p = (9.9 ± 1.8) x 103 dm3 mol-1 s-1. IPVE in benzene. Figure 2 shows that the dependence of R on m near mB is too illdefined to make a calculation of kp1+ W possible. However, a simple comparison of the rates RB at m = mB gives RB(IPVE)/RB(EVE) = 1600/55 ≈ 30. Because of the very low rates at m < 3 mol dm-3 a plausible value of k+p cannot be calculated reliably by the method used in the previous section, despite the apparent similarity of the plots. Estimates by means of various lines through the experimental points give values of k+p of (10 ± 5) x 105 dm3 mol-1 s-1. I do not propose any explanation for the great differences in kp1+ W, and therefore probably in the kp1+ , for the two VE, but the fact that both rate constants (k+p and kp1+ ) are so different indicates some profound difference in the kinetic properties of these two monomers. The exceptional kinetic position of secondary alkyl ethers is not news, since Eley & Saunders (1954) found cyclohexyl VE to be eight times more reactive than EVE in polymerizations initiated by iodine. The dramatic drop in rate at the first dilution step for IPVE is different in magnitude and shape from what was seen with EVE, and the ideas used in the following sections to explain apparently similar phenomena with other monomers and solvents do not seem to be applicable here; it remains a mystery.

ii) EVE in Et2O and diglyme The R against m plots for these two solvents (Figures 3 and 4) show that they behave differently. In view of the fact that the di(2-methoxyethyl) ether (diglyme) molecule is much larger than Et2O and contains three O-atoms, this is not too strange, and therefore I shall treat the systems separately. Et2O solvent. Figure 3 shows that R increases with m by a factor of ca. 40, whereas c decreases by a factor of ca. 1.8. The original authors concluded from their usual bilogarithmic plot that there is a normal bimolecular propagation over the whole concentration range, according to (4.15). However, my interpretation of the points in Figure 3 shows several regimes.

353

Developments in the Theory of Cationoid Polymerisations In the region of high m there are insufficient results to define the curve adequately for an interpretation like that given for EVE in benzene. At the other end one can use (4.15) and thus I found that as m goes from 1.4 to 3 mol dm-3, the k+p goes from 1.1 x 104 to 1.5 x 104 dm3 mol-1 s-1, which is the same as found by the original authors, and k+p continues to increase with growing m. For this change, at any rate throughout the region of bimolecular propagation, I suggest the following, fairly obvious, qualitative explanation. Since the dielectric constant (DC) of Et2O at the relevant temperature is ca. 5 and that of EVE is lower by about one unit, one may be seeing here the normal acceleration of an (ion + molecule) reaction as the DC of the medium decreases with increasing m. The sharp fall in rate as m goes from mB (10.5 mol dm-3) to 10 mol dm-3 can be explained in terms of my theory, as follows. Because both the monomer and the solvent have the same dipole moment of 1.14 Debye units (Taskinen et al. 1978) it cannot be due to a polarity effect and I conclude therefore that one has here the case discussed at the end of Section 3a, namely that this deceleration is a manifestation of the statistical factor. Diglyme solvent. The kinetic plot for this system (Figure 4) differs from those of all the other VE systems in several respects, and it shows clearly that the behaviour pattern consists of several parts. As the bulk monomer is diluted with diglyme, there is a marked rise in the polymerization rate, in contrast to the deceleration seen in all other VE systems, accompanied by a fairly steep rise in c down to m ≈ 8.5 mol dm-3. After a sharp maximum, the rate falls continuously but with an inflection towards m = 5.5 mol dm-3, and c rises less steeply and near-rectilinearly, as for the Et2O system. The interpretation of the behaviour from about 2 to 9 mol dm-3 might be by the same model as used by the original authors and by us for Et2O solvent, were it not for the inflection and that R/m increases by ca. 40 % with increasing m, whereas the coefficient of kp in (4.15), Am + B= c, decreases from around 5 x 10-10 to 2.5 x 10-10 mol dm-3. It follows that k+p must be increasing too. This, however, is contrary to the prediction of simple transition state theory, since for diglyme ε = 7.3 (Hsieh et al. 1982), so that as m increases, c falls. Probably one is seeing here an effect characterizing large solvents comprising several (in this case three) linked dipoles (CH2OCH2 groups), and which definitely fall outside the scope of the simple transition state theory. The k+p calculated by the original authors, ranging from 1.2 x 104 to 2.7 x 104 dm-3 mol-1 s-1 as m goes from 1.2 to 7 mol dm-3 appear to us to be valid. However, the behaviour near m = mB needs some other explanation. My proposal involves the specific solvation of the ‘backside’ of the carbenium ion by the strong dipole of the solvent; this displaces the monomer molecule which is located there in the absence of the solvent, so that the π-bond to the monomer at the ‘front’ is weakened and the unimolecular isomerization-propagation becomes accelerated, despite the statistical factor which, alone, would produce a deceleration, as explained at the end of Section 3a. As the dilution proceeds from m = mB downwards, the polymerization goes through a dieidic phase, in

354

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) which the unimolecular propagation by the species SvP+nM, which are ‘backside solvated’ by diglyme, coexists with bimolecular propagation by the species SvP+nSv, in which the Pn is completely solvated by diglyme. As m decreases, the polymerization becomes monoeidic, i.e., purely bimolecular, as discussed in the previous paragraph. The whole sequence of changes is illustrated in Table 4.

iii) EVE in CH2Cl2 The R against m plot for this system (Figure 5) resembles at first sight that for IPVE in benzene, and indicates a change of mechanism at very small dilution, i.e., very near m = mB. It is an obvious step to seek the explanation in terms of a preferential solvation of the propagating cation by the added solvent which has a dipole moment of 1.6 Debye units, whereas that of EVE is 1.14 Debye units . A similar view was expressed by the original authors (Deffieux et al. 1982). I am aware of CH2Cl2 being a much weaker donor than any ether (Gutmann 1978) and of the fact that near mB the ether monomer has the mass-action advantage. None the less, my view offers the following self-consistent picture. As CH2Cl2 is added progressively to the monomer, the ratio [P+nSv]/[P+nM] increases so that in the then dieidic polymerization the contribution from the fast unimolecular propagation diminishes so that the slower bimolecular propagation gradually takes over, and from m ≈ 5 mol dm-3 downwards the polymerization is monoeidic and bimolecular. This means that the only type of cation needing consideration is P+nSv and therefore from (4.15) R/mc = k+p. In other words, for the lower part of the concentration range the interpretation of the original authors is valid, their kp is our k+p, and it is what they believed it to be; its slight upward drift as m increases, i.e. as the mean ε of the mixture decreases, is what one expects for an (ion + molecule) reaction. The fact that even a small amount of CH2Cl2 admixed to another solvent reduces the rate to that prevalent in CH2Cl2 only has also been found in small-molecule kinetics and fits into the picture of specific or selective solvation (Clark & Wayne 1969).

Table 4 m/(mol dm-3) Propagators

2-4.5 +

SvPn Sv

4.5-10

mB = 10.5

SvPn+M

MPn+M

SvPn+Sv

Eidetity

Monoeidic

Dieidic

Monoeidic

Molecularity

Bimolecular

Unimolecular + bimolecular

Unimolecular

355

Developments in the Theory of Cationoid Polymerisations

c) Other monomers The polymerizations of hydrocarbon monomers by ionizing radiations differ from those of the VE in several respects which have been set out at the end of Section 2. I now show that the reaction patterns of the hydrocarbons and the ways in which they differ from those of the VE can be explained adequately by my theory. Unfortunately, c is not known for any of these systems, so that no rate-constants can be calculated by the established method, but another method has been devised based on DP information.

i) Styrene in solution The only extensive set of kinetic results, including DP, was obtained by Ueno et al. (1966a). Before these are analysed, the reader must be warned that they are presented in a dangerously misleading manner, because the rate is given in units of percent per minute as a function of mol (%) of monomer. In their Figure 4 the rate is 0.2% min-1 at m = 8 mol dm-3 and also at 6 mol dm-3; but at m = 8 mol dm-3, R = 2 x 10-3 x 8 = 1.6 x 10-2 and at m = 6 mol dm-3 it is 1.2 x 10-2 mol dm-3 min-1! Their kinetic results for styrene in toluene are shown, recalculated by us, in Figures 6 and 7 as R/(mol dm-3 s-1) against m/(mol dm-3). At first sight the two sets of points seem hardly compatible, but by my interpretation they can both be considered to evince the same reaction pattern which involves a change of kinetics near m = 5 mol dm-3. In terms of my theory we are seeing at high m a unimolecular propagation and at low m a normal bimolecular propagation, with a dieidic regime in between. In the same paper, Figure 6 purports to show that under similar polymerization conditions the dilution of styrene with CH2Cl2 produces a sharp increase in rate to a maximum RX and then a decrease. Figure 8, in which the same results are plotted as R/(mol dm-3 s-1) against m, shows this to be illusory, and in fact the dependence of R on m at high m is unknown. What is clear is that a drastic deceleration sets in at or above 5 mol dm-3, and that below ca. 3 mol dm-3 probably normal bimolecular propagation prevails. In section5b (ii) I show how the DP information for this system makes it possible to calculate a k+p.

ii) Isobutene in solution The influence of various solvents on the rate of polymerization of isobutene at –78 °C by ionizing radiation has been described by Ueno et al. (1966b). The dilution of isobutene with n-hexane, chloroform, CH2Cl2, or carbon disulphide accelerated the polymerizations, the effect increasing in the order given, and the acceleration by CS2 being much the greatest. The dependence of the rate on m appears to show two different behaviour patterns. Their Figure 4 shows that for CS2 and CH2Cl2 the rate increases with dilution

356

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993)

Figure 6 The dependence of R on m for styrene in toluene at I = 9.7 rad s-1

Figure 7 The dependence of R on m for styrene in toluene at I = 53 rad s-1

357

Developments in the Theory of Cationoid Polymerisations

Figure 8 The dependence of R on m for styrene in CH2Cl2 at I = 9.7 rad s-1 to a maximum, RX, near 5 mol dm-3 and then declines steeply to m = 2 mol dm-3. For CS2 the ratio RX/RB ≈ 3.2, for CH2Cl2 RX/RB ≈ 1.6. For CHCl3 and hexane, their Figure 7 appears to show that over the whole range of m the rate increases as m decreases, but in contrast to Figure 4 - the rate is given in percent per hour. When it is recalculated to mol dm-3 s-1 one finds that for these solvents, too, R goes through a maximum, near m = 7 mol dm-3, with RX/RB ≈ 2 for both solvents; see Figures 9 and 10. For the experiments with CH2Cl2, CHCl3 (e = 6.8), and CS2 the same explanation as used for styrene will serve, although the strong acceleration by CS2 seems odd at first sight in view of its zero dipole moment. However, because of its exceptionally high polarizability it behaves like a solvent of high ε, although its ε is only 2.6 (–78 °C). Its irregular behaviour in cationic polymerizations, as if it were a solvent of high polarity, has been known for many years (Hersberger et al. 1945). The similarity of the curves for the four solvents is remarkable, and the fact that the polyisobutene formed in CH2Cl2 is precipitated as a gel, whereas it is soluble in the other solvents, seems only to have distorted the relevant curve. However, the cause of the acceleration by the non-polar, non-polarizable hexane remains obscure. The increase in the rate of polymerization of isobutene as it is diluted with a polar solvent had been reported earlier by Popova et al. (1965). These authors found that for

358

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993)

Figure 9 The dependence of R on m for isobutene in CS2 (O) and CHCl3 (❑)

Figure 10 The dependence of R on m for isobutene in CH2Cl2 (O) and hexane (❑)

359

Developments in the Theory of Cationoid Polymerisations polymerizations with I = 70 rad s-1 at –78 °C the dilution with CH2Cl2 gave RX/RB ≈ 2 at ca. 50 mol (%) (ca. 7 mol dm-3), and dilution with CF2Cl2 gave RX/RB ≈ 5 at ca. 80 mol (%) isobutene. However, in one of the earliest studies of the effects of solvents on polymerizations by ionizing radiations (Stannett et al. 1964) it was found that the rate of polymerization of isobutene in CH2Cl2 at –78 °C and I = 5.6 rad s-1 with m = 9.5 and 11 mol dm-3 was only about one-third of the rate for bulk monomer. In view of the earliness of this investigation its disagreement with later results may not be significant, especially in view of the well-known difficulty of purifying adequately the CH2Cl2 available at that time. (The changes in the nature and amounts of the impurities in commercial chemicals, particularly solvents, with time, and differences between countries, are far too little known and appreciated.)

iii) 4-Methoxystyrene The polymerization of 4-methoxystyrene (MeOSt) by ionizing radiations at 20 °C in CH2Cl2 is reported briefly by Deffieux et al. (1980). Because this monomer resembles the VE in its polarity, one expects it to resemble these monomers in its polymerization behaviour. Indeed, as Figure 11 shows, the drop in rate, RB/R0.8B, between m = mB and the arbitrarily chosen m = 0.8mB is 4.3, and for EVE it is 2.5. There is no obvious inflection signalling the change of mechanism as there is for EVE, but the scanty points are certainly compatible with one. The behaviour is markedly different from that of styrene.

Figure 11 The dependence of R on m for 4-MeO-styrene in CH2Cl2

360

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993)

d) The rate constants in solution

i) The unimolecular rate constants The experiments show that the dilution of all the monomers leads to a change of rate, and I contend that at the earliest stage of dilution the polymerizations are still mainly unimolecular and I offer an explanation for the effects of solvents on the rate of the unimolecular reactions. Since the rate constants, kp1+ , are defined by (4.1) and (4.14) they can only be calculated if [P+nM] is known. As explained in Section 3b, there are reasons for believing that for cyclopentadiene and for isobutene [P+nM] = c, but for the former there are no results for solutions, and for the latter no c values are available, so that for these monomers kp1+ could only be calculated for the bulk polymerizations.

ii) The bimolecular rate constants According to my view, the polymerizations by ionizing radiations at the lowest m are bimolecular reactions, propagated by the species P+nSv. For these reactions there are no ambiguities, and [P+nSv] = c, so that k+p is defined by (4.1) and (4.15). The available values, including those calculated in this Section and in Section 5, are collected in Table 5. The new features of this Table are: (i) the values calculated by me (1, 2 and 3); (ii) the recognition that the values quoted apply only over a range of m which depends on the nature of the solvent; (iii) the k+p for styrene and EVE in solvents of low polarity are very similar. In my view none of these values and others in the literature are sufficiently reliable for any activation energies calculated from them to afford useful information. I have refrained from attempting a correlation of the rate constants with the dielectric constant of the diluent because in my view even the same cation in each different solvent is a different species, so that the fundamental hypothesis of theories of the Laidler type is not valid.

5 The degree of polymerization a) General treatment The DP of polymers formed by ionizing radiations is more difficult to interpret than that of polymers formed by chemical initiation, because after quite a low degree of conversion the degradation of the polymers by the radiation may become significant (Stannett et al. 1964; Deffieux et al. 1982). It is not known to what extent this fragmentation and to

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Developments in the Theory of Cationoid Polymerisations

Table 5 Values of kp kp/(dm3 mol-1 s-1) Diluent

This work a

Original authors

–7 8

CH2Cl2

104

-

2

10

Toluene

2.0 x 104

b

-

3

23

Toluene

3.2 x 104

c

-

Result

T,°C

References

Isobutene 1

Ueno et al. (1966b)

Styrene Ueno et al. (1966c)

Ethyl vinyl ether 4

20

Benzene

(1.5±0.8) x 104

0.7 x 10 4

5

23

E t 2O

(2.4±1.5) x 104

(1.2-2.6) x 104

6

23

Diglyme

(1.3±0.3) x 104

(1.2-2.7) x 104

7

22

CH2Cl2

(2±0.2) x 103

ca. 2 x 103

Deffieux et al. (1981) Hsieh et al. (1982) Deffieux et al. (1982)

Isopropyl vinyl ether 8

26

benzene (10 ± 5) x 105

(1.4-3) x 105

Deffieux et al. (1983)

a Calculated for m < mC b I = 9.7 rad s-1 c I = 53 rad s-1

what extent various transfer and termination processes are responsible for the welldocumented fact that the observed DP is generally smaller, in some systems very much smaller, than the ideal DP given by the ratio G(– m)/Gi, where G(– m) is the amount of monomer consumed and Gi is the yield of propagating ions per 100 eV (see (2.2)). In all the pioneering papers dealing with the bulk polymerizations, the lowness of the DP was attributed to the proton transfer to monomer that was well documented in the chemically initiated polymerizations, and was treated in terms of a bimolecular process. Therefore, those discussions, referring to bulk conditions and ignoring fragmentation, are of no relevance here. What we have to decide is whether all the DP information is to be ignored because of our ignorance of the extent of fragmentation in the different systems, or

362

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) whether we attempt a partial understanding by ignoring the possibility of fragmentation. Actually, the scant information available appears to be reasonably consistent, it can be interpreted by our theories, and some quantitative results can be extracted from it, so that it may be that the importance of the fragmentation has been exaggerated. To utilize the DP of the unimolecular reactions, the conventional theory, expressed essentially by the Mayo equation, had to be generalized to include the DP of polymers formed by a propagation of zero order with respect to monomer. This was done first in the context of a more general discussion (Plesch 1968), and the present treatment follows from it. This analysis starts conventionally. The DP is given by Rp/Rb, where Rp is the rate of propagation and Rb is the sum of the rates of all chain-breaking processes. In the systems considered here, Rp = R and is given by (4.1). As before, it is more useful to treat the two ends of the monomer concentration range separately. For the region m < mC where secondorder propagation by P+nSv predominates, the corresponding rate R2 is given by (4.15). At high m the species [P+nSv] is kinetically insignificant, so that c = [P+nM] + [P+nG] and correspondingly R1 is given by (4.14) in the form

R1 = kp+1cW

(4.14a)

Hence + R = kp1 cW + kp+ [Pn+ Sv]m

(5.1)

With regard to chain-breaking, note that in the systems under consideration here the dependence of the polymerization rate on I1/2 indicates that there are no terminating impurities, and that the principal termination is the neutralization of the cations by electrons. According to my view, and in contrast to the treatments by earlier authors, there are three such reactions, represented below:

Pn+ M + e − → Pn• + M

(5.Ia)

Pn+ G + e − → Pn• + M

(5.Ib)

Pn+ Sv + e − → Pn• + Sv

(5.II)

The fate of the radicals P•n (see (2.II)) does not concern us here. I know of no reason why the rate constants of these three diffusion-controlled reactions should be markedly different, and so they are given the same symbol, kt. If no cations 363

Developments in the Theory of Cationoid Polymerisations other than P+nM, P+nG and P+nSv are present, the concentration [A–] of terminating electrons attached to an acceptor A, is c, the total concentration of ions of either charge, and therefore

Rt = kt c 2

(5.2)

It will be convenient to replace only one of the c in (5.2) by means of (4.5) so that the rate of termination is then

Rt = kt ([Pn+ Sv] + [ Pn+ M] + [ Pn+ G])c

(5.3)

The total rate of chain breaking is the sum of the rate of termination and the rates of all other chain-breaking processes, Rr:

Rb = Rt + Rr

(5.4)

The most important of these in chemically initiated polymerizations are the transfer reactions with solvent, rate Rs, and rate-constant ks, and with monomer, rate Rm, and rate-constant km. Solvent transfer was shown to be important by Ueno et al. (1966c) for the polymerization of styrene in toluene, and it will be discussed below. The chemistry of the transfer with an aromatic compound ArH, discovered by Plesch et al. (Plesch 1953; Brackman & Plesch 1958; Penfold & Plesch 1961), can be represented as

Pn+ X + ArH → Pn ArH + X

(5.III)

Pn ArH + X + M → Pn Ar + HM + X

(5.IV)

where the reaction (5.III) is rate-determining. Therefore

Rs = ks [ Pn+ X][Sv]

(5.5)

where [P+nX] is any or all of the propagating cations. The chain transfer by non-aromatic solvents is of course chemically different, but the formalism is similar. The question to be decided now is which of the propagating species can take part in this type of transfer. Because in chemically initiated polymerizations ks is usually much smaller than k+p and k+p mB < kp1+ , we propose to neglect the solvent transfer at high m, i.e., when [Sv] is small; thus (5.5) becomes

Rs = ks [ Pn+ Sv][Sv]

364

(5.6)

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) Monomer transfer is a more difficult phenomenon to analyse, because in principle both P+nM and P+nG can react unimolecularly and bimolecularly thus:

and

Pn+ M or Pn+ G → Pn + HM +

(5.V)

Pn+ M or Pn+ G + M → Pn + HM +

(5.VI)

In view of the fact that proton transfer to monomer is the most general and effective alternative to propagation in chemically initiated bimolecular polymerizations, it seems sensible to include here the reactions (5.V). For m < mC we need to include the normal bimolecular process,

Pn+ Sv + M → Pn + HM +

(5.VII)

especially since monomer transfer was recognized as an important feature in the polymerization of IBVE in CH2Cl2 by Du Plessis et al. (1974). The bimolecular processes (5.VI) are neglected for the same reason that bimolecular propagation by P+nM and P+nG was discarded. It follows that the rate of chain breaking by monomer is given by

Rm = km [Pn+ Sv]m + kmM [Pn+ M] + kmG [Pn+ G]

(5.7)

By means of (5.3), (5.6) and (5.7) we obtain from (5.4) the general chain-breaking equation

Rb = kt ([Pn+ Sv] + [ Pn+ M] + [ Pn+ G])c + ks [ Pn+ Sv][Sv] + km [ Pn+ Sv]m + kmM [ Pn+ M] + kmG [ Pn+ G]

(5.8)

The general DP equation, derived from Rp/Rb by means of (5.1) and (5.8), is evidently cumbersome and not really useful because of the variation of all the rate-constants with m, especially when the polarities of M and Sv are very different. Recognizing this limitation, we shall once again consider separately the two ends of the range of m.

i) Bimolecular propagation For m < mC, where the only kinetically significant propagator is P+nSv, the DP is given by the second term of (5.1) divided by the appropriate modification of (5.8) in which [P+nM] = [P+nG] = 0, so that

365

Developments in the Theory of Cationoid Polymerisations

DP = kp+ m /( kt c + ks [Sv] + km m)

(5.9)

The inversion of (5.9) yields (5.10), which resembles the conventional Mayo equation, except that it contains the c:

1/DP = km / kp+ + ( ks [Sv] + kt c) / kp+ m

(5.10)

To visualize the dependence of the DP on m we need to substitute for c in terms of (4.12) and we thus obtain

1/DP = ( kt A + km ) / kp+ + ( kt B + ks [Sv]) / kp+ m

(5.11)

which has the same form (5.12) as the conventional Mayo equation:

1/ DP = α ′′ + β′′ / m

(5.12)

with α′′ and β′′ constant for high [Sv]; in contrast to the Mayo equation for chemically initiated polymerizations, α′′ may be negative, because we have seen that for some solvents, A is negative. For m > mC one can generalize (5.10) and (5.11) further by substituting for [Sv] in terms of (4.10). This procedure gives

1/DP = (km − ksvm / vs ) / kp+ + (ks /vs + kt c) / kp+ m

(5.13 a)

1/DP = (km A + km – ks vm vs-1 )/kp+ + (kt B + ks vs-1 )/kp+ m

(5.13 b)

These equations give the same dependence of the DP on m as (5.12), but one can only expect them to be valid over a range of m for which the DC of the reaction mixture remains sufficiently constant for the rate constants to be unaffected. Equation (5.13a) is used for the system styrene in toluene where this condition is fulfilled.

ii) Unimolecular propagation For the region of high m the rate of chain-breaking is given by

Rb1 = kt ([Pn+ M] + [ Pn+ G])c + kmM [ Pn+ M] + kmG [ Pn+ G]

(5.14)

Since there seems little prospect at present of being able to determine kmM and kmG separately, we will combine the second and third terms as km1 ([P+nM] + [P+nG]), and

366

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) since by hypothesis the two types of complexed cations are the only cations, (5.14) takes the simple form

Rb1 = ( kt c + km1 )c

(5.15)

Therefore, from (4.14a) (given at the beginning of this section) we obtain

and

DP = kp+1W /( kt c + km1 )

(5.16)

1/DP = kt c/kp+1W + km1/kp+1W

(5.17)

To find the dependence of the DP on m, we substitute for c from (4.12) and thus obtain

1 / DP = ( kt B + km1 ) / kp+1W + kt Am / kp+1W

(5.18)

which is of the form

1/ DP = α ′ + β′m

(5.19)

The corresponding equation for chemically initiated unimolecular polymerizations is of the same form (Plesch 1968), and it was pointed out on that occasion that in favourable cases one can discriminate between polymerizations of first and zero order with respect to m from the way the DP depends on m.

b) Applications of the DP equations

i) EVE in CH2Cl2 The results of Deffieux et al. (1982, Table 2) for EVE in CH2Cl2 are plotted according to (5.12) and (5.19) in Figures 12a and 12b. It is fortunate that the apparently off-the-line point near m = 5 mol dm-3 is reinforced by two further determinations (Deffieux et al. 1982, Table 3; Hsieh et al. 1982, Table 5), so that the general shape of the curve is fairly closely defined, except near mB. The original authors made no attempt at a detailed interpretation and presented the results once again as a log-log plot, thus obscuring their most interesting features. We know from the kinetic analysis that for m < 6 mol dm-3 the polymerization is bimolecular, so that (5.11) applies, and we are concerned with the right-hand side of Figure 12.

367

Developments in the Theory of Cationoid Polymerisations

Figure 12 Plot (a), 102/DP against 10/m and plot (b), 102/DP against m for EVE in CH2Cl2. Two additional points near m = 5 mol l-1 from Deffieux et al. (1982), Table 3 and Hsieh et al. (1982), Table 5

There is no means of knowing whether this is rectilinear, but if we assume it to be as shown, with minimum slope and minimum intercept, and make some simplifying assumptions, we can obtain an order-of-magnitude for kt. We assume that km = ks = 0 and thus obtain 1/DP = k+tA/k+p + k+tB/k+pm

(5.20)

Because for this system A is negative, the Figure 12a gives us the intercept

I20 = kt A / kp+ = –6.8 × 10 −2 and with A = –2.65 x 10-11 we obtain kt/k+p = 2.6 x 109. From the slope

S20 = kt B / kp+ = 7 × 10 −1 and with B = 6.7 x 10-10 we obtain kt/k+p = 1.0 x 109 and an average kt/k+p = 1.8 x 109. The value of k+p from the kinetic data is 2.2 x 103 dm3 mol-1 s-1 so that the average kt = 4 x 1012 dm3 mol-1 s-1. It is encouraging that our two values of kt/k+p agree within a factor of 2. One cannot use (5.10) in this instance to determine km by assuming c is constant, as I20 is negative. Deffieux et al. (1981) calculated kt from (2.8) as kt ≈ 4 x 1011 dm3 mol-1 s-1. In view of the assumptions involved in both calculations, the discrepancy is probably not significant.

368

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) Next, we examine the dependence of the DP on m in the region near mB, where (5.18) is applicable. Both the kinetic plot and Figure 12 show that the consequences of introducing even a very small quantity of CH2Cl2 into the EVE are so dramatic that an attempt to account for them by an equation is unpromising (consider, that one would need to know the d/dm for each of the rate constants and equilibrium constants). I conclude from this analysis that my theory, based on a change of propagation mechanism with decreasing m, can account adequately for the observations.

ii) Styrene in toluene The dependence of the DP of polystyrenes formed by ionizing radiations in toluene has been reported by Ueno et al. (1966c) in the form of plots of molecular weight against mole fraction of monomer for two values of I and slightly different T. These results, converted to DP dependence on m, are shown in Figures 13a, b and 14a, b. The rate curves discussed in Section 4b (i) indicate a marked change of regime near m = 5 mol dm-3, which I attributed to bimolecular propagation being prevalent below that, and unimolecular propagation being dominant at high m, and the DP plots can be interpreted in the same way. However, in contrast to the VE system discussed in the previous section, we have no information on c for this system, but since the yield of ions from a given dose-rate depends mainly on the dielectric constant, it can be assumed that in the mixtures of aromatic hydrocarbons with which we are dealing here, the c and the rate constants are independent of m, so that we can use (5.10) and (5.14), treating c as constant.

Figure 13 Plot (a), 103/DP against 10/m and plot (b), 103/DP against m for styrene in toluene

369

Developments in the Theory of Cationoid Polymerisations

Figure 14 Plot (a), 103/DP against 10/m and plot (b), 103/DP against m for styrene in toluene

However, (5.14) does not help to provide new information, because even if we assume kp1+ = k+Bp1 and calculate kt from the diffusion equation, we still have the two unknowns W and c. At low m, equations (5.13a, b) are relevant, and since A and B are unknown for this system, we shall use (5.13a). The intercepts for both systems (Figures 13a and 14a) are effectively the same, so that

I13 = (km – ks vm / vs ) / kp+ = (2 ± 0.5) × 10 −3 Since vm ≈ vs, the fact that I13 is positive shows that km > ks, which is in agreement with the results obtained by the original authors by a slightly different method (Ueno et al. 1966). The slope is

S13 = (kt c + ks / vs ) / kp+ from which we can estimate k+p if we assume that ks/vs can be neglected compared to ktc; this can be justified by reference to various findings from chemically initiated polymerizations. Further, at low m equation (4.1) gives c = R/mk+p, so that the above equation for S13 becomes

kp+ = ( kt R / S13 m)1 / 2

370

(5.21)

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) By means of (5.21) and the data in Table 6, together with the value of kt = 2 x 1011 dm3 mol-1 s-1 used previously, the two values of k+p shown in Table 6 have been calculated. Because both I and T are different, it is not possible to apportion the reasons for the difference in k+p if indeed it is significant. However, the close agreement as to order of magnitude of the two values obtained from the two sets of experiments is reassuring. It is unfortunate that for styrene in CH2Cl2 the results of Ueno et al. (1966b) are too scanty and too scattered to permit similar calculations.

Table 6 Values of k+p 102S13

(105R/m)/s-1

k+p/(dm mol-1 s-1)

13

1.13

2.3

1.0 x 104

14

1.16

6

3.2 x 1 0 4

Figure number

iii) Isobutene in CH2Cl2 Ueno et al. (1966b) have given results for the DP of polyisobutenes formed in CH2Cl2 at –78 °, which we show as plots of 1/DP against 1/m and 1/DP against m in Figures 15a and 15b. These can be exploited, together with the rate data for the same system (Figure 10), to obtain an estimate of k+p. Note that the rate goes through a maximum near m = 5 mol dm-3 (Figure 10) and that the DP has a maximum near 8 mol dm-3 (Figure 15). Equation (5.17) is more useful for this system than for most others, because for isobutene there is only one complexing site so that W = 1, and (5.17) takes the form

1 / DP = kt c / kp+1 + km1 / kp+1 (5.22) Since c = R1/ kp1+ , (5.17) gives for m = mB,

km1 = kp+1B / DPB – kt R1 / kp+1B (5.23) The original data give DPB = 1.5 x 103, R1 at m = mB as 1.7 x 10-6 mol dm-3 s-l, and k+Bp1 = 2 x 109 s-1 (Table 2), so that

371

Developments in the Theory of Cationoid Polymerisations

Figure 15 Plot (a), 104/DP against 10/m and plot (b), 104/DP against m for isobutene in CH2Cl2

km1 = 2 × 10 9 / 1.5 × 10 3 – 1012 × 1.7 × 10 −6 / 2 × 10 9 ≈ 10 6 s −1 This result means that at any rate for bulk isobutene at –78 °C the DP is governed by the unimolecular proton transfer to the monomer. To estimate k+p by means of (5.13a) we make the approximation ks/vs << ktc, replace c by R/k+pm and thus obtain the slope S13 as

S13 = kt ( R/m)/(kp+ )2 +

so that kp = ( kt R/S13 m)

1/ 2

(5.24)

With S13 = 1.82 x 10-3, R/m = 7.5 x 10-7, and kt = 2 x 1011 dm3 mol-1 s-1, we thus obtain k+p = 104 dm3 mol-1 s-1. This is of the same order of magnitude as the k+p = 1.2 x 104 dm3 mol-1 s-1 for isobutene in MeCl at –45 ° (Magagnini et al. 1977 and preceding papers). The rate-constant determined by these authors was identified as k+p by Plesch (1993). (The k+p calculated in this section was wrongly given as 105–106 by Plesch (1993).)

6 Conclusions In this paper many sets of results on the polymerization of various alkenic monomers by ionizing radiations from several research groups have been re-examined by means of a

372

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) new theoretical model which consists of several connected parts. The first comprises the idea that for polymerizations of monomers in bulk or in solution at high concentrations, the propagation is a unimolecular isomerization of a complex consisting of a monomer molecule which is π-bonded by its double bond to the carbenium ion at the growing end of the chain. This idea, due to Fontana et al. (1948, 1952), has not been used previously in the context of polymerizations by ionizing radiations, nor have its implications been examined before. The kinetic evidence shows that at conversions up to ca. 30 % the polymerizations are of zero order with respect to monomer, which supports my theory and indicates that the earlier interpretation of the rates in terms of a second-order reaction was erroneous. The new first-order rate constants, kp1+ , calculated by me from the published data, are collected in Table 2. The second part of the theory, which is a logical consequence of the first, is that monomers that have more than one basic site, e.g., an aromatic ring or an oxygen atom, can form more than one type of complex with the carbenium ion; this idea was first proposed by Plesch (1990) in the context of chemically initiated polymerizations. It helps to explain why aryl alkenes and alkyl vinyl ethers polymerize more slowly than isobutene and cyclopentadiene. The reason is that all the complexes formed by the alkyl alkenes are propagators, whereas for the aryl alkenes and vinyl ethers only a fraction of the population of complexes can propagate. To explain the very varied behaviour patterns shown by the various monomers in various solvents, use has been made of a further, hitherto unrealized, implication of the model, namely that the rate of the isomerization-propagation must depend upon the electrochemical environment of the complex. This vague idea has been given precision by concentrating attention on the species which occupies the site at the ‘back-side’ of the near-planar carbenium ion, the ‘front-side’ of which is π-bonded to the double bond of the monomer. The idea is that the stronger the dipole at the back, the weaker is the π-bond, and the lower is the energy of the transition state, and therefore the greater is the rate. As the dilution of the monomer progresses, the solvent takes over from the monomer as the principal solvator of the carbenium ions, and the propagation becomes of second order. The ensuing reaction pattern, i.e., the way in which the rate and the DP change with the monomer concentration, depends upon the relative polarity of the solvent and the monomer, and an understanding of these relations has made possible a self-consistent interpretation of the multifarious phenomena of these reactions. As far as possible these ideas have been expressed algebraically and rate constants have thus been extracted from the data (Table 5). The ideas propounded here about the solvation of carbenium ions in different circumstances are capable of further development. I hope that they will be tested and refined by a resumption of work in this now neglected field; in particular, it seems that

373

Developments in the Theory of Cationoid Polymerisations recent results on copolymerizations by ionizing radiations (Wood et al. 1989; Wood & Stannett 1992) will need to be re-assessed. The many results on polymerizations by ionizing radiations of monomers mixed with electron-acceptors should also now be re-examined in the light of the new theory. Further, it seems likely that its application to chemically initiated cationic polymerizations would be rewarding. It is a pleasure to acknowledge that this work would not have been possible without the old-fashioned, detailed publication of primary data by Stannett and his group and by the earlier workers; the currently fashionable omission of primary data by most authors is a serious obstacle to all investigations which involve the reinterpretation of established results. I also acknowledge with deep gratitude the generous advice and critical encouragement of many colleagues, especially (in alphabetical order) M. H. Abraham, A. Deffieux, A. Gandini, G. A. Salmon, V. T. Stannett and Ff. Williams. This is part XI of ‘Developments in the Theory of Cationic Polymerization’. For Part X see Plesch (1991) and for Part IX see Plesch (1990).

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374

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) Deffieux, A., Squire, D. R. & Stannett, V. 1980 Polymer Bull. 2, 469-476. Deffieux, A., Hsieh, W. C., Squire, D. R. & Stannett, V. 1981 Polymer 22, 15751579. Deffieux, A., Hsieh, W. C., Squire, D. R. & Stannett, V. 1982 Polymer 23, 65-68. Deffieux, A., Young, J. A., Hsieh, W. C., Squire, D. R. & Stannett, V. 1983a Polymer 24, 573 577. Deffieux, A., Stannett, V., Wang, A., Young, J. A. & Squire, D. R. 1983b Polymer 24, 1469-1472. Deffieux, A., Subira, F. & Stannett, V. T. 1984 Polymer 25, 1131-1135. Desai, V. R., Suzuki, Y. & Stannett, V. 1977 J. Macromol, Sci. A 11, 133-137. Dewar, M. J. S. 1951 Bull. Soc. Chim. Fr, 18, C79. DuPlessis, T. A., Stannett, V. T. & Goineau, A. M. 1974, J., Macromol. Sci. A 8, 1361-1373. Eley, D. D. & Saunders, J. 1954 J. Chem. Soc., 1672-1676. Fontana, C. M. & Kidder, G. A. 1948 J. Am. Chem. Soc. 70, 3745-3751. Fontana, C. M., Kidder, G. A. & Herold, R. J. 1952 Ind. Engng Chem. 44, 16881695. Goineau, A. M., Kohler, J. & Stannett, V. 1977 J. Macromol. Sci. A 11, 99-114. Gutmann, V. 1978 The Donor-Acceptor Approach to Molecular Interactions. London: Plenum Press. Hamann, S. D., Plesch, P. H. & Skinner, H. A. 1950 Proc. R. Dublin Soc. 25 NS, 4141. Hayashi, K., Yamazawa, Y., Takagaki, T., Williams, F., Hayashi, Ko. & Okamura, S. 1967 Trans. Faraday Soc. 63, 1489-1500. Hayashi, Ka. 1969 In IUPAC Int. Symp. on Macromolecular Chemistry, pp. 507528. Budapest: Akadémiai Kiadó. Hayashi, Ka., Hayashi, Ko. & Okamura, S. 1971 J. Polymer Sci. A 1, 2305-2321. Hayashi, Ka., Hayashi, Ko. & Okamura, S. 1973 Polymer J. 4, 426-436. 375

Developments in the Theory of Cationoid Polymerisations Hayashi, Ko., Irie, M. & Yawamoto, Y, 1977 J. Polymer Sci. Polymer Symp. 56, 173-182. Hayashi, Ko. 1980 Polymer J. 12, 583-596, Hersberger, A. B., Reid, J. C. & Heiligmann, R. G. 1945 Ind. Engng Chem. 37, 1073-1078. Higashimura, T., Masuda, T., Okamura, S. & Yonezawa, T. 1969 J. Polymer Sci. A 1, 2129-2141. Hsieh, W. C., Kubota, H., Squire, D. R. & Stannett, V. 1980 J. Polymer Sci, Polymer Chem. 18, 2773-2784. Hsieh, W. C., Deffieux, A., Squire, D. R. & Stannett, V. 1982 Polymer 23, 427430. Hubmann, E., Taylor, R. B. & Williams, F. 1966 Trans. Faraday Soc. 62, 88-96. Magagnini, P. L., Cesea, S., Giusti, P., Priola, A. & DiMaina, M. 1977 Makromol. Chem, 178, 2235. Ma, C. C., Kubota, H., Rooney, J. M., Squire, D. R. & Stannett, V. 1979 Polymer 20, 317-320, Matsusaki, K,, lchijo, C. & Kanai, T, 1981 Makromol. Chem. 182, 2919-2926. Penczek, S., Kubisa, P. & Matyjaszewski, K. 1980 Adv. Polymer Sci. 37, 64. Penfold, J. & Plesch, P. H. 1961 Proc. Chem. Soc. 311. Plesch, P. H, 1953 J. Chem. Soc. 1659-1661. Plesch, P. H. 1968 Cationic polymerisation. In Progress in High Polymers (ed. J. C, Robb & F. W. Peaker), vol. 2, pp. 137 188. Iliffe Books. Plesch, P. H. 1973 Brit. Polymer J. 5, 1-12. Plesch, P. H. 1984 In Cationic polymerisation and related processes (ed. E, J. Goethals), p. 1. Academic Press. Plesch, P. H. 1988 Makromol. Chem. Macromol. Symp. 13/14, 375-387. Plesch, P. H, 1989 Eur. Polymer J. 25, 875-877.

376

New Views on Cationic Polymerizations Induced by Ionizing Radiations (1993) Plesch, P. H. 1990 Makromol. Chem. Macromol. Symp. 32, 299-306. Plesch, P. H. 1992 Lecture to 10th Cationic Polymer Symposium, Balatonfuered 1991. Makromol.Chem. Macromol. Symp., 60, 1-35. Plesch, P. H. 1993 Prog. Reaction Kinetics 18, 1-62. Popova, A. I., Sheinker, A. P. & Abkin, A. D. 1965a Vysokomol. Soyed. 7, 15971603. Popova, A. I., Sheinker, A. P. & Abkin, A. D. 1965b Polymer Sci. USSR, 7, 17681776. Salomon, G. 1953 In Cationic Polymerisation and Related Complexes (Ed. P. H. Plesch), p. 57.Cambridge: W. Heffer and Sons. Stannett, V., Bahstetter, F. C., Meyer, J. A. & Szwarc, M. 1964, Int. J. Appl. Radiation Isotopes 15, 747 757. Suzuki, Y., Chudgar, A., Rooney, J. M. & Stannett, V. 1977, J. Macromol. Sci. A 11, 115-131. Szwarc, M. 1978 Macromolecules 11, 1053 1054. Taskinen, E., Kukkamaeki, E. & Kotilainen, H. 1978 Tetrahedron 34, 12031205. Taylor, R. B. & Williams, F. 1969 J. Am. Chem. Soc. 91, 3728-3732. Ueno, K., Yamaoka, H., Hayashi, K. & Okamura, S. 1966a Int. J. Appl. Radiation Isotopes 17, 513-519. Ueno, K., Yamaoka, H., Hayashi, K. & Okamura, S. 1966b Int. J. Appl. Radiation Isotopes 17, 595-602. Ueno, K., Hayashi, K. & Okamura, S. 1966c Polymer 7, 451-458. Ueno, K., Williams, F., Hayashi, Ko. & Okamura, S. 1967 Trans. Faraday Soc. 63, 1478-1488. Ueno, K., Hayashi, Ko. & Okamura, S. 1968 J. Macromol. Sci. A 2, 209-214. Williams, F., Hayashi, Ka., Ueno, K., Hayashi, Ko. & Okamura, S. 1967 Trans. Faraday Soc. 63, 1501-1511.

377

Developments in the Theory of Cationoid Polymerisations Williams, F. 1968 In Fundamental Processes in Radiation Chemistry (ed. P. Ausloos), ch. 8 (Principles of radiation-induced polymerization), p. 515-598. New York: Wiley Interscience. Williams, F. 1972 J. Macromol. Sci. Chem. A 6, 919-936. Wood, K. B., Stannett, V. T. & Sigwalt, P. 1989 Makromol. Chem. Suppl. 15, 71-78. Wood, K. B. & Stannett, V. T. 1992 J. Polymer Sci. A 30, 13-19. Yamamoto, Y., Marinaka, A., Irie, M. & Hayashi, Ko. 1977 Macromol. 10, 266268. Yoshida, H., Irie, M., Shimada, O. & Hayashi, Ko. 1972 J. Phys. Chem. 76, 3747-3750.

378

4.10

A General Theory Explaining Discontinuous Variations of the Degree of Polymerisation with the Concentration of the Reagents (1964) P. H. Plesch

First published in the Journal of the Chemical Society, 1964, 16, 1, 104-114. Reproduced with permission from the RSC, copyright 1964. This is Part IV of Developments in the Theory of Cationic Polymerisation.

Prologue Although the writer had not himself encountered the phenomena described in the title of this paper, he had become very familiar with them whilst writing the chapter on ‘Isobutene’, which is Section 3.1 in the present book. The absence of any coherent and general explanation of such a widespread phenomenon was a challenge, which occupied him for a long time. When it had been met he wrote to a friend ‘that he felt like Kepler did on finding his Third Law and had he been able to draw he would, like Kepler, have drawn a triumphal chariot in the margin of his manuscript’. It was all the more disappointing that this advance in understanding was largely ignored. The fact that the exposition did not appear in a polymer journal was partly made good by its main message being given as an Appendix to the ‘Isobutene’ chapter in the book mentioned earlier. The sad fact is that the key ideas involved may seem too complicated. They came to this writer when he was explaining to an undergraduate class the principle of conductimetric titration. The discontinuities, which this paper is about, are in fact titration end-points. The line of thought elaborated in this paper continues to be useful for assessing functionally the purity of reagents and solvents and the effectiveness of purification procedures; and the warning against spurious correlations remains topical. From the historical point of view it is interesting to note that there is here yet another, and new, demonstration that the concentration of the propagating species in cationic polymerisation must be much smaller than that of any of the reagents. A few technical comments:

379

Developments in the Theory of Cationoid Polymerisations 1. It is now known, mainly through this writer’s own work [104] that AlCl3 in alkyl chloride solvents is mainly monomeric. Therefore some of the detailed explanations need to be adjusted correspondingly. 2. This paper was written long before the ideas and the mathematics of Binary Ionogenic Equilibria (BIE) were developed [138]. 3. It is now clear that the equilibrium constant, which decreases with increasing temperature, is most probably that for the dissociation of ion-pairs. 4. The statement in the last paragraph of the paper, that benzene is unlikely to be a chain-breaker, is strange in view of the fact that this author himself discovered the alkylation of toluene (solvent) by the growing cation during cationic polymerisations [15-17, 28], which is a transfer reaction.

Abstract In cationic polymerisations it is commonly found that the degree of polymerisation (DP) changes abruptly as the concentration of one of the constituents of the reaction mixture is varied. These variations, especially the very sharp DP peaks, have not been explained hitherto in detail. A theory is developed which accounts quantitatively for all forms of DP variation in terms of neutralisation, or formation, or both successively, of chain-breaking agents, as the concentration of the relevant reactant is changed. The theory is illustrated by applying it to six examples from the literature. One of the most characteristic and common features of cationic polymerisation is that, as the concentration of one of the components of the reaction mixture is changed, the degree of polymerisation (DP) of the polymers varies in a manner such that the relevant curve shows a more or less abrupt, sometimes even catastrophic, change of direction and cannot be represented simply by the Mayo equation. It was realised that the phenomenon was probably due to impurities [2, 3d], and Ambroz, Kazda, Vesely, and Zlamal [2] investigated from this point of view the polymerisation of isobutene by aluminium chloride. A prominent feature of their results was that with increasing concentration of catalyst the DP went through a sharp maximum. Vesely attempted the formulation of a quantitative theory of this phenomenon [2b]. He suggested that the region where the DP decreases with the concentration of aluminium chloride is to be explained in terms of chain-breaking by ‘bases’, and that beyond the turning point of the curve 1/DP is proportional to Ke[AlCl3], where Ke was supposed to be a (composite) equilibrium constant

380

A General Theory Explaining Discontinuous Variations... governing the concentration of ‘bases’ (especially free anions) in the reaction mixture. Unfortunately the exposition of these interesting ideas is so condensed that the argument is obscure, and the many, apparently ad hoc assumptions make the validity of the conclusions far from obvious. There is also an implication that these ideas could be applied to other types of DP variation, but there is no attempt at elaboration; a more detailed discussion of the work of Vesely and his co-workers has been presented elsewhere [4]. The object of the present paper is to expound a theory which accounts in an algebraically precise manner for all known forms of DP curves. Four general types of such curves are known: (A) The DP goes through a maximum. (B) The DP rises to a maximum constant value. (C) The DP falls to a minimum constant value. (D) The DP goes through a minimum. These types are illustrated in Figures 1, 5-7. In a few systems the DP varies in a manner which can be considered as a combination of two of these types. The variation of the DP can be further classified into four categories according to the reagent, the variation of the concentration of which produces the change in the DP: (1) Catalyst (metal halide); (2) ‘Additive,’ which may be a co-catalyst; (3) Monomer; (4) Solvent composition. These categories are illustrated in Figures 1-4. The most striking and also the most enigmatic type of DP variation is type A, and it is also the most common in that it occurs in all four categories. For these reasons the theory will be explained in detail with reference to this type, and the other types will then be considered more briefly. After the development of the general theory, some examples of its application to results in the literature will be elaborated.

General theory Type (A) Variation. The essence of the theory is that curves such as those shown in Figures 1–4 are not considered as a whole, but are regarded as made up of two parts. Consider a generalised curve of this type which represents the variation of DP with the concentration of a reagent F. Let the concentration of this reagent be f, and let the value of f corresponding to the DP peak be g (Figure 8). For the branch of the curve representing values of f > g it is evident that an increase in f is producing an increase in the concentration of a chain-breaking reagent (in the following discussion we shall use the non-committal term ‘chain-breaker’ since it is not possible to determine from studies of DP alone whether such a one is a terminator or a transfer agent), which may be F itself, or a compound derived from F, the concentration of which is proportional to (f – g). If the DP of the polymer is governed by a number of chainbreaking reactions, the rates of which can be represented generally by terms of the form kx [X i] xi[Pn+], where kx is the rate constant for the reaction of growing chains of i

i

381

Developments in the Theory of Cationoid Polymerisations

Figure 1 Variation of the intrinsic viscosity of polyisobutene with concentration of AlCl3 [2a]. Temperature –78°. Solvent: ethyl chloride [CH2:CMe2] = 4.15 M

Figure 2 Variation of the molecular weight of polyisobutene with the ratio [Bun•CHO]; [AlCl3] [2c]. Temperature –78°. Solvent: ethyl chloride. [CH2:CMe2] = 2 M. [AlCl3] = 8.1 mM. [Bun•CHO] = 0 –10 mM

382

A General Theory Explaining Discontinuous Variations...

Figure 3 Variation of DP with concentration of isobutene [3e]. Temperature –78°. Solvent: methyl chloride. [AlCl3] = 3.76 x 10-4 M

Figure 4 Variation of the molecular weight of polyisobutene with the composition of the solvent [2f]. Temperature –80°. Solvent: ethyl chloride + ethane. [AlCl3] = 0.3% by wt. [CH2:CMe2] not given

383

Developments in the Theory of Cationoid Polymerisations

Figure 5 Variation of the molecular weight of polyisobutene with the concentration of of catalyst in the presence of diethyl ether [2b]. Temperature –78°. Solvent: ethyl chloride. [Et2O] = 16.2 mM. [CH2:CMe2] and vol. of reaction mixture not given

Figure 6 Mayo plot of 1/DP against catalyst concentration for the polymerisation of undiluted isobutene at –78° [3a]

384

A General Theory Explaining Discontinuous Variations...

Figure 7 Variation of the molecular weight of polyisobutene with solvent composition [2g]. Temperature –78°. Solvent: ethyl chloride + benzene. [CH2:CMe2] and [AlCl3] not given

Figure 8 Schematic representation of a type (A) variation of DP with concentration f of a reagent F

385

Developments in the Theory of Cationoid Polymerisations concentration [P+n] with the i-th chain breaking agent, Xi, and xi is the order of that reaction with respect to Xi, and if the rate of propagation is given by kp [P1] [P+n], then we can write the Mayo equation in the form

k f (f – g) 1 1 = + ⋅ DP kp [ P1 ] kp [ P1 ]

∑k

xi xi [ X i ]

(1)

i

where kf is the rate constant for the reaction between growing chains and F, or the compound formed from F. It follows, as is well established, that a plot of 1/DP against f gives a straight line from the slope of which kf /kp can be found. We next consider the rising branch of the DP curve for which f < g. This has been the main source of difficulty in understanding these curves. The difficulty is immediately removed if we consider that as f becomes less than g, the concentration of a chainbreaking agent G increases. We make the plausible assumption that the total concentration of this agent is g, and that it forms a complex H with F. If this complex contains equimolar quantities of F and G, and if it is very stable, then the concentration of agent which is free is simply (g - f), and the point g represents the exact ‘neutralisation’ of the agent. Let the rate of chain breaking by the agent G be given by kg(g - f) [Pn+]. Further, it is necessary to assume that the complex H formed can also act as a chain-breaking agent. Let the rate of the corresponding reaction be given by khf[Pn+] for all f < g, and khg[Pn+] for f > g. These relations are summarised in Table 1; the Mayo equation embodying them takes the following forms: For f < g:

1 / DP = kg (g – f)/kp [ P1 ] + kh f/kp [ P1 ] + Ji / kp [ P1 ]

(2)

and for f > g:

1 / DP = kg (f – g)/kp [ P1 ] + kh g/kp [ P1 ] + Ji / kp [ P1 ]

(3)

where the term Ji represents the summation in the second term of equation (1). Equations (2) and (3) can be transposed to the more useful forms

1 / DP = [(kh – kg )f + kg g + J i ]/ kp [ P1 ]

(4)

1 / DP = [k f f + (kh – k f )g + J i ]/ kp [ P1 ]

(5)

From equations (4) and (5) it follows that the slope of the left-hand branch of the Mayo plot gives (kh – kg)/kp, and that of the right-hand branch gives kf/kp. The two branches 386

A General Theory Explaining Discontinuous Variations... must meet at f = g at the value of 1/DP which we will denote by 1/DPc and is given by the equation

1 / DPc = (kh g + Ji ) / kp [ P1 ]

(6)

This means that, if a series of groups of experiments is conducted in such a way that in each experiment f is varied over the useful range and g is constant in each group, but is varied from group to group, then equation (6) described the variation of 1/DPc, with g among the different groups of experiments; in other words, equation (6) describes the locus of the apices of the Mayo plots. A set of results of this type is discussed in detail in Example 1.

Table 1 Scheme of chain-breaking (cb) reactions for different types of system F+G→H

Reaction Concentration of reagent when

f
0

f>g

cb rate-constant Case no.

Type

kf

kg

kh

1

A

+

+

+

0

+

0

0

+

+

0

0

+

2 B 3

4

C

g–f

f

f–g

0

g

kf

kg

kh

Condition

kp[P1]/DP – Ji =

f
kg(g – f) + khf

f>g

kf(f – g) + khg

f
kg(g – f)

f>g

0

f
kg(g – f) + khf

f>g

khg

f
k hf

f>g

khg

Additional reaction H + F → L, L is not cb: when f < g, h = f; when f > g, h = 2g – f 5

D

0

0

+

f
k hf

f>g

kh(2g – f)

It is assumed that the formation constants of complexes H and L are very large + denotes that the rate constant is finite

387

Developments in the Theory of Cationoid Polymerisations Generalised Treatment. The analogous argument for types B, C, and D has been set out in detail elsewhere [4]. Here we shall give a more general treatment. Consider that the concentration h of the complex H is governed by an equilibrium, so that

h = K(f – h)(g – h)

(7)

If F, G, and H (or substances originating directly from them) are (potential) chain-breakers, the DP will be governed by a Mayo equation of the form:

and

kp [ P1 ]/ DP – Ji = k f (f – h) + kg (g – h) + kh h

(8)

= ( kh – kg – k f )h + kg g + k f f

(9)

1

1

2

2

h = (K −1 + g + f ) – [(K −1 + g + f )2 – 4 gf ]

1 2

The minimum in the Mayo plot will now no longer be at f = g, but will be displaced in a direction and by an amount determined by the magnitude of K. Moreover, the more stable the complex, the more abrupt will be the change of slope of the DP curve. For the case of strong complexing (K great) and F, G, and H all chain-breakers, equation (9) reduces to equation (4) or (5). The forms which the right-hand side of equation (9) takes in various other cases (but all with large K) are set out in Table 1, and the corresponding phenomena are explained below. Type (B). DP growing to Maximum, Constant Value. The behaviour shown in Figure 5 indicates that the system contains a chain-breaker G at a concentration g and that reagent F, which is not itself a chain-breaker, combines with it, so that for f > g the concentration of chain-breaker is constant. If the complex H formed from the chain-breaking agent and reagent F is not itself a chain-breaker, we have case 2; if it is a chain-breaker, we have case 3 of Table 1. Type (C). DP falling to Minimum, Constant Value. In this case (Figure 6) there is present in the system a reagent, G (at a concentration g), which itself may or may not be a chainbreaker but forms a (more effective) chain-breaking reagent (complex) H with F, whilst F itself is not a chain-breaker (case 4 of Table 1). Type (D). DP passes through Minimum. This pattern, illustrated in Figure 7, can be interpreted on the supposition that as the concentration, f, of reagent F is increased the concentration of chain-breaking agent H increases. Since this does not continue indefinitely as f increases, it follows that the chain-breaking agent H is formed from F by reaction with a constituent of the reaction mixture, the concentration of which is g. When f > g,

388

A General Theory Explaining Discontinuous Variations... the excess of f reacts with the chain-breaking complex H to give a further complex L which is either not a chain-breaker or a much less effective one than H (see case 5 of Table 1). An instance of this behaviour is discussed in Example 6 below. Generalised Stoichiometry. The treatment can be generalised further by considering the formation of other than binary complexes, as illustrated in the equation:

xG + yF = zH In this case, if the formation constant K of H is very great h = zf/y when yg > xf, and

h = zg/x when yg < xf.

If K has an intermediate value, it is given by the equation:

K = h z /(f – yh/z) y (g – xh/z) x A detailed treatment of results obtained with systems of the kind discussed in Examples 5 and 6 may require the use of equations of this type. Spurious Correlations. If the reagent F which is, or which may form, or may react with, a chain-breaking agent, is contained as an impurity in the solvent, then increasing the monomer:solvent ratio will decrease f; if it is contained in the monomer, the reverse will happen. In this way a spurious variation of DP with monomer concentration may arise, which will be superimposed upon the normal effects due to variations in the rate of monomer transfer and solvent transfer with changing monomer concentration. Such effects can only be elucidated by the use of monomer and solvent specimens purified in different ways, as has been demonstrated very effectively by Zlamal, Ambroz, and Vesely (see Example 1). Fontana-Kidder Propagation. If the propagation is not the normal bimolecular reaction, but unimolecular, as first found by Fontana and Kidder in the polymerisation of propene, the rate of the propagation is given by

Vp = kp′ [ Pn+ ] The rate of chain-breaking is made up of the rates of unimolecular termination and monomer transfer, kt + km1 = Jo say, and the rate of bimolecular chain-breaking by various reagents, Ji. Thus

kp′ / DP = JO + Ji

389

Developments in the Theory of Cationoid Polymerisations so that the DP is independent of monomer concentration, provided that Ji does not contain a term involving [P1]. If, however, the monomer contains as impurity the reagent F, then the DP will show a dependence on monomer concentration, the form of which will be determined by the nature of F, and hence its reactions. Effect of Temperature. Another aspect of this matter is the effect of temperature on the pattern of the DP curves. One would expect the dissociation constant of the complexes involved to decrease with increasing temperature. In agreement with this expectation one finds quite generally that at higher temperatures, say between +30 °C and –30 °C, all the DP curves are much more rounded than in the temperature region below about –50 °C. Unfortunately, only two systems have been investigated over a wide temperature range (–30 °C to –125 °C), but the results show the effect very well; this is discussed in Example 5. Electrical Conductivity. A further topic which needs to be considered is the correlation found by Zlamal, Ambroz, and Vesely [2] between the specific conductivity of solutions (mainly in ethyl chloride) of aluminium chloride containing various quantities of a polar compound (acetonitrile, butyraldehyde, ethanol, etc.) and the DP of the polyisobutenes formed in these solutions. Over a certain range of concentrations there is an inverse correlation between the specific conductivity, which has a sharp minimum when the ratio [AlCl3]/[Additive] = 1, and the DP, which at the same composition shows a sharp maximum. This evidence indicates that the principal chain-breakers in these solutions are free ions and that the 1:1 complexes which are formed are much less ionised and are much less effective chain-breakers than the compounds (probably 2:1 and 1:2 complexes) which are prevalent on either side of the neutralisation point. This matter is discussed further in Example 5 below. The authors concluded from their results that the propagating species is also a free ion rather than an ion-pair. However, whilst this may be true, it does not follow from this evidence, since the cation in an ion-pair may well be able to react with a free anion. One further point needs to be made which has not been expounded previously and is essential to an understanding of these experiments: Since there is a very close correlation between the specific conductivity of the catalytic solutions, e.g., AlCl3, EtOH in ethyl chloride, and the DP of polyisobutenes obtained when isobutene is added to these solutions, it follows that the electrical condition of the solutions before and after the addition of the monomer must be essentially the same. This means that the number of solute molecules involved in the initiation of polymerisation

390

A General Theory Explaining Discontinuous Variations... must be negligibly small compared with the total. This is amply borne out when one calculates the number of polymer molecules formed in typical systems; it is several powers of ten smaller than the ‘catalyst concentration.’

Applications of the theory The literature contains a large number of examples of the patterns of DP variation which have been discussed above. A list of most of the examples available is given in Tables 2–5. The tables include only those systems in which the DP variation shows a turning point or discontinuity, so that it must be classed as ‘abnormal’ and is not amenable to analysis by the simple Mayo equation. It is, of course, impossible to discuss each in detail and those selected for such treatment in the following pages are marked in the tables by an asterisk. Example 1. Type (A). Category 1. Zlamal, Ambroz, and Vesely have reported [2a] that when isobutene is polymerised by aluminium chloride at –78° in ethyl chloride, the DP of the polymer passes through a maximum as the concentration of aluminium chloride is increased, and they showed that with progressive purification of the ethyl chloride the maximum DP increased and the concentration of aluminium chloride at which it occurred decreased. This concentration is to be identified with our g, and it is reasonable that it decreases with progressive purification of the solvent. The senior author later [2b] presented the same results in the form of Mayo plots, 1/DP against [AlCl3], and these agree with the predictions of our theory inasmuch as a) all the left-hand branches and all the right-hand branches of the plots are approximately parallel, and b) the points of intersection of each pair of branches increase linearly with the aluminium chloride concentration, g, at which they occur, thus confirming equation (6). A similar set of results, for polymerisations in methyl chloride, present essentially the same picture [2b]. Vesely [2b] concluded that since the value of 1/DP obtained (by extrapolation) at [AlCl3] = 0, was approximately the same as that obtained from Norrish and Russell’s results with stannic chloride [5], the fundamental mechanism of polymerisation by both catalysts must be the same. Whilst this may be so, it does not follow from this evidence, because the extrapolations are afflicted by considerable uncertainty and, moreover, it is now known that the transfer coefficients which determine the intercept depend on the nature of the catalyst. Example 2. Type (B). Category 1. It was found by Vesely [2b] that, when isobutene was polymerised by titanium tetrachloride in ethyl chloride at –78 °C in the presence of diethyl ether, the DP rose with increasing concentration of titanium tetrachloride until a maximum value was reached at [TiCl4]/[Et2O] approximately unity; thereafter it declined

391

Developments in the Theory of Cationoid Polymerisations

Table 2 Isobutene No.

Additive

Solvent

Type

Category

Ref.

1

C H 3 Cl

A

3

3e

2

C2H5Cl

A

3

3e

3

CH2Cl2

A

3

3e

4

C2H3Cl

A

3

3e

5

n-C5H12

A

3

3d, 3e

6*

C2H5Cl

A

3

3b

7*

C2H3Cl

A

3

3b

8*

None

C

1

3a

9*

C H 3 Cl

C

1

3a

10 *

C2H5Cl

A

1

2a

11 *

C H 3 Cl

A

1

2b

12

C3H7·CHO †

C2H5Cl

A

2

2c

13

(C2H5)2O

C2H5Cl

A‡

1

2d

14

CH3·O·C6H5

C2H5Cl

A‡

1

2d

15

C2H5OH

C2H5Cl

A

1

2e

16

C2H6 + CH3Cl

A

1

2f

17

C2H6 + CH3Cl

A

4

2f

18

C2H6 + C2H5Cl

A

4

2f

19

C6H6 + C2H5Cl

D

4

2g

20 *

C2H5Cl

B

1

5, 6

C2H5Cl

B

1

2b

CH2Cl2

A

2

§

21 * 22

(C2H5)2O

Catalysts: In systems 1-19 the catalyst was AlCl3; in number 20 it was SnCl4; in numbers 21 and 22 it was TiCl4 Co-catalysts: In systems 1-19 and 21 the co-catalyst is unknown. It may have been adventitious water, solvent (not in numbers 5 and 8), or the additive or an impurity contained therein; in systems 21 and 22 it was water Temperature: For systems 6 and 7 the temperature range was – 55 °C to – 125 °C; for system 22 the temperature was –13 °C; for all other systems it was – 78 °C to – 80 °C † In this paper another 18 compounds are mentioned which as additives gave type (A) curves ‡ These curves are unlike the normal type (A) curves in that the maximum is flanked closely by a minimum on each side § Biddulph, Plesch, and Rutherford, Symposium on Macromolecules, Wiesbaden, 1959, Paper III A 10. See no [54] in Publication List

392

A General Theory Explaining Discontinuous Variations...

Table 3 Styrene No.

Co-catalyst

Solvent

Type

Category

Ref.

23

ButCl

(CH2Cl)2

B

2

a

24

ButCl

(CH2Cl)2

B

1

a

25

H2O

(CH2Cl)2

A

2

a

26

ButCl

C6H5·NO2

A

2

b

27

PriCl

C6H5·NO2

A

2

b

28

Unknown

SO2

A

3

c

29

Unknown

SO2

C

1

c

In all experiments included in this table the catalyst was SnCl4, the temperature 25 °C a Colclough and Dainton, Trans. Faraday Soc., 1958, 54, 894 b Idem, ibid., p. 898 c Azami and Tokura, J. Polymer Sci., 1960, 42, 545

Table 4 Alkyl vinyl ethers, RO·CH:CH2 No.

R

Solvent

Type

Category

Ref.

30

Bui

n-C6H14 + CH3·C6H5

A

4

a

31

Bui

n-C6H14 + CH3·C6H5

A

4

b

32

Pri

n-C6H14 + CH3·C6H5

A

4

b

33

Et

n-C6H14 + CH3·C6H5

C

4

c

34

Et

n-C6H14 + CH2Cl2

C

4

c

The catalyst in systems 30-36 was BF3,Et2O; the co-catalyst is unknown, but was probably adventitious water; the temperature was –78 °C a Okamura, Higashimura, and Sakurada, J. Polymer Sci., 1959, 39, 507 b Okamura, Higashimura, and Yamamoto, J. Chem. Soc. Japan, Ind. Chem. Section, 1958, 61, 1636 c Higashimura, Sunaga, and Okamura, Chem. High Polymers (Japan), 1960, 17, 257

very slightly and then remained constant. Unfortunately the paper does not contain sufficient information to allow the calculation of kg/kp and Ji /kp. Example 3. Type (C). Category 1. Kennedy and Thomas [3a] showed that when isobutene was polymerised by aluminium chloride in ethyl chloride at –78 °C the DP decreased

393

Developments in the Theory of Cationoid Polymerisations

Table 5 α−Methylstyrene No.

Solvent

Type

Category

Ref.

35

n-C6H14 + CHCl3

A

4

d

36

n-C6H14 + CH3·C6H5

A

4

d

The catalyst in systems 30-36 was BF3,Et2O; the co-catalyst is unknown, but was probably adventitious water; the temperature was –78 °C d Okamura, Higashimura, and Imanishi, Chem. High Polymers (Japan), 1959, 16, 69

with increasing concentration of the catalyst up to a certain concentration, and at higher concentrations remained constant. This means that the system contained an impurity which reacted with aluminium chloride to give a chain-breaking agent. For experiments with an isobutene concentration of ~9.5 mole/l, the results do not permit precise determination of g, but this is probably in the region of 1.2 x 10-3 mole/l, whereas at a monomer concentration of about 4.6 mole/l, it is about 5 x 10-4 mole/l. Hence it is reasonable to suppose that the main source of the impurity was the monomer. This is borne out by the fact that other experiments recorded in the same paper, show g for undiluted monomer to be ~7 x 10-4 mole/l. In a later paper [3b] Kennedy and Thomas reported that, when undiluted isobutene was polymerised at –78 °C with aluminium chloride as catalyst, with the same range of concentrations as in the previous study, the DP was independent of the catalyst concentration. They did not comment on this discrepancy, but it can now be understood on the supposition that in the later work the monomer was so pure that g was lower than the lowest catalyst concentration used (~1.5 x 10-4 mole/l), so that all experiments fell into the ‘plateau’ region. These experiments are prima facie identical with those reported by Vesely [2b] and discussed in Example 1. However, the range of aluminium chloride concentration is very different, and so indeed is the behaviour of the DP. Whereas the concentrations used by Vesely ranged from ~0.02 to 0.2 mole/l, those used by Kennedy and Thomas lay in the range (2–20) x 10-4 mole/l. We must conclude that the materials used by Kennedy and Thomas were probably very much purer than those used in Vesely’s work. Example 4. Type C. Category 2. It was found by Norrish and Russell [5] that when isobutene was polymerised by stannic chloride in ethyl chloride at –78 °C the DP of the polymer fell rapidly with increasing water concentration until the ratio [H2O]/[SnCl4] was about unity, and remained approximately constant at all higher water concentrations. These results have been analysed and interpreted in detail [6]. It was concluded that the principal chain-breaking agent is a species whose concentration was proportional to

394

A General Theory Explaining Discontinuous Variations... that of stannic chloride monohydrate, and at first it was identified with the monohydrate itself, but a consideration of the kinetic information available subsequently led to the conclusion that the chain-breaking agent is the anion derived from stannic chloride monohydrate by loss of a proton, and that the reaction of this with the growing carbonium ion is a termination [4]. Example 5. TypeA. Category 3. The first reported instance of the ‘peak phenomenon,’ by Thomas et al. [3c] concerns the variation of the DP of polyisobutene with the concentration of monomer in reactions catalysed by aluminium chloride in an alkyl halide solvent at low temperatures. Subsequently, more detailed studies confirmed the existence of the phenomenon for reactions in pentane, methyl chloride, ethyl chloride, vinyl chloride, and methylene dichloride. It was also shown [3b] that for any one solvent the shape of the curve relating the DP to the monomer concentration depended on the temperature, in that the peak was the more prominent the lower the temperature; near –50 °C it was very small and near –30 °C it was absent, the DP increasing steadily with the monomer concentration to the value characteristic of polymers obtained from undiluted monomer. These findings agree with our theory according to which the sharpness of the peak is related to the magnitude of an equilibrium constant which diminishes with increasing temperature. The shape of the curve obtained at –78 °C was the same for all the solvents and shows a steep rise in the DP with increasing monomer concentration up to a maximum at a relatively low monomer concentration, followed by a more gradual fall to the DP characteristic of polymers obtained from undiluted monomer. The monomer concentration at which the DP maximum occurs varied from one solvent to another, as did the height of the DP peak. The explanation which we propose is that the solvents contained one or more impurities, the nature and concentration of which depended on the nature of the solvent and may have differed from one batch of solvent to another, and that these impurities reacted with, and thus rendered ineffective (‘neutralised’), a chain-breaking agent present in all the reaction mixtures. Thus the region where the DP rises from the value characteristic of polymers obtained from the undiluted monomer to its maximum can be described more logically as ‘an increase of DP with increasing diluent concentration’ rather than as ‘a decrease of DP with increasing monomer concentration.’ This effect is superposed on two others: the ‘normal’ change of DP with monomer concentration which shows itself in the region of lowest monomer concentrations, and an increase of DP as the decrease of the diluent concentration reduces the rate of chain-transfer by the diluent. A detailed analysis of the curves is further complicated by the fact that the magnitude of all the rate constants and any equilibrium constants involved may be affected by the change in the electrical properties of the medium with changing monomer:diluent ratio (except for the reactions in pentane). However, the experiments with pentane as diluent,

395

Developments in the Theory of Cationoid Polymerisations and others, showed that the change of medium - at least in terms of bulk dielectric constant - was not by itself responsible for the peak [3b]. The question now arises as to the origin and nature of the ubiquitous chain-breaking impurity. The clue to this is given by the experiments of the same authors discussed in Example 3. Our analysis shows that the monomer contained a substance which combines with aluminium chloride to give a chain-breaking agent. Let this be denoted by G, and let the active impurity in the solvent be G′. We propose that in the absence of solvent the ternary complex Al2Cl6,G predominates, and that this is an efficient chain-breaker, but that the binary complexes AlCl3,G and AlCl3,G′, which we suppose to be formed on addition of solvent, are very much less effective. As the ratio of solvent to monomer is increased, more of the ternary complex will be converted into the binary complexes, so that there is a progressive neutralisation of the most efficient chain-breaker. This suggestion would be no more than an ad hoc hypothesis were it not that the most likely impurities are water and other oxygen-containing compounds (alcohols, ethers); and that Zlamal had found that for isobutene in ethyl chloride at –78 °C the chainbreaking activities, given in our notation by kh/kp, of the complexes of aluminium chloride and ethanol had the values: Al2Cl6,EtOH kh/kp……………………. 1.5 x 10-2

AlCl3,EtOH AlCl3,2EtOH 7.4 x 10-5 1.6 x 10-3

Thus, when G is ethanol, the ternary complex is two-hundred times more effective than the binary complex and, moreover, the second ternary complex, AlCl3,2G is also a much more efficient chain-breaker. It seems very likely that for other oxygen compounds the situation is similar, since probably, not the complexes themselves, but anions derived from them are the true chain-breakers. The fall of the DP from the peak as the solvent:monomer ratio becomes very great (very low monomer concentration) may be at least partly due to the progressive formation of the ternary complexes of the type AlCl3,2G which are efficient chain-breakers. Example 6. Type D. Category 4. Zlamal and Kazda [2g] have reported that, when isobutene was polymerised by aluminium chloride at –78 °C in a mixture of ethyl chloride and benzene, the DP of the polymers went through a minimum when the solvent contained about 5% by weight of benzene. In conformity with the ideas developed in the previous example, we interpret this effect as being due to an impurity, G, in the benzene which reacts with aluminium chloride to form two complexes, thus:

Al 2 Cl 6 + G → Al 2 Cl 6 , G Al 2 Cl 6 , G + G → 2 AlCl 3 , G 396

A General Theory Explaining Discontinuous Variations... The supposition, made in the discussion of the previous example, that the ternary complex which is formed at first is a much more efficient chain-breaker than the binary complex which is formed subsequently, is adequate to explain the observed behaviour. In these experiments the concentration of aluminium chloride was 2 x 10-3 mole/l. In further experiments [2g], with the complex AlCl3,EtOH at a concentration of 24.6 x 10-3 mole/l. Zlamal and Kazda found that the DP of the polyisobutenes did not change significantly as the proportion of benzene in the solvent was raised from 0 to 15%. This is entirely in agreement with expectation based on our theory. Zlamal and Kazda attempted to explain these results and the differences between them and others, obtained with a mixed solvent containing hexane instead of benzene [2g], on the supposition that the benzene itself forms a complex with C2H5+ ions derived from the reaction of ethyl chloride and aluminium chloride, thus enhancing the dissociation of ion-pairs, and leading to a simultaneous increase in specific conductivity and decrease in DP. While the formation of C2H5+ ions under the relevant conditions is highly unlikely, the idea that they could form a complex with benzene rather than a C2H5,C6H6+ ion seems rather odd. However, ions of this type would serve the theory equally well, the criticism of which must therefore be based on the point that there is no evidence that benzene as such has a major effect on the DP and that the presence of active impurities in it at concentrations of the order of 10-3–10-2 mole/l seems very likely.

Acknowledgement I thank Professor F.S. Dainton, FRS, and the Referees for helpful comments and suggestions.

References 1.

Part III, Plesch, Ricerca Sci., 1955, 25, 140.

2.

a Zlamal, Ambroz, and Vesely, J. Polymer Sci., 1957, 24, 285. b Vesely, J. Polymer Sci., 1958, 30, 375. c Ambroz and Zlamal, J. Polymer Sci., 1958, 30, 381. d Ambroz and Zlamal, J. Polymer Sci., 1958, 29, 595. e Zlamal, Symposium on Macromolecules, Wiesbaden, 1959, Paper III A 14. f Zlamal, Ambroz, and Ambroz, Chem. Listy, 1955, 49, 1606. g Zlamal and Kazda, Symposium on Macromolecules, Moscow, 1960.

397

Developments in the Theory of Cationoid Polymerisations 3.

a Kennedy and Thomas, J. Polymer. Sci 1960, 46, 481. b Kennedy and Thomas, J. Polymer. Sci 1961, 55, 311. c Thomas Sparks, Frolich, Otto, and Muller-Cunradi, J. Amer. Chem. Soc., 1940, 62, 276. d Kennedy and Thomas, J. Polymer. Sci., 1960, 46, 233. e Kennedy and Thomas, J. Polymer. Sci., 1961, 49, 189.

4.

The Chemistry of Cationic Polymerization, Ed. P. H. Plesch, Pergamon Press, London, 1963, Chapter 4.

5.

Norrish and Russell, Trans. Faraday Soc., 1951, 48, 91.

6.

Biddulph and Plesch, J. Chem. Soc., 1960, 3913.

398

5

About Propagating Species and Propagation Rate-Constants in Cationic Polymerisations

The propagation rate-constants in cationoid polymerisations For a physical chemist a reaction is not completely defined until its rate-constant has been measured, preferably over a range of temperatures and in a variety of solvents. Despite enormous efforts towards this goal, it has been achieved for only very few cationoid polymerisations, and with respect to the cationic systems the quest could not be considered ended until the discrepancy between the best values of kp+ and the rate-constants k2 for the attack of small cations on alkenes under non-polymerising conditions had been resolved. This was done in the last of this author’s papers included here [154]. The papers grouped together in this section record the author’s successive efforts to define the problem and to assess the claims of others [(78), (88), (126), (139)], to make his own experimental contribution [(142), (145)], and finally to assess more comprehensively and critically than before the merits of other workers’ claims to have measured any of these rate-constants [(144)].

399

Developments in the Theory of Cationoid Polymerisations

400

5.1

The Propagation Rate-Constants in Cationic Polymerisations (1971) P. H. Plesch

This paper was first published in Advances in Polymer Science, 8, 1971, 137-154. Reproduced with permission from Springer-Verlag, Berlin. Copyright 1971.

Prologue In this first attempt at a systematic definition of the problem it is recognized explicitly that there may be a multiplicity of chemically distinct chain-carriers growing simultaneously in the same reaction mixture (enieidic polymerisation). The fact that these may include paired and unpaired ions is considered from the point of view of conventional ionic equilibria, and a warning is given that there may be tight and solvent-separated ion-pairs to be considered. This idea, taken over from the theory of anionic polymerisations, was shown much later to be inappropriate for cationic polymerisations {154}. It is shown that the carbenium ions cannot be considered ‘free’ except in a kinetic sense, but that they are strongly solvated by the solvent. Further, a clear mechanistic distinction is made between the nature of the propagation steps for carbenium and for onium ions, e.g., oxonium, which serves to explain the differences between the orders of magnitude of the corresponding rate-constants. Two further innovations are the consideration of polymerisations in which the kinetic order with respect to monomer may be different from unity, and that the very common alleged ‘effects of counter-ions’ might be due to a concurrent pseudo-cationic (cationoid insertion) polymerisation. There is also here a simple calculation whereby it is shown that propagation by paired cations cannot explain the monomer consumption which is attributed by this author to propagation by the ester. Many of the kp+ values accepted here were later shown to be wrong, including those derived from polymerisations by ionising radiations {146}.

401

Developments in the Theory of Cationoid Polymerisations The paper ends with two of this author’s favourite exhortations: ‘to clarify the chemistry before attempting the kinetics’ and closely related advice ‘to select far more carefully the systems chosen for study’. Both have been consistently ignored.

1 Introduction A polymer-forming chain reaction requires at least one rate-constant, namely that for propagation, kp, for its complete specification; in this simplest case there is only one type of propagating centre, all the centres are formed in a time which is negligible compared to the duration of the reaction, their concentration remains constant throughout the reaction (Stationary State of the Second Kind), and there is no transfer. In general, however, rate-constants for initiation, ki, for at least one termination, and for various transfer reactions must also be known. If the real initiator is formed from precursors by an antecedent reaction, such as

BF3 + H 2 O → BF3 ⋅ H 2 O or if it is involved in an equilibrium, for instance

SnCl 4 + PhOH ↔ SnCl 4 ⋅ PhOH

(a )

we require to know the corresponding rate or equilibrium constants; and if we have an enieidic [2] polymerisation, i.e., one in which more than one propagating species is involved, each of these must be presumed to have its own kinetic constants. In the present discussion we will confine attention to the propagation rate-constant kp. Once kp is known, the other rate-constants can usually be calculated from the chainbreaking coefficients obtained from, e.g., Mayo plots. For some non-stationary polymerisations ki and/or kt (initiation and termination) can be measured independently (see Section 4.1).

2 Why are we so ignorant about kp-s in cationic polymerisations? In any polymerisation for which the rate of propagation is given by the second-order equation

Vp = kp xm

402

(1)

The Propagation Rate-Constants in Cationic Polymerisations (1971) (Vp = rate of propagation, x = concentration of growing molecules, m = monomer concentration), the kp can be found if we know the rate-law, which is usually of the form

R = kc0i m j

(2)

(R = polymerisation rate, co = nominal concentration of catalyst or co-catalyst, or a known function of these), so that we can establish the relation between the coefficients of m in Equations (1) and (2), i.e., between kpx and kcoim j-1; and if we can determine x. The rate-law (2) can usually be established without too much difficulty by appropriate kinetic experiments, but it must be remembered that the same system may follow different rate-laws under different conditions, and it is evident that such kinetically complicated systems are generally unsuitable for attempts to determine the fundamental rate constants. However, a sufficient number of kinetically simple systems is now known which are much more useful for such studies. The real difficulty is the determination of x, because for this we must know: i) how many different types of growing centre exist; if there is more than one, say r, then we have an enieidic polymerisation for which Equation (1) takes the form:

Vp = m ∑ kpr xr

(1A)

r

ii) what they are: iii) how their concentrations are related to each other and to co. Most of the required information on x must come from other than kinetic measurements, e.g., spectra or conductivities. In a few favourable cases x can be obtained from a combination of kinetic with some other, e.g., electrochemical measurements. The problems (i)–(iii) are inextricably interrelated, because they all are, to some extent, of an analytical nature, and they have been solved satisfactorily only for relatively few systems. In particular, whether the propagating species are in fact ions, or whether they are highly polar covalent species, such as the esters of pseudo-cationic systems, has been clarified only for very few systems involving olefinic monomers; although for many such our general background information on the chemistry of the species concerned and the pattern of the polymerisations themselves make an ionic propagating species much more likely [3, 4].

403

Developments in the Theory of Cationoid Polymerisations As far as heterocyclic compounds are concerned (cyclic ethers and formals and some others) the situation is rather happier, since on general chemical grounds there is virtually no species other than -onium ions which need be considered as propagating species. If it is known that in a particular system the active species are, or include ions, and if we know the total concentration of chain-carriers - if, say, this can be proved to be equal to the ‘nominal’ concentration of catalyst, co, and does not vary throughout the reaction we are up against the electrochemical problem of discovering what proportion of the propagating ions is free, and what fraction is present as ion-pairs or as higher aggregates. And even when this is resolved, there remains the question whether there is only one kind of free cation, paired cation, etc., or whether each of these is involved in a solvation equilibrium with monomer or polymer which, in the nature of the situation, will be shifted as the reaction progresses and monomer is consumed. We must also remember that in some solvents both ‘tight’ and solvent-separated ion-pairs might be present, which we must expect to have different kinetic characteristics. Since these electrochemical problems are of dominant importance for the interpretation of the kinetic results and the evaluation of the propagation rate-constants, we must explore them before we can discuss determination of rate-constants and their significance.

3 Electrochemical considerations In the present context it will be useful to establish the conditions under which free cations or paired cations might be expected to determine the behaviour of a cationic polymerisation; some aspects of this problem have been discussed previously [5]. Consider a system in which Pn+ are the growing polymer molecules and A- is the anion derived from the catalyst or the syncatalytic system. Let [Pn+] + [Pn+ A-] = c, let [Pn+] = [A-] = i, [Pn+ A-] = q, and let K be the equilibrium constant for the dissociation of ion-pairs:

Pn+ A − ↔ Pn+ + A − It follows that

K = i 2 /q = i 2 /(c – i)

(3)

i = K 1/2 q1/2 = –K / 2 + ( K 2 + 4 Kc)1 / 2 / 2

(4)

and

404

The Propagation Rate-Constants in Cationic Polymerisations (1971) The rate of a polymerisation propagated by free ions and paired ions is

R = – dm / dt = kp′im + kp′′qm = R′ + R′′

(5)

where k′p and k′′p are, the propagation rate-constants for free and paired cations, respectively. We now examine how the ratio Q of the free-ion rate, R′, to the paired-ion rate R′′, varies with the conditions. If we define β = k′p/k′′p, then it follows from Equations (3), (4), and (5) that Q = R′/R′′ = 2 β /[(1 + 4c/K )1 / 2 – 1]

(6)

In order to examine the behaviour of Equation (6) we need to define likely values of c/K and β. For reasons which will be explained later, values of c greater than about 10-5 M need not be considered for carbenium polymerisations, and a useful lower limit is probably about 10-10 M. As far as K is concerned, in solvents such as ethylene and methylene dichloride, whose dielectric constant lies between ca. 9 and 16, according to the temperature, the evidence [6, 7, 8, 9] shows that under these conditions the dissociation constants (K) of trityl salts are in the range 10-4 to 10-5 M. This is the only information which we have on the K of carbenium salts, and+ it is of little direct relevance +to the likely K of ion-pairs involving cations such as –CH2 C HPh (from styrene), –CH2 C Me2 (from + isobutene), or –CH2 C HOR (from alkyl vinyl ethers), because all of these are much less bulky and have a considerably greater charge-density than the trityl cation. These two effects will make the K of the ion-pairs which comprise such ions much less than those for trityl salts. If, despite these uncertainties, we hazard a guess and take K between 10-5 and 10-7 M we find that c/K ranges from 10-5/10-7 = 102 to 10-10/10-5 = 10-5. For the largest value of clK the value of Q is β/9.5. Thus if β has the improbably low value 10, free ions and ion-pairs contribute equally to the rate; but if β is 100 or greater, which is much more likely in these systems, then Q ~ 10, and ion-pairs would contribute less than 10% to the total rate. For all smaller values of c/K the Q would be correspondingly greater and we may conclude therefore that in solvents of DC greater than about 10, ion-pairs are probably largely irrelevant to the polymerisations under a wide range of conditions. There are many papers which purport to record ‘the effect of counter-ion’ on such factors as transfer constants, co-polymerisation ratios, etc. It is significant that in most of these studies relatively high initiator concentrations have been used, so that counter-ion effects are more likely; but before accepting that the observed effects are indeed due to change of counter-ion (derived from different catalysts or co-catalysts) it must be ascertained that these polymerisations are in fact cationic and not pseudo-cationic - in which case the effects would stem from the different reactivities of different esters (see Section 5).

405

Developments in the Theory of Cationoid Polymerisations For reactions in solvents of much lower DC, such as chloroform or benzene, the situation is of course entirely different, because then ion-pairs, and perhaps higher aggregates, will dominate the reaction pattern, and in such circumstances counter-ion effects are of course quite plausible. However, at present we have no experimental information which would be of use in a more precise analysis of such systems. As far as the polymerisation of heterocyclic monomers is concerned, the situation is qualitatively similar, but quantitatively different. As a model for the active species in oxonium polymerisations, Jones and Plesch [10] took Et3O+PF6- and found its K in methylene dichloride at 0 °C to be 8.3 x 10-6 M; however, in the presence of an excess of diethyl ether it was approximately doubled, to about 1.7 x 10-5 M. This effect was shown to be due to solvation of the cation by the ether. Therefore, in a polymerising solution of a cyclic ether or formal in methylene dichloride or similar solvents, in which the oxonium ion is solvated by monomer, the ion-pair dissociation equilibrium takes the form

Pn+ ⋅ P1A − ↔ Pn+ ⋅ P1 + A − with a K of ca. 10-5 M. The initiator concentrations used for heterocyclic monomers are usually in the range 10-1 to 10-4 M, most frequently 10-2 to 10-3 M, and the total concentration of active centres, c, in polymerisations with manageable rates also lie in this range, despite the considerable wastage of initiator which may occur with some triethyl oxonium salts because of their instability and side-reactions [11, 12]. Thus for these systems c/K might range from 10-2/10-5 = 103 to 10, so that Q ranges from β/32 to β/2.7. Therefore an appreciable fraction of the rate would be due to ion-pairs, unless β were greater than, say, 100. However, the fact that over a wide range of initiator concentrations the rate is linearly proportional to it, proves [5c] that, roughly 0.1 <β< 10. At first sight this is unexpected, especially if one recalls the great differences between the reactivities of free and paired anions. However, in the oxonium polymerisations we are not comparing the reactivity of a paired ion with that of a ‘bare’ free ion, but with that of a free ion solvated by a highly polar monomer. This solvation results in a marked reduction in the charge-density of the ion, and hence in its reactivity, and the further reduction in charge-density, brought about by pairing of the solvated cation with an anion, is relatively insignificant when compared to the effect which pairing has on the reactivity of a ‘bare’ ion. We may thus conclude that although oxonium polymerisations are probably dieidic under most conditions, the reactivities of the two species may be so similar that to a first approximation these systems can be treated as monoeidic.

406

The Propagation Rate-Constants in Cationic Polymerisations (1971)

4 Some solutions to the problem of finding x The central problem of determining x (or ∑xr) has been solved in a fairly general manner for radical and anionic polymerisations, but no generally applicable method, such as the sector method for radical reactions, has yet established itself for cationic polymerisations. Moreover, because of the great variety of cationic polymerisations it seems unlikely that a single method will be found suitable for all of them. They fall into at least two groups which differ greatly in the concentration of growing centres. On the basis of the results to be described below, it appears that for olefin polymerisations k′p is of the order of 105 to 107 M-1 s-1, depending on the olefin and the solvent. (As explained above, these polymerisations are monoeidic in solvents of high DC, so that we can discuss x rather than ∑xr.) If the reaction obeys Equation (1) with Vp = R, and x is constant, the half-life is t1/2 = ln 2/k′px. If, for the sake of argument, one considers a minimum manageable halflife to be 10 s, x = ln 2/10 x 105 = ca. 10-6 M. This is the greatest likely concentration of growing centres, and for longer half-lives and/or greater values of k′p, x will be correspondingly smaller. This means that in order to determine x directly for this type of reaction, extremely sensitive analytical methods are required which can operate in the range 10-6 to 10-10 M. On the other hand, the results we have for heterocyclic systems indicate that for most of these the kp may be so small, that for manageable reaction rates ∑xr, is in the range 10-1 to 10-4 M, i.e., of the order of magnitude of the nominal catalyst concentration, and easily amenable to direct measurement. The methods of measuring x (or ∑xr) fall into two groups: a) One can attempt to determine the concentration of active ends by measuring some physical property of the polymerising solution which is characteristic of the growing ends, such as the UV spectrum or the conductivity. b) One can short-stop the polymerisation with a basic reagent which is so chosen that it combines with the growing centre and thus appears as an end-group in the dead polymer. We will discuss in outline the scope, limitations, and achievements of both methods.

4.1 The study of polymerising solutions Elementary considerations show that of all spectroscopic methods only the UV need be considered for olefin polymerisations. The reasons for the success of this method in the

407

Developments in the Theory of Cationoid Polymerisations study of anionic polymerisations are that many monomers give anions of high extinction coefficient (ε), that solvents of relatively low DC are used in which ion-pairs are dominant, and that the magnitude of k′′p is such that manageable reaction rates can be obtained with values of ∑xr which are large enough to be measurable by spectroscopy. No attempts at using the same type of flow method for cationic systems have been published, and in fact the prospects of success are not favourable, because although the ε of aromatic carbenium ions are not much different from those of the anions, the solvents usually used for these reactions (methylene and ethylene dichloride) give reactions in which - if ions are present at all - free ions are dominant (as explained in Section 3) so that kp = k′p is too great and correspondingly x is too small to be measurable. There appears to be no reason why one should not attempt to reproduce the conditions prevailing in the anionic polymerisations, by using solvents of much lower polarity, such as chloroform, chlorobenzene, or methylene dibromide, but this has not been done so far; it seems to be a line of work which merits attention. The only studies on olefin polymerisations in methylene dichloride in which kp was deduced directly from the rate of reaction were carried out by Ledwith and his collaborators [9, 13] with extremely low concentrations of monomer and catalyst. They polymerised isobutyl vinyl ether and N-vinyl carbazole in a Biddulph-Plesch calorimeter with trityl or tropylium salts and obtained the first-order rate constants k1 from the conversion curves. Since different catalysts gave the same ratio of k1/c0 they concluded that for each of them ∑xr = c0 and hence identified k1/c0 with kp which must in fact be k′p, as explained above. It seems unlikely that if several initiators give the same value of kp, they do so because they are all equally inefficient, and the inference that they do so because they are all 100% efficient, i.e., that for all of them x = c0, seems plausible - but it would be useful to have a direct check of this. The most successful attempts at determining the concentration of growing chains directly on polymerising solutions of olefins are due to the schools of Williams [14], and Okamura [15, 16]. The polymerisations were induced by high-energy radiation in bulk monomer and the concentration of ions was determined by extremely sensitive conductance measurements. The concentration of ions was so small (10-10 to 10-11 M) that despite the low DC ion-pairing could be neglected, and thus k′p values were obtained. Although these values will probably be corrected slightly by future work, we have no doubt that their orders of magnitude are correct, and in our opinion they provide a firm set of reference points by means of which the validity of all other alleged values of k′p for olefins can be assessed. [Author’s note: How wrong one can be! See Chapter 5.7] An ingenious method of measuring kp was evolved by Goethals [17] for the polymerisation of thietans by Et3O+BF–4. These polymerisations stop at incomplete conversion, because

408

The Propagation Rate-Constants in Cationic Polymerisations (1971) the sulphur atom in the polymer is more basic than that in the monomer, and therefore the reaction of a growing chain (II) with polymer yields a stable, non-propagating tertiary sulphonium ion (III), so that this reaction is kinetically a termination (suicidal polymerisation):

+ Pp – S

+ Pm+n+1 (II)

+ → Pp+1 – S

Pm

k1

(III)

(CH2)3Pn

It was shown by means of conductivity measurements that (∑xr)0 = c0, the initial catalyst concentration, and that initiation is almost instantaneous, but the question to what extent free ions and ion-pairs are involved is not yet entirely clear, though it seems probable that free ions are dominant; because of this uncertainty we will denote these propagation constants by kp. For rapid and completely efficient initiation, and termination by reaction with polymer

(lnR) / mc0 = lnkp – kt I

(7)

t

where I = ∫ ( mo – m )dt , which is the area under the conversion curve up to t. Hence kp o and kt were found from a plot of (lnR)/mc0 against I for increasing values of t. A similar technique was used almost simultaneously by Penczek [18, 19] for the polymerisation of bis-chloromethyl oxetan (BCMO) by (i-Bu)3Al-H2O in chlorobenzene. In this system, too, there is termination by reaction of growing centres with polymer, but initiation is slow and the equations are correspondingly more complicated. The authors believe that their value of the propagation rate-constant refers to ion-pairs and is thus k′′p, and we see no reason to disagree with their view; they also determined ki and kt. These two examples show that some non-stationary polymerisations, although unpromising at first sight, can be made to yield much useful information. For the polymerisation of 1,3-dioxolan and 1,3-dioxepan by HClO4 Plesch and Westermann [20] were able to show by conductivity measurement that ∑xr = [HClO4]0 and hence obtained values of kp. These values are probably composite, and the contributions from k′p and k′′p are not known, but is has been explained in Section 3 that they are unlikely to differ by more than one power of ten.

409

Developments in the Theory of Cationoid Polymerisations

4.2 The short-stop method The principle of the short-stop method of determining ∑xr, in cationic polymerisations is that to the polymerising solution a basic reagent Q is added which combines with the growing centre and thus forms an end-group in the dead polymer:

Pn+ + Q → Pn Q + How the dead species PnQ+ loses its charge will of course depend on the nature of Q and on the method of isolating the polymer. An analysis of the polymer for Q will give the concentration of growing centres at the instant at which the reaction was killed, and if the rate at that instant is known, kp can be calculated. One pre-requisite for the success of the method is that there should be no side-reactions, such as proton-abstraction from the growing centre: +

Pn ⋅ CH 2 ⋅ C HX + Q → Pn CH : CHX + HQ + This method has not been used so far for olefin polymerisations, but in fact the only difficulty in its application is that Q must be such that it can be detected in the very low concentrations (10-6 to 10-9 M) which x is believed to have in these reactions, for instance by activation analysis. For -onium polymerisations this technique has been used with ingenuity and success by Saegusa [21] who determined the concentration of oxonium ions in THF polymerisations in bulk by killing them with PhONa and counting the PhO groups in the polymer spectrophotometrically:

+ Pn – O

+ PhO- → Pn – O(CH2)4 – OPh

The question whether this reaction is monoeidic or enieidic was not discussed by that author, but in view of the low polarity of bulk THF it seems likely that the principal propagating species is ion-pairs; but since there is no definite evidence we will denote the rate constant by kp, but write the equations in terms of x rather than ∑xr. For this equilibrium polymerisation therefore

– dm / dt = kp x ( m – me )

(8)

and hence t2

ln[( mt1 – me ) /( mt 2 – me )] = kp ∫ xdt t1

410

(9)

The Propagation Rate-Constants in Cationic Polymerisations (1971) The x was determined throughout the reaction at increasing times, the resulting curve was integrated and the results plotted according to Equation (9) so that the slope of the line gave kp. It is evident that this classical piece of work has shown the way in which ∑xr, and hence kp, can be determined for many different systems. A closely related method was used by Jaacks and his collaborators [22] to determine the concentration of tertiary oxonium ions (IV) in the polymerisation of dioxolan. They did this by killing the reaction with EtONa, hydrolysing the polymer and determining the EtOH derived from the killing agent by gas-chromatography:

+ RmRnOCH2O(CH2)2Rp + EtO- → RmOCH2O(CH2)2Rp + RnOEt (IV) hydrolysis [m + n + p + 1] [(CH2OH)2 + CH2O] + EtOH R = –OCH2O(CH2)2– Thus the quantity of EtOH in the hydrolysate is equivalent to the number of tertiary oxonium ions; any secondary oxonium ions react with EtO- to give EtOH which is removed before hydrolysis of the polymer.

5 Pseudo-cationic polymerisations No account of the propagation rate-constants of cationic polymerisations would be complete without some discussion of pseudo-cationic polymerisations, since the first alleged kp values which looked reasonably authentic in fact belong into this category; they are for the polymerisation of styrene by sulphuric [23, 24] and perchloric acid [2532] in various polar solvents in the temperature range ca. 0 ± 20°. The story of why and how Gandini and Plesch evolved the theory of pseudo-cationic polymerisation has been told in detail and need not be repeated here [3, 4]. However, their ideas are still contested by various authors, and they have also been modified in the light of more recent results, so that it is appropriate in the present context to summarise the arguments which support the idea that pseudo-cationic polymerisation is a reaction-type sui generis. The most thoroughly studied system is styrene-perchloric acid in methylene and ethylene dichloride over the temperature range –90 °C to +30 °C. Most of the facts about this reaction are not in dispute and the essential features are these [25-32]:

411

Developments in the Theory of Cationoid Polymerisations i) When perchloric acid is added to a solution of styrene in CH2Cl2, the following phenomena are observable: At low temperatures there is an extremely fast reaction I (which may he accompanied by a flash of orange-red colour and a transient high electrical conductivity) and the extent of stage I diminishes with increasing temperature. It is followed by a much slower stage II, with an activation energy of 8–12 kcal mol-1 (depending on m). Part or all of stage II (according to the conditions) is internally of first order and its rate is given by

RII = k2 c0 m

(10)

where c0 is the initial concentration of the acid. When stage II is almost complete, the hitherto colourless solution suddenly turns yellow (stage III), there is a simultaneous increase in electrical conductivity, and the residual monomer is consumed extremely rapidly. The yellow colour and conductivity in stage III have been shown to be mainly due to the 3-aralkyl-1-phenylindanyl cation (V) [33]:

H

(CH2CHPh)nCH3 C

O

CH2 CH+

Ph

(V)

ii) If at near ambient temperatures, an excess of water over acid is added, the rate is hardly affected, but the stage III (formation of indanyl ions) is suppressed completely [31, 32]. If, in low temperature experiments, the solution contains more ethanol than acid, stage I is suppressed, stage II is slowed down but goes to completion, but there is no stage III [34]. iii) In the presence of an electrolyte with a common ion, (n-Bu)4N+ClO4- or Li+ClO4- at concentration s, k2 falls linearly with decreasing 1/s1/2 to a limiting value, k2L at ‘infinite’ s (1/s1/2 = 0), but the conversions in stage I are not affected [28]. iv) A careful reinvestigation of stage II with highly purified materials has shown that in fact it is of first order only during about the first half-life and thereafter the reaction accelerates steadily until stage III is reached [34]. There is general agreement that stages I and III are truly ionic reactions which are not due to the very abundant, colour-conferring indanyl ions, but to a very small concentration

412

The Propagation Rate-Constants in Cationic Polymerisations (1971) of oligostyryl cations which are in equilibrium with them [32, 33]. The current controversy is concerned with the mechanism of stage II and the interpretation of the rate constant k2, or rather of the coefficient of m, namely k2 c0. In fact, there are really two separate questions, which unfortunately have been much confused by most authors and commentators: a) Are the polymerisations due to a small concentration of free ions, i, or a large concentration x of some much less reactive species? In other words, is k2 c0 = kpi, or is k2 c0 = k′′′p x, where k′′′p is the rate constant of species X whose concentration x is approximately c0? b) If the reactions are carried by a species X of low reactivity, is this an ion-pair or an ester? When we proposed the pseudocationic theory originally we thought that in stage II the reaction is entirely due to a large concentration of the relatively unreactive ester oligostyryl perchlorate, CH3(CHPhCH2)nCHPh·O·ClO3. In view of the more recently discovered facts (iii) and (iv) we now prefer the view that a fraction of the rate is due to ester and the remainder is due to free ions, this fraction depending on the detailed circumstances and on the part of the stage II which is considered; at the start of the reaction the contribution from free ions is small or zero and it increases with conversion [34]. According to this interpretation the rate-constant of ester propagation is k′′′p = k2L. However, Pepper and his collaborators maintain that the k2L is the rate-constant of ionpair propagation, and they consider that the ester itself does not propagate [27, 28]. We will show below that ion-pairs are irrelevant in these systems, and it is essential to realise that this conclusion, based on elementary electrochemical arguments, is quite independent of all other aspects of the problem. In Section 3 it was shown that for those olefin polymerisations in solvents of DC about 10 which are ionic, propagation must be predominantly by free ions, under the usual polymerisation conditions. For the polymerisations by perchloric acid we can take a concrete numerical example by which it can be shown that ion-pairs (VI) cannot play any important part in the reaction. The relevant dissociation equilibrium is κ

CH 3 (CHPh ⋅ CH 2 ) n CHPh + ClO −4 ↔ CH 3 (CHPh ⋅ CH 2 ) n CHPh + + ClO −4 (VI ) The experimental rate-law [10) is valid over a wide range of conditions. From Equations (10) and (5) it follows that the half-life t1/2 , of the polymerisation is given by

413

Developments in the Theory of Cationoid Polymerisations

t1 / 2 = (ln 2) /( kp′ i + kp′′q )

(11)

and i is given by Equation (4) and q = c - i. If we assume for K the same low value as in Section 3, i.e., 10-7 M and give k′p the reasonable value 105 M-1 s-1, then calculation shows that if c = c0 = 10-4 M, the half-life of the reaction calculated only from the k′p term is less than ca. 30 seconds, which is far less than the observed half-life (ca. 103 seconds), and therefore, a fortiori, ion-pairs cannot be of any significance in these circumstances since, if we did take account of them, the half-life would be even shorter, and if c were much less, say 10-6 M - which would mean that only a small fraction of the acid actually forms ions of all kinds - then the concentration of the ion-pairs would be vanishingly small. In other words, the useful lesson from these simple considerations is that if the total ion concentration were of the same order of magnitude as the nominal acid concentration, the free ions alone would give a reaction rate far greater than that observed; and if the total concentration of ions were much less than the acid concentrations usually used, the concentration of ion-pairs would be so small that their effect would be quite negligible compared to that of the free ions. This means that whatever else may be going on in these reactions, ion-pairs are completely irrelevant. It follows therefore that the answer to question (b) is that if the reaction is not carried by free ions, the active species cannot be ion-pairs, but must be the ester. Thus question (a) becomes: free ions or ester? As happens so often in scientific controversies, it appears that the truth may embody both the extreme positions. The point (ii) above shows that at least one of the active species is insensitive to water and ethanol, and points (iii) and (iv) indicate that at least under some conditions stage II is dieidic. It is fairly evident that the species which is insensitive to water and ethanol must be the ester, and that the ‘second species’ which is suppressible by excess of common-ion electrolyte, and which is slowly formed during stage II, must be the free ions. We thus conclude that ester propagation (pseudo-cationic polymerisation) is indeed a reaction type sui generis, and that under certain circumstances it may be accompanied by free-ion propagation. The consequence of this view is that most of the observed k2 which Pepper interpreted as k′′p (ion-pairs) and which we interpreted as k′′′p (ester) are probably composite:

k2 = kp′i + kp′′′e

(e = concentration of ester)

(12)

and that therefore a detailed discussion of the actual values is presently not useful. It is however, worth noting that the k2 values reported are so small, compared to the known k′p values, that the first term in Equation (12) cannot be very great absolutely, but it may well be as great as, or greater than, the second term. For instance, if k′′′p = 10 M-1 s-1, e = 10-3 M,

414

The Propagation Rate-Constants in Cationic Polymerisations (1971) k′p = 105 M-1 s-1, then i = 10-7 M would make the two terms equal. It follows further that if we do want to obtain a genuine k′′′p value, we must use the Szwarc-Pepper common-ion extrapolation technique to obtain it as k2L, the limiting value at infinite salt concentration.

6 Comparison and discussion of some kp values 6.1 Dubious values of kp The literature contains a number of claims concerning kp values for a variety of polymerisation systems, which we will not discuss here. Examination of the original papers shows that most of these alleged kp values are derived on the basis of inadequately explored reaction kinetics and ill-substantiated mechanisms, some of which are now known to be wrong. It would not be useful to dissect each of these claims in detail, since we have provided the reader in the earlier parts of this paper with the critical apparatus required to do this for himself.

6.2 Comparison of some kp values Most of the kp values which seem reasonably reliable are shown in Tables 1 and 2. At first sight the kp values fall into two groups: For olefin polymerisations they lie between ca. 103 and 109 M-1 s-1 and for the O- and S-heterocyclics they lie in the range 10-3 to 10 (with the exception of 1,3-dioxepan). One can avoid wonderment at this great difference if one realises that one is dealing with two essentially different groups of reactions. The olefin polymerisations involve attack of a centre with high positive charge density on an atom which is the negative end of a feeble dipole, the major part of whose moment is induced by the attacking centre. The transition state for this reaction must be nearly linear and the activation energy, if any, is very small, in accordance with the prediction made many years ago by Evans and Polanyi [35]. On the other hand, when considering the propagation step for the cyclic ethers and thietans, one must remember that the -onium ion is strongly solvated by monomer, so that even if it is not paired, ‘free’ is not really an appropriate adjective for it, and therefore the chargedensity is much lower than for the carbenium ion. Secondly, the monomers have large dipoles and thus come in towards the positive -onium centre with the negative hetero-atom ‘forward’, and thirdly, for this reason the transition state cannot be linear and involves three centres, so that the entropy of activation, ΔS, is numerically relatively great, and it may in fact be considerably greater than the entropy of polymerisation, ΔS0ss.

415

Developments in the Theory of Cationoid Polymerisations

Table 1 Some k+p values for olefinic monomers (M-1 s-1) Solvent

T (°C)

Initiator

k+p

Ref.

c-Pentadiene

none

–78

Radiation

6 x 108

14

Styrene

none

15

Radiation

3.5 x 106

15

α-Me styrene

none

0

Radiation

4 x 106

15

i-Bu vi ether

none

30

Radiation

3 x 105

15

i-Bu vi ether

none

42.5

Pulse radiation

1 x 106

16

i-Bu vi ether

CH2Cl2

0

C7H+7SbCl6-

3.5 x 103

13

i-Bu vi ether

CH2Cl2

0

Ph3C+SbCl6-

3.5 x 103

13

i-Bu vi ether

CH2Cl2

–25

C7H+7SbCl6-

1.5 x 103

9

i-Bu vi ether

CH2Cl2

–25

Ph3C+SbCl6-

2 x 103

9

N-vi carbazole

CH2Cl2

0

C7H+7SbCl6-

4.6 x 105

9

N-vi carbazole

CH2Cl2

–25

C7H+7SbCl6-

1.5 x 105

9

Monomer

Table 2 Some kp values for heterocyclic monomers (M-1 s-1) Solvent

T (°C)

Initiator

kp a

Ref.

BCMO

PhCl

70

(i-Bu)3Al + H2O

8.5

18

THF

none

0

Et3Al + H2O + 3 promotersb

(6.4 ± 0.3) x 10-3

21

1,3-Dioxolan

CH2Cl2

0

HClO4

10

20

1,3-Dioxepan

CH2Cl2

0

HClO4

3 x 103

20

3,3-Dimethyl thietan

CH2Cl2

20

Et3O+BF4-

6.5 x 10-3

17

Thietan

CH2Cl2

20

Et3O+BF4-

>0.25

38

3,3-Diethyl thietan

CH2Cl2

20

Et3O+BF4-

3 x 10-5

38

3-Et, 3-n-Bu thietan

CH2Cl2

20

Et3O+BF4-

3 x 10-5

38

Monomer

a As explained in the text, the values for BCMO and THF are most probably k′′p and all the remainder are probably composite b With epichlorohydrin, or propene oxide, or β-propiolactone as promoters

416

The Propagation Rate-Constants in Cationic Polymerisations (1971) The propagation for cyclic formals also involves a solvated oxonium ion and a highly polar monomer [10, 12]. Since under optimum conditions the polymers are essentially free from any kind of end-group (except very small amounts of –OH) Plesch and Westermann [36, 37] concluded that they must be formed by a ring-expansion mechanism, involving a 4-centred transition state:

R — (CH2)2 O

R — (CH2)2

+O—H

O

O O

O

+O—H

O R = [–(CH2)2OCH2)–]n

Thus the reaction mechanisms for olefins and for the heterocyclic monomers are essentially different in all respects, and hence there is really no rational basis for comparing their kp values.

6.3 The effect of temperature and solvent polarity on kp Neither for olefins nor for heterocyclic monomers do we yet have a sufficiently extensive body of activation energies of the kp-s to make a detailed discussion profitable. It is worth noting, however, that for the cationic (as opposed to the pseudo-cationic) polymerisation of olefins in solvents of DC greater than about 10, it is likely that a reduction of the temperature does not affect the rate except through its effect on k′p, since these reactions are mainly carried by free ions only. For cationic polymerisation of olefins in solvents of DC appreciably less than ca. 10 and for those of heterocyclic monomers in all solvents of DC up to perhaps 15–20, this is not so. For such systems the polymerisations are probably at least dieidic (free ions and ionpairs) and a lowering of the temperature will increase the DC of the ion pairs. Thus in such systems the change of temperature affects not only k′p and k′′p, but also the relative abundance of the different types of chain-carriers; therefore the proper interpretation of the apparent activation energies is difficult and by no means obvious. In the foregoing discussions we have taken the DC as a measure of the polarity of a solvent, but it is of course no more than a rough make-shift, for lack of anything better. As to the effects of solvent polarity on kp, very much the same applies as was said about the effects of temperature. Attempts at correlating kp with solvent polarity (through the

417

Developments in the Theory of Cationoid Polymerisations DC or any other measure) are meaningful only so long as one is sure that one is dealing with a monoeidic system where kp = k′p. For all others one has the same problems as with the temperature effects: change of polarity will indeed affect the magnitude of k′p and k′′p, but its most important effect is likely to be on the relative abundance of the two (or more) active species concerned.

7 Conclusion An observer who is accustomed to the relative clarity and simplicity of radical and anionic polymerisations and the abundance of information about them might suggest that ‘Much Ado about Nothing’ would be an appropriate sub-title to this article. The fact is indeed that in the field of cationic polymerisation there are still only very few rate-constants which can be regarded as well substantiated. In this situation we have deliberately refrained here from quoting and criticising in detail each and every claim to have measured a rateconstant. Instead, we thought it more useful to explore the origins of the present unsatisfactory position, and to indicate some guide-lines which will help in the planning of future researches. It now appears that much more careful thought is required in the selection of systems which may offer the prospect of yielding unambiguous results. In particular, the choice of solvent and initiator must be considered very carefully, and features such as mechanisms of initiation, catalyst efficiency, nature of end-groups, and the internal order of reactions need to be explored much more thoroughly than has been customary in the past. Too much effort has been wasted by ignoring the precept: ‘First the Chemistry, then the Kinetics’.

Acknowledgement This article is based on a lecture delivered to the Polymer Division of the Royal Australian Chemical Institute, whose generous hospitality is gratefully acknowledged.

References 1.

Bauer, R. F., LaFlair, R. T., Russell, K. E., Can. J. Chem. 48, 1251 (1970).

2.

From Greek enioi = several, eidos = form or image, monoeidic = one form; dieidic = two forms.

3.

Gandini, A., Plesch. P. H.: SCI Monograph No. 20, p. 107, (1966).

418

The Propagation Rate-Constants in Cationic Polymerisations (1971) 4.

Plesch, P. H., Pure Appl. Chem. 12, 117 (1966).

5.

a. Szwarc, M., Carbanions, Living Polymers, and Electron-Transfer Processes, New York: Interscience 1968. b. Adv. Chem. Ser. 91, 263 (1969). c. Plesch, P. H.: Progess in High Polymers, Vol. II, 137- 288. Robb, J. C., Peaker, F. W., (Eds.), London: lliffe Books 1968.

6.

Longworth W. R., Mason, C. P., J. Chem. Soc. (A). 1164 (1966).

7.

Kalfoglou, N., Szwarc, M., J. Phys. Chem. 72, 2233 (1968).

8.

Lee, W. Y., Treloar, F. E., J. Phys. Chem. 73, 2458 (1969).

9.

Ledwith, A., Adv. Chem. Ser., 91, 317 (1969).

10. Jones, F. R., Plesch, P. H., Chem. Commun., 1018 (1970). 11. Jones, F. R., Plesch, P. H., Chem. Commun., 1231 (1969). 12. Jones, F. R., Plesch, P. H., Chem. Commun., 1230 (1969). 13. Bawn, C. E. H., Fitzsimmons, C., Ledwith, A., Proc. Chem. Soc. 391 (1964). 14. Bonin, M. A., Busler, W. R., Williams Ff., J. Am. Chem. Soc. 87, 199 (1965). 15. Williams, Ff., Hayashi, Kanae, Ueno, K., Hayashi, Koichiro, Okamura, S., Trans. Faraday Soc. 63, 1501 (1967). 16. Ueno, K., Hayashi, K., Okamura, S., J. Macromol. Sci. (Chem.). A 2,209 (1968). 17. Goethals, W. J., Drijvers, W., Makromol. Chem. 136, 73 (1970). 18. Penczek, St., Kubisa, P., Symp. on Macromols. Budapest, Paper 2/12 (1969). 19. Penczek, St., Kubisa, P., Makromol. Chem. 130, 186 (1969). 20. Plesch, P. H., Westermann, P. H.: to be published; Westermann, P. H.: Ph. D. Thesis, Keele (1967). 21. Saegusa, T., Matsumoto, S.. Hashimoto, Y.: Polymer J. 1, 31 (1970), and earlier papers. 22. Jaacks, V., Boehlke, K., Eberius, E.: Makromol. Chem. 118, 354 (1968).

419

Developments in the Theory of Cationoid Polymerisations 23. Pepper, D. C., et al., Proc. Roy. Soc. A. 263, 58, 63, 75, 82 (1961). 24. lkeda, K., Higashimura, T., Okamura, S., Chem. High Polymers (Japan) 26,364 (1969). 25. Pepper, D. C., Reilly, P. J., J. Polymer Sci. 58, 639 (1962). 26. Pepper, D. C., Reilly, P. J., Proc. Roy. Soc. A. 291, 41 (1966). 27. Darcy, L. E., Millrine, P., Pepper, D. C., Chem. Commun. 1441 (1968). 28. MacCarthy, B., Millrine, W. P., Pepper, D. C., Chem. Commun. 1442 (1968). 29. Gandini, A., Plesch, P. H., Proc. Chem. Soc. 240 (1964). 30. Gandini, A., Plesch, P. H., J. Polymer Sci. B., 3,127 (1965). 31. Gandini, A., Plesch, P. H., J. Chem. Soc. 4826 (1965). 32. Gandini, A., Plesch, P. H., European Polymer J., 4, 55, (1968). 33. Bertoli, V., Plesch, P. H., J. Chem. Soc. (B) 1500 (1968). 34. Mathias, E., Plesch, P. H.: to be published, Mathias, E.: Ph. D. Thesis, Keele (1970). 35. Evans, A. G., Polanyi, M., J. Chem. Soc. 252 (1947). 36. Plesch, P. H., Westermann, P. H., J. Polymer Sci. C., 16, 3837 (1968). 37. Plesch, P. H., Westermann, P. H., Polymer, 10, 105 (1969). 38. Goethals, E. J.: to be published; quoted by permission.

420

5.2

Nature of the Propagating Species in Cationic Polymerisationsa (1973) P. H. Plesch

This paper was first published in the British Polymer Journal, 1973, 5, 1, 1-12. Reproduced with permission from John Wiley & Sons, UK. Copyright 1973.

Prologue Once again, in this paper, the electrochemical aspects of the ions and their equilibria are prominent. The Fuoss-Kraus equation is applied to the pairing of the carbenium ions with the anions. It is shown that since an increase in the solvent polarity reduces the propagation rate-constant, the increase in rate in changing from a less polar to a more polar solvent must be due to the increase in polarity augmenting the ratio of the concentrations of unpaired to paired cations, (here called i/p and in later papers y/p) on the assumption that as in anionic polymerisations, the unpaired ions propagate faster than the paired ions. Another useful innovation is the formulation of an equation relating i/p to c /KD where c is the total concentration of the electrolyte and KD the dissociation constant of the ionpairs. In a later paper it will be noted that this is the reciprocal of a (much simpler) equation relating KD /c to p/i which had been derived previously by Bos and Treloar (A). It is astonishing in view of the importance of such equilibria, that this equation did not appear earlier and that even now it is not widely known. Its plot enables one to find very simply i/p if KD/c is known. There is also a simple calculation whereby it is shown that propagation by paired cations cannot explain the monomer consumption which is attributed by this author to propagation by ester. There is also here a detailed explanation of the reasons why a change of solvent, leading to a change of KD, can change the DP and why the same effect can result from a change in the size of the anion. a

An expanded version of the lecture delivered to the Lodz section of the Polish Chemical Society in March 1972.

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Commercial rubbers

Developments in the Theory of Cationoid Polymerisations

1 Nature of the problem In the present review we are concerned with the so-called cationic polymerisations [1] of olefins (isobutene, alkyl vinyl ethers, N-vinyl carbazole, etc.) and of heterocyclic compounds (oxetans, THF, thietans [2], cyclic formals, etc.) by protonic acids (e.g., HClO4), by metal halides MtXn which can act without co-initiators (e.g., AlBr3) and by those which require co-initiators (at least in some systems) such as Et2AlCl1k or TiCl4, by organic salts (e.g., Ph3C+ BF4-, Et3O+ SbF6-), by mixed anhydrides, such as MeCOClO4, and by various related compounds. Any theory of these reactions must explain their detailed features in terms of the minimum number of hypotheses, which must be compatible with the generally accepted principles of chemistry. The reactions with which we are concerned here can be represented by the general scheme:

Pn* + P1 → Pn +1 , k p

(1)

where P1 is the monomer, kp the propagation rate-constant, and the nature of the active species Pn* is the subject of the present discussion.

2 Outline of the historical development Probably the earliest quantitative experiments on what are now known as cationic polymerisations were made by Gwyn Williams (1938) with styrene and stannic chloride, and by the early 1940s the general belief had become established that in reactions initiated by metal halides the active species is a cation. It appears that Evans and Meadows [3] were the first to state specifically that in hydrocarbon solvents the propagating cations must be paired with the anions and Plesch [4] made the first attempt at calculating the dissociation constant, KD, for an ion-pair comprising a growing cation in a hydrocarbon solvent:

Pn+ A− ↔ Pn+ + A− , K D

(2)

Such calculations are based on the Bjerrum-Fuoss equation

log K D = 3 log a – A′ – B/εT a

(i)

where a is the distance of closest approach of the ions, ε is the dielectric constant of the solvent, T is the temperature, and A′ and B are positive quantities. Since to a first

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Nature of the Propagating Species in Cationic Polymerisations (1973) approximation a is independent of T and ε, and log a is negative, equation (i) can be used in the approximate form

– log K D = log K A = A + B/εT a

(ii)

where A is positive. This equation is, of course, the basis of the well-known generalisations to the effect that when one changes from a solvent of higher ε to one of lower ε, or if a larger anion is replaced by a smaller one, KD will be reduced. Despite the fact that the range of validity of equation (i) does not extend below ε values of about 5, calculations based on it for less polar solvents do give a rough indication of KD values, which shows that in hydrocarbons, for instance, the concentration of free ions (for all usual values of the total ionic concentration) would be a very small fraction of the total. Although this point seems to have been appreciated and understood very early on, it took an astonishingly long time for people to understand that in solvents of greater polarity, such as methylene dichloride, the electrochemical situation would be completely different from that prevailing in hydrocarbons. Although equilibria such as (2) are studied in the most elementary parts of all physical chemistry courses, their implications, expressed in the equivalent forms (iiia) and (iiib)

K D = α 2 c /(1 – α ) = i 2 / p

(iiia)

(c = [Pn+] + [Pn+ A-] = i + p, α = degree of dissociation,

i ≡ [Pn+ ], p ≡ [Pn+ A − ]

a

i/K D = –1 / 2 + (1 + 4c/K D )1 / 2 / 2

(iiib)

are even now not fully understood by some workers. In particular, it took a very long time before the kinetic implications of the electrochemical equilibria were appreciated. The curve in Figure 1 shows just how the ratio i/p varies with c/KD. It is simpler and more useful to take the dimensionless quantity c/KD as the independent variable, in place of c; the equation of the curve in Figure 1 is

i (1 + 4c/K D ) 1/2 – 1 = p 2c/K D + 1 – (1 + 4c/K D ) 1/2

(iv)

a In Reference 1f the symbol p was used for [P+], and q for [P+A–]. This confusing symbolism has been abandoned and the presently used symbols are recommended.

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Developments in the Theory of Cationoid Polymerisations

Figure 1 The dependence of the ratio of free ions to ion-pairs (i/p) on the relative concentration (c/KD)-see equation (iv) Since both elementary theory and experiments in small-molecule kinetics show that the reactivities of paired and free ions can be very different, the ratio i/p plays a dominant part in the kinetics of all ionic reactions and therefore we must start with a detailed consideration of this topic.

3 Unpaired and paired cationsa Until quite recently the heading to this section would have contrasted paired cations with free cations, but it has become increasingly obvious during the last few years that a For a detailed discussion of some aspects of this topic see M. Szwarc, Carbanions, Living Polymers, and Electron Transfer Processes, Interscience, New York, 1968 and Ions and Ion Pairs in Organic Reactions, Ed., M. Szwarc, Wiley-Interscience, New York, 1972.

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Nature of the Propagating Species in Cationic Polymerisations (1973) although a reactive cation may be free of the electrostatic influence of an anion, its behaviour may be modified by other interactions, such as a more or less close association with a polar or polarisable solvent, or with the monomer. Thus whilst an ion may be unpaired and therefore ‘free’ from a (perhaps rather naive) electrostatic point of view, the reactivity of such a ‘free’ ion may be different in different environments because of different degrees of solvation, which will alter both the geometry around, and the chargedensity at, the reactive site. For the present we will ignore the distinctions between differently solvated unpaired ions and discuss simply the kinetic and other consequences of the simultaneous occurrence of propagation by two reactive species, whose relative concentrations are governed by an equilibrium. This type of reaction is denoted by the term dieidic, this being a special case of the general class of enieidic reactions, i.e., those in which several (Greek enioi) forms (Greek eidos) of propagating species coexist. In dieidic reactions in which the propagating species are unpaired and paired cations, the total rate R is the sum of the rates R+ and R± of the reactions due to unpaired and paired cations, respectively. Thus, if equilibrium (2) is the only one involved,

R = R + + R ± = [k p+ αc + k p± (1 – α )c][P1 ]

(va)

= [k p± + α( k p+ – k p± )c][P1 ]c

(vb)

In its ‘mirror image’ form, for unpaired and paired anions, this equation has been used to good effect to determine the kp- and kp± in a large number of anionic polymerisations. In the field of cationic polymerisation, analogous studies have so far only been reported for thietans [2b] for which the kp+ and kp± do not differ very much; this seems to be a characteristic feature of heterocyclic systems which will be discussed below.b In the mid-1960s the first measurements of propagation rate-constants for unsaturated monomers became available, from polymerisations initiated by γ-radiation [5]. The circumstances of these experiments were such that it was immediately clear that these very high rate constants (106 to 108 l mol-1 s-1) were those of unpaired cations, kp+. All these reactions were carried out with bulk monomer, i.e., the polymerisations occurred in a medium of very low polarity (ε c. 2 for hydrocarbons and 5 to 6 for alkylvinylethers). Unfortunately, the γ-radiation method is not applicable to polymerisations in solution, especially in polar (usually alkyl halide) solvents. The methods which have been used to b In earlier publications kp+ was denoted by kp or kp′ and kp± by kπ or kp′′. The present nomenclature kp+ and kp± is clearer and in conformity with that used for anionic polymerisations and is recommended.

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Developments in the Theory of Cationoid Polymerisations determine kp values for olefins in such solvents are still rather unsatisfactory [1i], but it does appear reasonably certain now that in solvents of ε in the range 10 to 12, the kp+ values are in the range 103 to 106. This is, of course, expected, because it follows directly from Transition State Theory that for any reaction in which the transition state is less polar than the initial state (such as that of an ion adding to a molecule), an increase in the polarity of the solvent will stabilise the initial state more than the transition state, and thus raise the activation energy and lower the rate-constant (see Figure 2). The lowering of kp+ with increasing polarity (ε) of the solvent is apparently in conflict with the observation that most cationic polymerisations go faster (for the same monomer and initiator concentrations), the more polar the solvent is. This effect can have several explanations - for some systems it may be completely meaningless to compare the rates in two solvents of different polarity (even at the same concentrations of reagents), unless it is proved (a) that the kinetics (i.e., the order with respect to monomer and initiator) is the same in both solvents and (b) that the total concentration of growing chains produced by a given concentration of initiator is the same. However, if for two different solvents the kinetics and the initiator efficiencies are the same, and if equilibrium (2) is the only one involved, and if the more polar solvent gives a faster reaction, this means that the experimental second-order rate-constant [kp± + α(kp+ - kp±)] in equation (vb) is greater for the more polar solvent. Since theory (and experiment) tell us that for the more polar solvent kp+ and kp± are smaller than for a less

Figure 2 ΔΔHs(Pn+ + P1) is the difference between the solvation energy of (Pn+ + P1) in hydrocarbon solvent and in a polar solvent, and ΔΔHs‡ is the corresponding difference for the Transition State Complex (TrStC). Since ΔΔHs(Pn+ + P1) > ΔΔHs‡, the activation energy ΔH2‡ in the polar solvent is greater than that (ΔH1) in hydrocarbon solvent

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Nature of the Propagating Species in Cationic Polymerisations (1973) polar solvent, the greater rate in the more polar solvent must be due to α being greater in that solvent. Another way of saying the same thing is that an increase of polarity increases KD [equation (i)] and hence α, so that the consequent greater relative abundance of unpaired ions outweighs the effect which increasing ε has in diminishing both kp+ and kp±, as long as kp+ > kp±. One of the consequences of kp+ being greater (usually very much greater) than kp± is that in solvents of εc. 10, ion-pairs are largely irrelevant as far as the propagation is concerned. This can be illustrated by a simple example. Suppose that KD = 10-5, c = 10-3 mol l-1, then α ≈ 0.1. If kp+ = 106 and kp± = 104 l mol-1 s-1, we have a situation where the c. 10 % of unpaired ions contribute ten times as much to the rate as the 90 % of paired cations. The value of KD is typical for ions of the size and for the values of εT, which are relevant here, but c is rather large; typically it is probably below 10-5 mol l-1-which makes α even greater and the contribution of paired cations to the rate even smaller. The above demonstration that in a great many cationic polymerisation systems ion-pairs are of no importance as far as the rate of reaction is concerned, raises the question of how it can be explained that in many such systems the nature of the initiator, which determines essentially the nature of the anion, can influence the DP of the polymer formed. In principle, a change of anion, say from a smaller one, e.g., BF4-, to a larger one, such as SbF6- could influence the DP in a number of ways. However, probably the most important way is through the effect of ion-size on KD [equation (i)]. If, in seeking the origin of DP variations, we enumerate all the different types of chainbreaking reactions which can occur in cationic polymerisations, we find that only one is peculiar to the paired cation; that one is the unimolecular decomposition of the growing ion-pair and this seems to be in many systems the most important chain-breaking reaction. Suppose now that the rate of unimolecular chain-breaking in the ion-pair is ten times as great as the sum of the rates of all chain-breaking reactions which the unpaired cations can undergo; and suppose further that α = 0.1, so that any one cation spends one-tenth of its life unpaired. Since the probability of chain-breaking is ten times as great during the time when the cation is paired, as it is when it is unpaired, the ‘paired time’ is much more important than the ‘unpaired time’ from the DP point of view. Furthermore, a change in ion-size which changes α by only a few per cent, will have a disproportionately large effect on the DP by changing the ‘paired time’ of the cation during which chainbreaking is more likely to occur. In order to present a fair picture of the consequences arising from the pairing of ions it must be said at this stage that pairing is only the first of a succession of aggregations, and that as the polarity of the medium decreases, the free energy of an ionic solution is diminished by progressive clustering of the ions to triplets, quadruplets, and finally to large aggregates.

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Developments in the Theory of Cationoid Polymerisations These phenomena are well known, though by no means perfectly understood, in small molecule dynamics, and their role has been elucidated to some extent for anionic polymerisations, but for cationic polymerisations this is very largely uncharted territory. The limits to the validity of the Bjerrum-Fuoss equation (1) are set not so much by a breakdown of the model from which it is derived, as by the progressively increasing abundance of ternary and higher aggregates, as the dielectric constant of the medium is reduced.

4 Structure and reactivity of the cations 4.1 The carbenium ions Since in many of the polymerisations with which we are concerned here the active species are carbenium ions, it is relevant to discuss briefly their structures. Carbenium ions can be formed from olefins by the addition of a cation, such as a proton or some other carbenium ion. The cations formed from simple olefins are secondary or tertiary carbenium ions: +

CH 2 : CHPh + R + → RCH 2 ⋅ C HPh

(3)

I +

CH 2 : CMe 2 + R + → RCH 2 ⋅ C Me 2

(4)

II Conjugated olefins yield carbenium ions in which the charge is distributed over several centres:

+ RCH2•CH•CH•CH2 III

(5)

CH2:CH•CH:CH2 + R+ + CH2•CHR•CH:CH2 IV

(6)

+ CH2:CH•O•R′ + R+ → RCH2•CH•O•R′ V

428

(7)

Nature of the Propagating Species in Cationic Polymerisations (1973) The near-uniqueness of isobutene arises from the fact that in the substituted t-butyl cation II the charge is much more concentrated than in any of the other ions shown here, and yet it is stable because it cannot undergo any energetically favourable isomerisations, such as that of the ion VI derived from 3-methylpent-1-ene [6]: +

+

CH 2 : CH ⋅ CHMe 2 + R + → RCH 2 ⋅ C H ⋅ CHMe 2 → RCH 2 ⋅ CH 2 ⋅ C Me 2 VI

(8)

VII

The resultant ion VII is of course effectively the same as II. In the ions I, III and V the charge is more or less widely distributed over several centres or, in other words, the charge density at the centre of charge is much smaller than in the ions II or VII. The effect which variations in charge-density have on the electrical properties of ions is at present difficult to assess. From primitive electrostatic considerations one can conclude that diffuseness of charge is in some respects equivalent to an increase in ion size. From general chemical theory it follows that the more diffuse the charge, the more stable is the ion, and this of course is the driving force for the isomerisation of carbenium ions. It is important to realise that not only are the reactivities of carbenium ions far greater than those of carbanions, but the gradation in stability of carbenium ions covers a far wider range than that of carbanions; that is the reason why carbenium ion reactions are generally so much more complicatedthere is much greater scope and driving force for many types of side reactions.

4.2 Hetero-cations Hetero-cations, such as secondary or tertiary oxonium ions can be formed easily by the addition of a proton or a carbenium ion to an ether:

+ R+ + —O— → R – O VIII

(9)

If the ether is cyclic (oxetan, THF), the resulting oxonium ion is the propagating species in its polymerisation. The propagating species in the polymerisation of cyclic S– [2], N–[7, 8], and P– [9] compounds are formed by analogous reactions. In the polymerisation of compounds which polymerise through the carbonyl group, the active species is believed to be a carboxonium ion IX:

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Developments in the Theory of Cationoid Polymerisations +

R + + CH 2 O → R ⋅ O ⋅ C H 2

(10)

IX in which the charge is distributed over two centres. Thus, whereas in oxonium ions and ions of type VII the charge-density is high, since there is little, if any, scope for charge delocalisation, the carboxonium ions, such as IX, have a more diffuse charge. An interesting consequence of the high charge-density on oxonium ions and sulphonium ions, combined with the high dipole moment of the corresponding monomers, is that the ions are strongly solvated by monomer. This solvation was proved by model experiments with triethyl oxonium ion and diethyl ether [10]. The experiments illustrated in Figure 3 show that as the Et3O+ ion is titrated with Et2O, the equivalent conductance at zero

Figure 3 Titration of Et3O+PF6- in CH2Cl2 at 0 °C with Et2O. The equivalent conductance at zero concentration, Λ0/mho cm2 mol-1, and the dissociation constant KD/mol l-1 of the ion-pairs, as functions of the ratio [Et2O]/[Et3O+PF6-]

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Nature of the Propagating Species in Cationic Polymerisations (1973) concentration, Λo, decreases. This means that the average size of the cations increases and this is the cause of the concurrent increase in KD. This solvation of the propagating cation by monomer (and/or by polymer!) explains why in the polymerisation of cyclic oxygen and sulphur compounds the kp+ and kp± do not differ greatly. The solvation by monomer reduces the charge-density so much, that any further charge-dissipation by ion-pairing produces only a small further decrease in the reactivity.

5 Propagation mechanisms

5.1 Olefin polymerisations It is generally accepted that many olefin polymerisations proceed through carbenium ion chain-carriers, and in these reactions the propagation consists simply of the successive additions of a carbenium ion to the double-bond of the monomer. However, there are also many systems in which the evidence indicates that the propagating species cannot be a carbenium ion. Such reactions have been termed ‘pseudo-cationic’ and in these polymerisations the propagating species is believed to be an ester. The most thoroughly investigated systems comprise aromatic monomers (styrene, acenaphthylene [11]) and protonic acids (HClO4) or iodine [11] as initiators. The simplest representation of the propagation is as the addition of the ester (stabilised by four styrene molecules) across the double-bond of the monomer [12]:

(n + 7)CH2:CHPh + HClO4 → CH3•CHPh(CH2•CHPh)nCH2CHPh•O•ClO3)4C8H 8 CH2 : CHPh

(11)

→ CH3•CHPh(CH2•CHPh)n+1 – CH2CHPh•O•ClO3)4C8 H 8 Although the ester mechanism is not yet generally accepted, the evidence accumulating since it was first put forward is in its favour, and the evidence which is alleged to be against it, or which has been interpreted in terms of ion-pairs in place of the ester, is certainly compatible with the ester theory [13, 14, 15]. We note in passing an interesting application of the polymerisation of styrene by perchloric acid: it was used as an indicatorreaction in the enthalpy titration of weak bases [16].

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Developments in the Theory of Cationoid Polymerisations

5.2 Polymerisation of heterocyclics As far as the polymerisation of heterocyclic compounds with one hetero-atom is concerned (cyclic ethers and their analogues) there seems little doubt at present that the propagation involves a displacement at the positive propagating centre. The ring which is part of this -onium ion is opened between the charged atom and a carbon atom next to it, and this becomes attached to the hetero-atom of the monomer:

(12)

However, for a variety of reasons it seems extremely unlikely that the same mechanism is applicable to the polymerisation of cyclic formals and acetals. One reason is that these compounds cannot be co-polymerised with cyclic ethers; another is that the polymers are predominantly cyclic, with the number of end-groups far smaller than the number of growing chains. One mechanism which has been proposed and which accounts for most of the observations involves formation of an oxonium ion (X) from the initiator and the monomer, and a subsequent propagation by a ring-expansion reaction (see 13). This mechanism is still controversial and it will be some time before a definite decision between it and the rival mechanism, which is analogous to reaction (12), can be made, but the current evidence is in favour of the ring-expansion. No decisive new facts have come to light since this controversy was reviewed [1g].

6 Conclusion This short review is necessarily rather selective and presents an individual point of view. The author hopes nonetheless that he has presented a fair picture and, even more important, that he has shown up the current uncertainties which are the growing points of the subject.

7 Acknowledgements The author wishes to thank the Polish Academy of Science for its great hospitality which gave him the chance to present the substance of this article as one of the lectures which

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(13)

he gave in Poland in the spring of 1972. He thanks especially Professor St. Penczek for arranging this visit, for his constant and thoughtful care, help, and advice, and for translating this article into Polish; and the Editor of Polimeri for permission to publish this article in the original English.

References It was thought unnecessary to give references to work earlier than 1961, since these will be found in the author’s book The Chemistry of Cationic Polymerisation. As far as later work is concerned, the references are not intended to be exhaustive, but were selected so as to give the reader an easy entry into the literature. 1.

a. Kennedy, J. P.; Langer, A. W. Fortschr. Hochpolym. Forsch. 1964, 3, 508. b. Pepper, D. C. in Olah, G. A. (Ed.) Friedel-Crafts and Related Reactions. Interscience, New York. 1964. c. Plesch, P. H.; Gandini, A. S.C.I Monograph No. 20, Society of Chemical Industry, London. 1966, p. 107.

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Developments in the Theory of Cationoid Polymerisations d. Plesch, P. H. Pure Appl. Chem. 1966, 12, 117. e. Kennedy, J. P. in Kennedy, J. P. and Toernquist E. G. M. (Eds.) Polymer Chemistry of Synthetic Elastomers, Part 1, Interscience, New York. 1968, p. 291. f. Plesch, P. H. in Robb, J. C. and Peaker, F. W. (Eds.) Progress in High Polymers, Vol. 2, Iliffe Books, London. 1968, p. 137. g. Plesch, P. H. I.U.P.A.C. Symp. on Macromol. Chem., Budapest. 1969, p. 213. h. Tsukamoto, A.; Vogl, O. Progr. Polym Sci. 1971, 3, 199. i. Plesch, P. H. Fortschr. Hochpolym. Forsch. 1971, 8, 137. j. Kennedy, J. P. J. Macromol. Sci. Chem. 1972, A6, 329. k. Kennedy, J. P.; Gillham, J. K. Fortschr. Hochpolym. Forsch. 1972, 10, 1. l. Plesch, P. H., Main Lecture, IUPAC Symp. on Macromols., Helsinki. 1972. To be published in Pure Appl. Chem. 2.

a. Goethals, E. J.; Drijvers, W. Makromolek. Chem. 1970, 136, 73. b. Drijvers, W.; Goethals, E. J. IUPAC Symp. on Macromols., Boston. 1971, Preprints p. 663.

3.

Evans, A. G.; Meadows, G. W. Trans. Faraday Soc. 1949, 4, 359.

4.

Plesch, P. H. J. Chem. Soc. 1950, 543.

5.

See References quoted in Reference 1(i).

6.

Kennedy, J. P. Trans. NY Acad. Sci., Series 11. 1966, 28, 1080.

7.

Razvodovskii, E. F.; Nekrasov, A. V.; Pushchyaeva, L. M.; Markevich, M. A.; Berlin, A. A.; Enikolopov, N. S. IUPAC Symp. on Macromols., Helsinki. 1972, Preprint 1-122.

8.

Schacht, E. H.; Goethals, E. J. Makromolek. Chem. (in press).

9.

Lapienis, G.; Penczek, S. IUPAC Symp. on Macromols., Helsinki. 1972, Preprint 1-11 2.

10. Jones, F. R.; Plesch, P. H. Chem. Comm. 1970, 1018. 11. a. Giusti, P.; Puce, G.; Andruzzi, F. Makromolek. Chem. 1966, 98,170. b. Cerrai, P.; Andruzzi, F.; Giusti, P. Makromolek. Chem. 1968, 117, 128. 12. Gandini. A.; Plesch. P. H. Eur. Polym. J. 1968, 4, 55. 13

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a. Darcy, L. E.; Millrine, W. P.; Pepper, D. C. Chem. Comm. 1968, 1441. b. MacCarthy, B.; Millrine, W. P.; Pepper, D. C. Chem. Comm. 1968, 1442.

Nature of the Propagating Species in Cationic Polymerisations (1973) 14. Masuda, T.; Higashimura, T. Polymer Letters 1972, 9, 783. 15. Hamann, S. D.; Murphy, A. J.; Solomon, D. H.; Willing, R. I. J. Macromol. Sci. Chem.1972, A6, 771. 16. Greenhow, E. J. Chem. Ind. 1972, 466.

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5.3

Propagation Rate-Constants in the Cationic Polymerisation of Alkenes (1984) P. H. Plesch

This paper was first published in Cationic Polymerization and Related Processes, Ed., E. J. Goethals, 1984, IUPAC. Reproduced with permission from IUPAC, copyright 1984.

Prologue In this review there is for the first time a comparative discussion of the three propagating species: the unpaired cation, the paired cation and the ester formed from the monomer and an acidic initiator. The relative kinetic importance of these three under different conditions of temperature and of solvent polarity are discussed qualitatively and by means of a three-term rate-equation. From these considerations are derived the optimum conditions for achieving a monoeidic system with the aim of obtaining kinetically simple reactions. It is also emphasised that an initiation reaction that is fast compared to the propagation, and the chemistry of which is known and simple, is essential for the unambiguous determination of propagation rate constants. The effect of the dielectric constant D on enieidic polymerisations is analysed algebraically, with emphasis on the very complicated effect of D on the degree of dissociation of ion-pairs. The relevance to polymerisation kinetics of the Keele group’s polarographic measurements on various triarylmethylium ions in different solvents {137} is explained. A fundamental re-evaluation of the experiments with nitrobenzene solvent given in Section 5.5 should be noted. In particular, the argument at the end of sub-section 2 here is invalidated because the participation of the cationated solvent molecules in the propagation makes the polymerisations in nitrobenzene dieidic.

1 Introduction No doubt some will say: ‘What - again?’, since I first reviewed this subject of propagation rate-constants in cationic polymerisations in 1971 [1] and discussed it briefly in 1973 [2]. Of the other reviews which have dealt with this subject thereafter, that by D. J. Dunn

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Developments in the Theory of Cationoid Polymerisations [3] scores most highly under the headings of ‘comprehensiveness’ and ‘critical quality’, but since then more claims to the measurement of kp values have appeared which also ought to be reviewed comprehensively and critically, but that will not be the subject of this paper. My reason for discussing the rate-constants again, is that I am no longer a spectator, but have some of our own results to present which are the first products of a fairly recent research line [4, 5]. Let us be clear at the outset that the object of measuring rate-constants is to understand the phenomena of polymerisation in terms of models and to use these for predictive calculations and for the more efficient design of experiments and of polymer production methods. Therefore, it seems appropriate to start by attempting some clarification of concepts, but at this point I am compelled to voice the feelings of Goethe’s Faust embarking upon his translation of the Gospel according to St. John: ‘Hier stock ich schon’ - vulgarly: ‘I’m stuck already’. I’m stuck because it is very hard to go beyond a formal and probably oversimplified model representing the cationic polymerisation of alkenes as a trieidic reaction in which the total rate of consumption of monomer is represented as the sum of three terms:

– dm / dt = ( kp+ [ Pp+ ] + kp± [ Pp+ A − ] + kpE [ E])m

(1)

Here the three (potentially) propagating species: unpaired ions Pn+, paired ions Pn+A- and esters E, are assigned characteristic rate-constants kp± and kpE. As long as one considers a group of related alkenes giving ions of similar structure, e.g., substituted styrenes, and a group of related solvents, e.g., alkyl chlorides, and the same (or similar) anionic moieties A-, one may be reasonably confident that in comparing rate-constants of whatever type, one is comparing like with like. However, I feel acutely that as soon as I attempt to venture beyond this safe position, I am attacked by severe doubts and misgivings as to the appropriate choice of model, as far as solvent and solvation effects are concerned. A complicating factor is that the three principal propagating species are affected differently [6] by changes in the nature of the solvent. With regard to the unpaired cations, one might take the simplistic view ‘an ion is an ion is an ion’ whatever its environment or the circumstances of its reaction and attempt to understand the reactivity of that unchanging species by means of conventional rate theory. The extreme alternative is almost nihilistic in regarding every ion in every different condition as a species sui generis, thus giving up all attempts at generalisation. The approach of the reasonable chemist is somewhere between these extremes and, because it requires judgement, is both more interesting and more hazardous than either extreme. One of the principal difficulties is that there is very little, if any, background information

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Propagation Rate-Constants in the Cationic Polymerisation of Alkenes (1984) from small molecule kinetics to draw on, since unpaired carbenium ions are rare except in the context of radiation chemistry, and the carbenium ions familiar to the organic chemist in, for example, solvolyses, generally have a short and simple life very different from our ions in aprotic media. What the ‘reasonable chemist’ is actually hoping for is a set of kp+ values for at least one monomer in a range of solvents so that ‘conventional’ rate-theory can be tested and if necessary modified appropriately; this will be discussed further below. With regard to ion-pairs, there is much more information both from small molecule kinetics and from the anionic polymerisations, but it must be remembered that the solvents usable for the latter cover only a very small range of polarities, and an effective ‘transfer of skills’ between the two domains remains to be achieved. The reactivity of esters as propagating species is a subject awaiting the attention of a physical-organic chemist. First, there is an urgent need for an experimental approach to the ionisation of esters of strong acids which is almost uncharted territory, and then the organic chemist’s knowledge concerning the reactions of acids and esters with alkenes needs to be exploited. An interesting start in that direction has been made by Sigwalt [7]. When looked at from that point of view, some useful information will probably be obtainable from the great mass of results from Higashimura’s school on polymerisations which, to my eye, are partly or completely pseudocationic, i.e., propagated by esters. Starting with Pepper’s pioneering results on the polymerisation of styrene by perchloric acid in different solvents there is by now a body of kpE which probably merits a careful comparative analysis. Since all three types of rate–constants are essentially affected by the same factors - although in a different way - it may be useful as a background to the following discussion to specify briefly the principal variables which are now known to affect the phenomenology of any cationic polymerisation; these include the following: i) The structure and polarity of the monomer. ii) The chemical nature and permittivity D of the solvent and the variation of D with temperature. iii) The reactivity and size of the anionic moiety of the initiator system. iv) The nature and concentration of potential cation or anion complexing compounds which include the monomer itself, any initiator precursors such as metal halides MtXn, and added electron donors or acceptors.

439

Developments in the Theory of Cationoid Polymerisations

2 Choice of reaction conditions I will illustrate some of the problems involved in selecting suitable systems by means of our recent results on the determination of the kp+ of acenaphthylene [4] and styrene [5] in nitrobenzene. In planning this work I aimed at realising a system of such a kind that there would be no doubt about the two most essential matters: 1) The initiation +

R + + CH 2 : CXY → RCH 2 C XY

(A)

must consume all the initiator in a time short compared to the half-life of the polymerisation; this means that the initiator must be a stable salt of a reactive carbocation dissolved in a polar solvent. The most abundant propagating species must be the unpaired cation, i.e., the dissociation constant KD of the ion-pairs must be so great that the ratio y/p = [Pn+]/[Pn+A-] would be greater than 10, and preferably greater than 102.

Pn+ A − ↔ Pn+ + A − , KD

(B)

From the relation between y/p and c/KD [2, 8] (c = [Pn+] + [Pn+A-]) it is seen that for y/p ~ 10, c/KD ~ 10-1, so that if c = 10-4 mol l-1, KD would need to be not less than ca. 10-3 mol l-1. In order to achieve an adequately large KD, the adjustment of three variables is at our disposal, which are summarised in the Bjerrum-Fuoss equation (2) relating KD to D, the temperature T, and a quantity a which is determined by the distance of closest approach of the ions when paired:

–lnK D = 3lna + A + B/DTa

(2)

where A and B contain only universal constants [9]. As the denominator of the second term increases, the KD increases. Thus this equation expresses quantitatively the common experience that KD is generally greater, the greater D is (at constant T), or the lower the temperature (which for most polar solvents increases the product DT), or the larger the ions concerned (larger a). When selecting our reaction conditions we chose the most polar readily available solvent of adequate inertness, nitrobenzene, which has D = 34.82 at 298 K. Although CH3NO2 with almost the same D and C2H5NO2 (D ~ 28) are much easier to purify and to handle in vacuo, they cannot be used as they are not inert to carbocation

440

Propagation Rate-Constants in the Cationic Polymerisation of Alkenes (1984) salts. The addition of almost any cationic initiator to either of these solvents usually gives a large exotherm. Having fixed on the very polar nitrobenzene, any advantage to be gained by increasing the size of the anion is relatively unimportant but it is fortunate that the most stable anion, SbF6- is also relatively large. Our work with acenaphthylene [4] having shown that the nature of the anion is not important for polymerisations in nitrobenzene, we then fixed upon the SbF6- as the most useful anion; the nature of the initiating cation is of course irrelevant for the nature of the propagating species and we have found PhCOSbF6 to be easily prepared, stable, and as ‘clean’ an initiator for alkene polymerisations as for oxacyclic monomers. It is a useful coincidence that the choice of a highly polar solvent for electrochemical reasons also has as a consequence that in such a solvent the rate of an ion-molecule reaction, as in the propagation step, characterised by kp+, is reduced considerably from what it is in a less polar solvent. This follows from Transition State Theory and has been explained in the present context [9, 10]. In my reasoning, if the ‘electrochemical imperative’ had not pointed to the use of the most polar solvent available, in order to obtain a monoeidic system, the ‘kinetic imperative’ - the need to have rates adequately low for convenient measurement would have dictated the same choice.

3 The determination of kp+ We concluded - and our experiments have confirmed - that by polymerising an alkene in PhNO2 with, say, PhCOSbF6 as initiator (Int) we have achieved a monoeidic system in which the following conditions are valid: initiation is fast and complete so that we have a Stationary State of the Second Kind, and the following equations should apply:

– dm / dt = kp+ [ Pn+ ]m

(3)

[ Pn+ ] = [Int ]o

(4)

[ Pn+ ] ∝ t

(5)

The relations (3) and (5) imply a first-order reaction:

– dm / dt = k1m

(6)

k1 = kp+ [ Pn+ ]

(7)

with

441

Developments in the Theory of Cationoid Polymerisations With acenaphthylene under the best conditions the polymerisations were of first order internally up to ca. 70% conversion and with styrene they were of first order during the entire reaction. This means that condition (5) was satisfied. The condition (4) is never exactly valid, because every chemical system contains some impurities which inactivate the initiator. Some of the impurities come from the walls of the vessel, some from the solvent, and some from the monomer. We have shown how these can be determined (4) and it will suffice here to correct the equation (4) to the more realistic form (8):

[ Pn+ ] = [Int ]o – γ

(8)

Generally, γ depends on the purification methods and is a function of the monomer concentration; ideally it should be reproducible and not greater than 10% of [Int]o. On a plot of k1 against [Int]o the intercept on the [Int]o axis (the ‘impurity intercept’) due to solvent impurities is usually the major part of γ, the contribution from impurities of other origins being much smaller. To test whether equation (8) applies, one needs to find out first whether k1 is rectilinearly related to [Int]o. If it is so over a reasonable range of concentrations, one needs to settle whether [Pn+l is equal to [Int]o or whether a constant fraction of the initiator is being consumed by side-reactions, e.g., by cationation of an aromatic ring. The way of doing this is to use several initiators: if they all give the same result it is unlikely that they are all equally inefficient and one concludes therefore that they are all completely efficient. This is what we did with acenaphthylene and the kp+ was then confirmed by another worker using yet another initiator (11). Another way is to count the initial groups, e.g., PhCO, in the polymer, as we did with styrene. Ideally, it is the [Pn+] rather than the completeness of consumption of the initiator that should be checked. This can be done by tagging the end by means of an easily distinguishable and determinable highly reactive base, a technique known as short-stopping or end-capping and many different methods of doing this have been devised. Regrettably, most seem to have been applied to unsuitable systems, because these methods will not distinguish between paired and unpaired cations, and probably most propagating esters are also attacked by these bases. The distinctive information provided by conductivity (κ) measurements in this context deserves special mention because the κ is determined only by unpaired ions. In our work with styrene we found that the κ rose to its maximum and then constant value κf in less than 2 s for reactions taking 30–300 s for completion. This means, first, that mixing and initiation are fast. Since the molar conductivity (Λ) of the salt is given by Λ(PhCO+) + Λ(SbF6-) and is ca. twice that of the propagating ions which is Λ(Pn+) + Λ(SbF6-), the Λ( Pn+) being very much lower than both Λ(SbF6-) and Λ(PhCO+), a slow initiation would produce an initially large κ as the phial of initiator is broken into the monomer solution and then a slow fall as the PhCO+ are converted

442

Propagation Rate-Constants in the Cationic Polymerisation of Alkenes (1984) to the much more slowly moving Pn+ = PhCO(CH2CHPh)mCH2CHPh+. Furthermore, since κf is rectilinearly related to [PhCO+] over a considerable concentration range, it follows that there 1 is no important degree of ion-pairing; if there were, κf would be a function of [PhCO+] /2. We can conclude that our kp+ values (Table 1) are essentially sound, but of course the uncertainty limits may be reduced by technical advances.

4 Some kp+ values and the factors affecting them The kp+ for styrene Having obtained what I believe to be a sound value of kp+ for styrene in nitrobenzene, it is appropriate to attempt a comparison with values obtained in other solvents and in bulk. As for the latter, the radiation results still show a scatter over 2 orders of magnitude (2 x 106 to 4 x 108 l mol-1 s-1) without there being any evident reasons for narrowing the range by dismissing either of the extremes; however, the more recent results seem to be grouped near the lower value (3). As for values in solvents with intermediate D, (ca. 10–15) only a very few of the many claims to have obtained kp+ in such solvents can be taken at face value and their critical evaluation is beyond the scope of this article. Suffice it to say that the most credible values appear to lie in the range 104 to 106 l mol-1 s-1 for chlorinated solvents of D ca. 10 and ca. 300 K. It is therefore much too early yet to discuss whether these kp+ values conform to any of the theoretical relations between the rate-constant of an ion-molecule reaction and some function of D such as that of Laidler and Landskroener [12] or Hiromi [13] (see also [14]).

Dieidic systems involving kp+ and kp± Next, we consider the case where the first-order rate constant of a polymerisation increases with the polarity of the solvent or solvent mixture. This effect was first observed by Pepper with α-methylstyrene [15] and thereafter by very many others and I have discussed it briefly and qualitatively [2]. If this happens the system cannot be ‘pure kp+’, but it must

Table 1 The kp+ for acenaphthylene and styrene in PhNO2 at 298 K kp+ / l mol-1 s-1

Acenaphthylene (4)

Styrene (5)

23 ± 2

188 ± 9

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Developments in the Theory of Cationoid Polymerisations be either pure kp± or kpE or an enieidic system of some kind. In the following analysis we will confine our attention to a dieidic system involving unpaired and paired ions. The k1 is then given by:

k1 = αckp+ + (1 – α )ckp±

(9)

where c is as defined above and α is related to KD by the usual relation:

K D = α 2 c /(1 – α )

(10)

and KD is related to D by equation (2). Evidently, the relation between α and D is very complicated and that between k1 and D is even worse. However, the effect of changing D on k1 can be seen as follows:

(1 / c)dk1 / dD = dkp+ / dD + (dkp± / dD)(1 – α ) + ( kp+ – kp± )dα / dD

(11)

The first two terms represent the effects of changing D on kp+ and kp± and they have opposite signs since increasing D increases the rate-constant of a dipole-dipole reaction (in contrast to its effect on kp+). The third term represents the effect of D on α which is that α increases with D; but as explained above, their relation is complicated. It is, however, clear that any increase of k1 with D is likely to arise from a multiplicity of interrelated causes and cannot be amenable to any simple interpretation; moreover, since equation (11) contains both positive and negative terms there is scope for k1 to increase or decrease with increasing D and indeed for a maximum or minimum. It must be emphasised in this context that changing T also changes D and that whereas both kp+ and kp± will be reduced by the normal activation energy effect, the concurrent increase in D will also decrease kp+ but will increase kp±, thus counteracting the thermal deceleration of the ion-pair propagation. It was the need to explain Arrhenius plots which have a minimum and kinked ‘Arrhenius’ plots of DP (for isobutylene in CH2Cl2, TiCl4, H2O) [16] that produced the first detailed treatment of the temperature-dependence of the rate and DP in terms of a dieidic polymerisation by paired and unpaired cations. Actually, dieidic systems involving paired and unpaired cations are probably by far the most common of all cationic polymerisations. As for the effect of changing solvent polarity on the reactivity of paired cations, this is very much smaller than on the unpaired ion for simple electrostatic energetic reasons: the charge density is so very much smaller and there is less space around both ions to accommodate

444

Propagation Rate-Constants in the Cationic Polymerisation of Alkenes (1984) oriented solvent molecules. This matter came to our notice during polarographic studies on carbenium ions [17]. As the results in Table 2 show, the difference ΔE1/2 in half wavepotential (measured against the E1/2 of the Ph3C+ ion) for (4-ClC6H4)3C+ is almost the same in MeCN (D = 37) as it is in CH2Cl2 (D = 9), and this is also true of the (4-MeOC6H4)3C+ ion. Since for any one ion in solvents I and II the ΔI–IIΔE1/2 is given by

FΔ I − II ΔE1 / 2 = Δ I − II ΔGsθ

(12)

(F = Faraday, ΔGsθ = standard free energy of solvation of the ion), the observed ΔE1/2 indicate the near-identity of the solvation energies in the two solvents. For comparison, we may calculate the ΔI–IIΔE1/2 for the same ions in the unpaired state by Abraham’s equation [18] and this gives a value between 0.1 and 0.2 V, the uncertainty being due to ambiguities about the significant dimensions of the triaryl methyl ions.

Complexation of growing ends The effects on rates and DP of complexing by various reagents with both cations and anions have been studied by many authors, and therefore once again there is scope for an analysis of the scattered and varied results. Here we can do little more than point out the consequences of the different types of complexation. The formation of a complex between the propagating end and one or more molecules of monomer can have two extreme consequences. If the incorporation of a monomer molecule from the solvation shell of the cation is the growth-rate determining step, the propagation becomes a unimolecular reaction and the rate of polymerisation becomes of zero order with respect to monomer concentration. Such a model was developed by

Table 2 E1/2/V for three triarylmethyl ions in two solvents Solvent

CH2Cl2 [17]

MeCN [19]

Ion

E1/2

ΔE1/2

ΔI-IIΔE1/2

E1/2

ΔE1/2

(4-ClC6H4)3C+

0.60

0.14

0.03

0.38

0.1 1

(C6H5)3C+

0.46

0.00

0.00

0.27

0.0 0

(4-MeOC6H4)3C+

0.00

–0.46

–0.01

–0.20

–0.47

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Developments in the Theory of Cationoid Polymerisations Fontana to explain the kinetics of the polymerisation of propene [20] and it has since been used by other authors. If the monomer molecules are fairly firmly attached to the growing end, as are the four styrene molecules which stabilise the propagating polystyrylperchlorate ester, then propagation remains of first order with respect to monomer; the depletion of the monomer causes the ester to ionise near the end of the reaction, and the resulting carbenium ion then consumes the residual monomer rapidly [21, 22]. Complexation by monomer will be most prevalent with polar monomers, e.g., alkyl vinyl ethers, and also with less polar monomers in solvents of low polarity and polarisability, such as alkanes, because in these conditions the monomer is the most polar or polarisable part of the system and thus primarily involved with the solvation of the ions. Complexation by reagents other than the monomer usually has several consequences: the reduction of the charge density by the complexant and the increase in the effective size of the ion will both increase the KD of the propagating ion-pair so that y/p increases; and also the unpaired ion is now ‘encumbered’ by something different from the solvent molecules which solvate it in the absence of complexant, and one cannot predict generally whether the balance of these effects will augment or diminish the propagation, transfer, and termination rates. In certain systems the initiator may have the dual role of producing the initiating cation and also of complexing with, and thus stabilising, the anion derived from it. In the recent literature the best documented example is the conjugation of the CF3SO3- ion (A-) with the parent acid AH to give A2H- [7]. This phenomenon, well known for a long time to occur in solvents of moderate polarity, also occurs in nitrobenzene and produced unresolvable ambiguities when we attempted to use CF3SO3H and HClO4 for the determination of kp+ [11]. Many attempts are on record to influence copolymerisation ratios, DP, and yields and their temperature coefficients by the addition of electron-donors or electronacceptors to reaction mixtures, the presumption being that the additives affect the nature and relative abundance of the chain-carriers (see for example [23]). The theory of most of these attempts is - to say the least - obscure. However, a detailed theoretical treatment has been given of the effect of a strong complexing agent on a pure kp± system and it was tested successfully in rationalising the effect of thiophene on the polymerisation of styrene by SnCl4 [24]; it would be desirable to test it on a wider range of systems.

446

Propagation Rate-Constants in the Cationic Polymerisation of Alkenes (1984)

5 Where do we go from here? Selection of initiators Having given a rather impressionistic analysis of where we are now with respect to kp determinations, a useful service can perhaps be rendered by specifying systems that are best avoided and, to be more positive, summarising what has emerged as useful. The basis of my arguments are largely the earlier parts of this paper and our analysis of how to improve initiators [25]. First, the complications arising from a multiplicity of propagating species can be reduced considerably if initiators are used which cannot form esters; in other words protonic oxo-acids and the mixed anhydrides and salts derived from them, such as triflates and perchlorates, are not useful for attempts to measure kp+ and kp± for three reasons: i) Except under very special conditions which can be recognised from the results of Pepper, Higashimura, and others, they do not give monoeidic systems (the main guide is the nature of the DPD curve). ii) In general, these systems are not stationary, i.e., the ratios [Pn+]: [Pn+A-]: [E] are not constant throughout the life of the polymerisations [22, 26]. iii) As mentioned above, the conjugation of the acids with their anions introduces a totally unnecessary - and almost irresolvable - uncertainty as to the effective concentration of the initiator. In order to rationalise and facilitate the selection of suitable initiators, we can apply to the initiation reaction (A) the Polanyi Principle [27] of the antibatic correlation between standard enthalpy ΔHθ of a reaction and its activation energy ΔH≠. We are thus led to select those initiating cations R+ which give the largest possible |ΔHθ| so as to obtain a correspondingly low ΔH≠ and thus a fast initiation. Our calculations have shown that from this point of view R+ = Ph2CH+ has an advantage of ca. 80 kJ/mol over Ph3C+ [25]. The low ΔH for Ph3C+, leading to a relatively high ΔH≠ gives slow initiations and therefore great scope for side-reactions. A significant improvement, easy to implement experimentally, can be obtained by using (4-ClC6H4)3C+ salts or PhCO+ salts; the former has the additional advantage that side-reactions involving attack on one of the phenyl groups are inhibited. It should be noted that Dorfman’s rates of addition of PhCH2+ and Ph2CH+ to alkenes point in the same direction, the former giving rates ca. twice those given by the latter [28].

447

Developments in the Theory of Cationoid Polymerisations A note on kp+ Several workers have attempted to use the ‘common ion’ technique to depress [Pn+] and thus to achieve a monoeidic Pn+A- system, as was done so successfully for anionic systems. However, because generally the solvents used for cationic polymerisations are much more polar, the KD of the chain-carriers and of the common-ion salts are considerably greater than in the anionic systems. Therefore the electro-chemical situation is likely to be complicated by triple ion formation and the effects of ionic strength on the KD and on the rate-constants, so that any results obtained by extrapolations to ‘infinite ionic strength’ need to be scrutinised most carefully.

Conclusion I hope that my analysis has clarified some obscure matters, helped colleagues to think along new lines, and indicated how further progress with the measurement of the different kinds of kp can be accelerated. I look forward to hearing of many new, soundly established results when we all meet again.

References 1.

P. H. Plesch, Advances in Polymer Science, 1971, 8, 137.

2.

P.H. Plesch, British Polymer Journal, 1973, 5, 1. (This paper contains the incorrect statement that kp± decreases with increasing D).

3.

D. J. Dunn, Developments in Polymerisation. (Ed. R. N. Haward) Applied Science Publ., London (1979), Vol. 1, p. 45.

4.

S. D. Pask, P. H. Plesch, and S. B. Kingston, Makromol. Chemistry, 1981, 82, 3031.

5.

G. E. Holdcroft and P. H. Plesch, submitted to Macromol. Chemistry.

6.

J. E. Gordon, The Organic Chemistry of Electrolyte Solutions, J Wiley and Sons, New York, (1975).

7.

P. Sigwalt and G. Sauvet, Polymer Journal, 12, 651 (1980).

8.

P. H. Plesch, Journal Polymer Sci. Symp., 56, 373 (1976).

9.

R. Fuoss, Journal of the American Chemical Society, 1958, 80, 5059.

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Propagation Rate-Constants in the Cationic Polymerisation of Alkenes (1984) 10. C. E. H. Bawn, C. Fitzimmons, A. Ledwith, J. Penfold, D. C. Sherrington, and J. A. Weightman, Polymer, 12, 119 (1971). 11. G. E. Holdcroft, Ph.D. Thesis, Keele (1983). 12. K. T. Laidler and P. A. Landskroener, Transactions of the Faraday Society, 1956, 52, 200. 13. K. Hiromi, Bulletin of the Chemical Society of Japan, 1960, 33, 1251. 14. S. G. Entelis and R. P. Tiger, Reaction Kinetics in the Liquid Phase, J. Wiley, New York (1976). 15. D. C. Pepper, Nature, 158, 789 (1946); Transactions of the Faraday Society, 45, 397 (1949). 16. R. R. Biddulph, P. H. Plesch, and P. P. Rutherford, Journal of the Chemical Society, 1965, 275. 17. P. H. Plesch, unpublished. 18. M. H. Abraham and J. Liszi, Journal of the Chemical Society, Faraday Transactions, 1978, I, 7, 1604; Journal of Chemical Physics, 1979, 70, 2491. 19. H. Volz and W. Lotsch, Tetrahedron Letters, 1969, 2275. 20. C. M. Fontana and G. A. Kidder, Journal of the American Chemical Society, 1948, 70, 3745. 21. A. Gandini and P. H. Plesch, Europ. Polymer Journal, 1968, 4, 55. 22. D. J. Dunn, E. Mathias, and P. H. Plesch, European Polymer Journal, 1976, 12, 1. 23. G. Heublein and R. Wondraczek, Journal Polym. Sci. Symp., 56, 359 (1976). 24. P. H. Plesch, Progress in High Polymers, Volume 2, Ed., J. C. Robb and F. Peaker, Iliffe Books Ltd., London, 1968, p.137. 25. S. D. Pask and P. H. Plesch, European Polymer Journal, 1982, 18, 839. 26. D. C. Pepper, Journal of Polymer Science Symp., 1976, 56, 39. 27. M. G. Evans and M. Polanyi, Transactions of the Faraday Society, 1936, 32, 1933; 1938, 34, 22. 28. Y. Wang and L. M. Dorfman, Macromolecules, 1980, 13, 63.

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Developments in the Theory of Cationoid Polymerisations

450

5.4

An Account of the Propagating Species in Cationic Polymerisations (1989) P. H. Plesch

This paper was first published in the European Polymer Journal, 1989, 25, 7/8, 875877. Reprinted with permission from Elsevier Science, Copyright 1989.

Prologue The present short inventory of possible propagating species in cationoid polymerisations was contributed to a ‘Festschrift’ for Professor J. C. Bevington. Since he made his reputation with the radical polymerisations, this writer thought it appropriate to contrast the paucity of radical-species with the ‘zoo’ of cationoid species, which have been his concern. There is here also a consideration of the properties of anions that may influence the course of cationic polymerisations. This enumeration should be useful for any beginner who will find his attention directed towards the most relevant parts of classical physical chemistry.

Abstract The different types of cations, anions, and other species likely to be involved in the cationoid polymerisations of alkenes are discussed, with special reference to their relative abundance under different conditions. In the context of this celebration which is dedicated to a distinguished radical monger, it may be useful to outline the intellectual plight of the cation mongers who are concerned with the polymerisations of alkenes. The essential features of radical chemistry seem to be determined principally by the relative strengths of chemical bonds and the activation energies of their rupture, with electrostatic effects, especially solvation energies, playing at most a secondary role. In contrast to this, the ion monger is always concerned with at least two charged species; one of these is responsible for the growth of the polymer chain and also chain-breaking and side reactions, and the other may influence critically the activities of the former. In addition, the elusive quality of a solvent, its polarity (natural or induced), influences all features of these polymerisations. Especially in weakly polar 451

Developments in the Theory of Cationoid Polymerisations or polarisable solvents, the intense electric field around cations (especially) causes strong interactions with all polar or polarisable constituents of the solution, which can influence profoundly the whole pattern of reaction. This means that in cationoid polymerisations the kinetic situation can be vastly more complicated than in radical polymerisations. As a result of the insights gained in the last ca. 40 years, we cation mongers must now reckon with very many different species of propagating centre, even after some ruthless wielding of Occam’s Razor. Since each of the species concerned will have its own rateconstants for propagation, transfers of various kinds, and terminations, and their relative abundance will be governed by a corresponding number of equilibrium constants, the potential ‘worst case’ complications can be imagined. This is the first occasion when this worst case has been set out explicitly, and it is done with the aim of clarifying a rather confused field. It must be understood, however, that in any one polymerisation system, the number of kinetically important species present simultaneously is unlikely to be greater than at most 3 or 4. Therefore the interested investigator should not be scared off, but should use his physico-chemical understanding to maximise the concentration of the most wanted species. The following enumeration aims to set out the author’s views without concern for priorities or current controversies or providing detailed justifications. We now recognise that when an ion R+, e.g., Ar2CH+, reacts with an alkene M, e.g., styrene or an alkylvinyl ether, in a solvent, the resultant growing carbenium ion RM+ (which forms the growing Pn+), and the inevitably present anion A− can form any or all of the species listed below. It is implicit in the symbol Pn+ that the ion is solvated by the solvent, and therefore only solvators other than the solvent will be specified; the solvation of the anion which has often been neglected, is almost equally important, and again solvation by the solvent will be implicit in the symbol A−. For brevity, the picture is presented essentially in electrostatic terms, but such effects as hydrogen bonding and charge-transfer interactions are deemed to be included. The propagating species, in order of increasing complexity, comprise 1. The cation Pn+, e.g., –CH2CMe2+ 2. The paired cation Pn+A-. The relative concentrations of the paired and unpaired cations are governed by an Ostwald-type equilibrium with dissociation constant KD. The magnitude of this is governed by the size and shape of the ions and the dielectric constant of the solvent. In contrast to anionic polymerisations, there is no definite evidence for distinguishing between ‘tight’ and ‘solvent-separated’ ion-pairs. 3. The monomer-solvated cation Pn+M. Although this species first appeared in 1948, its importance was not realised until comparatively recently. Provided that its

452

An Account of the Propagating Species in Cationic Polymerisations (1989) propagation rate-constant kp+M is less than that of the uncomplexed cation, kp+, the formation of this species by an equilibrium Pn+ + M ↔ Pn+M (equilibrium constant KM) can explain why an apparent propagation rate-constant, kpA, becomes greater, the smaller the [M] is. The potential trough responsible for the formation of Pn+M can have different origins, depending on the nature of M: for homo-alkenes, the interaction may be similar to that of Ag+ with a double-bond or an aromatic ring; for hetero-alkenes, such as alkyl vinyl ethers, it involves the much stronger C–O–C dipole. 4. The cation which is both solvated by M and paired: Pn+M·A-. Whichever way one thinks of this species, the positive charge-density of the Pn+M is low compared to that of Pn+ so that for this reason and because of the mass-action effect the abundance of Pn+M·A- is likely to be much less than those of Pn+A- and Pn+M. 5. Unless the monomer contains a hetero-atom, the polymer is likely to be much less polar and polarisable than the monomer and the solvent and therefore negligible as an ion solvator; but for monomers such as p-MeO-styrene, the alkyl vinyl ethers, or N-vinylcarbazole, the polarity of their polymers is such that they can make a significant contribution to the solvation of Pn+, especially if the solvent is of low polarity. Therefore the species Pn+Pm and, presumably, Pn+PmA- must be considered as parts of the ionic population in certain systems. 6. If the nature of the anion is such that the cation can form an ester with it, then under appropriate conditions this ester can be a cationoid propagating species, producing a pseudo-cationic polymerisation. The best known example is poly(styryl) perchlorate –CH2-CPhH-OClO3. The propagation takes place by the insertion of the monomer into the C-O bond. This system is exceptional in that this very unstable ester falls apart into ions rapidly unless it is stabilised by monomer. The more usual pattern is that an ester, such as poly(alkylvinyl ether) trifluoroacetate, needs to be activated by protonation, or the corresponding iodide which needs to be activated, e.g., by I2, so that the propagating species is –CH2CH(OR)I·I2. The growth occurs by the insertion of the monomer into the C–I bond, and this type of system can be so stable as to produce living polymerisations. A possible variant on the ester theme may be the formation of highly polar complexes from metal halides and water: Pn+ + SnCl4OH- → PnOH.SnCl4, with growth taking place by the insertion of the monomer into the C-O bond of the polymeric carbinol activated by the metal halide. If this idea proves to be useful, the mechanism would be clearly related to the pseudo-cationic syncatalytic systems comprising BCl3 and an ester, which can yield living polymerisations.

453

Developments in the Theory of Cationoid Polymerisations Whereas all the species mentioned under (1) to (5) are involved in normal equilibria, it is a peculiar feature of pseudo-cationic systems that the esters are generally formed rapidly, in some systems by the observable collapse of an ion-pair, and then remain stable until the end of the polymerisation, or ionise slowly and irreversibly, forming propagating cations. This is one example of how the ionic population may change during the course of a polymerisation. 7. As far as the anions are concerned, some form of homo-conjugation is the most common variant. For example, the poor efficiency of many oxo-acids AH as initiators is (partly) due to the formation of the homo-conjugate anion A2H-. Evidently, because the effective size of the A2H- ion is greater and its charge density less than for A-, its ion-pair formation constant will be smaller. 8. In the presence of deliberately added electron-acceptors, X, e.g., tetracyanoethylene, the anion forms a complex XA-. Because of the greater size and lower charge-density of this complex anion, the fraction of unpaired cations will be increased, with consequent effects on rate, DP, copolymerisation ratios, tacticity, etc., of the polymers. The list may yet be incomplete, but it involves nothing that is not familiar from other parts of chemistry and is free from any ad hoc inventions. It helps one to realise that most cationoid polymerisations under most conditions are likely to be eniedic and that consequently the rate equations will contain several terms. Therefore the corresponding propagation rate-constant is an ‘apparent’, composite quantity, difficult to define, and consequently any alleged measurements of this kpA or its components are likely to be doubtful; thus one can understand the wide discrepancies in the reported values of alleged ‘kp+’. So where does our analysis leave the investigator? Not necessarily ‘up the creek without a paddle’; we can adapt Mme. de Stael’s famous phrase to ‘Tout comprendre, c’est tout controller’. The object of understanding is mastery, and once we are aware of the physicochemical influences at work in the cationoid systems, we can attempt to adjust the conditions in such a way that we achieve monoeidic systems on which we can make unambiguous measurements. Another aspect of chemical mastery is the ability to make wanted products, and if we understand the factors influencing the composition of the ionic population, it will be possible to make materials of different tacticity, DPD, etc., from the same monomer, and quite different copolymers from the same two monomers, by a well-informed choice of reaction conditions.

454

5.5

The Propagation Rate Constants of the Cationic Polymerisation of Alkenes - Part III. Indene, Two Vinyl Ethers and General Discussion* (1990) P. H. Plesch and S. H. Shamlian

This paper was first published in European Polymer Journal, 1990, 26, 10, 1113-1120. Reproduced with permission from Elsevier Publishers, copyright 1990.

Prologue to Sections 5.5 and 5.6 These two papers, which belong together, will be introduced together. The first work records the author’s final experimental venture in the quest for the elusive kp+ and a summing-up of the results obtained with five monomers in nitrobenzene solvent [116, 125, 142]. He has followed his own advice with regard to choosing initiators which give very fast initiation, has monitored the ionic population by conductivity measurements during the reactions, correlated the kp+ values with the (partly new) polymerisation enthalpies for the five monomers and in other ways had squeezed from the results all that they could yield, including some un-understood facts - except the last drop. In particular, he had concluded through some detailed arguments that rate-constants are genuine kp+. The ‘last drop’, however, which was squeezed from the results became the core of the second paper, and it contains the clues to the falsification of his conclusion; and because it eventually led to a fruitful new insight, it was not a bitter drop. At the instigation of two critical and knowledgeable colleagues this author re-examined his justification of the unexpected smallness of the alleged kp+ and realised that he had wrongly ‘explained away’ the effects of the strong basicity of his chosen solvent, nitrobenzene. When he then took into account the cationation of nitrobenzene he realised that propagation by the resulting cation most plausibly involved a cyclic transition state, similar to that involved in living cationoid insertion polymerisations. This new mechanism proved to be a useful innovation because it also accounted very plausibly for other previously unexplained phenomena and it was developed further in a subsequent critical review of his own results [144]. * Refs [1] and [2] are Parts I and II of this series. These papers together show convincingly how useful it can be to publish all sound results, irrespective of whether one understands them.

455

Commercial rubbers

Developments in the Theory of Cationoid Polymerisations Regrettably, the insight and new understanding provided by Section 5.6 invalidate the calculation and conclusion in the last paragraph of Section 5.5. This is because we know too little about the propagating species in polymerisations initiated by SnCl4 in nitrobenzene.

Abstract We report on the measurement of the propagation rate constants kp+ of styrene, indene, phenyl vinyl ether (PhViE) and 2-chloroethyl vinyl ether (CEViE) in nitrobenzene at (mostly) 298 K with 4-ClC6H4CO+SbF-6 as initiator. The dependence of the conductivity on the [4-ClC6H4CO+SbF-6] = c0 helped to establish that [Pn+] = c0 and thus to validate the foundation of this work. It is shown that most probably the propagating species are the uncomplexed, unpaired, solvated carbenium ions. Some new enthalpies of polymerisation have been found.

Monomer

Styrene

Indene

PhViE

CEViE

kp+/dm3·mol-1·s-1

195 ± 15

373 ± 15

1450 ± 200

ca. 104

–ΔHp/kJ·mol-1

64 ± 2.5

56 ± 0.5

110 ± 10

80 ± 8

Introduction This is the third report on attempts to measure the propagation rate constant, kp+, for the cationic polymerisation of various monomers in nitrobenzene by reaction calorimetry. The first two were concerned with acenaphthylene (ACN) [1, 2] and styrene [2]. The present work is concerned with attempts to extend the method to more rapidly polymerising monomers. With these we were working at the limits of the calorimetric technique [3] and therefore consistent kinetic results could be obtained only for indene and for phenyl vinyl ether (PhViE), the slowest of the vinyl ethers; 2-chloroethyl vinyl ether (CEViE) proved to be so reactive that only a rough estimate of kp+ could be obtained. Most of our results were obtained with 4-chlorobenzoyl hexafluoroantimonate (1), and some with tris-(4-chlorophenyl)methyl hexafluorophosphate (2). A general discussion of the significance of all the kp+ values obtained in this work is presented.

456

Indene, Two Vinyl Ethers and General Discussion (1990)

Experimental procedures

Materials Solvents. For the early part of the work, nitrobenzene was purified as described [1, 2] and with this solvent, which had a conductivity of 10-6 S⋅m-1, ‘impurity intercepts’ of ca 2 x 10-4 mol⋅dm-3 were obtained, similar to those found in previous work [1, 2]. However, since we needed to use very low initiator concentrations because of the high reactivity of the monomers which we were aiming to study, we eventually found a method of reducing the impurity level in the nitrobenzene by about the required factor of 10. The improved method consists of crystallising the PhNO2 thrice, then distilling it in vacuo with a temperature not above ca 50 °C, stirring the distillate with well-baked Al2O3 for ca 10 h, and filtering it in vacuo into a reservoir which was then fused to a gravity-fed vacuum burette. The conductivity was still ca 10-6 S⋅m-1, but the ‘impurity intercept’ for polymerisations carried out in this solvent was ca 1/10 of the previous value. (The ‘impurity intercept’, ci, is the intercept on the c0-axis of a plot of the first-order rate constant k1 versus c0, the concentration of initiator. It represents the quantity of initiator rendered ineffective by adventitious impurities.) EtNO2 was fractionally distilled and the last 15%, which was free from impurities detectable by gas liquid chromatography (GLC), was stirred with baked Na2SO4 in a reservoir attached to the vacuum line.

Initiators Compound (1) was prepared conventionally from 4-chlorobenzoyl fluoride and SbF5 and dissolved in EtNO2. The solution was distributed into phials by the usual tipping device [4]; the content of the phials was obtained by the mid-point method [4, 5], and the initiator concentration was determined as described [2].

Monomers Styrene was purified and dosed as described [2]. Indene (99% + pure, Aldrich, Gold Label) was dried on CaH2 and dosed into evacuated phials. Ethyl vinyl ether and CEViE were Aldrich products. They were dried on CaH2 and used without further treatment. PhViE was prepared and purified essentially according to the method described [6] and stored over CaH2.

457

Developments in the Theory of Cationoid Polymerisations

Apparatus and procedure All the kinetic experiments were done either in the original Pask-Plesch calorimeter [3] of ca 35 ml capacity or in a larger apparatus of the same design with a capacity of ca 90 ml. The output from the ‘Grapple’ linear resistance bridge [7] was fed to a chart-recorder. For the experiments with styrene and indene, an instrument with a maximum speed of 20 cm⋅min-1 was used, but for the vinyl ethers a faster instrument with a maximum chart speed of 100 cm⋅min-1 was required. The signal from a WPA Scientific Instrument CMD 400 digital conductivity meter was fed to another recorder. At the end of each experiment, the electrical conductivity, κf, of the reaction mixture was determined accurately with a Wayne-Kerr Autobalance bridge. The CEViE was distilled into the calorimeter from a hanging burette; the other monomers were charged into breakable phials which were placed into the phial-magazine of the calorimeter in such a way that first the monomer phial and then the initiator phial could be pushed by a magnet into the breaking tube. After the phial-magazine had been charged with the required phials, the calorimeter was evacuated for several hours; if a volatile monomer was to be used it was distilled in, and the nitrobenzene was added from its reservoir. Then the jacket of the calorimeter was evacuated, the phial of monomer (if a monomer of low volatility was being used) was pushed into the breaker-tube and broken, and then the phial of initiator was pushed into the breaker-tube. When the temperature was constant (usually at 298 or 283 K), the phial of initiator was broken and the breaker dropped rapidly a second time to help the mixing-in of the initiator solution. If all went well, the conductivity rose from the initial, very low, level without acceleration to a maximum and constant value in less than ca 5 seconds (90% in 3 seconds), and this time was the best-possible indication that the speed of mixing-in of the initiator was adequate. Further, it shows that the rate of initiation was also great enough, because if this had been too low, the initially high conductivity would have fallen noticeably as the small, fast initiating cations were replaced by the large, slow oligomeric and polymeric cations. The temperature record showed a more variable pattern. For the relatively slowly polymerising styrene and indene, the initial reaction rate was always so much less than the rate of mixing-in of the initiator solution, even with high initiator concentrations, that the reaction curves showed good first-order behaviour from the start. For the more reactive monomers, all the reaction curves were sigmoid, with a marked but variable acceleration lasting rarely more than 3 seconds. The behaviour of the conductivity mentioned above indicates that this is not due to the slowness of the initiation reaction,

458

Indene, Two Vinyl Ethers and General Discussion (1990) but is an artefact due to a slight delay in the thermal equilibration between the solution and the hardware. Since only the part of the reaction curve beyond the inflection point was of first-order and since there was thus less of the reaction curve to analyse, the resulting first-order rate constants, k1, for these monomers are less accurate. The reaction curves, together with a conventional electrical calibration, also yielded an enthalpy. From this and the initial concentration of monomer, m0, and the quantity of unreacted monomer determined by GLC (always less than ca 5%), the enthalpy of polymerisation, ΔHp, was calculated. The final conductivity, κf, and the slope of its plot against c0, which is the final molar conductivity Λf, proved to be very useful diagnostic quantities. After the polymerisations were complete, the mixtures were quenched by crushing a phial of quenching agent, the product was made more tractable by evaporating off most of the solvent, and it was then treated as appropriate. The polymers precipitable in aqueous EtOH (polystyrene and polyindene) were isolated by precipitation, washed and prepared for analysis. The poly (vinyl ethers) were isolated by pumping off the solvent at ca 40 °C, redissolving the polymers in a more volatile solvent and then pumping that away. All the products were sent to Rapra Technology Limited for determination of the DP and DPD by GPC with poly(styrene) standard.

Results General introduction Provided that the time-temperature curve obtained from the calorimetric experiments is wholly of first-order, or comprises a first-order section, usually after the inflection point of sigmoid reaction curves, a conventional analysis yields a first-order rate constant k1, which is related to the concentration of monomer, m, and the initial concentration of initiator, c0, by the equations

– dm / dt = k1m = k2 (co – ci )m

(1)

where ci is the ‘impurity intercept’; and if

[ Pn+ ] = co – ci

(2)

459

Developments in the Theory of Cationoid Polymerisations then

k2 = kp+ = k1 /(co – ci )

(3)

Before kp+ can be calculated for any system, the validity of equation (2) needs to be established. Also, as pointed out previously [2], it may be that ci is a composite quantity, comprising impurities in the solvent and in the monomer (and possibly also the initiator solution). In the present work the high reactivity of the monomers gave little scope for varying m0, since m0 < 0.1 mol⋅dm-3 would have given a low DP and too little polymer to be analysed, and m0 > ca 0.2-0.4 mol⋅dm-3 (depending on the monomer) would give too fast reactions, even with the lowest usable c0. Therefore the question of impurities in the monomers could not be investigated by our suggested method [2], and so all impurities are comprised in the ci term. The success of our improved purification technique in reducing ci to ~0 (i.e. <10-5 mol⋅dm-3) indicates that at least the purity of the PhViE was adequate. Some exploratory experiments with ethyl vinyl ether showed that it polymerised too rapidly for our method to be useful. The polymerisation of 2-methyl butene-2 had a manageable rate but the results showed inconsistencies which we did not have time to resolve, as this was the last monomer to be studied.

Styrene In order to establish a correlation with the previous results, a few runs were done with styrene and (1) as initiator. The results are collected in Table 1 and shown in Figure 1. The plot gives ci = 1.3 x 10-4 mol⋅dm3 and kp+ = 212 ± 10 dm3⋅mol-1⋅s-1 compatible with our previous [2] value of 188 ± 9 dm3⋅mol-1⋅s-1, giving a weighted mean best value of 195 ± 15 dm3⋅mol-1⋅s-1. The agreement of the two values obtained by different workers with different apparatus establishes the continuity of the present results with those obtained

Table 1 The polymerisation of styrene by (1) in PhNO2 at 298 K Exp. No. 104c0/mol·dm-3 104κf/S·m-1

102k1/s-1

–Δ ΔHp/kJ·mol-1

DPn

DPw

37

4.13

7.28

6.11

60.6

22

46

38

6.32

10.88

11.72

65.8

25

48

34

6.70

11.22

10.64

64.3

25

46

m0 = 0.2 mol·dm-3 Averages DPw/DPn = 1.94

460

Indene, Two Vinyl Ethers and General Discussion (1990)

Figure 1 The first-order rate constant, k1, and the final conductivity, κf, for the polymerisation of styrene by (1) in PhNO2 at 298 K, as functions of c0 = [(1)]

earlier. The average ΔHp = –63.6 ± 2.5 kJ⋅mol-1 is compatible with the previously determined value of –67.3 ± 1.8 kJ⋅mol-1 obtained for polymerisations in CH2Cl2 [8]. All the polystyrenes had unimodal DPD. This finding and the average DP n = 24, agree with previous findings: DP w / DP n = 1.94. Λf = (1.73 ± 0.05) x 10-3 S⋅m2⋅mol-1 is close to the value (1.84 x 10-3S⋅m2⋅mol-1) which can be calculated from Figure 3 of Reference [2] and the theoretical value - see Discussion.

Indene The results for indene are shown in Table 2 and Figures 2 and 3. The results of line A of Figure 2 were obtained with PhNO2 purified in the same way as that used for the styrene; the line B results were obtained with PhNO2 dried by the improved technique. The lines

461

Developments in the Theory of Cationoid Polymerisations

Table 2 The polymerisation of indene by (1) in PhNO2 at 293 K 104c0/mol·dm-3

104κf/S·m-1

102k1/s-1

–Δ ΔHp/kJ·mol-1

DPn

DPw

DPw / DPn

40

5.4

12.6

8.2

56.5

29

104

3.6

39

7.2

16.7

13.0

56.6

33

101

3.1

42

10.4

23.5

27.6

57.0

26

101

3.9

41

13.2

28.6

65.2

—

32

104

3.2

66

3. 5

6.8

7.15

54.3

33

109

3.3

64

5.0

10.8

13.6

56.4

28

94

3.3

56

8.2

18.2

24.5

(63.6)

29

96

3.3

65

8.9

21.1

46.5

58.4

34

100

2.9

56.5

30

10 1

3.3

Exp. No.

Average

m0 = 0.2 mol·dm-3 Experiments (39-42) with standard dried PhNO2, experiments (56, 64-66) with PhNO2 purified further (see text)

have the same slope, giving kp+ = 373 ± 15 dm3⋅mol-1⋅s-1. In this calculation the two points representing very high rates have been ignored, as they may be artefacts due to the apparatus working near the limit of its range; but the fact that this apparent anomaly occurred twice may be significant. However, the plot of Λf against c0 (Figure 3) shows these experiments to have been normal with regard to the initiator concentration, and the ΔHp of the one of these experiments for which this is available, also shows no abnormality. The average enthalpy of polymerisation is ΔHp = –56.5 ± 0.6 kJ⋅mol-1 (if the ΔHp of experiment 56 is ignored). This value is compatible with the two values obtained in CH2Cl2, –58.1 ± 2.5 at 203 K [9] and –55.7 at 263 K [10]. All the DPD curves were unimodal. The DP shows no drift with c0, nor is it affected by the further purification of the solvent. DP n = 30 ± 4; DP w / DP n = 3.3 is remarkably constant. The conductivity plot, Figure 3, shows that the improved purification technique for PhNO2 did not affect the conductivity of the polymerisation product, and the fact that it does not give an impurity intercept but goes very close to the origin indicates that the neutralisation reaction of the impurities with the initiator yields ionic reaction products. Λf = 2.6 x 10-3⋅S⋅m2⋅mol-1. 462

Indene, Two Vinyl Ethers and General Discussion (1990)

Figure 2 The k1 as a function of c0 for the polymerisation of indene by (1) in PhNO2 at 298 K. Line A, PhNO2 purified by the standard method; line B, PhNO2 subjected to further drying (see text)

Phenyl vinyl ether The results obtained with PhViE in the ‘extra dry’ PhNO2 are listed in Table 3 and are plotted in Figures 4–6. All the reaction curves were sigmoid and k1 was evaluated by the usual first-order analysis of the reaction curves beyond the inflection point (line A in Figure 4) and also from the relation

463

Developments in the Theory of Cationoid Polymerisations

Figure 3 Plot of κf against c0 for the polymerisation of indene by (1) in PhNO2. O as for line A, Δ as for line B in Figure 2

Figure 4 The dependence of k1 on c0 for the polymerisation of PhViE by (1) in PhNO2. Line A corresponds to column (a), line B to column (b) in Table 3

464

1.83

1.95

2.80

3.43

3.74

9.77

94

95

96

97

92

91 0.10

0.11

0.13

0.15

0.10

0.10

0.10

mo/mol·dm-3

22.1

6.16

7.36

6.44

4.41

4.49

4.03

104kf/S·m-1

10.1

4.23

3.00

4.25

2.30

2.72

1.9

a

14.1

6.0

5.0

5.5

3.2

3.0

3.2

b

110

120

119

10 5

110

108

10 6

101

–Δ ΔHp/kJ·mol-1

: k1 obtained by first-order analysis of the reaction curves beyond their inflection point : k1 calculated from Rmax as described in the text, equation (4)

b

a

Average

1.44

104co/mol·dm-3

93

Exp. No.

10k1/s-1

6.1

7.1

6.1

6.25

6.4

5.7

5.8

5.25

DPn

9.5

10.9

9.2

10.1

10.5

9.2

9.3

7.7

DPw

Table 3 The polymerisation of phenyl vinyl ether by (1) in PhNO2 at 293 K

1.57

1.53

1.50

1.62

1.63

1.61

1.61

1.47

DPw / DPn

Indene, Two Vinyl Ethers and General Discussion (1990)

465

Developments in the Theory of Cationoid Polymerisations

Figure 5 The dependence of κf on c0 as for Figure 4

Rmax = k1mmax

(4)

where Rmax and mmax are, the rate and the m at the inflection point of the sigmoid reaction curves, respectively. Experiment 91 with an exceptionally high c0 has been left off the plots in Figure 4 to keep its scale reasonable, but the corresponding points fall close to the lines A and B. The scatter in the plots is partly due to the very great rate of reaction,

466

Indene, Two Vinyl Ethers and General Discussion (1990)

Figure 6 The dependence of the enthalpy of polymerisation on DPn of the polymer, as for Figure 4

the uncertainties arising from having only a part of the reaction curve available for analysis, and especially the necessity to use very low c0 in order to obtain manageable reaction rates. The consequence is that, even with the specially purified PhNO2 with no ci detectable from Figure 4, one is still working with initiator concentrations uncomfortably close to the necessarily rather irreproducible, although very small, ci. The effect involved can be illustrated thus: Figure 3 and Figure 3 of Reference [2] show that the κf plot is normally a good straight line and Figure 5 confirms this, except that one point (experiment 92) is off the line. If we take this to indicate that the actual c0 was smaller by 1 x 10-4 mol⋅dm-3 than the nominal value, and move the corresponding points in Figure 4 to their new ordinate, the scatter is reduced. If equal weight is given to the lines, they yield the best value for kp+ = 1450 ± 200 dm3⋅mol-1⋅s-1. The enthalpy of polymerisation also shows a scatter, probably mainly due to instrument errors, and the best value is ΔHp = –110 ± 10 kJ⋅mol-1; no other measurements of this quantity appear to be available. A curiosity, difficult to understand if proved to be genuine, is that ⎪ΔHp⎪ appears to increase slightly with increasing DP n , see Figure 6; for sterically hindered polymers, such as isobutene and α-methylstyrene, the opposite trend prevails, with ⎪ΔHp⎪ decreasing asymptotically with increasing DP n from that for dimerisation to that for the formation of high polymer. The only trend of the ΔHp is that just mentioned, and it shows no trend with c0, k1, or k1/c0. This is an adequate justification for using reaction calorimetry to obtain kp+, despite the reaction products being oligomers.

467

Developments in the Theory of Cationoid Polymerisations The average DP n = 6 but the variations of c0 and m0 are insufficient to establish by means of Mayo plots what kind of chain breaking process is responsible for this low value. The DPD are unimodal, and as for indene, DP w / DP n is very consistent but very much lower (1. 57 ± 0.05). The Λf = 2.26 x 10-3S⋅m2⋅mol-1 (Figure 5).

2-Chloroethyl vinyl ether CEViE was the first vinyl ether whose polymerisation was attempted in this work. With the initiator (2) dissolved in PhNO2, manageable reaction rates and reasonably consistent values of k1/c0, were obtained (Table 4). However, when we attempted to check these results by means of the initiator (1), the reactions were uncontrollably fast and, as is seen from the last two entries in Table 4, k1/c0 is ca ten times as great as with the other initiator, so that we can only say that kp+ is of the order of 104dm3⋅mol-1⋅s-1. Work with this monomer was abandoned. The inefficiency of the initiator (2) is noteworthy. A new feature is that the DPD of the polymers is bimodal, for both initiators. The evidence is insufficient to construct an explanation, and the phenomenon appears to merit further study (Figure 7).

Figure 7 Examples of the bimodal DPD curves for poly(2-chloroethyl vinyl ether) obtained with (4-ClC6H4)3C+ PF6- (curve a, experiment 24) and with 4-ClC6H4CO+ SbF6- (curve b, experiment 74)

468

21

11

9

10

7

9

21

23

24

28

73

74

(1)

(2)

Int.a

1.05

0.35

3.70

2.63

1.26

2.94

33.2

104co/mol·dm-3

0.10

0.10

0.10

0.11

0.11

0.23

0.20

mo/mol·dm-3

1.0

0. 7

0.38

0.36

0.22

0.20

0.37

k1/s-1

1

2

0.10

0.14

0.17

0.07

0.01

(10k1/co)/dm3·mol-1·s

: Initiator, (4-ClC6H4)3C+PF6- (2); initiator, 4-ClC6H4CO+ SbF6- (1) : H and L designate the DPn corresponding to the two peaks of the DPD

b

a

Average

20

T (°C)

20

Exp. No.

Table 4 The polymerisation of CEViE in PhNO2

80 ± 8

75

71

87

86

–Δ ΔHp/kJ·mol-1

/ 38

107

/ 40

122 / 50

103 / 38

89

113 / 36

DPnb H / L

Indene, Two Vinyl Ethers and General Discussion (1990)

469

Developments in the Theory of Cationoid Polymerisations ΔHp = -80 ± 8 kJ⋅mol-1 is to be compared with the values of Ledwith et al.: – 80.5 + 6 at 0 °C and –61.5 ± 10 at 11.8 °C [11].

Discussion The following discussion will deal with all the results of this series of experiments which are collected in Table 5.

1 The ionic conductivity after polymerisation The ionic conductivity at the end of a polymerisation is due to whatever cations Pn+ are formed or left when the monomer is exhausted and the anions A– of the initiating salt, plus a very minor contribution from the ions formed from impurities, which will be ignored. In order to analyse the relation between the observed κf, c0 and the ionic conductivity Λi of the electrolyte, it is necessary to clarify the electrochemistry of the solutions. We note first that the polymeric cations, whatever their structure, (i.e., as they were when propagating or subsequently isomerised), are much larger than the anions, SbF6, so that these carry virtually all the current so that Λi ≈ λ (SbF6), and therefore Λi can be calculated-see below. Next, we note that all the κf – c0 plots, including that reported earlier [2], are rectilinear. This means: a) that the extent of formation of ion-pairs must be negligibly small over the whole range of c0; and b) that the only ionic equilibrium which can prevail in these solutions is the binary ionogenic equilibrium (BIE)

Pn+ + MtX-n+1 ↔ PnX + MtXn, K11 for which Λf is given by the following equation [13]:

Λ f = κ f / c o = K111/ 2 Λ i /(1 + K111/ 2 )

(5)

If Λi ≈ λ (SbF6-), as explained above, we can estimate it from the Stokes-Einstein equation for univalent ions

λ i = F 2 / 6 πLri η

(6)

where F = Faraday’s constant, L = Avogadro’s constant, ri is the radius of the ion, and η is the viscosity of the solvent. For PhNO2 at 25 °C (η = 1.811⋅10-3 Pa⋅s) and ri = 250 pm, the 470

25

Styrene

20

7-21

PhViE

CEViE

0.1–0.2

b

: Reference [12], in CH2Cl2 : This work c : Bimodal DPD

a

0.2

20

lndene

0.1–0.15

Best value

Styrene

0.2

0.065–0.5

25

Styrene

0.5

Best value

25

ACN

0.1–0.5

mo/mol·dm-3

ACN

25

T (°C)

ACN

Monomer

0.35–33

1.4–10

3–9

4–7

2–9

2–30

2–14

104co

6-10 —

23.3 ± 2 23.2 ± 2

24

212 ± 10

30 6 107H-40Lc

373 ± 15 1450 ± 200 ca. 104

195 ± 15

26

188 ± 9

23 ± 2

DPn

kp+/dm3·mol-1s-1

1.57

3.3

1.94

—

—

n

/ DP

—

DPw

2.26 —

80 ± 8

2. 6

1.72

1.84

—

—

103Λf/S·m2 mol-1

110 ± 10

56.5 ± 0.6

63.6 ± 2.5

—

—

85.4 ± 2a

–Δ ΔHp/kJ·mol-1

Table 5 Summary of results from this work and the previous papers [1, 2]

b

b

b

b

[2]

[2]

[1]

Ref

Indene, Two Vinyl Ethers and General Discussion (1990)

471

Developments in the Theory of Cationoid Polymerisations λ (SbF6-) = 1.81⋅10-3 S⋅m2⋅mol-l, which agrees well with the experimental values from the styrene polymerisations, and it means that K11 >> 1, i.e., the ionisation is virtually complete. The calculation also shows that [SbF6-] = c0, therefore the concentration of cations must be the same; since the smallness of the impurity intercepts shows that the wastage of cations is insignificant, we can accept this as evidence that the fundamental assumption of this work, expressed by equation (2), is valid. The two somewhat greater values of Λf for indene and PhViE cannot be explained at present, since K/(1 + K ) cannot be greater than unity. They cannot be due to the slightly lower temperature, since this would increase η and thus reduce Λi. If a reinvestigation confirms this phenomenon, its cause may be sought in the formation of small cations which can contribute noticeably to Λi during the final phase of the polymerisation, e.g., protonated monomer generated by proton transfer from growing cations.

2 The state of the cations in solution The significance of the second-order rate constants, which we believe to be kp+, needs some discussion. As has been shown above, one can have considerable confidence that, in all the experiments of this series, the propagating species are unpaired cations and that their concentration is very close to that of the initiator. Therefore the only question still needing clarification is that of the state of these cations in solution. This problem has been discussed extensively by the senior author [14-17], and many others, e.g., [18]. There are at present four distinct possibilities to be considered. i) The cation may be surrounded by solvent molecules in what one might call a ‘normal’ state of solvation, without being especially attached to any one solvent molecule. ii) The cation has formed a covalent bond to one O-atom of one solvent molecule, so that its charge is distributed over a

—C—O+—N = O group. iii) The propagating cation is solvated or complexed with unreacted monomer. iv) It is solvated or complexed with a segment of polymer. The models (ii), (iii) and (iv) of course also involve a normal solvation by the solvent of the ions resulting from the processes (ii)–(iv) which have a much lower charge density.

472

Indene, Two Vinyl Ethers and General Discussion (1990) The process (ii) would produce a species (3)

+ Pn+ + O2NPh ↔ Pn —O—N—Ph (3)

O

which might propagate very slowly or not at all, so that the propagation would be carried predominantly by the very small equilibrium concentration of free Pn+. This view, expressed in many discussions but never in print, is based on the observation [19] that PhNO2 is Ocationated by MeF and EtF in SO2 + SbF5. The relevance of this observation is doubtful because of the long extrapolation from SO2 + SbF5 to PhNO2 solvent. Two observations speak against the model (ii): the mobility of the Ph3C+ ion in PhNO2 is completely normal, whereas that of species (3) (with Ph3C in place of Pn) would be much less; and the spectrum of Ph3C+ in PhNO2, although shifted, is not changed much, whereas the spectrum of Ph3COH2+ is quite different from that of Ph3C+ [20]. We recognise that it is hazardous to draw conclusions from the behaviour of the bulky trityl ion with a rather diffuse charge to that of the much ‘sharper’ secondary ions involved in polymerisations; but we must also point out that there is no evidence whatever in favour of the model (ii) and therefore we will ignore it henceforth. Models (iii) and (iv). Strictly, the only way of finding out definitely whether there is any complexation between the growing cation and the monomer or the polymer, or both, is to investigate whether (and if so, how) the apparent k p+ depends on monomer concentration [16, 17]. We have such evidence only for ACN and styrene and for these the value of kp+ does not depend on m. This is in accord with the prediction [15, 17] that in a highly polar solvent the complexation of Pn+ by a π-donor monomer or its polymer is likely to be negligible. The likely behaviour of the n-donor vinyl ethers and their polymers is less clear, but a consideration of the dipole moments and concentrations involved makes it extremely unlikely that these monomers or their polymers could compete successfully for a place in the solvation shell of the growing cations. We conclude therefore that in our systems the Pn+ ion, solvated normally, is the propagating species, and that what we have measured are the true kp+ in that solvent.

3 The kp+ values The values of kp+ summarised in Table 5 need little comment. The ‘best’ value for styrene is the weighted mean of both determinations. As these values are unaccompanied by activation enthalpies and entropies, they are, unfortunately, rather uninformative. The only clear correlation is an antibatic one with

473

Developments in the Theory of Cationoid Polymerisations ⏐ΔHp⏐, both for the three hydrocarbons and for the two vinyl ethers (Figure 8). This is the exact opposite of what is usually found. For normal addition reactions of similar compounds, an increase in ⏐ΔH⏐ produces a decrease in the activation enthalpy ΔH‡ and thus an increase in the rate constant (Polanyi principle). The main characteristic of our results is that they stand alone in two respects:

Figure 8 The variation of kp+ with ΔHp for all five monomers listed in Table 5

474

Indene, Two Vinyl Ethers and General Discussion (1990) i) because no other results obtained in PhNO2 solvent are available; and ii) because they cannot be compared simply with alleged kp+ values obtained in other solvents. The reason is that these alleged kp+ values are mostly composite, comprising the rate constants of propagation of uncomplexed Pn+, paired Pn+ (Pn+A–), and Pn+ complexed with monomer or polymer or both, without or with an associated A– [17]. Even when we will eventually have genuine kp+ values for solvents other than PhNO2, it will not be possible to draw many (or any?) very firm conclusions because the only theoretical treatments of the variation of rate constants with solvent polarity for (ion + molecule) reactions are concerned with spherically symmetrical ions, and the charge distribution in the cations of concern to us is anything but spherically symmetrical. Finally, the availability of the value of kp+ for styrene in PhNO2 enables us to solve an old mystery, namely, what is the concentration of growing ions in polymerisations initiated by SnCl4 with a co-initiator? Dainton and Colclough [22] reported on the polymerisation of styrene by equimolar concentrations of SnCl4 and t-BuCl in PhNO2 at 25 °C. Their Figure 3 shows that for m = 0.8, the rate R = 1.28 x 10-3 mol⋅dm-3⋅s-1. If we take kp+ = 200, we get

[ Pn+ ] = R / kp+ m = 1.28 x 10 −3 / 200 x 0.8 = 8 x 10 −6 mol ⋅ dm −3 Since [SnCl4] = [t-BuCl] = 10-3 mol⋅dm-3, this calculation, rough though it is, shows that only ca 1% of the components of the catalytic system was effective.

Conclusion The work reported here is the last experimental study of the Keele Polymer Group which came to an end in 1985. The senior author believes that he has achieved one of his principal chemical objectives, to determine some credible kp+ values and to discover the optimum conditions. He hopes that others will adopt the use of highly polar solvents and will explore a wide temperature range. For low temperatures, the eutectic mixtures of PhNO2 with one of the nitronaphthalenes or dinitrobenzenes will be needed. Another useful, highly polar, solvent is SO2. The nitroalkanes should be avoided. The initiator of choice should be an aroyl salt of a stable anion, and it is clear that the ideal such salt has not yet been found, but useful guidelines for finding improved initiators (in terms of speed of reaction, shelf-life and solubility) are available [21].

475

Developments in the Theory of Cationoid Polymerisations

Acknowledgements PHP acknowledges gratefully an SERC grant (to SHS) and a Leverhulme grant which facilitated the publication of this paper, and he thanks Dr S. Holding of RAPRA Technology Limited, for the DPD measurements and help with their interpretation.

References 1. S. D. Pask, P. H. Plesch and S. B. Kingston, Makromolek. Chem., 182, 3031 (1981). 2. G. E. Holdcroft and P. H. Plesch, Makromolek. Chem., 185, 27 (1984). 3. S. D. Pask and P. H. Plesch, Chem. Ind. (London) 331 (1981). 4. P. H. Plesch, High Vacuum Techniques for Chemical Syntheses and Measurement, Cambridge University Press, Cambridge (1989). 5. S. D. Pask, P. H. Plesch and M. Di Maina, Chem. Ind. (London) 329 (1981). 6. S. M. McElvain and B. Fajardo-Pinzon, J. Am. Chem. Soc., 67, 650 (1945). 7. P. K. Grannell, S. D. Pask, P. H. Plesch and G. E. Holdcroft, Chem. Ind. (London) 441 (1983). 8. R. H. Biddulph, W. R. Longworth, J. Penfold, P. H. Plesch and P. P. Rutherford, Polymer, 1, 521 (1960). 9.

H. Cheradame, J.-P. Vairon and P. Sigwalt, Eur. Polym. J., 4, 13 (1968).

10. H. J. Prosser and R. N. Young, Eur. Polym. J., 11, 403 (1975). 11. A. Ledwith, E. Lockett and D. C. Sherrington, Polymer, 16, 31 (1975). 12. M. S. Anasagasti and L. M. Leon, J. Polym. Sci.; Polym. Lett., 21, 979 (1983). 13. D. W. Grattan and P. H. Plesch, J. Electroanal. Chem., 103, 81 (1979). 14. P. H. Plesch in Cationic Polymerisation and Related Processes (edited by E. J. Goethals), p. 1. Academic Press, London (1984). 15. P. H. Plesch, Eur. Polym. J., 25, 875 (1989).

476

Indene, Two Vinyl Ethers and General Discussion (1990) 16. P. H. Plesch, Makromolek. Chem., Macromolec. Symp., 33, 299 (1990). 17. P. H. Plesch, Progress in Reaction Kinetics (in preparation). 18. G. Sauvet, M. Moreau and P. Sigwalt, Makromolek. Chem., Macromolec. Symp., 3, 33 (1986). 19. G. A. Olah, J. R. DeMember, R. H. Schlosberg and Y. Halpern, J. Am. Chem. Soc., 94, 156 (1972). 20. P. H. Plesch (unpublished data). 21. S. D. Pask and P. H. Plesch, Eur. Polym. J., 18, 839 (1982). 22. R. O. Colclough and F. S. Dainton, Trans. Faraday Soc., 54, 898 (1958).

477

Developments in the Theory of Cationoid Polymerisations

478

5.6

The Propagation Rate-Constants of the Cationic Polymerisation of Some Alkenes in Nitrobenzene - IV. Not the Real kp+ *† (1993) P. H. Plesch

This paper was first published in European Polymer Journal, 1993, 29, 2/3, 121-124. Reproduced with permission from Elsevier, copyright 1993.

Prologue: See Previous Section

Abstract The cationic polymerisation of several alkenes, including vinyl ethers (VE), by carbenium and carboxonium salts in nitrobenzene had given propagation rateconstants which were interpreted by us as being the kp+ as defined by the equation -dm/dt = kp+ [Pn+]·m, where [Pn+]. is the concentration of unpaired, uncomplexed propagating cations. The purpose of the present paper is to show that our own work contains evidence, not understood and neglected at the time, indicating that this is not correct. An interpretation has been devised which is compatible with all the facts, including the very low values of the rate-constants (now called kp+A), the bimodal DPD of the poly(2-chloroethylvinyl ethers), and the antibatic correlation between the kp+A and the enthalpy of polymerisation for three hydrocarbons and two VE. This is based on the idea, introduced by others, that the propagating carbenium ions cationate the solvent, Sv, giving the ions PnSv+, i.e., PnON+(O)C6H5, which are in equilibrium with the Pn+. The observed kp+A are weighted means of the propagation rate-constants of the two propagating species. A propagation mechanism for the PnSv+has been suggested which resembles closely that for pseudocationic polymerisations [8].

* Ref [1] is Part III of this series. †

This is Part XII of ‘Developments in the Theory of Cationic Polymerisations’. For Part XI see [9].

479

Developments in the Theory of Cationoid Polymerisations

1 Introduction The present author wanted to determine the propagation rate-constant, kp+, for the cationic polymerisation of various alkenes (this term here includes vinyl ethers, VE) under such conditions that the interpretation of the measurements should be as unambiguous as possible. If there are no complications from the complexation of the propagating species with constituents of the reaction mixture, the rate of such polymerisations is given generally by equation (1):

– dm / dt = R = kp* ⋅ [ Pn* ] ⋅ m

(1)

[ Pn* ] = [ Pn+ ] + [ Pn+ A − ]

(2)

where

and m = [monomer]. The Pn+ is a growing carbenium ion, A- is the corresponding anion derived from the initiator, the dissociation constant, KD of the ion-pairs is given by equation (3):

KD = [ Pn+ ][A − ]/[Pn+ A − ]

(3)

and kp* is a composite quantity. The aim was to achieve a monoeidic polymerisation with the unpaired, uncomplexed cation Pn+ as the only propagator, so that the rate, R, would be given by equation (4):

R = kp+ ⋅ [ Pn+ ] ⋅ m

(4)

In order to achieve this, the KD must be made as large as possible; and to avoid complications from Pn+ complexed with other constituents of the reaction mixture it is also necessary to minimise the formation of Pn+M from Pn+ and M, and the formation of Pn+P by the complexing of the Pn+ with π- or n-donors in the pendent groups of the polymers. Such a simplification of the polymerizing systems can be achieved in principle by the use of a highly polar solvent which would monopolise the solvation shell of the cation with effective exclusion of the competing anion, monomer, and any pendent polar groups [2]. The use of a highly polar solvent would have the additional advantage that in it the propagation rate-constants for the 3-centre (ion + molecule) reactions would be considerably lower than in less polar solvents, since according to Transition State theory for such reactions, kp+ is proportional to 1/D (D = dielectric constant). As a result of these considerations, PhNO2 was chosen as the solvent. To achieve our objective we considered it essential to select reaction conditions such that the rate of polymerisation would be given by the rate of propagation, with first-order kinetics throughout; this means fast initiation and no termination during virtually the whole of the polymerisations. In order to create these simple conditions, we used as initiators various carbenium and carboxonium salts of the inert and stable anions PF6- and SbF6-. Conductivity

480

The Propagation Rate-Constants of the Cationic Polymerisation... measurements showed that [ions] = c0, the concentration of initiator, and the kinetic measurements showed that the reactions were internally of first order so that

R = k1 ⋅ m

(5)

and that

k1 = k ⋅ (co – ci )

(6)

where ci is the concentration of cations which are scavenged, but not neutralised, by the inevitable impurities. In the earlier publications [1, 3, 4] the rate-constant k was designated as kp+, but as the whole point of the present paper is to show that it is not the real kp+, as defined by equation (4) [2], we will denote it here by kp+A. For ease of reference, these kp+, determined in the earlier work, together with the enthalpies of polymerisation, ΔHP, are presented in Table 1. It is evident immediately that the kp+A are much smaller than the ‘accepted’ kp+ for CH2Cl2 solutions, especially for the three hydrocarbons, which were believed to be of the order of 104 to 106 l·mol-1·s-1 [2]. Although a reduction of the kp+ in changing from solvent CH2Cl2 to the much more polar PhNO2 was expected and was one reason for choosing PhNO2, two critics in particular held the opinion that the reduction in the rate-constants was far greater than could be accounted for by the dielectric constant effect alone [5]. They suggested that one or both of the following effects could be reasons for the low values of kp+A. The first is a reduction in the reactivity of the monomers due to the expected complexation between the electron acceptor PhNO2 and the electron donor monomers, and the second is the possible complexation of the propagating carbenium ions with the solvent. In our previous discussion [1] the first point was ignored, and we adduced circumstantial evidence that the second was probably invalid, whence we

Table 1 Summary of results* T (°C)

kp+A/l·mol-1·s-1

–Δ ΔHp/kJ·mol-1

Acenaphthylene

25

23 ± 2

85. 4 ± 2

Styrene

25

195 ± 15

63. 6 ± 2.5

Indene

20

373 ± 15

56. 5 ± 0.6

PhVE

20

1450 ± 200

11 0 ± 10

CEVE

7–21

ca. 104

80 ± 8

Monomer

*From Table 5 of Reference [1]

481

Developments in the Theory of Cationoid Polymerisations concluded that our rate-constants were indeed genuine kp+. The detailed considerations to be explained below have shown that the first objection is probably unimportant, at least for hydrocarbon monomers, but that the second one is indeed valid, and that actually our results themselves contained evidence, unrecognised at the time, supporting that view; in other words, in this respect our critics are right, though for reasons which they did not suspect. The rest of this paper is concerned with developing the relevant arguments.

2 The possible complexation between the monomer and the solvent The first objection needs to be discussed in terms of the formation of a charge-transfer (CT) complex MSv between an alkene monomer M and the solvent Sv, with the formation constant KMS. Since

KMS = [MSv]/[Sv] ⋅ m and

mo = m + [MSv] KMS = [MSv]/( mo – [MSv]) ⋅ [Sv]

(6)

so that

[MSv] = KMS ⋅ mo /( KMS ⋅ [Sv] + 1)

(7)

There is sufficient information on CT complexes of this kind in Foster’s book [6] for the KMS to be estimated. By extrapolating from 1,3,5-trinitrobenzene and 1,4-dinitrobenzene to PhNO2 for any one electron donor (mesitylene or hexamethyl benzene), and from CCl4 to solvents of D > ca 10, we find that at least for the three hydrocarbon monomers it is very unlikely that KMS > 10-2 l·mol-1. Therefore, since [Sv] = ca 10 mol·l-1 ([molar vol]-1), we find for m = 1 mol·l-1, that [MSv] < 0.1 mol·l-1, which means that for these monomers >90% of the monomer is not bound in a CT complex, and the first objection is therefore not relevant. For the monomers containing both π- and n-donor groups, i.e., the VE, the KMS may well be greater, and therefore the formation of CT complexes may be important for these.

3 The nature of the propagators The second objection amounts to saying that our kp+A are not kp+ because we had calculated them from equation (4) on the assumptions that Pn+ is the only propagator and that its concentration is given by equation (8):

482

The Propagation Rate-Constants of the Cationic Polymerisation...

[ Pn+ ] = co – ci

(8)

when actually there are reasons for believing that these assumptions are not valid. We will therefore examine the consequences of this idea, starting with the reasonable suggestion of the objectors [5] that the carbenium ions would cationate the solvent to give a species PnSv+, a likely structure for which is Pn·O·N+(O)C6H5 (I). This idea is based on the observation of Olah et al. [7] that PhNO2 can be methylated and ethylated in a mixture of SbF5 and SO2. The formation constant of (I), KSv, is given by equation (9):

KSv = [ Pn Sv + ]/[Pn+ ] ⋅ [Sv]

(9)

so that

[ Pn+ ] = (co – ci )/(KSv ⋅ [Sv] + 1)

(10)

We now consider the following two possibilities: i)

The Pn+ is the only propagator and PnSv+ is inert.

ii)

Both Pn+ and PnSv+ are propagators.

Our last paper [1] contains three facts which we could not explain at the time and which we think now shed light on the question of the number and nature of the propagators. The first is that with the 2-chloroethylvinyl ether (CEVE) the initiator 4-ClC6H4CO+SbF6- (1) dissolved in EtNO2 gave polymerisations too fast to be measured reliably, whereas the initiator (4-ClC6H4)3C+PF6- (2) dissolved in PhNO2 gave polymerisations with a lower and conveniently measurable rate. The second unexplained feature is that the polymers obtained with both initiators had a bimodal DP distribution (DPD). The polymer from (2) contained about equal amounts of high (DP = 113) and low (DP = 36) polymer, but the polymer from (1) contained much less of the low DP materials (DP = 50) (high DP = 122). As it seems unlikely that any explanation of a bimodal DPD can be devised on the basis of a monoeidic polymerisation mechanism, we reject the alternative (i) and will investigate the usefulness of (ii). An important, though not absolute, constraint on the choice of the second species participating in the formation of the polymers, is that it must be ionic, since the ionic conductivity of the reaction mixture corresponds closely to that calculated from co as shown in Reference [1]. The model (ii) implies that in PhNO2 solutions the species Pn+ and PnSv+ coexist and that both are propagators which are normally in equilibrium according to equation (9). The

483

Developments in the Theory of Cationoid Polymerisations propagation by Pn+ is the conventional 3-centre addition of the growing cation to the double-bond, but the propagation by PnSv+ is different. We find that the most plausible mechanism for this involves a 6-centre cyclic transition state, very similar to that of the pseudo-cationic polymerisations [8], which can be pictured as (II) in the following reaction (Scheme 1):

Scheme 1 We now suppose that the initiator 1 in EtNO2 has formed the cationated aci-acid 4ClC6H4C(O)-ON+(:CHMe)OH (III) and that this initiates a normal cationic polymerisation by protonating the monomer which then propagates to give Pn+ (Scheme 2):

Scheme 2

484

The Propagation Rate-Constants of the Cationic Polymerisation... The initial high [Pn+ ] thus formed produces a fast consumption of a large part of the monomer, thus generating the polymer of high DP early in the life of the polymerisation. At the same time the species (I) is formed which propagates much more slowly (Scheme 1), the equilibrium (9) is established, and thus the polymerisation becomes dieidic, so that then each polymer chain is formed partly by Pn+ and partly by PnSv+ [which is (I)]. In contrast to this, we have the much slower polymerisations ensuing when the initiator is 2 in PhNO2. In our view this is because the storage of 2 in PhNO2 produces the species (4-ClC6H4)3CON+(O)Ph which, after the first propagation step, yields I. The dilution of the initiator solution upon breaking the phial into the monomer solution shifts the equilibrium in favour of the Pn+ ,which is a relatively slow process. Therefore, in this system the polymer formed first is that of low DP, and subsequently the higher polymer is formed by the dieidic polymerisation by Pn+ and PnSv+. Kinetically, the situation during the later part of the polymerisations by both initiator systems therefore resembles very closely the irregularly alternating propagation by unpaired and paired cations contributing to the formation of any one chain in a solvent of intermediate polarity. The obvious question why only the CEVE gave polymers with a bimodal DPD can be answered with the tentative suggestion that for the other monomers the charge-density on the Pn+ is relatively so great that the ratio [Pn+]/[PnSv+] is too small for a monoeidic polymerisation by Pn+ to play any important part. It would not be difficult to test our ideas experimentally. A further argument against our original view can be deduced from the third originally unexplained fact, the correlation between our kp+A and the enthalpy of polymerisation, ΔHp, which is shown in Figure 8 of Reference [1]. If we assume that the dependence is rectilinear, i.e., of the form

log[kp+ A / l ⋅ mol −1 ⋅ s −1 ] = a ⋅ ΔHp + b then for the three hydrocarbons

a = 4.22 × 10 −2 / kJ ⋅ mol −1 , b = 4.97 and for the two VE

a = 2.80 × 10 −2 / kJ ⋅ mol −1 , b = 6.24

485

Developments in the Theory of Cationoid Polymerisations In simple terms, this correlation means that the more negative the ΔHp, the smaller is kp+A. However, the normal correlation for a series of 3-centre reactions of the same type is that a more negative enthalpy is associated with a smaller activation energy and therefore a greater rate-constant (Polanyi’s Principle). The most obvious conclusion is that the rate-determining step in our reactions is not a simple 3-centre process, such as the addition of a carbenium ion to a double-bond, as we had supposed originally, and therefore it follows that our kp+A - whatever else they may be - are not kp+.

4 What next? The physico-chemical considerations on the basis of which PhNO2 was selected as solvent for the determination of kp+ were correct and relevant, but they were inadequate. We now know that a solvent is needed which in addition to having a large dipole-moment must be invulnerable to attack by cations. The requirement of high polarity implies the need for a dipole whose negative end is ipso facto prone to cationation. It should, however, be possible to produce adequately polar solvents whose negative end is protected sterically from such electrophilic attack. The easy, obvious solutions to this problem are 2,6-di-tbutyl nitrobenzene and 2,6-di-t-butyl pyridine. Similarly, sterically protected ketones, e.g., 2,2,6,6-tetraisopropyl cyclopentanone, or similarly protected cyanides may be the answers to the frustrated kineticist’s dream. There is much scope here for progress by ingenious selection of solvents.

Acknowledgement This paper is dedicated to my ever-helpful friend, John C. Bevington.

References 1.

P. H. Plesch and S. H. Shamlian, Eur. Polym. J., 26, 1113 (1990). Note that in Table 4 the heading to column 7 should be (10-4 k1/c0)/dm3·mol-1·s-1.

2.

P. H. Plesch, Progr. Reaction Kinetics, 18, 1 (1993).

3.

S. D. Pask, P. H. Plesch and S. B. Kingston, Makromolek. Chem., 182, 3031 (1981).

4.

G. E. Holdcroft and P. H. Plesch, Makromolek. Chem., 185, 27 (1984).

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The Propagation Rate-Constants of the Cationic Polymerisation... 5.

K. Matyjaszewski and S. Penczek. Private communications. Although it is unusual to heed unpublished critical comments, it will be seen that the privately expressed views of these experienced colleagues have catalysed a useful advance in our understanding.

6.

R. Foster (Ed.), Organic Charge-Transfer Complexes, Academic Press, London (1969).

7.

G. A. Olah, J. R. DeMember, R. H. Schlosberg and Y. Halpern, J. Am. Chem. Soc., 94, 156 (1972).

8.

P. H. Plesch, Makromolek. Chem., Macromolec. Symp., 60, 11 (1992).

9.

P. H. Plesch, Phil. Trans. R. Soc., London, A342, 469-504 (1993).

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Developments in the Theory of Cationoid Polymerisations

488

5.7

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) P. H. Plesch

This paper was first published in Progress in Reaction Kinetics, 1993, 18, 1-62. Reproduced with permission from Science and Technology Letters, copyright 1993.

Prologue In the mid-1980s, this writer realised that the area of polymer chemistry defined by the title to this paper was in a mess and greatly confused and that therefore a very thorough, very critical review was necessary. Whilst he was considering such an enterprise which would be a culmination of his earlier attempts, he received an invitation from one of the Editors of Progress in Reaction Kinetics to undertake just this assignment; in other words, there was the prospect of being paid for what he had been wanting to write anyway. In the event, between invitation and publication five years elapsed, two of which were taken up with attempts to understand the polymerisations by ionising radiations which at the time had been believed to be well understood, and which yielded the first comprehensive theory of these reactions and a better understanding of the subtleties of the carbenium ion in solution [146]. The review which eventually emerged, is not an uncritical juxtaposition of all the claimed rate-constants, but a record of the very detailed scrutiny of each work, on the basis of which the claimed rate-constants were eventually accepted or rejected. The review opens with a discussion of the nature and relative abundance of the various propagating species found in different systems under different conditions. This is followed by an account of various kinetic patterns and a description of the experimental methods used, and of their merits and deficiencies. One of the innovations in this work was that the author calculated wherever necessary and possible the original experimental rate-constants, and this enabled him to see kinetic irregularities that had been unrecognised or at least had not been reported by the original workers; and in many cases these eventually provided new insights by which the validity of their claims could be assessed.

489

Developments in the Theory of Cationoid Polymerisations A useful discovery was that the paradigm which had explained the phenomenology of the polymerisations of isobutene by AlCl3 [112] was also useful for understanding why in the polymerisations of, for example, styrene by strong protonic acids, only a very small fraction of the acid is consumed, for which no plausible explanation had been put forward previously. It involves the formation of strong complexes also by protonic acids whith the alkenic monomers. However, the discovery with the most far-reaching consequences arose from the close scrutiny of the results of Kunitake and Takarabe on the polymerisation of styrene by trifluoromethyl sulphonic acid. It became evident to the reviewer that in these reactions an important contribution to monomer consumption must have been made by the ester, and he was able to extract from the results the corresponding propagation rate-constants, kpE, for that cationoid insertion polymerisation. This became one of the most convincing supports for the author’s views on cationoid insertions. The most important casualties of this campaign are the rate-constants much quoted in textbooks but shown here to be unacceptable; these comprise most of those from Bawn’s group and those derived from radiation polymerisations. Neither of these groups of results had previously been scrutinised so closely. The paper ends with some practical advice on how to obtain reliable rate-constants, but the writer is not too optimistic about finding his view heeded, because most practising chemists are too much in love with their own methods, and seem not to mind squandering resources on re-inventing the wheel. On re-reading what is one of his longest works the author found the reason why it seems to have made little impact on his colleagues. It is that this type of meticulous critical interpretation, although didactically useful, and necessary for good science does make rather dull reading.

1 Introduction

1.1 Preamble The present reviewer has struggled with the practice and theory of cationic polymerisations since 1944, and he has evolved a view of these ionic reactions in solution which is sufficiently simple and flexible to be heuristically useful. The present critique of his colleagues’ and his own results is founded in his accumulated experience and involved

490

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) much thought, which led him to some new views expressed here for the first time. He hopes that his work will be a useful guide to contemporary and future workers in this promising, but difficult, area of physical chemistry. This review is concerned with the propagation rate-constants of a particular category of cationoid polymerisations. The term ‘cationoid’ is used to designate polymerisations which may involve any or all of the following species: unpaired cations, paired cations, complexed cations, and (modified) esters. The cationic polymerisations are the reactions in which a positively charged propagating species Pn+ is generated from the reaction of a pre-existing cation, e.g., ArCO+, or a precursor such as a simple protonic acid, (e.g., CF3CO2H), or a complex protonic acid, (e.g., BF3H2O), or a mixed anhydride, (e.g., MeCO2ClO3) or a positively charged species generated by ionising radiation, with a polymerisable alkene M, as shown in Scheme 1. In the present context the term ‘alkene’ includes vinyl ethers and aryl and alkoxy-aryl alkenes. We hold the opinion that pseudo-cationic polymerisations which are propagated by a modified ester (Plesch, 1992) form a reaction category sui generis, and that the living cationic polymerisations belong to that category, and therefore they will not be considered in the present work. The concept of the chain-carriers in the cationic polymerisations has become increasingly sophisticated over the last five decades. The view that the chain-carrier in the polymerisations initiated by, e.g., AlCl3 is a carbenium ion (then known as a carbonium ion) evolved around 1940, and by the end of the decade the need to consider the pairing of ions, especially in non-polar solvents, had been generally accepted. The idea that the cations can form donor-acceptor bonds with the monomers originated in 1947, but its full implications were not appreciated until very much later. Because of these developments and for other reasons, the propagation rate-constants of such cationoid polymerisations

Initiator ArCO+MtX–n+1 CF3CO2H + nM → Pn+ + BF3H2O MeCO2ClO3

Anion* MtX–n+1 CF3CO2– BF3OH– ClO–4

* Conjugate anions A2H– are ignored here Scheme 1

491

Developments in the Theory of Cationoid Polymerisations have proved to be very elusive quantities. The literature contains many claims to have measured one or more of them, but most of these claims now appear rather unconvincing. There are numerous reviews which contain compilations of rate-constants (Dunn, 1979; Gandini and Cheradame, 1985; Kennedy and Maréchal, 1982; Ledwith and Sherrington, 1974, 1975; Plesch, 1968, 1971, 1973, 1984; this enumeration of reviews is not intended to be exhaustive), but these earlier reviewers, and indeed the present reviewer in his earlier efforts, found far more of the claims to be acceptable than we do now. Our objective here has been to circumscribe and define the subject, to outline the physical chemistry involved, to show the practical and the theoretical difficulties of obtaining satisfactory, intelligible measurements, and to scrutinise the major claims to have determined rate-constants. Finally, we have assembled in Section 5 those rate-constants which in our opinion can be categorised with confidence as kp+ or kp±, the propagation rate-constants of unpaired and paired cations. We have given reasons for our acceptances and rejections, many of which are based on time-consuming recalculations and plottings of graphs. We could have ignored all those claims which we rejected, but we have thought it more useful to show why we now consider worthless some of the alleged kp+ and kp± values which had gained a certain credibility by being apparently of the ‘right’ order of magnitude, and by being quoted repeatedly by less critical reviewers. Our efforts should be read in conjunction with the critical assessment of initiation mechanisms of Gandini and Cheradame (1980). We do not claim to have found and examined every report that a rate-constant has been measured. Therefore the non-appearance of any such claim in this review may mean either that we have not seen it or that we did not deem our rejection of it to be worth recording. Seeing the enormous effort which has been reviewed here, the harvest of results is meagre, and for a few, easily identifiable, reasons. Too many investigators have ignored the wise kineticist’s maxim: first attempt to clarify the chemistry, then study the kinetics. The facile assumption that all cations react in the same way with all monomers has led to much wasted effort. Many studies were too ‘quick and dirty’ to yield useful conclusions, i.e., insufficient measurements were made to establish firmly the kinetic dependences, and/or materials were purified inadequately. Another frequent source of trouble has been the lack of thought devoted to the selection of a suitable chemical system. Whilst, at the time, Pepper’s selection of protonic acids for study as initiators was rational, as was Bawn’s choice of stable cations, it was hardly wise for others to use protonic acids and their derivatives once pseudo-cationic polymerisations had been identified, and for many investigators to continue with the use of trityl salts and SbCl6- once it had become known that their reactions with alkenes are neither fast nor necessarily simple; but hindsight is

492

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) a wonderful thing, and this writer is not without his own regrets concerning projects that might have been planned better. Many unsound numbers and ill-founded conclusions have been due to the failure by experienced investigators to insist that their young collaborators always plot the primary data, i.e., the rate against whatever variable was being studied; because whenever the first plot made is of Rate divided by some Concentration, or worse, a Rate-Constant divided by ..., the most important source of information has been discarded. Much of the new information in this review has come from our unscrambling such results, whenever sufficient data had been made available in the publications. The modern practice of withholding the primary data from the reader, so that no conclusions other than those of the original author can be devised, is a serious obstacle to progress. We have tried to acknowledge adequately the work, and especially the ideas, of others, but inevitably there will be omissions, mis-attributions, and errors of emphasis, and for these we apologise. The long delay since we started this work, of which numerous colleagues are aware, was principally due to the fact that when we attempted to review the polymerisations by ionising radiations, which we thought was a well-established field that would present few problems, we found that in fact there was no general theory of these reactions and that most of the allegedly and apparently well-established numbers were wrong. So we interrupted the composition of this review, whilst we evolved a new theory of that class of polymerisations (Plesch, 1993). It turned out to have been time well spent, because the insights gained, especially concerning the effects of solvents and the range of conditions in which the complexing of the monomer with the carbenium ion is important, helped greatly towards a better understanding of the chemically initiated polymerisations. Some readers may regret that we have taken our title so literally that we have not included the rate-constants of dimerisation, e.g., for diphenylethylene; nor those for initiation by preformed cations (except marginally); nor the rate-constants for the addition of aryl and di-aryl cations to alkenes, established so elegantly by Wang and Dorfman (1980) and by Mayr and his collaborators (Mayr, 1990; Bartl et al., 1991 and numerous earlier papers). In our view these subjects are sufficiently interesting and important to be reviewed together in their own right. We acknowledge with appreciation some stimulating discussions with K. Matyjaszewski during the early part of this enterprise. We are greatly indebted to P. Sigwalt and J.-P. Vairon for their painstaking analysis of the sections concerning the work of their group and much else, and we are happy to thank D. C. Pepper for his shrewd comments on the whole work.

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Developments in the Theory of Cationoid Polymerisations

1.2 Glossary and list of symbols Although every symbol and unusual term is defined at its first occurrence in the present work, a list is given here for the reader’s convenience.

Rate-constants and propagating species kp

Shorthand for ‘propagation rate-constant’ without specific assignment to any one propagating species.

kp +

The propagation rate-constant for an unpaired carbenium ion Pn+, solvated mainly by solvent. It may, in certain circumstances, include a contribution from the carbenium ion complexed with a pendent group from the polymer, represented as Pn+P, because the corresponding kp+p cannot, at present, be separated from the kp+.

kp+P

See above.

kp+M

The propagation rate-constant of a carbenium ion complexed with monomer, Pn+M.

‘kp+’ kp±

An alleged or putative kp+ The propagation rate-constant for a carbenium ion paired with an anion, represented as Pn+ A-.

kp *

A composite rate-constant given by kp*=(kp+[Pn+]+kp±[Pn+A-])=R/m·[Pn*] and [Pn*]=[Pn+]+[Pn+A-]

kp E

The propagation rate-constant of an activated polymeric ester.

kp

+A

An apparent propagation rate-constant comprising possible contributions from kp+ and kp± and kpE

k+p1

The rate-constant for the unimolecular propagation by isomerisation of Pn+M to P+n+1 in solution.

kp1+B

The k+p1, in bulk monomer.

ki

Rate-constant for initiation.

km

Rate-constant for proton transfer to monomer.

kt

Rate-constant for termination.

Equilibrium constants KD

Dissociation constant of an ion-pair, KD=[Pn+]·[A-]/[Pn+A-]

KM

Formation constant for the complex between a propagating cation and the monomer, M, of concentration m. KM=[Pn+M]/[Pn+]·m

K′M

K′M=[A-Pn+M]/[Pn+A-]·m

Concentrations c

Concentration of the initiator.

co

Initial value of c; in some contexts it denotes the total concentration of propagators.

494

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) ci

Part of co neutralised by impurities, whose concentration is [Imp].

m

Concentration of monomer, i.e., [M]. m in bulk monomer, i.e., (molar volume)-1.

mB +

-

p=[Pn A ] +

y=[Pn ]

Concentration of paired ions. Concentration of unpaired ions.

Miscellaneous a

Distance of closest approach of ions.

A

Optical absorbance.

Amphibainic ‘Going both ways’, derived from Greek amphibaina, an animal with a head at each end. In a polymer context a chain with a propagator at each end. BIE

Binary lonogenic Equilibrium: A+B↔Q++R-, K11 k11 = [Q].[R-]/[A]·[B].

D

Dielectric constant.

DPD

Degree-of-polymerisation distribution, used in preference to molecular weight distribution, MWD.

R

Rate of polymerisation = -dm/dt.

Mono-, di-, eni-eidic

From Greek word eidos, meaning image or form; in the context of polymer chemistry eni-eidic means ‘having one, two, several types of propagating species’.

ε (epsilon)

Optical extinction coefficient = molar decaidic absorption.

κ (kappa)

Electrical conductivity.

ρ (rho)

Density.

2 Theoretical background - critical definitions of terms and problems 2.1 The fundamental equations and definitions The title of this review means literally the rate-constant of the process by which the molecule of an alkene becomes attached to a carbenium ion at the end of a polymer chain with the re-formation of an identical ion. The simplest representation of this process is Equation (1):

Pn+ + M → Pn++1 , kp+

(1)

The rate of this reaction is given by Equation (2):

R = – dm / dt = kp+ ⋅ [ Pn+ ] ⋅ m

(2)

where m is the concentration of M and kp+ is the rate-constant of the process.

495

Developments in the Theory of Cationoid Polymerisations The statement above and the Equations (1) and (2) are over-simplified and ambiguous, and therefore they need clarification. This is because the determining factor for the chemistry and kinetics of the polymerisations is the composition of the ionic population in the polymerising solutions. We need to think in terms of ionic populations because many cationoid polymerisations are enieidic, i.e., such that more than one propagating species participates in the consumption of monomer. This fact generates the questions discussed in the following sections. The most fundamental question is whether any one ion is to be regarded as always the same species, irrespective of its environment and condition, e.g., solvent, temperature, pressure? The general answer is ‘No’. Every ion in every environment is different, and different from every other ion. The cations and anions, i.e., the organic salts Pn+, A-, owe their presence in solution to the free energy of solvation of both ions, but because in most systems of concern to us the charge density on the cations is much greater, the solvation of the anions can be neglected in the present considerations. The nature of the solvated species, which is determined by the nature of the ions and by the composition and structure of their solvation shell, depends on the solvent, on all the species in the solution, and on the temperature and pressure, and it is therefore one of the most difficult and complicated questions to be faced. Polymerisations of undiluted, bulk monomer are rare except for those initiated by ionising radiations and they require a special treatment which will be given later. The most common situation is to have the propagating ions in a mixture of monomer and solvent, and as the solvation by the solvent is ubiquitous and may dominate over that by other components of the reaction mixture, mainly because of the mass-action effect, it will not be noted by any special symbol, except in a few instances. This means that we adopt the convention that the symbol Pn+ denotes a growing cation solvated mainly by the solvent; correspondingly kp+ denotes the propagation constant of this species, subject to the proviso at the end of Section 2.3. Its relative abundance depends upon the abundance of the various other species in which the role of the solvent as the primary solvator has been taken over by any or all of the anion or the monomer or the polymer. The extent to which this happens depends on the ionic strength (essentially the concentration of the ions), and the polarity of the solvent, the monomer and the polymer, and their concentrations.

2.2 The solvation of Pn+ by monomer The solutions in which cationic polymerisations take place contain at least three species, in addition to the solvent, which can interact with the growing cation more or less strongly according to the circumstances; in other words, they can contribute to the solvation energy of the cation. These are the anion, the monomer, and the polymer. The complexing of the growing end by the monomer has been a feature of cationic polymerisations since it was suggested by Fontana and Kidder (1948, 1952) to explain why the polymerisation of propene

496

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) in propane by AlBr3 + HBr at –77 ºC is of zero order with respect to monomer. Their explanation is that the monomer is involved in an equilibrium (3) with the ion-pair Pn+ A-

Pn+ A − + M ↔ M ⋅ Pn+ ⋅ A −

(3)

where A- is the anion (in their system AlBr4-), the M·Pn+·A- is a ternary aggregate and K′M is the equilibrium constant, given by

KM′ = [M ⋅ Pn+ ⋅ A − ]/[Pn+ A − ] ⋅ m

(4)

and the rate-determining growth step is the unimolecular isomerisation of the ternary complex, as shown in Equation (5):

M ⋅ Pn+ ⋅ A − → Pn++1A −

(5)

with first-order rate-constant kp1+. The resultant ‘drained equilibrium’ kinetics, similar to the Michaelis-Menten enzyme kinetics, gives the rate-equation:

R = – dm / dt = kp+1 ⋅ KM′ ⋅ m ⋅ co /(1 + KM′ ⋅ m)

(6)

co = [M ⋅ Pn+ ⋅ A − ] + [ Pn+ A − ]

(7)

where

From (6) we see that if K′M·m>> 1, then

R = kp+1 ⋅ co

(8)

i.e., the reaction is of first order, whereas if the reverse is the case

R = KM′ ⋅ kp+1 ⋅ co ⋅ m

(9)

so that then the reaction is of second order, with a second-order, composite rate-constant K′M·kp1+. The inversion of Equation (6) to

co /R = 1 / KM′ ⋅ kp+1 ⋅ m + 1/kp+1

(10)

shows how the constants can be determined if co is known. Irrespective of whether co is known, if a plot of 1/R against 1/m gives an intercept at 1/m = 0, this indicates that there

497

Developments in the Theory of Cationoid Polymerisations is a contribution to the rate from a first-order reaction. Since the complexing of Pn+Awith M was first suggested, the idea of complex formation between the (unpaired or paired) cation and the monomer has been used by many authors to explain a variety of phenomena, see especially Pepper (1975), Chmelir (1976), Stannett and Deffieux (1984), Sauvet et al. (1986) and Plesch (1990a). A further consequence of the complexing of Pn+ by the monomer is that there may be a difference between the ionic population in stopped-flow experiments (and others) in which m is very small and in normal kinetic experiments with m in the range 0.1–2 mol·l-1. Therefore the ‘kp+’ obtained from the two types of experiment need not necessarily be the same; see for example Leon et al. (1980). It is clear from the foregoing discussion that although the first sentence of Section 2.1 is adequately general, Equations (1) and (2) are really inadequate, as they represent the restricted view of propagation as a bimolecular reaction, but in this Section that view has been expanded to include a unimolecular propagation mechanism; the kinetics of the corresponding reactions will be discussed in Section 2.5.2.

2.3 The solvation of Pn+ by polymers In addition to the species Pn+ and Pn+ M, one must consider the complexes formed by the carbenium ions with other π- or n-donors in the system, in particular the polymers formed from monomers containing aromatic groups or hetero-atoms. This means that the polymers formed from non-aromatic hydrocarbons, e.g., isobutene, form a distinct class of noncomplexing polymers; we will call these the Class A polymers. It is likely that the internal double-bonds in, for example, poly-(cyclopentadiene) are such poor complexors for steric reasons, that polymers containing them can be placed into the same class. The polymers containing pendent π- or n-donor groups form Category B, for example poly(styrene) and the poly(vinyl ethers). The carbenium ions at the growing end of such polymers can either complex with a donor group on its own chain (intramolecular complexing), or with such a group from another chain (intermolecular complexing); except in very concentrated solutions, this latter process is probably negligible. There may well be a Category C, consisting of chains which are so stiff that intermolecular complexing is more probable than the intramolecular process, but we will not consider them here. The distinction between these classes was introduced by Plesch (1990a), but the complexing of the carbenium ions with pendent groups of the polymer had been considered previously by several authors (Subira et al., 1988; Deffieux et al., 1983a; Stannett and Deffieux, 1984) to be a significant feature of the kinetics, but they did not elaborate the full consequences of their view. To us, the important aspects of this complexation are:

498

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) i) It is only possible for Class B polymers. ii) It is unimolecular: P+n ↔ P+nP. iii) The ratio [P+nP]/[ P+n] = Kp depends only on the nature of the pendent groups, the solvent, and the temperature and pressure, but not on any concentration. In the formation of Pn+P the pendent group is in normal competition with the solvent and/or the monomer and/or the anion, and therefore [P+nP] depends on the nature and concentrations of these; in other words, the formation of P+nP can only be minimised by means of an adequately polar solvent which can replace energetically and thus displace physically the pendent groups; this idea seems to have originated with Deffieux et al. (1983a). iv) The species P+nP participates in the normal exchanges characterising a normal equilibrium, but it may have the benefit of a kind of cage effect because ‘it is there’, and so the species P+nP may in some systems be more abundant than the formal concentration of the complexing group indicates. (v) The cations P+n and P+nP must have different propagation rate-constants, say kp+ and kp+P but there is at present no way known to us in which they can be separated. Therefore it does not seem sensible to write

R = (kp+ ⋅ [Pn+ ] + kp+ P [Pn+ P]) ⋅ m and so we adopt the convention that our symbol k+p is in fact a quantity which for Class A polymers is simple, but for Class B polymers may be composite, the ratio of its components depending on the nature of the monomer, the solvent and the physical conditions. It is essential to keep this in mind when attempting to compare k+p values.

2.4 Electrochemical considerations Because our main concern is the composition of the ionic population of the polymerising solutions, we need to consider the principal factors which affect it, namely the polarity of the solvent and the ionic concentration with particular reference to the formation of ionic aggregates. The simplest of these are the ion-pairs, and we will not consider any higher aggregates because the ionic concentrations are usually far too low for their formation to be significant. This means that we are concerned with the equilibrium (11):

Pn+ A − ↔ Pn+ + A − , KD

(11)

where A- is the anion originating from the initiator, and

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Developments in the Theory of Cationoid Polymerisations

KD = [ Pn+ ][A − ]/[Pn+ A − ]

(12)

In the present context P+n A- might be poly(iso-butyl)+ AlCl4-. For the simple case of spherical ions, the dissociation constant, KD, of ion-pairs is governed by the BjerrumFuoss Equation (13):

log( K D / mol ⋅ l −1 ) = –3 log( a / cm ) – 21.4019 – 7.2558 × 10 −4 /( DT / K )( a / cm ) (13) where D is the dielectric constant of the solvent and a is the distance of closest approach of the ions. If no cations other than P+n are present, the ion-pairing can be discussed in terms of the dissociation constant KD of the ion-pair, and the ratio p/y, where p = [P+n A-] and y = [P+n]. The most direct approach to this simple situation is by Bos and Treloar’s equation:

p/y = –1 / 2 + (1 / 4 + co / KD )1 / 2

(14)

(Bos, 1971; Bos and Treloar, 1978; as explained and exploited by Plesch, 1973, 1976.) This equation relates p/y to KD and co , where

co = y + p

(15)

i.e., the total concentration of the salt P+n, A-. The Equation (14) is useful in estimating how, for such simple systems, the KD and co need to be adjusted to achieve a desired value of y/p. Unfortunately, the real systems under consideration here differ from the simple ones described by the above equations in several ways. The first is that most cations are neither spherical nor even symmetrical, and the second is that in many systems the ionic population contains more than one kind of cation, for example P+n and P+nP, and more than one kind of anion, e.g., A- and A2H- if the initiator is a protonic acid AH (see, for example, Sigwalt and Sauvet, 1980), or AlCl4- and Al 2Cl 7- from AlCl 3. Further complications can arise if the anion is one which can participate in Binary Ionogenic Equilibria (BIE), (Grattan and Plesch, 1979; Plesch, 1990b). We consider first the problem arising from the nature and shape of the cations. Many workers have attempted to estimate the KD of the ion-pair P+nA- for various growing cations with various A-, basing their estimates on the KD of the corresponding trityl salts in the same solvent. These attempts were misguided because of the geometrical and electrostatic differences between the propeller-shaped trityl cation and the most common

500

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) propagating cations which are secondary, especially the poly(styryl) and those from alkyl vinyl ethers; the C-H dipole of these, and the close approach possible for the A- have the effect of reducing the KD from that of salts containing the trityl cation. This is analogous to the large difference between the KD of quaternary and tertiary ammonium salts. On the other hand, under polymerisation conditions the possible participation of the species P+n M and P+n P would yield the three-component ion-pairs M·P+n A- and P·P+n A-, but their KD are likely to be greater than that of P+n A-. Experimental evidence for this comes from Bos and Treloar (1971, 1978) who showed that the addition of styrene to a solution of Ph3C+ HgCl3- in (CH2Cl)2 increased the KD. The reason is this: the model developed by Plesch (1993) to account for the effects of various solvents on the rate of unimolecular propagation in the polymerisations initiated by ionising radiations enables us to picture the three-component ion-pairs as having the non-ionic component (M or P) on one side of the trigonal, planar carbenium ion and the anion on the opposite side; and of course all potential solvators/complexors are competing with the solvent for these positions of minimum potential energy. The formation of the ternary complexes can be thought of as involving the displacement of solvent, Sv, from P+nA- by M or by P; this means that the P+n–M or P+n–P binding is stronger than the P+n–Sv was, which means that thereby the P+n–A- - binding becomes weaker, so that KD becomes greater-as stated above. Changing our point of view to considering the complexing of M or P with P+n, we see that such binding would be weaker for the paired cation than for the unpaired. It therefore seems a reasonable approximation to neglect the ternary complexes as contributors to the consumption of monomer, except in non-polar solvents. The foregoing considerations can be expressed quantitatively by means of the following equations: The monomer-complexing Equations (16) and (17) for unpaired ions [corresponding to (3) and (4)] are

Pn+ + M ↔ Pn+ M

(16)

KM = [ Pn+ M) /[Pn+ ] ⋅ m

(17)

the mass-balance Equation (18) corresponding to (7) and (15) is

co = [ Pn+ M] + [ Pn+ A − ] + [ Pn+ ]

(18)

and the rate-equation (19) corresponding to (2) and (6) is

– dm / dt = R = kp+1 ⋅ [Pn+ M] ⋅ + kp+ ⋅ [Pn+ ] ⋅ m + kp± ⋅ [Pn+ A − ] ⋅ m

(19)

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Developments in the Theory of Cationoid Polymerisations This is not the whole story, as we have omitted the formation of conjugate anions, which, however, in view of the low ionic concentrations involved, is probably a sound approximation. It is evident that the rate-equation comprising all possible participants would have been so complicated and would involve so many constants as to be useless, but Equation (19), based on chemical common sense and admittedly likely to be valid only for the range of conditions given, can be used, as will be shown in the next section. However, before the kinetics we need to discuss one more electrochemical matter, namely how the dielectric constant D of the whole reaction mixture affects the rate-constants kp1+, kp+ and kp±. Because of the irregular shape of the cations, it is unlikely that this influence will obey the appropriate Laidler equations (k varies as 1/D). For the kp±, the appropriate equation would be that for a dipole-dipole reaction, which predicts an increase of the rate-constant with increasing D. The effect of solvents on the kp1+ is discussed by Plesch (1993). The participation of the growing end in a BIE, of the type

Pn+ + MtX −n +1 ↔ Pn X + MtX n

(20)

is an electrochemical phenomenon, and it affects the kinetics, because if it exists in a system, the [P+n] cannot generally be equated to co, the concentration of an initiator salt such as Ph3C+SbCl6-, even if the rate of initiation is great compared to the rate of polymerisation. Various groups of workers have attempted to determine the kp±, by the use of commonion salts so as to repress the dissociation of the ion-pairs at the growing end. In this context the two types of initiator pose different, but related, problems. If the initiator is a protonic acid AH, as in most of the stopped-flow experiments, the greatest part of the AH does not participate in the initiation (see Section 4.3.2). In these systems, therefore, conjugate ions A2H- can be formed from the added salt Bs+A- and therefore the effective [A-] < [Bs+A-]o. In the usual plots [Equation (23) below] of kp* (defined in Section 2.5.3) versus [Bs+A-]o-1/2 this uncertainty will not affect the intercept kp±, at [Bs+A-]o-1/2 = 0, but it will make the slope, from which the kp+ can be found, smaller, so that the resulting kp+ will be an underestimate. If the anion is complex and reactive, e.g., SbCl6-, then the parent SbCl5 formed by a BIE, at the growing end can complex with the SbCl6- from the added salt Bs+SbCl6- to form Sb2Cl11-, and it can act as initiator. This source of uncertainties can be avoided if inert anions, such as SbF6-, are used for the initiator.

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The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993)

2.5. Kinetics

2.5.1 Introduction From the earlier parts of this chapter it should be obvious that enieidic polymerisations are likely to be more common than monoeidic reactions, or - from a different point of view - that special conditions need to be arranged if one form of propagator is to dominate a polymerisation and all others are to be made kinetically insignificant. It has also been shown that there are two principal categories of propagation, unimolecular and bimolecular, and these will now be considered in greater detail.

2.5.2 Unimolecular propagation As mentioned in Section 2.2, the complexing of carbenium ions with monomers is a well-accepted feature of the theory of cationic polymerisations, but it has not been realised clearly until recently that this implies the coexistence of first-order and second-order propagation reactions in certain systems over certain concentration ranges, i.e., the existence of (at least) dieidic polymerisations. The first detailed discussion of the complexing of a carbenium ion with monomers was given by Plesch (1990a), but there was little information about the conditions under which this reaction would be kinetically important. One could, of course, predict from general principles that this complexing will be the more important, the more polar the monomer, the less polar the solvent, and the larger the anion; in other words the factors which diminish the formation-constants of the solvent-solvated cation and of the ionpairs favour the competing monomer as complexor of the cation. The first systematic information on this matter has come from the analysis by Plesch (1993) of the kinetic results on the polymerisation of various monomers by ionising radiations. This matter is discussed in some detail in Section 4.1; here it is sufficient to note that for various alkyl vinyl ethers (VE), styrene, and isobutene the dependence of R and DP on m indicates clearly that the nature and relative abundance of propagating species change drastically as m changes. The critical m, below which there is only the solvent-solvated cation propagating by a second-order reaction, denoted by mC, is given in Table 2, but it is illdefined because the radiation chemists usually did not use m < 2 mol·l-1. The results of Plesch’s analysis (1993)indicate that for the VE the mC is ca. 2 mol·l-1 in benzene, diethyl ether, and diglyme, possibly as high as 9 mol·l-1 in CH2Cl2; for styrene

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Developments in the Theory of Cationoid Polymerisations in toluene probably less than 2 mol·l-1, but in CH2Cl2 between 2 and 3 mol·l-1; and for isobutene about 2 mol·l-1 for CS2, CHCl3, 3–4 mol·l-1 for CH2Cl2, but below 1 mol·l-1 for hexane. Even though it is approximate, this last result especially seems plausible, as the monomer complexing must persist to the lowest concentrations in the least polar solvents. It is uncertain how good a guide these observations are for chemically initiated polymerisations, because in that work the propagation was by unpaired cations. However, we can use general principles to predict how the presence of anions, and an ionic concentration in the range from 10-5 mol·l-1 upwards, would affect the complexation by the monomer, remembering that in the polymerisations by ionising radiations there were no anions, and the ionic concentration was of the order of 10-10 mol·l-1. First, because neither the formation of P+nM nor the formation of P+nP involves a change of charge, the effect of changing the ionic concentration from 10-10 to, say, 10-4 mol·l-1 on the equilibrium constants is likely to be negligible. On the other hand, the effect of ionpairing on the complexation may be considerable; in terms of our previous terminology we are now comparing K′M [Equation (4)] with KM as defined by (16) and (17). The arguments in the previous section showed that in polar solvents the ternary complexes are probably kinetically negligible. They are only likely to be important in hydrocarbon solvents and for Class A polymers because then the only polar or polarisable species is the monomer; under these conditions also the unpaired cation is kinetically unimportant, compared to the paired cation. It is significant that the complexing of P+n by monomer was noted first for just such a system, propene in propane, and at low temperature. It follows from these considerations and from the mC quoted earlier that in solvents of D above, say 6 and at less than, say, 2 mol·l-1, even for the VE the contribution to the rate from a unimolecular mechanism is likely to be negligible. It is tempting to conclude that in that range of conditions P+nP is also likely to be kinetically unimportant, but that does not follow necessarily, because for the polymers of Class B the penultimate pendent group, e.g., OEt from EVE, is always available by an intramolecular binding, and such a unimolecular process is generally kinetically favoured over a bimolecular reaction, such as the complexing of a molecule of monomer or solvent. We conclude that the unimolecular isomerisation-propagation predominates at high m, and that it is the only mechanism in bulk monomer. Such propagation reactions are discussed in detail in Section 4.1. It also follows from this discussion that for the range of conditions indicated, which are those most frequently used for kinetic studies, the propagating species which are likely to be significant participants in second-order propagation are P+n, P+nA-, and P+nP, but the last of these, for the reasons given, is included with P+n.

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The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993)

2.5.3 Bimolecular propagation We start the generalisation of the fundamental bimolecular kinetic Equation (2) by introducing the conclusion from the previous section, namely that for the most common range of polymerisation conditions only the propagators P+n and P+nA- need to be considered, so that

R = m ⋅ ( kp+ ⋅ [ Pn+ ] + kp± [ Pn+ A − ])

(21)

Thus we have arrived back at a simple dieidic system-but we now know under what conditions this is appropriate. It is convenient to define a quantity [Pn*], the total concentration of growing ionic species which may, or may not, equal co , the total concentration of initiator, and which for most systems of interest to us is given by

[ Pn* ] = [ Pn+ ] + [ Pn+ A − ]

(22)

Whenever unpaired and paired cations co-exist as propagators in dynamic equilibrium any one chain will have been formed by an irregular alternation of growth steps involving unpaired and paired ions. This means that the resultant polymers carry the marks (tacticity, co-polymerisation ratios, etc.) of both types of propagation. The Equation (14) teaches us that in order to obtain a polymer formed purely by unpaired cations, one needs to decrease co /KD, by using a very low co with a highly polar solvent and a large anion to increase KD; and to obtain a polymer formed overwhelmingly by paired cations, one needs to work with solvents of low D or with a high concentration of common-ion salt to reduce y/p in a solvent of intermediate polarity. For such dieidic systems we can define a composite rate-constant kp*, given by the traditional equation introduced originally for anionic polymerisations

R/m = kp*[Pn* ] = αco (kp+ – kp± ) + co kp±

(23)

α = [ Pn+ ]/ co

(24)

where

Following the lead in the study of anionic polymerisations, several workers used commonion salts to shift equilibrium (11) in attempts to determine kp+ and kp± by means of

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Developments in the Theory of Cationoid Polymerisations Equation (23), [e.g., Lorimer and Pepper with styrene (1976), Rooney with NVC (1976), Kunitake and Takarabe with styrene (1979a, b).]

2.5.4 The life-time of kinetic species With regard to all the kinetic species considered in this section, P+n, P+nM, P+nP, P+nA-, the question of their lifetime is important, because various authors have attributed the formation of several distinct polymer populations (multimodal DPD) to the persistence of different types of growing ends throughout the lifetime of a chain. In our opinion this view is hazardous for the following reason: at each propagation step the attachment of the solvators at the C+ concerned is loosened because as the charge holding them moves elsewhere, the charge density is reduced in the transition state, and the newly formed C+ at the far end of the incorporated double-bond assembles its own solvators. It seems possible that an anion or a monomer molecule is actually ‘handed along’ the growing chain during several successive monomer additions, but this cannot apply to the P+nP species, as a penultimate pendent group is left behind and the next one takes its place; so to ascribe the formation of a particular polymer population to the species P+nP, as has been done (Sauvet et al., 1986) does not seem plausible to us. The general conclusion is that any one polymer chain is formed by a cation whose state of solvation (including pairing) changes irregularly during the life-time of that chain, and the average state of solvation depends on the prevailing circumstances. This point was made at the end of the previous section with regard to ion-pairing.

2.5.5 Conclusion Finally, we need to clarify how the total concentration of propagators is related to the processes of initiation (rate Vi, rate-constant ki) and termination (rate Vt, rate-constant kt). Until the early 1970s it was generally thought that if a cationic polymerisation is internally of first order, i.e.,

– dm / dt = k1 ⋅ m z

(25)

with z = 1, then the stationary state evinced by this behaviour is of the First Kind, i.e., one in which Vi = Vt ≠ 0, as in radical polymerisations. Under these circumstances, k1 is some function of ki, kp, kt and of the concentrations of initiator or co-initiator or both. However, about the mid-1970s several workers realised that for many cationoid polymerisations, which are internally of first order, the stationary state might be of the Second Kind, i.e., Vi = Vt = 0, throughout the greater part of the reaction; in other words Vi is so great that the initiation is complete in a time which is small compared to the life 506

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) of the polymerisation (‘bang initiation’), as in many anionic polymerisations. The idea that some cationic polymerisations proceed without a termination was formulated explicitly by Plesch (1956), but it took a long time for its implications to be understood and accepted. The term ‘stationary state of the Second Kind’ implied originally that the concentration [P+n] of the propagating species, believed at that time to be unique, remained constant throughout the life of the reaction, and that therefore the rate is determined only by the propagation rate constant. We now know that the kinetic situation may be more complicated, with several species sharing in the consumption of the monomer, and their relative concentrations liable to change during the life-time of the polymerisation. In view of the prevalence of such enieidic polymerisations, it is all the more important to select for attempts at determining propagation rate-constants such systems as do not involve complications from relatively slow initiation or fast termination, or both. For a successful measurement of kp+ it is essential that the initiation reaction should be well understood, which rules out most of the claims pertaining to systems involving an initiator and a co-initiator. It is almost equally important that the kinetics of the polymerisation should be simple. ‘Simplicity’ means that the polymerisation should be of a simple order internally, with respect to the monomer concentration, such that in Equation (25) z = 0 or 1, and that k1 should be independent of mo and should depend rectilinearly on the concentration of the initiator. Unfortunately, very few of the attempts at measuring kp+ are concerned with simple systems of this kind; many workers have preferred to struggle with the complications of interpreting kinetically obscure polymerisations to searching out chemically and kinetically simple systems. It is evident from the foregoing exposition that almost all the discussions in the literature about the propagation rate-constants of cationic polymerisations are defective, and that most attempts at their measurement are flawed in some more or less important respect. The present author notes with regret that his own earlier writings on the subject are no more than preliminary approaches, and he quite expects that even the present, much more profound, discussion may yet turn out to be defective in some essential respect.

3 Critical account of methods In this section we describe the methods which have been used for measuring R and by which measurements of [P+n]and [P+nA-] were attempted.

3.1 Measurement of the polymerisation rate In chain reactions of the type considered here, the rate of polymerisation is the rate of consumption of monomer. This can be determined directly by measuring the concentration of the residual

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Developments in the Theory of Cationoid Polymerisations monomer or of the polymer formed as a function of time by some form of spectroscopy or chromatography, or by the weight of the polymer isolated (usually by precipitation) from aliquots of the reaction mixture. However, the precipitation method can give misleading results because of the non-precipitability of some oligomers in the most common precipitant, ethanol; therefore the choice of the precipitant is important. The most common indirect methods involve following the change of density of a polymerising mixture under isothermal conditions or the change in temperature under adiabatic conditions. Densitometry and calorimetry work on the principle that the change in the physical quantity measured, i.e., density or temperature, is directly proportional to the change in the concentration of monomer. This is not valid for the first few steps of polymer formation, because both the change of density ρ with conversion, Δρ/ Δm, and ΔT/Δm are greatest for the formation of dimer and diminish asymptotically with increasing DP, becoming constant at about DP = 5. This means that unless the DP of the polymer exceeds ca. 40, the measured dρ/dt and dT/dt depend on the DP and may differ significantly from the values relevant to the formation of high polymers. It is this factor which limits attempts to slow down polymerisations by using a very low mo , because this generally leads to products with a low DP.

3.1.1 Densitometry The density measurement by means of a dilatometer (reviewed by Plesch, 1986) is being superseded by the Kratky vibrator method (Trathnigg, 1980a, b; Trathnigg and Schneditz, 1982). Densitometry is only really useful if the density of the reacting solution is rectilinearly related to the degree of conversion of monomer to polymer, which is not true of all systems (Treloar, 1960); but few investigators have tested this point.

3.1.2 Adiabatic calorimetry If a polymerisation is too fast for the reaction mixture to be kept isothermal, then the rate of temperature rise under adiabatic conditions can be used with advantage as a measure of the rate of the reaction. By means of a conventional electrical calibration and the experimentally established relation between Δm and ΔT, the rate of temperature change, dT/dt, is converted to –dm/dt, and the enthalpy of the polymerisation, ΔHp, can be found as well. A version of the technique suitable for cationic polymerisations was developed by Biddulph and Plesch (1959) and subsequently used by many workers; substantial improvements were made by Sigwalt’s group (Cheradame et al., 1968; Favier et al., 1974) and by Pask and Plesch (1989). The method is most useful for reactions which have half-lives in the range of 5 to 300 s, and

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The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) for mo in the range from about 0.05 to 2 mol·l-1. The lower limit is given by the consideration that the ΔT due to the polymerisation must exceed any temperature changes due to adventitious causes. Also, for monomers which give polymers whose DP is proportional to mo , a too low mo may yield polymers (oligomers) of such low DP (< ca. 20) that the assumption Δm = k·ΔT no longer holds, because the ΔHp for the formation of oligomers decreases asymptotically from DP = 2 to a constant value at DP ca. 5. It is also essential that the polymerisations go to completion. The critical test, omitted by many users of calorimetry, is that the relation between ΔT and Δm be a straight line through the origin. Our own experience of reaction calorimetry has taught us that the consistency (or lack thereof) of ΔHp values (or ΔT values) is a very reliable guide to the quality of such an investigation. The upper limit to mo is set by the need to avoid a too great increase in the viscosity of the reaction mixture or gel formation, especially at very low temperatures.

3.1.3 The stopped-flow technique The cationic polymerisations which are too fast for adiabatic calorimetry must be studied by other techniques, and prominent amongst these is the stopped-flow method. The idea behind this is that two reagents are mixed very rapidly and efficiently in a small volume and the resulting mixture is forced to flow along a tube containing one or more observation points. When the flow is stopped, the course of the subsequent reaction is recorded at the observation point. The most common observation method is UV-visible spectroscopy, and by this means the concentration of reactive species with suitable chromophores, e.g., aromatic carbocations, and the concentration of some monomers, typically aryl alkenes, can be monitored; ideally, both should be recorded simultaneously. If this is done, dAm/ dt and A* and dA*/dt are available, where Am is the absorbance due to the monomer and A* is that of all the growing species containing P+n at the wavelength λx of the absorbance maximum. Since

m = Am / εm ⋅ l

(26)

where εm is the molar extinction of M at λx and l is the pathlength, and

[ Pn* ] = A * / ε * ⋅ l

(27)

all the elements required for the calculation of kp* by means of the Equation (23) are available – in principle. However, although εm is easily measured, the determination of ε* is usually difficult, and the main weakness of this method arises at this point.

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Developments in the Theory of Cationoid Polymerisations

3.2 Determination of the nature and concentration of growing species

3.2.1 Outline After what has been explained in the earlier sections, it must be clear that most of the attempts at measuring kp+ have been misdirected. All but a few investigators assumed that at most two propagating species, P+n and P+nA-, were involved in their systems. Therefore we will need to examine for each report, first what were the most likely chaincarriers, i.e., what was the probable principal component of Pn*, and to what extent our assessment agrees with the opinion of the original workers; and then we need to examine how adequate were the measurements of [Pn*] and of the rate of polymerisation. An account of the attempts at determining [Pn*] must be prefaced by an enumeration of the various reactions which can frustrate such attempts. As we are only interested in ionic propagating species, we have to consider P+n, P+nP, P+nM, P+nA-. As explained in Section 2, the P+nP must at present be included with P+n and the P+nM is generally negligible in solvents of D above ca. 6 at m < ca. 2 mol·l-1. A danger which has not been encountered before is that the initiating or the propagating cation may form a complex P+nSv with a very polar solvent, Sv, that is so strong that it is not a propagator. The present author was caught in this trap when he chose nitrobenzene for the measurement of the kp+ of various monomers. In this highly polar solvent the formation of P+nM, P+nA- and, presumably also of P+nP was suppressed, but the kinetic results indicated that a considerable fraction of the cations had been inactivated by cationation of the solvent (see Section 4.2.3); therefore the real [P+n] was less than that calculated and so the calculated kp+ are too low. The methods for determining [Pn*] fall into two principal categories. One of these consists of making ‘plausible guesses’ about [Pn*] from the quantity of initiator and/or co-initiator, generally without any direct, rigorous check; the fundamentally sound method involves attempts at measuring [Pn*]. This can be done by at least three procedures. The first involves counting the number of initiator fragments present in a sample of polymer. If the initial groups derived from the initiator are not suitable for such an analysis, one can use the second method. This consists of ‘short-stopping’ the reaction, i.e., feeding into the polymerising solution a basic reagent which reacts cleanly, completely and irreversibly with the growing carbenium ions and thus produces an identifiable end-group, whose concentration can be measured. As such bases react equally well with P+n, P+nA- and PnA (ester), this method can give [Pn*] only in the absence of any ester; see reaction scheme (28) and Section 4.3.4:

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The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993)

Pn+, APnSv+, APn–A

PnNR3+, A-

R3N →

+ ArO-, Mt+

PnOAr, A-, Mt+

(28)

A third type of procedure is aimed at determining the [Pn*] in the reacting solution by measuring some physical property, such as the conductivity or the UV-visible spectrum. Only the conductivity method can distinguish between the sum of the concentrations of the species with a net charge (including the inert P+nSv defined above) and the nonconducting P+nA- and ester PnA. Although there must be differences between the spectra of the various species containing P+n they are far too subtle to have been detected in the work under review, so that these spectroscopic measurements gave the total [Pn*]; the spectroscopic difference between a paired and an unpaired carbenium ion was not found until recently (Schneider et al., 1987). Another method, kinetic titration, is discussed in Section 4.2.8.

3.2.2 Initial group determinations It has of course been understood ‘from time immemorial’ that if one could count the number of initiator fragments attached to the polymer chains then, in the absence of kinetic termination, one could thus find [Pn*] via the initial groups; or if one could be sure that there is no chain-transfer, a counting of initial groups or of the number of chains would provide the same information. Many qualitative identifications of initial groups derived from a putative co-initiator were attempted quite early {see for example Dainton and Sutherland (1949), [D in oligo-isobutenes from D2O co-initiator]; Plesch (1953) [end-groups derived from alkyl halide solvents in polystyrenes made with TiCl4]; Kennedy (1959) [Et groups labelled with 14C in poly(isobutyl vinyl ether) made with labelled BF3·Et2O]; Kennedy and Thomas (1960) [Me groups labelled with 14C in poly(isobutene) made with AlCl3 in labelled MeCl as solvent]}. It is difficult to understand now why these attempts were not developed to the quantitative level. One reason was probably the technical difficulty of such analyses at the time, and probably a more cogent reason was the realisation that even if groups derived from a co-initiator were found, only very detailed experiments could determine whether they had got into the polymer by initiation or by a transfer reaction with the putative co-initiator; the possibility of such reactions invalidates all the experiments quoted above.

511

Developments in the Theory of Cationoid Polymerisations In our opinion, the attempts to determine [Pn*] by means of initial trityl groups originating from a trityl-containing initiator are not always convincing and should be regarded with suspicion, because if a mixture of a trityl compound and a metal halide, MtXn, is used, e.g., Ph3CCl + SnCl4, then the Ph3C+ may not react cleanly and rapidly with many alkenes. The reasons for this include the involvement of the initiator in a BIE, as discussed below; steric inhibition due to the shape and size of the trityl cation, complexation of Ph3C+ with M, complexation of M with the MtXn and electron transfer giving the radicalcation ·M+. Very few systems are as well documented as the initiation of the polymerisation of cyclopentadiene by Ph3+SbCl6- and its bifunctional analogue (–CH2·C6H4CPh2+)2 2SbCl6-; there is no transfer and all the chains are started by the addition of the trityl cation to the monomer (Villesange et al.,1980). The determination of initial carbonyl groups derived from aroyl salt initiators, ArCO+MtX-n + 1, was used to confirm that with styrene in nitrobenzene these initiators give fast and complete initiation and form the initial group ArCOCH2CHPh– (Holdcroft and Plesch, 1984). Several attempts have also been made to count the number of chains initiated by iodine, before it was understood that in the I2 + alkene systems the real initiator is a proton from HI, and that any iodine in the polymer was either part of the growing end of a pseudo-cationically growing chain (Giusti and Andruzzi, 1966), or was incorporated by the iodination of double-bonds which originated from a proton transfer reaction at the growing end.

3.2.3 The short-stop (end-group) method The short-stop method of measuring [Pn*] was developed to produce an easily determinable end-group in systems in which the ‘natural’ end-groups are unsuitable for accurate, quantitative determination. It was first used by Jaacks et al., (1968) to determine the concentration of tertiary oxonium ions during the polymerisation of 1,3-dioxolan, and by Saegusa et al., (1968) for similar studies on tetrahydrofuran. For the polymerisation of alkenes it has only been used on two occasions. i) Higashimura et al. (1971) used 2-bromothiophene to stop the polymerisation of styrene in benzene solvent by BF3, cocatalysed by controlled quantities of water at 30 ºC. The idea was to determine the bromine content of the polymer by radioactivation analysis. The four experiments quoted showed a very large discrepancy between [H2O] and [Pn*], and the full publication announced never appeared. The kp of the order of 0.25 mol·l-1·s-1 is far too small to be kp+ in view of the low polarity of the solvent. ii) Sawamoto et al., (1983) used sodium naphthoxide to short-stop the polymerisation of styrene by MeCO2ClO3 in solvent mixtures of DC from 6.4–10.7 at 0 ºC. The end-

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The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) groups were counted spectroscopically by means of the absorption of the 2-naphthoxy group. The authors showed clearly that the polymerisations were dieidic, and the circumstances indicate that the participating species were probably the ester and the unpaired ions; therefore the ‘kp+’ calculated could not be assigned to any one type of active species (Section 4.3.4). It is strange that the elegant and sensitive method developed by Penczek’s group, which involves trapping oxonium ions by reaction with tert. phosphines, appears not to have been applied yet to carbenium ion polymerisations; this method too, however, would not distinguish between ions and esters as propagating species (Brzezinska et al.,1977).

3.2.4 Spectroscopic determination of growing ends The principal difficulty with the spectroscopic identification and estimation of the propagating ends is that under most conditions the reaction of an aryl alkene with any acidic reagents yields several products, most or all of which absorb in the same region of the spectrum, and the relative amounts of which change with the extent of reaction and with time (see for example Kunitake and Takarabe, 1976). This means that even if one is dealing with a monoeidic system, and even if the absorption spectrum of the propagating species is known, one cannot know without elaborate experiments what fraction of the absorbance found at any particular wavelength is due to the propagating species, and it is generally not known whether this fraction remains constant as the reaction progresses. However, since the total number of cations of all kinds generated per mol of initiator probably remains fairly constant with time, and since the extinction coefficients of the various ions are generally very similar, it is easy to see that ∫A·dλ can be approximately constant with time and proportional to the concentration of the initiator, without thereby giving an unambiguous measure of [Pn*]. Quite generally, if the A at λ* is due not only to the growing ends but also contains contributions from some or all of the other cations present in the solution, then the calculated [Pn*] will be too great, and consequently the kp* will be too small. The multiplicity of ions stems from polymerisations and degradative reactions which are strongly temperaturedependent, and for this reason the results obtained below ca. –50 ºC are easier to interpret and more reliable. The literature on the multiplicity of ions which can be formed from styrenes is extensive and some papers of direct relevance include Bertoli and Plesch (1968, 1969), Gandini and Plesch (1968), Moreau et al., (1987), Matyjaszewski and Sigwalt (1987). Although all the facts quoted here have been known for a long time, they have not been given proper consideration by some users of the stopped-flow method, and consequently their work has contributed little to the quest for sound kp+ values.

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Developments in the Theory of Cationoid Polymerisations

3.3 Sources of uncertainty and errors

3.3.1 Uncertainty about the nature of the initiator All the attempts to determine kp+ for systems in which BF3 or BF3Et2O was used as initiator can be ruled out because either the assumption was made that [P+n] = [BF3] or it was assumed that [P+n] = [BF3Et2O]. Since we now know that neither BF3 nor BF3Et2O is an initiator, but that the activity of BF3 depends on the presence of water (Giusti et al., 1970; Moulis et al., 1980; Gandini and Martinez, 1988), all experiments in which the water concentration was unknown (and that is the vast majority) can be ignored. Very similar considerations allow us to discard many experiments in which other metal halides were used which require a co-initiator (most frequently SnCl4), because even though the concentration of co-initiator (water, phenol, acid) may have been known, the relation between the concentrations of initiator and coinitiator and the resulting [Pn*] was not established experimentally, nor were the components of the [Pn*] and their concentrations.

3.3.2 Impurity effects Even if the nature of the initiation reaction is well-established, e.g., the initiation by a carbocation such as ArCO+, the [Pn*] cannot be assumed to be equal to the concentration, co , of the initiating species. Allowance must be made for the amount of initiator which is lost by reaction with basic impurities (concentration, ci), so that in reality

[ Pn* ] = co – ci

(29)

This of course applies especially to work done with very low co or with poorly purified solvents and reagents. Few investigations contain a plot of a rate or a rate-constant against co , from which ci can be determined as the intercept on the co axis (the impurity intercept). A kinetic method of determining the concentrations of the impurities in solvent and monomer has been described (Holdcroft and Plesch, 1984).

3.3.3 Sequestration of the initiator The two most common classes of initiator, metal halides and protonic acids, can both react with alkenes to give non-ionic products, whereby their effective concentration is diminished. The metal halides can form inert complexes, which explains why for example, isobutene and AlCl3 can co-exist in a non-reacting solution (Grattan and Plesch, 1980). In the stopped-

514

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) flow experiments with for example, CF3SO3H and styrene-type monomers, usually the [Pn*] << [AH]0; this may be because of ester formation, which is obviously important, irrespective of whether the ester can propagate polymerisation; or the [Pn*] may be less than [AH]0 because of the formation of conjugate anions A2H-,especially if a common-ion salt is used; a third reason is mentioned at the end of the next section. However, these phenomena would not affect any results obtained by those methods, e.g., stopped flow, which involve the direct counting of the cations by spectroscopic means.

3.3.4 The initiator and/or the growing end is involved in a BIE Until recently the possibility was ignored that initiators involving metal halides MtXn and organic halides, such as Ar3CX, or complex salts formed from these may be involved in a BIE, (Grattan and Plesch, 1979; Pask and Nuyken, 1983), e.g.,

Ar3CX + MtX n ↔ Ar3C + + MtX n− +1

(30)

When such an initiator is introduced into the monomer solution only the ions present at that moment can react with the monomer to give the propagating cation:

Ar3C + + M → Ar3CM +

(31)

the remainder of the initiator then ionises by the shifting of equilibrium (30). This type of reaction is relatively slow, and in the presence of an alkene monomer the formation of ions is even slower, because the concentration of the MtXn is reduced by its complexing with the alkene monomer

MtX n + M ↔ MtX n ⋅ M

(32)

Therefore, if the polymerisation initiated by the existing ions is fast, the ions formed after the mixing of the reagents find little or no monomer left to attack. In other words, this is another reason for [Pn*] being less than co . This consideration affects all experiments done with ‘stable carbenium ion salts’, which are vitiated by the fallacious belief that because a complex salt is completely ionic as a solid, it will remain completely ionised in solution; MeCO+SbF6-, for example, is a salt for which this is not true (Nuyken and Plesch, 1973). Sigwalt’s group, whose preferred initiator was Ph3C+SbCl6-, have cited evidence showing that this salt is completely ionised and dissociated under the conditions relevant to their polymerisations; this is discussed in Section 4.2.2.2. There may be differences in this respect between the Ph3C+ and the C7H7+ salts which could account for some features of the results of the Bawn group and others.

515

Developments in the Theory of Cationoid Polymerisations The BIE, are of course equally relevant to those systems in which a metal halide initiates by a cation which is formed in a self-ionisation BIE reaction, e.g., AlCl3 (Grattan and Plesch, 1980):

2 AlCl 3 ↔ AlCl 2+ + AlCl 4−

(33)

AlCl 2+ + M → AlCl 2 M +

(34)

Although an initiator may have reacted completely with monomer to yield P+n, the end of the growing chain may be involved in a BIE, so that the stationary concentration [P+n] is then less than the original concentration, [Int+]o = co , of the initiator:

A − + Int + + M → IntM + + A −

(35)

and if A- = MtX-n + l, and we denote IntMn+ by P+n.

Pn+ + MtX −n +1 ↔ Pn X + MtX n

(36)

This effect, too, will cause the [P+n] to be less than co . It is an as yet open question whether the complexed growing cations P+nM and P+nP can participate directly in BIE, The argument has been conducted in terms of unpaired ions, but paired ions may also be involved, so that there are concurrent Unary (Ostwald type) and BIE, However, this makes no difference in principle, as can be seen from the treatments of BIE, with ion-pairs by Grattan and Plesch (1979), Pask and Nuyken (1983) and Holdcroft and Plesch (1985). The common finding, discussed in the previous section, that when cationic polymerisations are initiated with protonic acids, HA, as in the stopped-flow experiments, the [Pn*] << [HA]o can be explained along the same lines, as will be shown in Section 4.3.2. We have here a useful discriminatory test, because in the pseudocationic polymerisations initiated by HA (with or without a modifier, such as an organic sulphide), the concentration of growing ester is equal to [HA]o (Plesch, 1992).

4 Results 4.1 Polymerisations initiated by ionising radiations 4.1.1 Introduction In this section we deal with the cationic polymerisations initiated by gamma rays, e.g., from a 60Co source, or by high energy electrons. Both types are treated together because

516

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) the phenomenology of the reactions is essentially the same. We shall deal separately with the polymerisations of undiluted monomers and those of monomers in solution. Our Section 2.5.2 will have alerted the reader to the peculiarity of bulk polymerisations, so that this division needs no further explanation. What does need explanation, however, is the revaluation, in the light of our new understanding, of a group of results which have been taken for many years as bench-marks in a dubious and contentious area of physical chemistry. The ‘father’ of the subject is F. Williams, because he was the first to devise how to obtain kp+ values from rate measurements on the polymerisation of an alkene (cyclopentadiene) by ionising radiation (Bonin et al., 1965), and he wrote what is still the most comprehensive and critical account of a difficult subject (Williams, 1968). He refers characteristically to ‘. . . an alarming number of misinterpretations and errors . . .’. Other, shorter, expositions have been given by Metz (1968), Hayashi (1971, 1980) and Stannett and Silverman (1983). The subject was popular until the end of the 1970s, but although many groups contributed to the elucidation of the chemistry and mechanisms of reactions caused by ionising radiations, only four of them have measured ‘kp+’ values. A scrutiny of the References section shows that three, which we will designate by the names of their leaders, Williams, Hayashi, and Stannett, interchanged personnel, a practice which led to a certain homogeneity of outlook, methods and, fortunately, also of critical standards. It was agreed by the mid-1960s that ionising radiations can generate radicals, cations, and anions as well as radical-ions, and that in order to obtain polymerisations in which the propagation by carbenium ions is dominant, the systems need to be freed from ion scavenging impurities, especially water, to an extent rarely, if ever, required or achieved in any other branch of chemistry at that time. It was also recognised that under prolonged irradiation the polymers formed could be fragmented, yielding growth-inhibiting impurities, or grow grafts, or both, so that the DP of the polymers was not as informative as that of polymers made by chemical initiation. The theoretical framework within which the polymerisations by ionising radiations were interpreted was developed to account for the reactions of bulk monomers, and the assumption was made that the propagation reaction is bimolecular, as for a chemically initiated polymerisation. That this assumption was incompatible with many conversion plots which are rectilinear to high conversions, and in some instances show accelerations, was ignored. When eventually polymerisations by ionising radiations were done in various solvents, the theory was extended somewhat uncritically to these, but no general theory comprising bulk polymerisations and the highly diverse effects of different solvents was ever developed. During the preparation of this review the present writer became aware of this unsatisfactory situation. He also saw that if one could understand the very varied phenomena occurring in polymerisations by ionising radiations, one would gain insight into many of the problems presented by the chemically initiated polymerisations. He therefore interrupted the composition of this review for ca. 18 months whilst he developed

517

Developments in the Theory of Cationoid Polymerisations a comprehensive interpretation of the polymerisations by ionising radiations (Plesch, 1993). The interpretations of the rate measurements, i.e., the conclusions concerning rateconstants, given in this section are based on that work. For reasons of consistency within the present review, some of the symbols used in this section differ from those used in the original publication (Plesch, 1993) on which it is based.

4.1.2 Theory of bulk polymerisations The rather complicated theory developed by the authors quoted earlier can be summarised thus: both in bulk monomers and in solutions of monomers the incident radiation creates a mixture of radicals and organic cations and electrons. Most of the cations recombine very rapidly with electrons (geminate recombination), but some remain free for a sufficient time to propagate a cationic polymerisation which is eventually terminated by combination with an electron. Provided that the cations are not deactivated by adventitious impurities, the ensuing polymerisations will have a cationic component. Since even at the highest dose rates the concentration of growing chains is less than 10-7 mol. l-1, the pairing of ions can be neglected and one can understand why high purity is required to obtain effectively monoeidic cationic polymerisations, in which the contribution from the much slower radical polymerisations can be neglected. If the monomer is polymerisable anionically as well as cationically, the anionic polymerisation can be suppressed, and it is always slower than the cationic reaction. Elaborate experiments by several groups had shown that with progressive purification the polymerisations became faster and the index n in Equation (37)

R ∝ In

(37)

tended to 0.5; here R is the rate of polymerisation and I is the dose-rate of the radiation. The one-half order with respect to I arises from the fact that the termination reaction is a bimolecular neutralisation:

Pn+ + Q − → Pn Since the propagating species was known to be an unpaired ion, P+n the rate-equation was written conventionally as

R = kp+ ⋅ [ Pn+ ] ⋅ m

(38)

The R was always sufficiently low for it to be measured by dilatometry. The great attraction of these polymerisations for the kineticists was the possibility of estimating or measuring the total concentration of cations in the reaction mixtures. Several different methods of

518

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) doing this were devised by different groups, which yielded reasonably concordant results; for the details of the methods the original publications must be consulted. There was general agreement that all the cations would very rapidly form polymers with cationic ends, all of them assumed to be growing; in other words, all the authors identified their concentration, [C+], with [P+n], and by means of Equation (39) they calculated their kp+. All these results are shown in Table 1. At this point we leave the conventional kinetic theory and turn to the substance of our Section 2.5.2. The principal point made there is that for polymerisations in bulk the propagation reaction is not bimolecular but unimolecular, so that the rate is given by Equation (39):

R = kp+1B ⋅ [ Pn+ M]

(39)

The symbol kpl+B denotes the first-order rate-constant of the bulk polymerisations. If M is a mono-alkene, we have the simplest case, with no aromatic groups or hetero-atoms in monomer or polymer, so that

[C + ] = [ Pn+ M] + [ Pn+ ]

(40)

where now [P+n] is the (notional, very small) concentration of uncomplexed P+n.

Pn+ + M ↔ Pn+ M so that

[ Pn+ M] = KM ⋅ [ Pn+ ] ⋅ m

(41)

For this simple case

[Pn+ M] = [C + ]

(42)

so that the rate-equation (39) becomes

R = kp+1B ⋅ [C + ]

(43)

which is related to the conventional rate-equation (38) by (45):

kp+1B = kp+ ⋅ mB

(44)

519

Developments in the Theory of Cationoid Polymerisations

Table 1 Alleged rate-constants ‘kp+’ for bulk polymerisation and firstorder kpl+B calculated from them Result No.

T, °C

mB/mol·l-1

'kp'/l·mol-1·s-1 a

kp1+B/s-1

b

References

1 Cyclo-pentadiene 1.1

–78

13.6

5.8 x 108 ± 1

7.9 x 109

Bonin et al. (1965)

2 Isobutene 2.1

0

11.0

1.5 x 108

1.6 x 109

Taylor and Williams (1969)

2.2

–78

12.6

1.5 x 108

1.9 x 109

Taylor and Williams (1969)

3.1

40

8.54

(2.9 ± 1) x 106

2.5 x 107

Ka. Hayashi et al. (1973)

3.2

25

8.66

(2.4 ± 0.9) x 106

2.1 x 107

Ka. Hayashi et al. (1973)

3.3

15

8.75

(2 ± 0.5) x 106

1.8 x 107

Williams et al. (1967)

3 Styrene

4 α-Methylstyrene 4.1

0

7.75

4.4 x 106

3.4 x 107

Williams et al. (1967)

4.2

35

7.58

6.5 x 105

3.0 x 106

Chawla and Huang (1975)

4.3

20

7.71

9.9 x 105

7.6 x 106

Chawla and Huang (1975)

4.4

0

7.75

1.30 x 106

1.0 x 107

Chawla and Huang (1975)

4.5

–20

8.05

1.18 x 106

9.5 x 106

Chawla and Huang (1975)

7.45

3 x 106

2.2 x 107

Deffieux et al. (1980)

5 4-Methoxy-styrene 5.1

20

6 Ethyl vinyl ether 6.1

30

10.3

9.4 x 104

9.7 x 105

Hsieh et al. (1980)

6.2

23

10.5

3.5 x 104

3.7 x 105

Hsieh et al. (1982)

6.3

20

10.54

2.9 x 104

3.1 x 105

Deffieux et al. (1981)

6.4

0

10.8

7.2 x 103

7.8 x 104

Goineau et al. (1977)

6.5

0

10.8

8.3 x 103

9.0 x 104

Suzuki et al. (1977)

520

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993)

Table 1 Continued Result No.

T, °C

mB/mol·l-1

'kp'/l·mol-1·s-1

a

kp1+B/s-1 b

References

7 Isopropyl vinyl ether 7.1

30

8.65

1.3 x 106

1.1 x 107

Hsieh et al. (1980)

7.2

26

8.72

1.2 x 106

1.0 x 107

Deffieux et al. (1983)

7.3

0

9.0

9.0 x 105

8.1 x 106

Goineau et al. (1977)

7.4

0

9.0

9.2 x 105

8.3 x 106

Hsieh et al. (1980)

8 Isobutyl vinyl ether 8.1

50

7.3

6 x 10 5

4.4 x 106

Ka. Hayashi et al. (1971)

8.2

42.5

7.4

1.1 x 106

8.1 x 106

Ueno et al. (1968)

8.3

30

7.6

3.4 x 105

2.6 x 106

Williams et al. (1967)

8.4

25

7.6

1.2 x 105

6.2 x 105

Ka. Hayashi et al. (1971)

8.5

0

7.9

3.8 x 104

3.0 x 105

Ka. Hayashi et al. (1971)

8.6

0

7.9

3.8 x 104

3.0 x 105

Goineau et al. (1977)

5 x 10 4

4 x 104

Goineau et al. (1977)

9 Tert. butyl vinyl ether 9.1

0

ca. 8.0

a

: The ‘kp’ are the constants calculated by the original authors : The kp1+B are the unimolecular rate-constants calculated by Equation (44). As explained in the text, they are probably minimum values, except for monomers Nos 1 and 2 b

The theory of unimolecular propagation for the cationic polymerisation of a bulk monomer was first developed by Szwarc (1978), and Equation (44) introduced by him has been named Szwarc’s equation (Plesch, 1993). The values of kpl+B calculated according to Equation (44) are also listed in Table 1. They show the same ranking as the kp+, since the mB only vary from ca. 7–11 mol·l-1 but as they are first-order constants they cannot be compared with any second-order rateconstants obtained for the same monomers by chemical initiation. Therefore all the many attempts in the literature to make such comparisons are futile.

521

Developments in the Theory of Cationoid Polymerisations In developing his theory of the polymerisations by ionising radiations Plesch now distinguishes between the mono-alkenes and other monomers, thus: if a monomer, such as styrene, contains two donor groups, then both of these can be involved in the complex formation with the carbenium ion, but only the π-complex involving the double-bond can propagate. This means that Equation (40) must be replaced by

[C + ] = [ Pn+ M] + [ Pn+ G] + [ Pn+ ]

(45)

where P+nG is the non-propagating complex between P+n and M. For the VE, which have a π- and an n-donor group, the same considerations, also expressed by Equation (45), apply. It follows that for monomers other than the mono-alkenes the concentration of +B growing chains, [P+nM], is less than [C+], and consequently the kp1 calculated by means of Equation (43) are too small. If the formation of the non-propagating complex P+nG is described by Equation (46):

Pn+ + M ↔ Pn+ G, KG

(46)

so that

[ Pn+ G] = KG ⋅ [ Pn+ ] ⋅ m

(47)

the elimination of [Pn+] and [Pn+G] gives

[ Pn+ M] = KM ⋅ [C + ] ⋅ m /([ KM + KG ] ⋅ m + 1)

(48)

This expresses quantitatively by how much the rate-constants calculated on the basis of (40) for aryl alkenes and VE by the original investigators could be underestimated, and this effect +B must account-at least in part-for the great differences in the kp1 recorded in Table 1.

4.1.3 The hydrocarbon monomers and 4-methoxystyrene in bulk The first determination of a kp+ by ionising radiation was achieved by Bonin et al., (1965) for bulk cyclopentadiene; the second, for isobutene, also came from Williams’ group (Hubman et al., 1966). The very high values would not have been taken seriously if the methods had been less rigorous or the accounts less detailed. It was generally thought that these rate-constants were as near as one could get to the propagation constant of a ‘bare’ cation reacting with an alkene, not least because the associated activation energies are near zero. In our view we see here rates of isomerisation which are only prevented from being even greater by the considerable negative activation entropies, which arise

522

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) from the incorporation of the monomer and the immobilisation of a replacement in the solvent shell of the cation. After Williams’ initial reports (Bonin et al., 1965; Hubman et al., 1966), the most detailed account of the methods used for determining kp+ is in the group of three papers resulting from the cooperation of Williams with Okamura’s group in Kyoto (Ueno et al., 1967; Hayashi et al., 1967; Williams et al., 1967); in these the kp+ of styrene, α-methylstyrene and isobutyl vinyl ether were reported. The bulk polymerisation of styrene and of αmethylstyrene gave kp+ values of the same order of magnitude (ca. 106) and two orders of magnitude less than those for cyclopentadiene and isobutene; the same is true for our +B kp1 shown in Table 1. A study of the polymerisation of α-methylstyrene by 60Co radiation at between –20 ºC and 35 ºC is described in great detail by Chawla and Huang (1975). The results in Table 1 +B show that their kp+ and our kp1 increase as the temperature is reduced; the change for +B + kp1 is greater than for kp because mB increases with falling temperature. The fact that the activation energy is negative (Ep = –13 kJ·mol-1 if Williams’ result is included) indicates that the propagation is very unlikely to be a simple bimolecular reaction. The bulk polymerisation of 4-methoxystyrene (Deffieux et al., 1980) also gave a ‘kp+’ of the same order of magnitude, but to calculate it from their less detailed measurements the authors had to assume values for the rates of initiation and termination in order to obtain ‘[P+n]’, and they chose to use those for styrene. It seems to us that it would have been more logical to take the rates of initiation and termination for another ether, e.g., IBVE, but in fact according to our calculations the resulting ‘kp+’ is only ca. 50% greater, a difference which is hardly significant in the present context.

4.1.4 Alkyl vinyl ethers in bulk The alkyl vinyl ethers are the most thoroughly studied class of compounds as far as their polymerisation by ionising radiations is concerned, and these studies have provided some of the best insights into the chemistry involved. The first one was a part of the classical work of Williams with the Kyoto group (Williams et al., 1967), but the largest body of results originates from the group of Stannett, who has also produced several summarising and comparative accounts which also comprise their work with alkyl vinyl ethers in solution, to be discussed below (Stannett et al., 1976, 1979, 1989; Goineau et al., 1977; Stannett and Silverman, 1983; Stannett and Deffieux, 1984); all results in Table 1. The first member of the series, methyl vinyl ether (MVE) provided an interesting lesson, because although it can be polymerised cationically by chemical initiators, its exposure to ionising radiations produces only a radical polymerisation. Desai et al.

523

Developments in the Theory of Cationoid Polymerisations (1977) showed that this is due to the formation of fragmentation products which inhibit the cationic reaction. The formation of inhibiting impurities also affects the later stages of the polymerisation of ethyl vinyl ether (EVE), but extrapolations to zero time gave the dose-rate dependence of the rate as n = 0.51 (Suzuki et al., 1977). By assuming that the initiation and termination rates are the same as those found by Williams et al. (1967) for isobutyl vinyl ether, a rateconstant and an activation energy were calculated. In the same paper these authors also reported on isopropyl vinyl ether (IPVE), isobutyl vinyl ether (IBVE), and tert. butyl vinyl ether (TBVE). The results for IPVE are in satisfactory agreement with those from the first and most thorough study (Williams et al., 1967).

4.1.5 Discussion of bulk polymerisations +B In our view all these results should be presented as our kp1 . As explained above, the differences, especially the very low values for the VE, are to be attributed very largely to the assumption that the concentration of propagating ions is equal to the calculated total concentration of ions, when in fact a large fraction of these is engaged in complexes which are unable to propagate, and only the remainder is complexed with double-bonds and thus able to isomerise-propagate. Any further discussion is inhibited by our ignorance of the structural and electronic factors which affect the rate of the rate determining isomerisation, and the magnitude of the formation-constants of the various complexes involved. Much research needs to be done in this area.

4.1.6 Theory of polymerisations in solution Most of the work on polymerisations by ionising radiations in solution was done by the Kyoto group and by Stannett’s group. The physics of the elementary reactions is essentially the same as for the bulk polymerisations, but the chemistry is affected by the fragmentation of the solvent and by the change in the solvation of the cations with changing composition of the reaction mixture. The point of view of the radiation chemists is the reverse of that familiar to ‘normal’ solution kineticists. These are accustomed to working with m from, say, 0.1 mol·l-1 up to such concentrations as still proved manageable by whatever technique was being used, usually not greater than ca. 3 mol·l-1 (L to R in Figure 1). The radiation chemists, on the other hand, starting with bulk monomers, diluted these until the polymerisations became too slow to be followed conveniently, usually at ca. 3–2 mol·l-1 (R to L in Figure 1). Therefore, there is little overlap between the results obtained on the same systems by the two different methods of initiation, and the two types of kineticists think in opposite directions.

524

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993)

Figure 1 Schematic representation of the variation of the polymerisation rate, R, with monomer concentration: A, EVE in benzene; B, EVE in diglyme; C, EVE in CH2Cl2; D, styrene in CH2Cl2; E, isobutene in CS2

In his general theory of polymerisations by ionising radiations, Plesch (1993) has analysed and rationalised in some detail the changes consequent upon dilution of the monomers by various solvents, but only two aspects of his theory are relevant in the present context. These are the state of solvation of the cations and how this changes with concentration for a variety of solvents. The plots of R versus m for different monomers and solvents, some of them shown schematically in Figure 1, have very different shapes, and from the changes of slope one can deduce approximately the concentration, mC, above which the solvation by solvent only is replaced by other forms of solvation, eventually finishing more or less close to mB with solvation by M only. These critical monomer concentrations, mC, which are necessarily rather vague, are listed in Table 2, and they have also proved to be useful in thinking about the significance of all the results obtained by chemical initiation. The information on the variation of the DP with m, scanty though it is, also indicates clearly that there is a change of polymerisation mechanism as m changes. Although the polymerisations were externally of an order greater than one with respect to m, the Stannett group treated them as if they were of first order, i.e., of second order overall; and they assumed that the polymerisations obeyed the normal bimolecular kinetics

525

Developments in the Theory of Cationoid Polymerisations

Table 2 Values of kp+ from polymerisations initiated by ionising radiations T, °C

Diluent

mc/mol·l-1

kp+/l·mol-1·s-1

–78

CH2Cl2

6

9.1 x 103

Ueno (1966b)

a

2

23

Toluene

2

3.5 x 104

Ueno (1966c)

a

3

10

Toluene

3

2.3 x 104

System no.

References

Isobutene 1 Styrene

Ethyl vinyl ether 4

20

Benzene

4

(1.5 ± 0.7) x 104 Deffieux (1991)

5

23

Et2O

5

(2.4 ± 1.5) x 104 Hsieh (1982)

6

23

Diglyme

4

(1.6 ± 0.2) x 104 Hsieh (1982)

7

22

CH2Cl2

4

Benzene

3

(2 ± 0.2) x 104

Deffieux (1983)

Isopropyl vinyl ether 8 a

23

(2.2 ± 0.8) x 105 Deffieux (1983)

: The analysis of the original data which yielded the kp+ is given by Plesch (1993)

according to Equation (38), which is only correct for m<mC. The apparent kinetic contradiction can be resolved by means of the Stannett group’s own results. When plotted by us, these showed that the [C+] for a given, fixed dose-rate changes with the monomer concentration approximately rectilinearly (in most systems up to quite high m), so that in view of their identification of [C+] with [Pn+],

[ Pn+ ] = A ⋅ m + B

(49)

where for some solvents A is positive, for others negative; however, they did not make use of this implication of their results. By means of Equation (49) and Equation (38) we obtain Equation (50)

R = kp+ ⋅ ( A ⋅ m 2 + B ⋅ m)

(50)

R/m = kp+ ⋅ ( A ⋅ m + B)

(51)

and

526

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) In this way the observed deviation from external first-order kinetics finds a natural explanation. Plesch’s substitution for [C +] helped towards a clearer understanding of these polymerisations, and it also enabled him to obtain slightly better defined values of kp+ from Stannett’s data; these are shown in Table 2 and they will be discussed in the following sections.

4.1.7 Alkyl vinyl ethers in solution EVE in benzene. (Deffieux et al., 1981). Below mC the plot according to Equation (51) gives kp+ from the slope as 2.3 x 104 and from the intercept as 7 x 103 1·mol-1·s-1, giving the average shown in Table 2, kp+ = (1.5 ± 0.7) x 104 l·mol-1·s-1. IPVE in benzene (Deffieux et al., 1983a). The results below mC are rather irregular, but a calculation similar to that for EVE gives kp+ = (10 ± 5) x 105 l·mol-1·s-1. In order to +B understand why both kp+ and kp1 are so much greater for IPVE than for EVE we would need more information, such as activation energies and their co-polymerisation ratios in dilute solution and in bulk. EVE in diethyl ether (Hsieh et al., 1982). The method used for EVE in benzene gives kp+ from the slope as 3.8 x 104 and from the intercept as 9.1 x 103, average kp+ = (2.4 ± 1.5) x 104 l·mol-1·s-1, for m < 2.5 mol·l-1. EVE in diglyme (Hsieh et al., 1982). The R/m versus m plot is too scattered, but a direct calculation from the R versus m plot below mC = 4 mol·l-1 gives k p+ = 1.6 x 10 4 l·mol -1·s -1. EVE in CH2Cl2 (Deffieux et al., 1982b). The R versus m plot gives kp+ = (2 ± 0.2) x 103 l·mol-1·s-1 for m < 4 mol·l-1.

4.1.8 Other monomers in solution Styrene in toluene (Ueno et al., 1966a). From the rate and the DP data, Plesch (1993) has diagnosed a marked change of mechanism near m = 5 mol·l-1, and by exploiting both types of information he has calculated kp+ = 2.3 x 104 at 10 ºC and 3.5 x 104 l·mol-1·s-1 at 23 ºC for m up to ca. 3 mol·l-1. Isobutene in CH2Cl2 (Ueno et al., 1966b). By means of the same method as used for styrene, Plesch (1993) calculated a kp+ at –78 ºC of 9.1 x 103 l·mol-1· s-1.

527

Developments in the Theory of Cationoid Polymerisations

4.1.9 Discussion of solution rate-constants The rate-constants in Table 2 calculated by Plesch for the VE do not differ greatly from those calculated by the original authors, but the range of m to which they apply is more closely defined. These kp+, like those for styrene and isobutene, suffer from the lack of observations at low m, and because of this, no account could be taken of the change of the dielectric constant, D, of the reaction medium with changing m. When comparing the kp+ of polymerisations by ionising radiations for different monomers it is essential to remember that for monomers containing more than one π-donor group or an n-donor group, the [P+n] does not equal the [C+] on which the calculation of the kp+ is based, so that for these monomers the kp+ are minimum values. The effect of D on kp+ was discussed by Stannett et al. (1979) in some detail, and they concluded that their results, shown as a plot of ln kp+ versus 1/D, agree with Laidler’s equation, according to which ln kp+ varies rectilinearly with 1/D. Their Figure 3 shows results for EVE and IPVE which include their rate-constants for the bulk polymerisations which we now know should be characterised by a first-order rate-constant, and it includes results obtained at a very high concentration of monomer, where the significance of the formal kp+ is far from obvious. Therefore their conclusion cannot be accepted now, and it is clear that the relation between kp+ and D needs to be investigated with a Class A monomer, e.g., isobutene, and at low m.

4.2 Calorimetry and densitometry

4.2.1 The Bawn - Ledwith - Sherrington group Because of the continuity of the methods and ideas involved in the work initiated by Bawn, and continued by Ledwith and Sherrington, the results obtained will be treated together in this section. Bawn’s group was the first to claim the measurement of kp+ values with the Biddulph-Plesch reaction calorimeter and by chemical initiation (in contrast to initiation by ionising radiation) (Bawn et al., 1964). Because these results appeared to be reliable and plausible, they have been quoted frequently, so that it is appropriate now to scrutinise them carefully. The principal innovation was to use trityl or tropylium hexachloroantimonates and other salts as initiators instead of the then customary syncatalysts consisting of a metal halide and a co-initiator, such as water. Thus the authors hoped to obtain a known concentration of growing chains. In the first of two papers on alkyl vinyl ethers (Bawn et al., 1971) the experimental technique and the method of evaluating the results are explained and illustrated by measurements on isobutyl vinyl ether (IBVE), the second contains measurements on other vinyl ethers (Ledwith et al.,

528

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) 1975); results on N-vinyl carbazole were reported by Bowyer et al. (1971); Goka and Sherrington (1975) reported the alleged kp+ for 4-MeO-styrene, and De Mola et al. (1978) reported rate-constants for N-ethyl, 3-vinyl carbazole.

4.2.1.1 Alkyl vinyl ethers The ethers discussed in the second paper were MVE, EVE, 2-chloroethyl (CEVE)-, cyclohexyl (CHVE)-, and tert. butyl (TBVE) vinyl ethers. The kinetic characteristics of the various monomers, as far as they concern the present subject, are shown in Figure 2. The reaction curves for all the ethers except MVE were sigmoid and the rate-constant, kp(obs) (the authors’ symbol, our kp+A) identified tentatively by the authors with our kp+, was obtained from the maximum rate on the assumption (i) that there was no termination, and (ii) that [Pn+] = co , the concentration of the initiating salt. Some experiments with second additions of IBVE provided evidence for the first assumption for that monomer, but the cessation of polymerisation at yields of 50% or less for CEVE showed that for this monomer the assumption did not hold. The validity of this assumption for the other monomers was not discussed. No evidence was offered for the assumption (ii) which is central to the whole interpretation of the results and the calculations of rate-constants. It was shown later by other investigators, including Sigwalt’s group, that neither of the assumptions is valid for the VE with Ph3C+ in CH2Cl2 (see, for example, Subira et al., 1976). The dependence of kp(obs) on mo and co , and other features of the reactions displayed in Figure 2, have been extracted by us from the published data, but they were ignored by the authors and apparently by most of those who have quoted and used their results. The most important of these features is the dependence of the kp(obs) on the concentration of monomer and of initiator. Before engaging in a detailed analysis of the results, we quote the authors’ disarming disclaimer from the second paper: ‘Apart from the possible relative variations considered above, all the data as a whole may be affected in a systematic way by the presence of adventitious impurities. As a result, this set of data should be considered as a valuable guide to orders of magnitude . . .’. It was, however, strange that the authors refrained from mentioning explicitly that for all systems for which sufficient data are presented, their kp(obs) increase strongly with mo , and they also vary, more weakly, but definitely, with co . In six of the systems recorded, kp(obs) goes through a shallow minimum and in three, in which co was not varied over an adequate range, a decrease of kp(obs) with increasing co probably represents the descending branch of such curves; there are also several instances of maxima. A single occurrence of such variations could justifiably be ignored, but their appearance in all systems indicates that they are significant. Moreover, the curves of kp(obs) versus mo or co obtained with any one monomer and different cations (C7H+7 and Ph3C+) and different anions (SbCl6- and BF4) do not coincide. All these features mean that the simple theoretical basis for the kinetic

529

Developments in the Theory of Cationoid Polymerisations analysis is inadequate and that therefore (i) the kp(obs) cannot be identified with any form of kp, and (ii) that the unknown components of this ‘constant’ are probably different for each one of the monomers and initiators. Even the authors’ claim to have provided a ‘guide to orders of magnitude’ cannot be sustained, because for those systems for which kp(obs) increases with mo , i.e., for which kp(obs) = kx . mo z, where z > 1, it follows that

– dm / dt = kx ⋅ moz ⋅ m ⋅ co so that kp(obs) is a rate-constant of at least third order (if z = 1), and therefore it cannot be a guide to the magnitude of even our second-order rate-constant kp+A, much less any individual kp contained in kp+A. Therefore the authors’ attempts to ascertain the contributions of kp+ and kp± to their ‘constants’ are pointless, and so are the attempts by the authors to account theoretically for the relative reactivities allegedly revealed by the kp(obs). This over-riding flaw in these results makes it superfluous to discuss the effects of other factors neglected by the authors, such as the possible intervention of BIE, and possible differences in the initiating efficiencies of C7H+7 and Ph3C+. For all these reasons this group of much-quoted results will not be included here.

4.2.1.2 N-vinyl carbazole The calorimetric method was applied by Bowyer et al. (1971) to the polymerisation of N-vinyl carbazole (NVC) by tropylium hexafluoroantimonate and perchlorate in CH2Cl2 at 0 ºC and –25 ºC. The reactions were very fast and the reaction curves had a monotonically decreasing rate from the start. The initial reaction rate, Ro, was correlated with the initiator and monomer concentrations by the equation

Ro = kp ⋅ co ⋅ mo and co was identified with [Pn+] and thus the kp was calculated. These values are much more consistent than those for the alkyl vinyl ethers, they show no trend with mo or co (although for some sets of results the range of both is possibly too small to reveal any trend), and they therefore seem much easier to interpret. The co are in the range (0.7– 11.5) x 10-6 mol·l-1, so that the participation of paired cations is likely to be unimportant. The assumption that there is no termination, though plausible, is not well substantiated. There are not sufficient data to construct reliable First Mayo Plots (1/DP versus 1/mo ) and the DP results are rather scattered for both SbCl6- and ClO4- and at both temperatures. The DP values obtained with the perchlorate at both 0 ºC and –25 ºC give good Second Mayo Plots (1/DP versus co ) from which it is evident that there is an important chainbreaking reaction by a species whose concentration is proportional to that of the initiator;

530

Figure 2 Plots constructed from data in Bawn et al. (1971) and Ledwith et al. (1975). The authors’ kp(obs) are the ordinates, the mo and co are abscissae. The details and scale factors are given in Table 2. For any one monomer, the scale factors are the same for all plots. The units for kp(obs) are l·mol-1·s-1, for mo and co mol·l-1 . See page 532 for the data used to construct these plots

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993)

531

Developments in the Theory of Cationoid Polymerisations

Figure 2 Plots constructed from data in Bawn et al. (1971) and Ledwith et al. (1975). The authors’ kp(obs) are the ordinates, the mo and co are abscissae. The details and scale factors are given below. For any one monomer, the scale factors are the same for all plots. The units for kp(obs) are l·mol-1.s-1, for mo and co mol·l-1 Monomer MVE

EVE

Plot

TBVE

CHVE

T, ºC

Cation

Anion

A

C7H7+

SbCl6-

0

B

C7H7+

SbCl6-

11.8

C

C7H7+

SbCl6-

0

A

C7H7+

SbCl6-

0

B

C7H7+

SbCl6-

11.8

C7H7+

SbCl6-

A

Ph3C+

B

Scale factors x for kp(obs)

mo

co

10-2

102

104

10-3

-

1 04

0

10-2

102

SbCl6-

0

10-3

102

105

Ph3C+

SbCl6-

–25

C

C7H7+

SbCl6-

0

D

C7H7+

SbCl6-

–25

E

C7H7+

SbCl6-

0

F

C7H7+

BF4-

0

G

C7H7+

SbCl6-

–25

A

C7H7+

SbCl6-

0

10-3

102

105

B

C7H7+

SbCl6-

11.8

A

C7H7+

SbCl6-

0

10-3

102

105

B

C7H7+

SbCl6-

11.8

CEVE IBVE

Initiator

the significance of this feature will appear shortly. It is regrettable that there are insufficient data for Second Mayo Plots for the experiments with the hexachloroantimonate, so that a comparison with the perchlorate results cannot be made. The authors wrote: ‘Data for the two catalysts are in good agreement …’, although those obtained with the perchlorate are about half of those obtained with the other initiator.

532

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) The same phenomenon was found by Holdcroft and Plesch (1984) for the polymerisation of styrene by benzoyl hexafluoroantimonate and by perchloric acid: the kp+ obtained with HClO4 was exactly one-half of that found with the hexafluoroantimonate. This was attributed to the formation of the conjugate anion A2H- which reduces by half the ‘available’ [AH] and thus the kp+; the same reaction can occur when a perchlorate salt is used:

2 Pn CH 2 CH(Cbz)+ + 2 A − → Pn CH = CH(Cbz) + Pn CH 2 CH(Cbz)+ + A 2 H − Most probably, it is the conjugate anion which is the chain-breaking species mentioned above whose presence is signalled by the Second Mayo Plot. All these considerations indicate that the rate-constant designated by the authors as kp is likely to be our kp+. The results which we consider reliable and significant are shown in Table 3. In view of the large uncertainties in the rate-constants, the difference in the activation energies is unlikely to be significant. [Note that Cowell et al. (1970) had shown that the polymerisation of NVC can be initiated by SbCl6-.]

Table 3 Propagation rate-constants for the polymerisation of NVC in CH2Cl2 by tropylium salts Anion

102 mo/mol·l-1

106 co/mol·l-1

T, °C

10-5 kp

10-5 kp+

Ep+/kJ·mol-1

10-5 k+p/l·mol-1·s-1

SbCl6-

ClO4-

(a)

(b)

2.7–5.4

0.75–1.0

0

4.6 ± 0.3

4.6 ± 0.3

2.7–5.4

1.0–2.0

–25

1.6 ± 0.4

1.6 ± 0.4

2.7–5.6

2.6–5.6

0

2.2 ± 0.7

4.4 ± 1.4 c

3.0–5.7

3.4–11.5

–25

27

24

0.66 ± 0.2 1.3 ± 0.4 c

10-5 k+p/l·mol-1·s-1

E+p/kJ·mol-1

0 °C

4.6 ± 0.3

27

–25 °C

1.6 ± 0.4

Most probable values:

a Authors’ values (Bowyer et al., 1971) b Our values c Calculated as kp+ = 2kp. Since the factor relating co to [P+n] is unlikely to be exactly 2, and probably varies with T, the values obtained with the perchlorate salt have not been included in arriving at the most probable values

533

Developments in the Theory of Cationoid Polymerisations

4.2.1.3 4-MeO-Styrene A very detailed account of the polymerisation of 4-MeO-styrene by C7H7+SbCl6- in CH2Cl2 at 10 ºC, 0 ºC and –25 ºC has been given by Goka and Sherrington (1975). The experiments were done with the Biddulph-Plesch vacuum calorimeter and polymerisations are said to have gone to completion, but the large scatter of the ΔHp values at all three temperatures arouses suspicion about this. The sigmoid reaction curves were analysed by the method of Bawn et al. (1971) to give a kpobs = [–d ln m/dt]max/co . At all three temperatures the k1 (calculated by us as kpobs ·co ) increased rectilinearly with mo , so the kpobs is not a normal second-order rate-constant. With increasing co the kpobs went through a sharp maximum at co < 10-4 mol·l-1. The reason for this became clear when we found that the k1 went through a maximum near co = 1.5 x 10-5 and a minimum near 3 x 10-5 mol·l-1 at both 10 ºC and 0 ºC, and then rose to a plateau, which also happened at –25 ºC (insufficient results at low co to show maximum or minimum). The behaviour was in fact very similar to that found by Rooney for NVC (see Section 4.2.5). The authors did not notice that at all three temperatures the DP went through two maxima with increasing co . This, as pointed out by Plesch (1964), signals the intervention of chain-breaking impurities. Despite the kinetic anomalies, the authors attempted to justify treating the kpobs as a second-order rate-constant. Their bafflement by the observations is expressed in a long and inconclusive discussion, and their tentative values of kp+ and kp± are not adequately established.

4.2.1.4 N-ethyl, 3-vinyl carbazole De Mola et al. (1978) have reported kinetic studies by reaction calorimetry on N-ethyl, 3-vinyl carbazole (NE3VC), polymerised by C7H+7SbCl-6 in CH2Cl2 at 0 ºC. The reactions were fast, and the colour of the yellow reaction mixtures changed rapidly to green or blue after the end of the reactions; these changes were studied spectroscopically, with attempts to extrapolate the spectra back to t = 0; the DP of the polymers obtained from the kinetic experiments was too great to be determined accurately (MW > 106). No primary kinetic data are given, only the unsupported statement: ‘…recorder traces yielded kp+ = 2 x 104 l·mol-1·s-1 at 0 ºC in CH2Cl2 and the enthalpy of polymerisation was estimated as 17 kcal·mol-1.’ So, presumably, ΔHP = –17 kcal·mol-1 = –71 kJ·mol-1. The work appears to contain an internal inconsistency: a strong absorption at λmax = 468 nm is attributed to the propagating species and it is stated that ‘Estimated values of optical density at zero time for the peak at 468 nm were apparently not influenced by the presence of added salts.’ This finding seems to confirm the general experience that the absorption spectrum of an unpaired cation resembles very closely that of the same ion when paired, i.e., for unit path-length the absorbance A = ε·([Pn+] + [Pn+A-]) = ε·co . Yet, the authors found that the curve relating the A468, to co was concave to the Co -axis, but that the A468.

534

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) depended rectilinearly on αco , where α is the degree of dissociation of a (hypothetical) ionpair, calculated with KD = 1.9 x 10-5 mol·l-1, which would mean that the A468 is due only to the unpaired cations. In view of this uncertainty and the absence of any primary data, the validity of the kp+ value is somewhat dubious, but it seems not implausible.

4.2.2 P. Sigwalt’s group

4.2.2.1 Preamble The group of Sigwalt is distinguished for having developed very elaborate and rigorous techniques for investigating cationic polymerisations and they have used them for studying a variety of monomers (Cheradame et al., 1968). A later version of their reaction calorimeter (Favier et al., 1974) permits the simultaneous measurement of the temperature rise due to the polymerisation and the spectroscopic measurement of the change in the concentration of the initiator, trityl hexachloroantimonate, as well as the recording of the electrical conductivity of the solutions (Subira et al., 1976, 1988). However, the many reports are all short of primary data, so that one can neither assess their reproducibility, nor analyse them in any ways different from those used by the authors; however, the lack of scatter on those plots which are shown is impressive. The authors have used a common form of analysis for all the non-stationary reactions initiated by Ph3C+ SbCl-6 which involves a slow initiation by the addition of the trityl cation to the monomer, a fast propagation and (in most instances) two chain-breaking reactions, a transfer (of a proton) to monomer and a termination. They write (typically Subira et al., 1988): ‘. . . unimolecular termination (assumed) Pn+ → Pn, kt.’ What their symbolism actually means is a ‘first-order’ reaction with respect to growing chains. No mechanism for this type of inactivation is suggested, nor any evidence adduced, which is particularly puzzling, as for several systems they conclude that the dominant propagators are unpaired cations. This difficulty can be overcome simply by writing their kt = kt2. [X], where X is an unknown reagent which neutralises or inactivates the growing centre; this possibility is actually mentioned by Cotrel et al. (1976). In fact, the termination reaction, although kinetically not unimportant in most systems, hardly affects the kp. These are calculated from the maximum rate and the m and [Pn+] prevailing at that point, as well as from the values during the whole of the reactions; the best explanation of this dual method is given by Subira et al. (1976). Sauvet et al. (1986) concluded that more consistent results can be obtained (for 4-MeO-styrene) by omitting the termination. A more serious and pervasive criticism of this work, and indeed of all studies with trityl cations as initiators, is that the rate of initiation is set equal to the rate of consumption of

535

Developments in the Theory of Cationoid Polymerisations Ph3C+ ions, though in some papers misgivings about a possible wastage of initiator are expressed. This is a weakness, as the critical quantity [Pn+] at any time t is always calculated as [Pn+]t = [Ph3C+]o–[Ph3C+]t. Yet another source of misgivings is the possibility of termination by a chloride ion from SbCl-6.

SbCl 6− + Pn+ → Pn Cl + SbCl 5 and a subsequent initiation by SbCl5 (Fleischfresser et al., 1968; Bracke et al., 1969):

SbCl 5 + M → ClM + + SbCl −4 This is a transfer reaction, yielding polymers without initial trityl groups. However, these reactions were considered to be too slow to affect the kinetic results (private communication). For a non-additive reaction of the Ph3C+ ion with NVC see Section 4.2.8. That this ion does add quantitatively to cyclopentadiene was shown by Villesange et al., (1980).

4.2.2.2 Alkyl vinyl ethers The earlier paper (Subira et al., 1976) contains results on isobutyl vinyl ether (IBVE) which are republished together with new measurements on methyl (MVE)–, ethyl (EVE)–, and isopropyl (IPVE)–vinyl ethers in CH2Cl2 over the temperature range 0 ºC to –40 ºC with m = (2–15) x 10-2, [Ph3CSbCl6] = (5.5-8) x 10-5 mol·l-1 (Subira et al., 1988). The rate of disappearance of the Ph3C+ ion in the presence of the monomer is considerably smaller than the rate of consumption of the monomer under all conditions, and as mentioned above, the authors identify the rate of disappearance of the trityl cation with the rate of initiation, in our notation

– dc / dt = ki ⋅ m ⋅ c = Ri Values of ki are obtained from the plots of Ri/mo versus co and Ri/co versus mo . Those at –20 ºC for MVE give good straight lines through the origin (Figure 1 of Subira, 1988) but the plots for IBVE at 20 ºC, 0 ºC, and –25 ºC (Figure 1 of Subira, 1976) show an inflection. The analogous information for monomers and temperatures other than those mentioned is not available. The authors admit that these inflections could be due to side reactions of the trityl cations, but they do not say whether inflections occur with any vinyl ethers other than MVE and EVE. The significance of the measured kp values is discussed at great length in the second paper. The authors are aware that their kp is a composite quantity and they analyse it in

536

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) terms of the participation of an unsolvated cation, a cation solvated by the solvent (our Pn+) and a cation solvated by the oxygen atom of the penultimate monomer unit of the polymer, our Pn+P. This analysis seems to us flawed, because the existence in kinetically significant quantities of a positively charged organic species without an attached solvent or other basic molecule is unlikely, even if it is an oxocarbenium ion with a relatively diffuse charge. The authors are fully aware of certain inconsistencies and some unexplained features and actually get very close to our view when they write: ‘This might mean that intrasolvation (formation of our Pn+P) is not the only-and even not the prevalent-factor governing the kinetics of these ‘chemically’ initiated polymerisations in CH2Cl2.’ The role of ion-pairs is discussed at some length. Conductivity measurements on polymerised solutions of EVE with successive dilutions gave results from which ion-pair dissociation constants KD were calculated conventionally by means of Shedlovsky plots. However, since the conductivity of solutions of the model system EtOCHMe+ SbCl6- can be interpreted much more plausibly in terms of a BIE (Plesch and Stannett, 1982),

EtOCHMe + + SbCl 6− ↔ EtOCHClMe + SbCl 5 , K11 it seemed probable that the poly(ethyl vinyl ether)+SbCl6- behaved similarly. When this reviewer replotted the conductivity results for this polymeric ‘salt’ from the Thèse de Doctorat d’Etat of F. Subira (kindly supplied by Professor Sigwalt) as κ versus co , straight lines were obtained for all temperatures from 0 ºC to –50 ºC over a 6-fold range of concentration. This indicates either that the ionisation and dissociation are complete, or that the ionisation involves a BIE, without ion-pairs. Whichever may be the case, therefore, the calculations and arguments of the original authors based on the participation of ionpairs are ill-founded. However, we concur with the eventual conclusion that ‘… it appears obvious that the free-ion contribution controls the propagation kinetics’, with the proviso that we would write ‘unpaired’ for ‘free’. In Table 4 we reproduce their rate-constants, kp+A in our symbols which, according to the authors, are close to kp+ (Subira et al., 1988). The one comparable result (EVE; 7 x 103 at 0 ºC) is of about the same order of magnitude as the kp+ obtained from

Table 4 The kp+A for the alkyl vinyl ethers in CH2Cl2 at 0 ºC. Initiation by Ph3C+SbCl6- (Subira et al., 1988) Monomer 10-3 kp+A/l·mol-1.s-1 Ep+A/kJ·mol-1

MEVE

EVE

IPVE

IBVE

0.26

7

11.2

15.4

53

52

17

26

537

Developments in the Theory of Cationoid Polymerisations polymerisation by ionising radiation (2 x 103 at 22 ºC) (Table 2). Since, however, neither the original authors nor we are able to assign these ‘constants’ confidently to any one species, they are not included in our final list.

4.2.2.3 4-MeO-styrene A study of the polymerisation of 4-MeO-styrene by trityl hexachloroantimonate in CH2Cl2 between 25 ºC and –15 ºC by the combined calorimetric and spectroscopic technique was reported by Cotrel et al., (1976), and a more detailed and elaborate investigation of the same system at 10 ºC was made by Sauvet et al., (1986); both papers contain few primary data. In the earlier paper the method of analysing the kinetic data is essentially the same as that used for the alkyl vinyl ethers. A rate-constant corresponding to our kp+A was calculated by the same two methods as used for the VE and these are given in Table 5; they yield an activation energy of EpA 25 ± 4 kJ·mol; both ki and km (transfer to M) have positive activation energies and Et is about 0. In order to explain the negative EpA the authors consider two alternative explanations. The first is a complexation between the growing cation and the monomer which involves essentially the approach of Fontana and Kidder (see Section 2.2). This implies that their ‘rate-constants’ are the product of a rate-constant and an equilibrium constant [Equation (12)], which could account for the negative EpA, because this would be the sum of the positive activation energy corresponding to the rate-constant and the negative enthalpy of the complexation. Since in this work m <8 x 10-2 mol·l-1, this explanation does not seem likely to us. Their other alternative is based on the well-known fact that for ionpairs in polar solvents the KD increases with decreasing T. Therefore [Pn+]/[Pn+A-] increases and if kp+ > kp±, the rate increases as T falls. This explanation for a negative activation energy was first proposed by Biddulph et al., (1965) and it remains plausible. Indeed, in

Table 5 The kp+A for 4-MeO-styrene in CH2Cl2 T, °C

102·m/mol·l-1

105·[Ph3C+SbCl6-]

10-4·kp+A

mol·l-1

l·mol-1·s-1

25

4.0

8.6

1.4 ± 0.2

10

1.5–8

2.5–11

2.6 ± 0.7

–2

4.1

7.2

3.5 ± 0.5

–15

4. 2

6.5

7.4 ± 0.1

Data from Table 1 of Cotrel et al., (1976); the kp+A shown here are the means of those obtained by two methods

538

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) the introduction to the second study (1986) the authors favour this electrochemical explanation. It induced them to study the effects of varying concentrations of the commonion salt (i-Amyl)3n-BuN+SbCl6- (TABN+SbCl6-)on all the variables. T h e s e i n c l u d e t h e – d [ P h 3 C + ] / dt (once again taken as equal to Ri), –dm/dt and the DPn and the DPD, both as a function of the degree of conversion. The most remarkable finding is that the DPD curves show several inflections, which were resolved into four Gaussian distributions. The same type of curve was obtained with tropylium SbCl6- and trityl SbF6-, so that this phenomenon is unlikely to be associated with either the initiating cation or the anion. The DP of the four fractions (DPi, i = 1–4) do not vary significantly with the degree of conversion. Under typical conditions (mo = 2.5 x 10-2, co = 5.8 x 10-5 mol·1-1) the following results were obtained: DP1 = 5200, DP2 = 1700, DP3 = 450, DP4 = 80. The amount formed of the populations 1–3 increases steadily from the start, but population 4 only begins to be significant when the conversion reaches 80%.

Table 6 The alleged propagation rate-constants of the species contributing to the polymerisation of 4-MeO-styrene in CH2Cl2 at 10 ºC by Ph3C+SbCl6- according to Sauvet et al., (1986) Species No.

Designation of species in symbols used

Designation of rateconstants

10-4·'kp'/l·mol-1·s-1 according to original authors

by original authors

in this worka

by original authors

in this work

1

P+, M, SbCl6-

M·Pn+·A-

kp1±

b

4.2

2

P +, M

Pn+A-

kp1+

kp+M

36

3

P+, CH2Cl2, SbCl6-

Pn+A-

kp2±

kp±

1.4

4

P+,CH2Cl2

Pn+

kp2+

kp+

12

5

P+, SbCl6-

c

kp3+

-

0.83

6

P+, P

c

kp3+

-

1.6

7

Average for all paired ions

kp+

-

1.1

8

Average for all unpaired ions

kp+

-

16

a

: According to our view Pn+, Pn+A-, Pn+M and Pn+P are all solvated by CH2Cl2 and this is not represented explicitly in our symbols, see Section 2.1 b : This species was considered by us to be kinetically insignificant c : This species which is not solvated by the CH2Cl2 is not included amongst the propagators considered in this work

539

Developments in the Theory of Cationoid Polymerisations The abundance of the other three populations is 2 >> 3 > 1. Their formation is attributed to three pairs of propagating species which are given in the authors’ and in our notations in Table 6. Each of the populations is regarded as being formed by an ion characterised by a state of complexation or solvation which is believed to retain its identity for a time which is long compared to the time required for the formation of each polymer chain; further propagating species are said to be formed by the ion-pairing process. These species are said to be (the numbers refer to Table 6): The paired (1) and unpaired (2) monomer-complexed cation; the paired (3) and unpaired (4) solvent-complexed cation; the paired cation (5); and the unpaired polymer-complexed cation (6). By an ingenious method which is not easy to understand, the authors calculated a kp value for each of the principal propagating species. These kp are then plotted against the α, the average degree of dissociation for all the species calculated from a KD = 3 x 10-5 mol·l-1, (which is also an average) and the prevailing ionic concentration. The resulting linear plots are extrapolated to α = 0 and α = 1 to give the corresponding kp± and kp+ values. We consider that these results are amongst the most interesting and challenging obtained anywhere in recent years and that they demand confirmation and extension. The authors’ treatment and explanation of the results can be criticised on the following grounds: i) The growing chain-end is most likely involved in a BIE, so that calculations of the concentrations of unpaired and paired ions would be faulty, even if there were only one kind of cation; but by the authors’ own hypothesis there are several kinds of cation, each with different electrochemical properties. ii) As explained in Section 2 and mentioned above, at the very low m used, the existence of Pn+M in kinetically significant concentrations is unlikely. iii) The persistence of so many types of solvates (we include ion-pairs in this term) with only very slow exchanges of solvators seems unlikely. We must conclude that there are good reasons for doubting the correctness of the assignment of the rate-constants to the species indicated by the authors, even if their magnitude were adequately established. Finally, it is worth noting that whilst many of the DPD curves for poly-(4-MeO-styrene)s produced under many different conditions by Higashimura’s group are asymmetrical, which indicates the coexistence of at least two propagating species, none appear to show the inflections found by Sigwalt’s group (see References in Section 4.3.4 and Higashimura et al., 1979). The reasons for this difference probably include the difference in the initiators used and the fact that the experimental techniques and standards of purity of the Paris group are far more rigorous.

540

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993)

4.2.2.4 Cyclopentadiene A dilatometric study of the polymerisation of cyclopentadiene by trityl hexachloroantimonate in CH2Cl2 between + 10 ºC and –70 ºC was reported by Sauvet et al. (1969, 1974). In the earlier paper, experiments are reported with high co /mo ratios, so that the initial groups could be counted spectroscopically. The DP found by osmometry (26), NMR (29), and IR (35) were all much higher than the theoretical, Δm/Δc which was 5. The rateconstant for the disappearance of the trityl cation by a second-order reaction was again taken to be ki. This was used in the later paper to give a set of kp+A ranging from 1 at 10 ºC to 45 l·mol-1·s-1 at –50 ºC. The reaction was interpreted as due to propagation by unpaired ions and by ions forming part of loose and intimate ion-pairs, with the major contribution being due to the unpaired ions. The reason why these rate-constants are so implausibly low is most likely to be found in the criticisms specified in the earlier sections.

4.2.2.5 α-Me-styrene The polymerisation of α-Me-styrene in CH2Cl2 by n-BuOTiCl3 and H2O or HCl was studied calorimetrically by Villesange et al., (1977), mainly at –70 ºC at which temperature complete conversions were obtained; the reaction rate decreased with increasing temperature, and at –50 ºC and –30 ºC conversions were incomplete; m was between 0.06 and 0.3 mol·l-1; the conversion curves had inflections, and at –70 ºC the reactions were ca. 90% complete in ca. 6 s. By an ingenious kinetic analysis, a set of kp values was obtained, which have a negative activation energy; the two possible causes for a negative Ep, which were explained in Section 4.2.2.3, are considered, without a definite conclusion being reached. The rate-constant, which we would call kp+A, obviously a composite quantity, is given as (2.2 ± 1.1) x 104 l·mol-1·s-1 at –70 ºC.

4.2.3 P. H. Plesch’s group Plesch chose nitrobenzene as the solvent for kinetic studies aimed at measuring the kp+ of several alkenes. The reasons for selecting this highly polar solvent (D = 35 at 25 ºC) were that, according to transition state theory, the kp+ would be considerably smaller than in, e.g., CH2Cl2 (D = 10–15 over the usual temperature range) - the kinetic imperative; that ion-pairing would be negligible - the electrochemical imperative; and that any complexing of the propagating carbenium ion with the monomers would be minimised-the thermodynamic imperative. The monomers studied successfully were acenaphthylene,

541

Developments in the Theory of Cationoid Polymerisations styrene, indene, phenyl vinyl ether, and chloroethyl vinyl ether; no useful results could be obtained from ethyl vinyl ether, as its polymerisation was too fast. The initiators were salts with reactive cations and stable and inert anions, so that the initiation should be fast and as unambiguous as possible, and there would be no scope for any BIE, involving the growing ends. Some exploratory experiments with HClO4 and HSO3CF3 showed that these are unsuitable for kinetic work, because of the formation of conjugate anions of the type A2H-. The kinetic techniques were densitometry and reaction calorimetry, and the electrical conductivity, κ, was monitored for most systems; the calorimetric measurements also yielded the enthalpies of polymerisation (ΔHp). Analysis of the polymers provided information on initial groups, DP, and DPD for many of the products. The determination of the quantity and origin of kinetically significant impurities is a feature of this work, because much of it was done with initiator concentrations, co , between 10-4 and 10-3 mol·l-1, and the measured impurity levels, ci, ranged from 10-4 down to 10-5 mol·l-1. The results were reported in three papers: acenaphthylene (Pask et al., 1981), acenaphthylene and styrene (Holdcroft and Plesch, 1984), styrene and all other monomers mentioned above (Plesch and Shamlian, 1990); the last paper also contains a general summary and discussion. The features which distinguish this work from most other such studies can be summarised thus: i) The results for acenaphthylene obtained in the first work were reproduced in the second, and in the third one the results for styrene obtained in the second one were reproduced. Thus the continuity of the measurements by a succession of workers with different apparatus and different initiators was established. ii) Coincident results were obtained by densitometry and calorimetry. iii) Coincident results were obtained with initiators consisting of a variety of cations and anions, which showed that the nature and concentration of the propagating species is independent of the nature of the initiator. iv) From the change of the electrical conductivity with time and the dependence of the final κf of the polymerised solutions on co , it was established that in all systems the initiation was fast and complete, and that the charges remained unchanged after the end of the polymerisations; and the actual κf corresponded closely to that calculated for the anion, which showed that the positive charge remained on the (effectively non-conducting) polymer. A rate-constant, k1, was calculated from the first-order conversion curves, and this was related to what Plesch believed to be the kp+ by the conventional relation:

542

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993)

R = k1 ⋅ m = kp+ ⋅ [ Pn+ ] ⋅ m on the assumption that

[ Pn+ ] = co – ci

(52)

where ci is the concentration of initiator scavenged by impurities. The results obtained in this way are shown in Table 7. As there are reasons now, explained below, for believing that Plesch’s rate-constants are not kp+, they will be designated here by ‘kp+’. It is immediately evident that these values are much lower than those obtained in other solvents of lower D. Although qualitatively this reduction was expected from transition state theory, and indeed was one of the reasons for choosing PhNO2, the extent of the reduction appeared to require for its explanation some additional effects. S. Penczek and K. Matyjaszewski (private communication) suggested that there are two such which need to be considered: deactivation of the monomer by complexation, and a reduction in the reactivity and/or the concentration of the growing centres. We will discuss first the well-known formation of charge-transfer (CT) complexes between π- or n-donors and nitrobenzene. This raises the question whether any alkenic monomers in nitrobenzene solvent are the ‘same’ monomers as in, say, CH2Cl2, and therefore whether any kp+ determined in a strong acceptor solvent can be compared validly with those determined in solvents which are not electron-acceptors. Because the monomer population comprises the uncomplexed M and the M involved in the CT complex with the solvent, MSv, the answer depends on the magnitude of KMS, the formation constant, which is given by

KMS = [MSv]/( mo – [MSv]) ⋅ [Sv] so that

[MSv] = KMS ⋅ mo ⋅ [Sv]/([Sv] ⋅ KMS + 1) The KMS can be estimated as follows: an extrapolation of the KMS for the CT complex formed by any one donor, such as mesitylene or hexamethylbenzene, with 1,3,5-trinitrobenzene and 1,4-dinitrobenzene to PhNO2, and an extrapolation from solvent CCl4 to one of DC > ca. 10 (Foster, 1969) shows that for our system KMS is very unlikely to be greater than 0.01 l·mol-1. Therefore, with m = 1 mol·l-1, and [Sv] = 10 mol·l-1, [MSv] < 0.1 mol·l-1. This means that for styrene and other π-donors effectively all the monomer is free. For n-donor monomers such as the VE, however, the fraction of uncomplexed monomer may be somewhat smaller. Therefore it appears that the formation of CT complexes probably did not affect significantly at least the results for the three hydrocarbon monomers.

543

Developments in the Theory of Cationoid Polymerisations The second argument advanced by Penczek and Matyjaszewski was that in PhNO2 solvent there is an equilibrium between the normally solvated cation Pn+ and the cation covalently bound to the solvent, Pn+-ON(O)Ph, +

Pn+ + O 2 NPh ↔ Pn – O N Ph, i.e. Pn+ Sv || (Sv) O and that the cationated solvent either does not propagate at all, or only very slowly compared to the Pn+. In his third paper, Plesch adduced circumstantial conductimetric and spectroscopic evidence against this suggestion, and he emphasised that the opinion that his kp+ are ‘too small’ arises from a misunderstanding of Laidler’s theory relating kp+ to D. However, there are two lines of experimental evidence against Plesch’s original view, which we will now explain. The formation of PnSv+ is expressed quantitatively thus:

[ Pn Sv + ] = KSv ⋅ [ Pn+ ] ⋅ [Sv] and

co – ci = [ Pn+ ] + [ Pn Sv + ] so that then

[ Pn+ ] = (co – ci ) /(1 + KSv ⋅ [Sv])

(53)

Since [Sv] = 10 mol·l-1 [(molar volume)-1], a KSv of ca. 1 would suffice to increase the ‘kp+’ by a factor of ca. 10. However, the only thing we can say with confidence about KSv is that it is likely to be different for every monomer, because of the different charge density and steric characteristics of the corresponding Pn+. This means that Plesch’s simple view, expressed by (52) would be falsified if the ranking of the ‘kp+’ in some inert solvent were different from that shown in Table 7. The only results suitable for this test are compiled in Table 8. If we assume that a change from benzene to toluene would not change the kp+ by an order of magnitude, we see that in hydrocarbon solvent the kp+ for EVE is about one half of that for styrene, whereas in nitrobenzene the ‘kp+’ of EVE is greater than that of styrene by more than two powers of ten. This evidence, therefore, falsifies Plesch’s assumption and supports the criticism of Penczek and Matyjaszewski.

544

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993)

Table 7 Rate-constants for polymerisations in nitrobenzene at T ca. 25 ºC (Plesch et al., 1981, 1984, 1990) Monomer

Acenaphthylene

Styrene

Indene

PhVE

CEVE

23 ± 2

195 ± 15

373 ± 15

1450 ± 200

ca. 104

‘kp+’/l·mol-1·s-1

The ‘kp+’ are minimum values for our kp+

Table 8 Comparison of approximate rate-constants/l·mol-1·s-1 Solvents Rate-constants

PhNO2

Toluene

Benzene

‘kp+’

kp+

kp+

25

22

20

2 x 102

3.5 x 104

T, ºC Monomers Styrene PhVE

1.5 x 103

CEVE

104 > 104

EVE References

Plesch (1981, 1984, 1990)

1.5 x 104 From Table 2

Actually, Plesch’s results themselves contain a clue relevant to this problem, the significance of which he did not appreciate at the time; that is the unusual antibatic correlation between log ‘kp+’ and ΔHp (enthalpy of polymerisation) which is shown in Figure 8 of the third paper. If the correlation is rectilinear, the lines are given by the Equation (54):

log[(' kp+ ' ) / l ⋅ mol −1 ⋅ s −1 ] = a ⋅ ΔHp + b

(54)

with, for the three hydrocarbons

a = 0.0422 / kJ ⋅ mol −1 , b = 4.97 and for the two VE

a = 0.0280 / kJ ⋅ mol −1 , b = 6.24

545

Developments in the Theory of Cationoid Polymerisations The significance of this correlation can be seen from the following analysis. For reactions with activation enthalpies ΔH* greater than, say, 20 kJ·mol-1, one can usually assume Polanyi’s relation, which says that the more negative ΔH, the smaller is ΔH*, and therefore a greater ΔH means a greater rate-constant, i.e., the opposite of the experimental results described by (54). Unfortunately, we do not know the values of the ΔH* corresponding to kp+, but they are likely to be of the same order of magnitude as the term T·ΔSp*, so that the argument needs to be conducted in terms of the ΔGp*. It can, however, be taken a little further towards the resolution of the contradiction noted above. If we abandon Plesch’s initial assumption expressed by (52) and replace it by (55), a simplified and plausible form of (53), then

[ Pn+ ] = (co – ci ) / KSv ⋅ [Sv]

(55)

and the coefficient of the concentration terms is

' kp+ ' = kp+ / KSv

(56)

Since ln kp+ = –ΔGp*/R·T and

ln KSv = – ΔGSvo / R ⋅ T ln ' kp+ ' = – ΔGp* / R ⋅ T + ΔGSv0 / R ⋅ T Therefore, the apparent free energy of activation, corresponding to ‘kp+’, is ΔGp*– ΔGoSv which may well be of a sign and magnitude compatible with (54). So this line of evidence, too, points to Plesch’s assumption (52) being invalid, and it follows that the ‘kp+’ in Table 7 are minimum values of kp+. However, if one were to measure the corresponding KSv, one could thus obtain the true kp+ from Plesch’s values of ‘kp+’ by means of (56). This matter is discussed in detail in a forthcoming paper (Plesch, 1993).

4.2.4 V. T. Stannett’s group Chung et al., (1975) have reported briefly on attempts at measuring the kp+ of EVE and IBVE, polymerised in CH2Cl2 by Ph3C+SbCl6- at –25º, 0 ºC and 15 ºC; the mo was in the range 0.06 to 0.2 mol·l-1 and co from (0.4–2.5) x 10-4 mol·l-1; they used a BiddulphPlesch reaction calorimeter. Only one reaction curve is given, there are no primary data,

546

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) for IBVE there is only one experiment at each of the three temperatures, and for EVE there are 2 at –25 ºC, 4 at 0 ºC, and 4 at 15 ºC. No DP are reported. The kinetic results are interpreted according to the equation

– dm / dt = k1 ⋅ m = kp+ co ⋅ m (our symbols). The mo , co , kp+ (without units), and ΔHp are listed. The wide scatter of the ΔHp values and the fact that for EVE the kp+ at any one temperature vary by more than a factor of 2 aroused our suspicion. Upon calculating the k1 from the data, we found that the plots of k1 against mo at all three temperatures are strongly curved upward, so that instead of being independent of mo , the k1 varies with mz, where z > 1. This is not unlike what was found by the Bawn group (Section 4.2. 1) and makes it pointless to quote the alleged k which are evidently not second-order rate-constants.

4.2.5 J. M. Rooney i) The polymerisation of N-vinyl carbazole (NVC) was studied by Rooney (1976, 1978a) by adiabatic calorimetry with CH2Cl2 as solvent and a variety of initiators over a range of temperatures. The rate of disappearance of Ph3C+, identified with the rate of initiation, was measured by a stopped-flow apparatus; however the plots of log [Ph3C+] versus time were strongly curved, although [Ph 3C +] o << m, and this remains unexplained. A serious source of trouble is signalled by the wide scatter of the ΔHp values which conflicts with the statement that the polymerisations went to completion. The conversion curves had an inflection (initial acceleration) and first-order constants k1 were evaluated from the subsequent linear part of the log m versus t plots, but these are not listed. In the first paper a very elaborate method is used to obtain a kp (our kp+A); in the second paper the kpobs is obtained as k1/co where co = [C7H7+SbF6-] or [C7H+7AsF6-]. For both initiators the plot of kpobs versus co shows a maximum and a minimum, see Figure 3, and the values at very low and very high co (the putative kp+ and kp±) are indeterminate. If, in the light of this evidence, one now examines Figures 4 and 5 of the first paper, one finds exactly the same pattern; because the maximum is so close to the origin, the effect is actually much clearer from plots of kpobs versus 1/co . The DP at 0 ºC and 20 ºC goes through a marked minimum, whereas the DPs obtained at –40 ºC with the C7H7+ salts go through a maximum. The causation of such DP variations by impurities has been explained by Plesch (1964). It is clear from this internal evidence, largely ignored by the author, that the kinetic situation was far more complicated than he suspected. The author’s use of nitromethane to dissolve the tropylium salts. and the impurity in NVC which cannot be removed by crystallisation from hexane (Hamid et al., 1970) may be at least partly responsible for this. The

547

Developments in the Theory of Cationoid Polymerisations discrepancies between these results and those of Sections 4.2.1.2 and 4.2.8 also indicate that Rooney’s are not acceptable. The lesson is: If an anomaly happens Once - it may be ignored; Twice - it deserves attention; Thrice - it signals an important problem. ii) Rooney (1978b) reported a dilatometric study of the polymerisation of anethole (4MeO, β-Me styrene) by Ph3C+SbF6- in CH2Cl2, mostly at 25 ºC, with co = (2-8) x 10-4 and m = 0.33-0.66 mol·l-1. Since both ki and the alleged kp+ increase strongly with co , the interpretation of the kinetics once again seems far too naive, and the values obtained cannot be considered well established. Actually, the variation of the rate-constants kpobs and ki with co are quite similar to those found by Rodriguez and Leon (Section 4.2.8), and a similar interpretation might be applicable, but the scatter of the results is too great to warrant this.

Figure 3 The dependence of the author’s kpobs (O SbCl6-, AsF6-, and DP ( ▲ AsF6-) on co from Tables 2 and 4 of Rooney (1978a)

548

• SbCl

6

-

,

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993)

4.2.6 P. Giusti’s group In the course of a long and thorough study of the polymerisation of isobutene (IB) by syncatalytic systems based on aluminium-organic compounds (Magagnini et al., 1977 and preceding papers) measurements were made by a Biddulph-Plesch type reaction calorimeter fitted with conductivity (κ) electrodes on polymerisations of IB by Et2AlCl + Cl2 in MeCl at –45 ºC, from which a kp+A value could be obtained. The reactions and procedures can be summarised as follows: When Cl2 is added to a quiescent mixture of IB and Et2AlCl in MeCl at low temperature, a fast polymerisation ensues, the κ increases rapidly, and both the conversion and the κ versus t curves show a short, irreproducible accelerating phase. The first reaction is

Cl 2 + Et 2 AlCl ↔ Cl + + Et 2 AlCl 2− ↔ EtCl + EtAlCl 2 In the presence of the monomer the equilibria are drained by the consumption of the Cl+ which is the true initiator: nIB

Cl + + IB → ClCH 2 CMe 2+ → ClPn+ The cationation of IB by Cl+ is very fast, so that the rate-determining step is the formation of Cl+ which continues until all the Cl2 has been consumed. However, some of the Cl+ are scavenged by adventitious impurities; also, some of the Cl2 is consumed by a direct addition to the monomer. A slightly complicated, but realistic, argument in which the conductivity plays an essential part, leads to the conclusion that for [IB]o = 0.1, [Et2AlCl]o = 1.8 x 10-4, [Cl2]o = 1.2 x 10-4 mol·l-1, the [Pn+] = (1.3–2.3) x 10-1 mol·l-1 and ki = (3–3.7) x 102 l mol-1·s-1. By means of an integrated rate-equation the authors obtained a kp which, in our symbols, is kp* = (1.2 ± 0.3) x 104 l·mol-1·s-1. They wrote: ‘…the method ... is rather inaccurate ... This makes it useless ... to speculate upon the nature of the propagating species (paired or unpaired cations).’ In view of the high polarity of the solvent MeCl (D = 14.4 at –45 ºC), the small [Pn*], and the fact that the poly-(isobutyl)+ is tertiary and therefore its salts will have a KD substantially greater than those of the secondary ions, we consider that the dominant component of kp* is kp+, and we consider it reliable. It must be said that the general theory upon which these calculations are based seems sound because it accounts well for the great variety of observations on a complicated system.

4.2.7 M. Marek and M. Chmelir These authors (1968) reported on the polymerisation of isobutene in heptane by AlBr3 with an excess of TiCl4 at –14 ºC. The conversion curves indicating a non-stationary

549

Developments in the Theory of Cationoid Polymerisations reaction (Y < 100%) obtained by reaction calorimetry were interpreted by the kinetic scheme developed by Pepper (Burton and Pepper, 1961; Hayes and Pepper, 1958, 1961). However, the kp was derived on the assumption that [Pn+] = [AlBr3]o; this was based on the assumptions (i) that the formation of the initiating species TiCl3+ by the BIE reaction

TiCl 4 + AlBr3 ↔ TiCl 3+ ⋅ AlBr3Cl − is rapid, and (ii) that therefore the rapid consumption of TiCl3+ by the initiation reaction (the nature of which was not specified), would produce a [Pn+] = [AlBr3]o. The kp derived on this basis, probably kp± in our symbols because of the low polarity of the solvent, was ca. 6 x 103 l·mol-1·s-1. This must be regarded as a minimum value, because it was shown subsequently (Grattan and Plesch, 1977) that at any rate for the self-ionisation of AlBr3 in MeBr the binary ionisation is a slow reaction (on the time-scale of the isobutene polymerisation), and because the sequestration of AlBr3 by its complexing with the isobutene (Grattan and Plesch, 1980) has been ignored.

4.2.8 M. Rodriguez and L. M. Leon The study of the polymerisation of NVC in CH2Cl2 by Ph3C+ AsF6- and PF6- at 0 ºC and 20 ºC by reaction calorimetry reported by Rodriguez and Leon is one of the most thorough done with this monomer (Rodriguez and Leon, 1983a, b). The first paper contains the kinetics; although no primary data are given for the ΔHp, the concordance and small spread of the values inspire confidence (at 20 ºC – 92.4 ± 3.3 and at 0 ºC – 94.9 ± 3.3 kJ·mol-1). After a short acceleration the following ca. 80% of each reaction was internally of first order, and the first-order rate-constants k1 (the authors’ kap) for the polymerisations of second portions of monomer were close to those of the first polymerisations; both these features indicate the absence of termination. Even with the lowest concentrations of initiator, co, the polymerisations went to completion. The authors calculated their kp from kp = k1/co, assuming that [Pn+] = co, and found that this kp fell from a highest value at the lowest co asymptotically towards the co axis. The authors showed convincingly that their results are incompatible with an interpretation in terms of a dieidic mechanism, with ion-pairs taking over as co increased from 0.5 x 10-5 to 9 x 10-5 mol·l-1; but assuming plausibly that the value at the lowest co would be nearest to the value for unpaired ions, they calculated kp+ = 9.5 x 105 at 20 ºC and 4.8 x 105 l·mol-1 s-1 at 0 ºC. From some very scattered results with co in the range of (0.2-5) x 10-3 mol·l-1 they concluded that kp± would be less than 102 l·mol s-1. Unfortunately, by omitting to plot the primary data, i.e., k1 versus co, they missed the most interesting feature of their results and were misled by the plots of kp. Their results plotted by us are shown in Figures 4 and 5, where we see that with increasing co the k1 550

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) rises, and from co = c′0 it becomes (more or less) constant. If the authors’ assumption [Pn+] = co had been justified, k1 would have been proportional to co over the whole range of co . The observations indicate that the cation or the anion of the alleged initiator (the Ph3C+ salt) reacts with an impurity, Imp, in the system to give the real initiator, and c′0 = [Imp]. We have in fact a kinetic titration of the Imp. From our plots we have obtained: k1/s-1

c′′o/mol·l-1

kp+/l·mol-1·s-1

20 ºC

6

1.0 x 10-5

6 x 105

0 ºC

5

1.5 x 10-5

3.3 x 105

T

These results are of course very similar to those of the authors, but we think that they are more soundly based. It is obvious now from our plots why the authors’ kp fall from their highest values near co = 0 towards an asymptote. If the cocatalytic impurity had been in the monomer, the c′o and the maximum, constant, k1 would have been proportional to mo , as was reported by Hamid et al., (1970); these authors found, when studying the polymerisation of NVC by HgCl2, that the monomer

Figure 4 The k1 as a function of [Ph3C+AsF6-] at 20 °C. m = 0.061 (O) and 0.122 mol·l-1 ( ). (Rodriguez and Leon, 1983a)

551

Developments in the Theory of Cationoid Polymerisations

•

Figure 5 Same as Figure 4, at 0 °C, with m = 0.061 (O), 0.122 ( ) and 0.244 ( ) mol·-1

contained (at least) one cocatalytic Imp which was removable by crystallisation from hexane, and one which could not be removed in this way. In the present instance there is insufficient evidence to indicate the origin of the cocatalytic impurity, and there are no indications as to its nature. Our consequent ignorance of the initiation mechanism is especially regrettable, as in their second paper the authors conclude from their monitoring of the [Ph3C+] and from the DPD of the polymers that the initiation does not involve the addition of the trityl cation to the monomer. They suggest that all their observations are explicable if the initiation is an electron transfer from the monomer to an acceptor A, and that the resulting radical-cations then dimerise in the well-known manner. The di-cations thus formed grow by amphibainic* propagation:

NVC + A → A − + • CH 2 ⋅ C + HCbz 2 • CH 2 ⋅ HCbz → CbzC + H ⋅ CH 2 CH 2 ⋅ C + HCbz * The amphibaina is a two-headed animal which goes both ways.

552

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) In their view the A is the trityl cation, which is regenerated at the end of the polymerisation. As we have shown, it is unlikely that the Ph3C+ itself is the initiator, so the chemistry of the real initiation remains unknown.

4.3 Stopped-flow and related methods

4.3.1 D. C. Pepper’s group The first measurements by the stopped-flow technique are due to Pepper and various collaborators (De Sorgo et al., 1973; Lorimer and Pepper, 1976; Pepper, 1974, 1975, 1976; Leon et al., 1980). The work is principally concerned with the polymerisation of styrene in methylene chloride by perchloric acid over a range of temperatures from 0 ºC to –97 ºC. The last papers give the senior author’s final conclusions which differ in several respects from his earlier views. Pepper took trouble to establish that the absorption at 340 nm, which he was observing, was the only one in the region between 300 and 500 nm, and he made out a good case (since supported by many observers) that it is due to the polystyryl cation at the growing end of the polymers. The only apparent weakness in the work is that an εmax = 104 l·mol-1·cm-1 (equal to the ε of the polystyryl anion) was assumed; since the ε of the polystyryl cation may be nearer 3 x 10 4 l·mol-1·cm-1, all the rate-constants may be too small by a factor of 3. The rate of change of [P n +] and m were monitored spectroscopically. The spectroscopic measurements were supplemented by conductivity measurements, and the DP and DPD of the polymers were measured. Also, the work included experiments with an added common-ion salt (n-Bu 4 N + ClO 4- ) and a non-common ion salt (PhCH 2NMe3+SbF6-). This very thorough study led the authors to the conclusion that propagation by unpaired and paired ions and by perchlorate ester can co-exist, and that their relative importance is affected by all the reaction parameters, including the ratio m/[HA]0 (where HA = HClO4), which of course falls as a reaction progresses. The reaction patterns were all complicated and sensitive to conditions, but somewhat simpler at –60 ºC and –80 ºC, at which temperatures the pseudo-cationic contribution is not important. Pepper paid particular attention to the contribution from non-ionic propagation. The rate, RM when [Pn*] = [Pn+] + [Pn+A-] is at its maximum [Pn*]M, was given by

RM / mM ⋅ [ Pn* ]M = kap = k/mM ⋅ [ Pn* ]M = kp* where k was proportional to [HA]2o. The kp* was expressed as usual by the equation

553

Developments in the Theory of Cationoid Polymerisations

kp* = kp± + α ⋅ (kp+ – kp± ) and it gave a good correlation for α values calculated from [Pn*] and KD = 5 x 10-7 mol·l-1 at –60 ºC and 1 x 10-7 mol·l at –80 ºC. These very low values are only astonishing if one does not consider that the salts of sec. carbenium ions, like those of tert. ammonium ions, with hydrogen-bondable anions such as ClO4- have much lower KD than those of fully substituted cations (Kraus, 1956). The derived constants given in Table 9 are put forward by Pepper with very explicit reservations as to their accuracy; they are included in our list of acceptable results. The great difference between kp+ and kp± at the low temperatures can be misleading if one disregards the difference in the corresponding activation energies. Lorimer and Pepper point out that their results indicate that at ca. 20 ºC kp+ and kp± would be about equal.

4.3.2 A digression on initiation Pepper and all subsequent workers with the stopped-flow technique observed that the ratio [Pn*]/[HA]o was generally ca. 10-2 at around 20 ºC, and Vairon et al., (1992) found that it increases markedly as the temperature is reduced. There has been much speculation about the reasons for this, and Sigwalt and Sauvet (1980) have investigated in some detail the formation of conjugate anions, but it is clear that this effect, though important in several systems, cannot account for the very low ion yields observed by many workers. We offer here an additional new explanation which is based on known chemistry, is testable, and is analogous to one that has served well in a closely related area: the addition of a solution of AlCl3 to one of isobutene leads to a short-lived polymerisation consuming very little of the AlCl3 followed by the ‘peaceful coexistence’ of the residual isobutene and AlCl3. Grattan and Plesch (1980) showed experimentally that these phenomena are due to the formation of AlCl2+ + AlCl4- from AlCl3 by a BIE, in the initiator solution, the initiation by the addition of AlCl2+ to IB, and the complexation of the un-ionised AlCl3 with the IB; this complexation reduces drastically the formation of more ions by the BIE, and so only a very small fraction of the AlCl3 is consumed by the initiation (see Section 3.3.4).

Table 9 Rate-constants for the polymerisation of styrene by HClO4 in CH2Cl2 (Pepper, 1976) T, °C –60 –80

554

10-4·kp+/l·mol-1·s-1

10-3·kp±/l·mol-1·s-1

Ep+/kJ·mol-1

Ep±/kJ·mol-1

2.5 2

3 1

4

13±3

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) We suggest that what happens with the protonic acids is very similar: In the initiator solution we have the BIE,

2HA ↔ H 2 A + + A − , K2

(57)

followed by nM

H 2 A + + M → HM + + HA → Pn+ + HA and

HA + M ↔ HA ⋅ M

(58)

Neither the equilibrium (57) nor the complexation (58) are new; what is new is their combination here in the form used for the AlCl3 + IB system. The central idea is that only the ions due to the BIE, which are present at the moment of mixing can be effective initiators, because the subsequent regeneration of ions by the BIE is far too slow to affect the very fast polymerisation. Concerning the details of the initiation, we do know from the polarographic studies of Kabirud-Din and Plesch (1978) that for CF3SO3H in CH2Cl2 at ca. 20 ºC, at any rate in the presence of the base electrolyte needed for polarography (0.1 mol·l-1 (n-Bu)4N+BF4-), the K2 for (57) is 7.2 x 10-3, and that there is no formation of HA2-; in the absence of the baseelectrolyte, K2 is likely to be smaller because of the ionic-strength effect. Therefore, since

[H 2 A + ] = K21 / 2 ⋅ [HA]

(59)

an [HA] = [HA]o = 10-3 mol·l-1 gives [H2A+] = 8.5 x 10-5 mol·l-1. If the H2A+ is converted rapidly and completely to [Pn*], then [Pn+]/[HA]o = 10-1. This is well within the range of the reported values, and it evidently depends on the value of K2. The increase of [Pn+]/ [HA]o with decreasing temperature is due to the fact that for most BIE, in polar solvents the K2 increases strongly with falling T. One can also reverse the calculation: from Kunitake and Takarabe (1979a), Figure 3, we see that for [CF3SO3H]o = 2.4 x 10-3 mol·l-1, the [Pn+] extrapolated back to t = 0 gives [Pn+] = ca. 10-4 mol·l-1. If we take this as [H2A+]o, we get from (59) that K2 = ([H2A+]o/ [HA]o)2 = 1.7 x 10-3 for the CF3SO3H in (CH2Cl)2 at 10 ºC. From Figure 5 of Kunitake and Takarabe (1979b) we get by the same method K2 = (3.5 x 10-4/5.4 x 10-3)2 = 4.2 x 10-3 at 20 ºC, again of the same order of magnitude as the polarographic value. In view of the uncertainty of the manual extrapolations, the agreement is satisfactory, and this indicates that our idea is compatible with the facts.

555

Developments in the Theory of Cationoid Polymerisations Several authors have attempted to calculate the rate-constant for initiation from their observed d[Pn+]/dt. However, it follows from our theory that the alleged ki, which we designate by kiA and which was calculated from

d[ Pn+ ]/ dt = kiA ⋅ [HA]o ⋅ m is not valid, because in our view

d[ Pn+ ]/ dt = ki ⋅ [H 2 A + ] ⋅ m = ki ⋅ K21 / 2 ⋅ [HA]o ⋅ m so that actually the kiA is

kiA = ki ⋅ K21 / 2 For example, if kiA = ca. 10 l·mol-1·s-1 (Kunitake and Takarabe, 1979a), ki = 10/8.5 x 10-2 = ca. 120 l·mol-1·s-1. Unfortunately, the situation can be much more complicated, with some, or most, of the acid forming an ester with the monomer which then contributes to the rate by pseudocationic consumption of monomer. It is ironic that the protonic acids, which were chosen originally by Pepper as apparently offering the best prospect of simplest kinetics, have turned out to be fundamentally unsuitable for kinetic work because of the multiplicity of their possible reactions with monomers, and the formation of conjugate anions.

4.3.3 T. Kunitake and K. Takarabe Kunitake and Takarabe reported studies on the polymerisation of styrene (1978, 1979a, b) and of α-Me-styrene (1981) in (CH2Cl)2 by CF3SO3H, carried out by a combination of the stopped-flow and rapid quenching techniques over the temperature range –1 to +30 ºC. For styrene they used [HA]o = (3–10) x 10-3 mol·l-1 and mo = 0.01 to 0.4 mol·l-1. The concentration of the ions, [Pn*], and of the monomer were followed spectroscopically. It was ascertained that during the polymerisation the only absorption was that at 340 nm, identified as due to the polystyryl cation, for which an ε = 104 l·mol-1·cm-1 was assumed, i.e., the same as that used by Pepper. After the completion of the polymerisation, an absorption due to indanyl cations appeared. The yield of polystyryl cations, [Pn*]/[HA]o, was always between 1 and 5%, and a reason for this has been suggested in Section 4.3.2. These papers lack primary data, but they contain two diagrams showing the simultaneous changes in m and in [Pn*] = [Pn+] + [Pn+A-] The absorption due to the [Pn*] rises very

556

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) rapidly to a sharp peak and then falls approximately exponentially to an asymptote; the conversion curve, after the first half-life which corresponds to the attainment of the peak absorption, is approximately of first order. Introducing their method of interpreting the results the authors wrote: ‘The CF3SO3Hstyrene system appears to be advantageous over the HClO4-styrene system for a detailed kinetic analysis, since there is no ambiguity concerning the carbocationic nature of the propagating species’. This is intended to indicate that there are no complications from a pseudo-cationic contribution to the rate. The statement is completely unsupported by evidence, and it is actually in blatant conflict with their own results, as we will show below. The authors used a rate-equation involving [Pn*] = constant, to analyse the results near the peak where this is approximately valid, and one involving the integration of [Pn*] for parts of the reaction where this quantity changes noticeably, and these two treatments yield fairly concordant results, which are shown in Table 10 (taken from Tables V and VI of Kunitake and Takarabe, 1979b). The authors realised that their rate-constant kp,app is composite and they assumed that it is given by the conventional Equation (60) in terms of kp+ and kp±, obviously ignoring any possible contribution from an ester:

kp* = kp± + kp+ ⋅ KD1/2 /[Pn* ]1 / 2

(60)

Table 10 Rate-constants for the polymerisation of styrene by CF3SO3H in (CH2Cl)2 (Kunitake and Takarabe, 1979b) 10-5 kp.app/ l·mol-1·s-1 a

10-5 kp+/ l·mol-1·s-1 a

10-5 kp±/ l·mol-1·s-1 a

30

2.1

29 ± 7

1.2 ± 0.2

20

1.6

12 ± 4

1 ± 0.2

10

1.0

5.1 ± 3.2

0.74 ± 0.05

–1

0.55

2.5 ± 1.5

0.43 ± 0.04

T, °C

10-5 kp*/ l·mol-1·s-1 b

0.36

a : Authors' values which are over-estimates because of the neglect of the pseudocationic component b : Calculated in this work

557

Developments in the Theory of Cationoid Polymerisations The plots of the data according to this equation were rectilinear for polymerisations at –1 ºC, 10 ºC, 20 ºC and 30 ºC, so that values of kp± and kp+·KD1/2 could be obtained. The authors then used the common-ion salt (n-Bu)4N+ CF3SO3- and interpreted the kinetic results by the equation

kp* = kp± + kp+ ⋅ KD / so ⋅ z

(61)

where s0 = [n-Bu4N+CF3SO3-]o and z = [CF3SO3-]/[n-Bu4N+CF3SO3-]; the z was calculated by means of the dissociation constant of the salt. From the plots of the kp* according to (61) a further set of kp± was obtained, which agreed well with those obtained without salt. From the slopes of both sets of plots, the kp+ and KD could be separated. The results are given in Table 10. The value of KD is of the same order of magnitude (ca. 10-7 mol·l-1) as that found by Pepper for poly(styryl)+ ClO4- (Section 4.3.1); this may be a useful confirmation of a rather astonishingly small value, but one must keep in mind the uncertainty arising from the possible formation of conjugate ions with the added salt. We now note that in analysing their results the authors have ignored completely that after the peak absorbance has been passed and the [Pn*] declines exponentially, the conversion curves are of approximately first-order, as we have ascertained by detailed measurements on the first of the two published curves (Figure 3 of Kunitake and Takarabe, 1979a; see below about Figure 1 of Kunitake and Takarabe, 1979b). Evidently, this implies that there is a kinetically dominant chain carrier whose concentration remains constant, which must be the ester. Therefore we are dealing here with trieidic polymerisations (Pn+, P n+A- and ester), and the contribution to the rate from the ions, given by kp*, has been overestimated because the contribution from the ester was ignored; therefore all the kp+ and kp± are maximum values. One actual value of kp* can be calculated from the figure mentioned previously by the following analysis which also yields the partial rate, RE, due to the pseudo-cationic polymerisation. The total rate R = R* + RE; the Rx at X% conversion were obtained from the slopes of the tangents to the curves at X = 25, 50, 75%. If the RE is given by RE = k1E·m * R50 = R50 + R50E = kp* ⋅ [ Pn* ]50 ⋅ mo / 2 + k1E ⋅ mo / 2

R75 = kp* ⋅ [ Pn* ]75 ⋅ mo / 4 + k1E ⋅ mo / 4 Therefore from Figure 3 of Kunitake and Takarabe (1979a), at 10 ºC

558

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993)

k *p = (R 50 – 2 R 75 ) /(mo / 2)([Pn* ]50 – [Pn* ]75 ) = (0.751 – 0.566) / 0.196 × (5 – 2.4) × 10 −5 = 3.63 × 10 4 l ⋅ mol −1 ⋅ s −1 This is the rate-constant of the combined ionic contributions to the rate, and it must be compared to the authors’ kp,app = 8.9 x 104 l·mol-1·s-1 which they believed was due entirely to ions. (The R25 is too inaccurate to be useful for an analogous calculation.) The same treatment applied to the results at 20 ºC gives a smaller kp*, we believe because the reaction does not go to completion, i.e., there is a termination, and the fundamental assumption of our treatment, that [E] = const., is not valid (see Figure 1 of Kunitake and Takarabe, 1979b). In order to discover the proportion of kp+ and kp± in our kp* we use the Equation (14) with co =[Pn*] which between X = 50% and 75% is ca. 3 x 10-5 mol·l-1. Hence y/p = 0.06, i.e., kp* is probably close to kp±. The magnitude of the error caused by ignoring the pseudo-cationic polymerisation can be shown by calculating the rates due to the ionic and covalent propagation mechanisms, thus: We obtain Rx* from the equation

Rx* = kp* ⋅ [ Pn* ]x ⋅ mx by means of our value of kp*, the [Pn*]x taken from the graph, and the approximate mx. Since RE = R - R*, therefore at the conversions listed below, the rates and component rates are:

% Conversion, X

R

RE

R* -1

mol·l ·s

-1

RE/R

kpE/ l·mol-1·s-1

25

1.17

0.74

0.43

0.37

611

50

0.75

0.36

0.39

0.52

831

75

0.283

0.085

0.20

0.71

852

559

Developments in the Theory of Cationoid Polymerisations These results show that even at the greatest ion concentration one third of the monomer consumption is due to the ester. Since the rate-constants calculated by Kunitake and Takarabe for styrene contain unknown contributions from at least three propagators, they cannot be included in our final table of results. It is also evident that the variation of the rate-constants with temperature cannot provide any useful information, because the relative contributions from the different propagators change with temperature. A further advantage of our treatment of the styrene results is that we can obtain a first-ever estimate of the minimum value of kpE for the poly(styryl)triflate ester of ca. 750 1·mol-1·s-1 (from kpE = RE/m·[E], assuming that [E] = [HA]o), which is ca. 100 times as great as the kpE for poly(styryl)perchlorate ester. The same group reported a study by the same method in the same solvent of the polymerisation of α-methylstyrene by CF3SO3H and H2SO4 at 30 ºC (Takarabe and Kunitake, 1981). However, the single result for CF3SO3H differs by a factor of 100 from the mean of the three results with H2SO4 so that one can have no confidence in these results.

4.3.4 T. Higashimura’s group The work on rate-constants by Higashimura’s group includes studies by the stopped-flow technique and also by the end-capping technique, and these are included in this section.

4.3.4.1 Stopped-flow technique A group of papers by Sawamoto and Higashimura (Sawamoto and Higashimura, 1978a, b; 1979; Higashimura and Sawamoto, 1978) contains reports on stopped-flow studies of the polymerisation of 4-methoxystyrene in (CH2Cl)2 and in mixed solvents by several initiators. One of the main differences from the work of Kunitake and Takarabe is that mo was 5 x 10-3 mol·l-1, whereas the mo in Kunitake and Takarabe’s work was of the order of 0.1–0.4 mol·l-1. In the work under review the primary observables were the absorbance at 380 nm, allegedly due to the propagating cation, and the rate of consumption of the monomer, also monitored spectroscopically, and the DPD. The identification of the peak at 380 nm as due to the poly(4-methoxystyryl) cation is, unfortunately, erroneous. De Sorgo et al. (1973) had given the λmax of this ion as 340 nm, which was confirmed by McClelland et al. (1991), and it has been shown that the absorption at 380 nm is due to a tertiary ion, the model for which is (Me2AnisC)2C+Anis, where Anis = 4-MeO-C6H4- (Moreau et al., 1987; Sigwalt et al., 1988); this ion is formed

560

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) by the abstraction of a hydride ion from the chain. Because of this mis-identification of the absorption of the propagating species, the kinetic measurements cannot yield any kind of propagation rate-constants, and they will therefore not be quoted. It is ironic that Higashimura, who was amongst those pointing out that an absorption at 430 nm was due, not to the poly(styryl) cation, as previously believed, but to derived ions, then himself fell into the same trap with regard to the poly(4-MeO-styryl) cation (for full references see Bertoli and Plesch, 1966, 1968). The large amount of information especially on the DP and DPD of the polymers obtained under different conditions indicated to Higashimura’s group that an ‘invisible’ species was contributing to the consumption of monomer. This was interpreted by others (see for example, Pepper, 1974 and subsequent papers) as a rediscovery of the pseudo-cationic polymerisations by activated esters, discovered in the 1960s by Gandini and Plesch. Since the activated esters contribute to the rate of polymerisation but are not included in the spectroscopic count of growing chains, even if the kinetic measurements had been made at the correct wavelength, the calculated kp for those systems in which esters can be formed would have been faulty.

4.3.4.2 End-capping technique The same group developed an end-capping method of counting the number of growing centres which they applied to the polymerisation of styrene by acetyl perchlorate (Sawamoto et al., 1983). It involves adding sodium naphthoxide to a polymerising mixture, so that all growing molecules are converted to poly(styryl)naphthyl ether, and the naphthoxy groups are then counted spectrophotometrically. By a suitably subtle GPC technique the DPD of the growing chains (those with naphthoxy end-groups) and the dead chains without naphthoxy groups (transfer-terminated) were found. The kp were calculated conventionally. The work was aimed at finding the effect of dielectric constant, D, on kp. The D of the solutions was calculated taking into account the styrene. Experiments were done with mo = 0.5 mol·l-1 in CH2Cl2 + CCl4 (D = 6.4), CH2Cl2 only (D = 8.3), and with mo = 0.05-0.5 mol·l-1 in CH2Cl2 + PhNO2 (D = 10.7) at 0 ºC. The kp in CH2Cl2 was 1.49 mol·l-1·s-1, i.e., of the same order of magnitude as found by Pepper, Gandini and Plesch, and others for the pseudo-cationic polymerisation of styrene by HClO4. Our plots of the results in their Table 11 show that as mo increases, the [Pn*] increases asymptotically to a level which may be the co = 4 x 10-4 mol·l-1, whilst the kp falls off over the same range of mo . As the rates are not given, one cannot find out to what extent this change was due to a change of rate or to the increase in [Pn*]. Since this polymerisation is probably trieidic, with the relative contributions from unpaired and paired cations and from activated ester unknown, the kp is completely uninformative, and so is the effect on it of the solvent composition. In addition, we now know from

561

Developments in the Theory of Cationoid Polymerisations Plesch’s work with styrene in PhNO2 (Section 4.2.3.) that this solvent inactivates a large and unknown fraction of the carbenium ions. For all these reasons none of this work can contribute to our stock of well-established rate-constants.

4.3.5 J-P. Vairon’s group Under the leadership of Vairon of Paris and in cooperation with van Beylen’s group at Louvain a new style of stopped-flow apparatus was developed which was especially designed for the proper study of cationic polymerisations (Villesange et al., 1991); it appears to be as much of an advance on previous designs as the Paris reaction calorimeter was on its predecessors. The first results obtained with the new device are concerned with the polymerisation of styrene by CF3SO3H in CH2Cl2 over a wide range of temperatures, with mo in the range (1–40) x 10-3 and [HA]o = (0.5–3) x 10-3 mol·l-1 (Vairon et al., 1992; we thank Professor Vairon for giving us the text of this work, which is his lecture at the 10th Symposium on Cationic Polymerisation, 1991, in advance of publication). The primary data from this work are the changes with time of the absorption at 340 nm due to the poly(styryl)+ and of the absorption due to the monomer at 290 nm; the ε340 is assumed to be 104 l·mol-1·cm-1, the value used by Pepper and by Kunitake and Takarabe. The propagation rate-constant, our kp+A, denoted by kp,app, was calculated from the [Pn*]max (their [Pn+]max) and the corresponding rate Rmax and m = mmax. Since the [Pn*]max decreased from 36% of [HA]o at –55 ºC to 4% of [HA]o at 0 ºC, the kp+A could only be determined below –10 ºC, because above –10 ºC the [Pn*]max was too small to be measured accurately. The results are shown in Table 11, and they correspond to an Ep+A of 43 kJ·mol-1. The kinetics of the formation and disappearance of the ions and the kinetics of the polymerisation are both complicated, and so the interpretation of the kp+A is far from clear. We have at least two complications to contend with. One is the extent to which a pseudocationic polymerisation contributes to the rate, the other is the relative importance of unpaired and paired cations. Neither of these questions is addressed by the authors, but we can attempt to resolve them in the light of what we discovered by analysing Kunitake and Takarabe’s results obtained with what was ostensibly the same system.

Table 11 Rate-constants for the polymerisation of styrene by CF3SO3H in CH2Cl2 (Vairon et al., 1992) T, ºC 10-4·kp+A/l·mol-1·s-1

562

–10

–22

–32

–62

9.7 ± 1.3

3.7 ± 0.2

1.5 ± 0.1

0.1 ± 0.01

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) Our finding that at 10 ºC there is a substantial contribution to the rate from a pseudocationic polymerisation makes it advisable to ignore at present all but the result at the lowest temperature, –62 ºC. The experience with poly(styryl)perchlorate suggests that also with the triflate the pseudocationic contribution to the rate at that temperature is likely to be small; therefore we can take kp+A = kp* and we can attempt to determine the relative contributions to it from kp+ and kp±. Once again we can find [Pn+]/[Pn+A-] = y/p from Equation (14). From the paper we take [Pn*] = 6.75 x 10-4 at –55 ºC, as it is not given for –62 ºC; this is the co of Equation (14). From Kunitake and Takarabe’s work we can take KD as ca. 10-7 mol·1-1 although at the much lower temperature it is likely to be greater. Hence co /KD = 7 x 10-3 and y/p = 1.2 x 10-2, and even if KD is as great as 10-5, y/p = 0.12. This means that the authors’ kp* is likely to be closer to kp±, but because of the evidently speculative nature of this assessment we cannot include it in our final table. Because most probably the contribution from pseudo-cationic polymerisation increases and the ratio kp+/kp± changes with increasing temperature, the quoted activation energy cannot be considered significant.

5 Summary of rate-constants

5.1 First-order rate-constants The first-order rate-constants kp1+B for polymerisations in bulk initiated by ionising radiations are summarised adequately at the end of Section 4.1.

5.2 Second-order rate-constants The second-order rate-constants kp+ and kp± for polymerisations in solution which we consider reliable are summarised in Table 12. The initiators used by the various investigators have not been listed, because by definition kp+ and Ep+ must be independent of these; and there are insufficient data to permit any firm conclusions about the effects of the nature of the anion on kp± and Ep±. When considering the rate-constants in this Table it must be remembered that all of them, except those for isobutene, probably comprise a contribution from the polymer-complexed cation, kp+P, greater or smaller according to circumstances (see Section 2.3), and correspondingly the activation energies would contain a term Ep+P and an enthalpy of complexation; further, for the reason explained in Section 4.1.9, the kp+ from ionising radiation experiments are minimum values. These less than 20 rate-constants which in our opinion can be assigned with confidence to a particular ionic propagating species evidently do not permit any generalisations. We

563

Developments in the Theory of Cationoid Polymerisations note that there is agreement between two authors, at least as regards the order of magnitude, concerning the kp+ of N-vinyl carbazole in CH2Cl2. It is particularly regrettable (and significant!) that for the most popular of monomers, styrene, only two sets of reliable results are available. We would like to emphasise that if some result not included in Table 12 happens to agree with one that is included, this agreement does not suffice to validate the excluded result. In the present state of immaturity of the subject, every result

Table 12 Rate-constants and activation energies for cationic polymerisations of alkenes in solution kp±/ l·mol-1·s-1

T/K

kp+/ l·mol-1·s-1

MeCl

22 5

1.2 x 104

4.2.6 (Giusti)

CH2Cl2

195

9.1 x 103

4.1.8 (Ueno)

213

2.5 x 104

3 x 103

193

2 x 104

1 x 103

296

3.5 x 104

283

2.3 x 104

C6H6

293

1.5 x 104

Et2O

296

2.4 x 104

Diglyme

296

1.6 x 104

CH2Cl2

295

2 x 1 03

299

2.2 x 105

4.1.7 (Stannett)

273

4.6 x 105

4.2.1 (Bawn)

248

1.6 x 105

27

293

6.0 x 105

19

273

3.3 x 105

Solvent

Ep+/kJ·mol-1 Ep±/kJ·mol-1

Section reference

Isobutene

Styrene CH2Cl2

CH3Ph

4.3.1 (Pepper) 4

13 4.1.8 (Ueno)

EVE 4.1.7 (Stannett)

IPVE C6H6

N-vinyl carbazole CH2Cl2

CH2Cl2

564

4.2.8 (Leon)

The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) must derive its validity from its own origin, and only when, some time in the future, there is an agreed corpus of numbers, as there is for radical and anionic polymerisations, can a new claimant be admitted on grounds of its agreement with ‘accepted’ values. Evidently, there are insufficient results to make any comparisons worth while, because a ranking in terms of rate-constants at any one, arbitrary, temperature is at best uninformative and at worst misleading. What can be done to augment our knowledge? Recognising that it is mostly fruitless for one investigator to prescribe to others how to proceed, we will nonetheless enumerate a few points which we think will be helpful in future research; some relevant points have already been made in Section 2.5.5. With regard to initiation, this must be fast compared to the life-time of the polymerisation because it is difficult enough to study one reaction (propagation) without having to grapplequite unnecessarily-with concurrent and consecutive reactions. The initiator should preferably be a species which is identifiable as a chain-end; and the nature of the initiation reaction must be established beyond doubt for every system. In this way the number of initially growing chains can be ascertained. We would favour chemically or radioactively tagged or labelled aroyl+ SbF6- or PF6- salts and possibly arylmethyl or diarylmethyl cations generated in situ by flash photolysis. Certainly the anion must be both inert and stable; this requirement eliminates as initiators the organic salts of chlorometallates and oxo-acids as suitable initiators. Some quantitatively based guidance in the choice of initiator can be found from Pask and Plesch (1982). It should be clear from what has been written here, that the use of any kind of protonic acid is a waste of time. The quenching or ‘killing’ reagent should be a base, such as the naphthoxy anion used by Higashimura (see Section 4.3.4.2) which gives a countable end-group, and not the conventional, but useless, ethanol or methanol. The kinetic measurements must be accompanied by conductivity measurements, and the electrochemistry, i.e., the composition of the ionic population, and any equilibrium constants such as K D must be established by measurements during and after polymerisation and with model compounds, and secondary effects, such as that of m on KD, must be investigated. The preferred general method is the vacuum reaction calorimeter because of its wide range and flexibility, and because the enthalpy of the reactions is a good indicator of whether a polymerisation has gone to completion; in any case, tests for residual monomer by glc must not be omitted. The complete reaction curve, however acquired, can reveal not only the internal order of a reaction, and whether it changes with conversion, and it is a far firmer base for calculating rate-constants than the initial rate or a maximum rate.

565

Developments in the Theory of Cationoid Polymerisations The choice of solvent is extremely difficult and is of course partly determined by what kind of question the study is aiming to answer. One must recognise that there is no such thing as an ‘ideal’ solvent, although CH2Cl2 comes near to it. Some guidance on the choice of solvents has been given by Plesch (1963) and advice on their purification has been brought up-to-date (Plesch, 1989). For studies of the effect of dielectric constant it is advisable to adhere to one family of compounds; for example for a VE one could use (D/T in parentheses): Diglyme (7.3/20 ºC) Et2O (4.3/20 ºC) and 1,4-dioxan (2.2/25 ºC); MeCN (37/25 ºC) and PhCN (25/25 ºC); for vinyl and vinylidene hydrocarbons in chlorinated solvents one can use MeCl (12.6/–20 ºC), PhCl (6.15/0 ºC), 1,2dichlorobenzene (11/0 ºC). There is here great scope for imaginative innovation. Finally, the dependence of the DP and DPD on conversion, on mo and on co must always be obtained, so that chain-breaking reactions can be identified by means of Mayo plots. We hope that some colleague, adequately equipped with enthusiasm, skill, and facilities and the necessary persistence will rise to the challenge implicit in this review, and produce some more reliable propagation rate-constants.

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Developments in the Theory of Cationoid Polymerisations T. Higashimura and M. Sawamoto,. Polymer Bulletin,. 1, 11 (1978). G. E. Holdcroft and P. H. Plesch, Makromolekulare Chemie, 185, 27 (1984). G. E. Holdcroft and P. H. Plesch, Journal of Chemical Research, (S), 1985, 36; (M) 0401 (1985). W. C. Hsieh, H. Kubota, D. R. Squire and V. T. Stannett, Journal of Polymer Science, Chemistry, 18, 2773 (1980). W. C. Hsieh, A. Deffieux, D. R. Squire and V. T. Stannett, Polymer 23, 427 (1982). E. Hubmann, R. B. Taylor and F. Williams, Transactions of the Faraday Society, 62, 88 (1966). V. Jaacks, K. Boehlke and E. Eberius, Makromolekulare Chemie, 118, 354 (1968). Kabir-ud-Din and P. H. Plesch, Journal of Electroanalytical Chemistry, 93, 29 (1978). J. P. Kennedy, Journal of Polymer Science, 38, 263 (1959). J. P. Kennedy and R. M. Thomas, Journal of Polymer Science, 45, 227 (1960). J. P. Kennedy and E. Maréchal, Carbocationic Polymerisation, Wiley, London, (1982). C. A. Kraus, Journal of Physical Chemistry, 60, 129 (1956). T. Kunitake and K. Takarabe, Journal of Polymer Science, Symposia, 56, 33, (1976). T. Kunitake and K. Takarabe, Polymer Journal, 10, 105 (1978). T. Kunitake and K. Takarabe, Macromolecules 12, 1061 (1979a); 12, 1067 (1979b). A. Ledwith and D. C. Sherrington in Reactivity, Mechanism, and Structure in Polymer Chemistry, Eds., A. D. Jenkins and A. Ledwith, Wiley, London, p.244 (1974). A. Ledwith and D. C. Sherrington, Advances in Polymer Science, 19, 2 (1975a).

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The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) A. Ledwith, E. Lockett and D. C. Sherrington, Polymer 16, 31 (1975b). L. M. Leon, P. Altuna and D. C. Pepper, European Polymer Journal, 16, 929 (1980). W. R. Longworth and P. H. Plesch, Proceedings of the Chemical Society, 117 (1958). J. P. Lorimer and D. C. Pepper, Proceedings of the Royal Society, A351, 551 (1976). C. C. Ma, H. Kubota, J. M Rooney, D. R. Squire and V. T. Stannett, Polymer, 20, 317 (1979). P. L. Magagnini, S. Cesca, P. Giusti, A. Priola and M. Di Maina, Makromolekulare Chemie, 178, 2235 (1977). M. Marek and M. Chmelir, Journal of Polymer Science, C22, 177 (1968). G. Maschio, F. Artigiani, M. Di Maina and P. Giusti, Journal of Polymer Science, 29, 1215 (1984). K. Matyjaszewski and P. Sigwalt, Macromolecules 20, 2679 (1987). H. Mayr, Angewandte Chemie, International Edition, 29, 1371 (1990). H. Mayr, R. Schneider and R. Pock, Makromolekulare Chemie, Macromolecular Symposia, 3, 19 (1986). R. A. McClelland, C. Chan, F. Cozens, A. Modro and S. Steenken, Angewandte, International Edition, 30, 1337 (1991). D. J. Metz, Advances in Chemistry Series, 91, 202 (1968). M. Moreau, K. Matyjaszewski and P. Sigwalt, Macromolecules, 20, 1456 (1987). J. M. Moulis, J. Collomb, A. Gandini and H. Cheradame, Polymer Bulletin, 3, 197 (1980). O. Nuyken and P. H. Plesch, Chemistry and Industry (London), 379 (1973). S. D. Pask and O. Nuyken, European Polymer Journal, 19, 159 (1983). S. D. Pask and P. H. Plesch, Chemistry and Industry (London), 331 (1981).

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Developments in the Theory of Cationoid Polymerisations S. D. Pask, P. H. Plesch and S. B. Kingston, Makromolekulare Chemie, 182, 3031 (1981). S. D. Pask and P. H. Plesch,, European Polymer Journal, 18, 839 (1982). D. C. Pepper, Makromolekulare Chemie, 175, 1077 (1974). D. C. Pepper, Journal of Polymer Science Symposia, 50, 51 (1975). D. C. Pepper Journal of Polymer Science Symposia, 56, 39 (1976). P. H. Plesch, Journal of Polymer Science, 12, 481 (1953). P. H. Plesch, Zeitschrift fur Elektrochemie, 60, 325 (1956). P. H. Plesch, (Ed.) The Chemistry of Cationic Polymerisation, Pergamon, p.678 (1963). P. H. Plesch, Journal of the Chemical Society, 104 (1964). P. H. Plesch, Cationic Polymerisation in Progress in High Polymers, Vol. 2, Eds., J. C. Robb and F. W. Peaker, Iliffe Books Ltd, London, p.137 (1968). P. H. Plesch, Advances in Polymer Science, 8, 137 (1971). P. H. Plesch, British Polymer Journal, 5, 1 (1973). P. H. Plesch, Makromolekulare Chemie, 175, 1065 (1974). P. H. Plesch, Journal of Polymer Science Symposia, 56, 373 (1976). P. H. Plesch and S. H. Shamlian, European Polymer Journal, 26, 1113 (1990). P. H. Plesch and V. T. Stannett, Journal of Macromolecular Science, Chemistry, A18, 425 (1982). P. H. Plesch in Cationic Polymerisation and Related Processes, Ed., E. J. Goethals Academic Press, p.1 (1984). P. H. Plesch, International Laboratory, 18, (1986). P. H. Plesch, High Vacuum Techniques for Chemical Syntheses and Measurements, Cambridge University Press (1989). P. H. Plesch, Makromolekulare Chemie, Macromolecular Symposia, 32, 299 (1990a).

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Developments in the Theory of Cationoid Polymerisations R. Schneider, H. Mayr and P. H. Plesch, Berichte der Bunsen Cesellschaft, 91, 1369 (1987). P. Sigwalt and G. Sauvet, Polymer Journal, 12, 651 (1980). P. Sigwalt, Polymer Journal, 17, 57 (1985). P. Sigwalt, K. Matyjaszewski and M. Moreau, Makromolekulare Chemie, Macromolecular Symposia. 13/14, 61 (1988). V. Stannett, H. Kubota, W. C. Hsieh and D. R. Squire, Proceedings of the Sixth International Congress of Radiation Research, Tokyo, Japan, 366 (1979). V. Stannett and J. Silverman in Initiation of Polymerisation, Ed., F. E. Bailey, Jr., American Chemical Society Symposium Series, 212, 435 (1983). V. Stannett and A. Deffieux, in Cationic Polymerisation and Related Processes, Ed., E. J. Goethals, Academic Press, p.307 (1984). V. T. Stannett, J Silverman and J. L. Garnett in Comprehensive Polymer Science, Ed., G. Allen Pergamon Press, New York, p.317 (1989). F. Subira, G. Sauvet, J. P. Vairon and P. Sigwalt, Journal of Polymer Science Symposia, 56, 221 (1976). F. Subira, J. P. Vairon and P. Sigwalt, Macromolecules, 21, 2339 (1988). Y. Suzuki, A. Chudgar, J. M. Rooney and V. Stannett, Journal of Macromolecular Scienc, A11, 115 (1977). M. Szwarc, Macromolecules, 11, 1053 (1978). K. Takarabe and T. Kunitake, Makromolekulare Chemie, 182, 1587 (1981). R. B. Taylor and F. Williams, Journal of the American Chemical Society, 91, 3728 (1969). B. Trathnigg, Makromolekulare Chemie, 181, 1979 (1980a); Angewandte Makromolekulare Chemie, 88, 127 (1980b). B. Trathnigg and D. Schneditz, Makromolekulare Chemie, Rapid Communications, 3, 597 (1982). F. E. Treloar, Polymer, 1, 513, (1960).

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The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes (1993) K. Ueno, K. Hayashi and S. Okamura, Polymer, 7, 451 (1966a). K. Ueno, H. Yamaoka, K. Hayashi and S. Okamura,. International Journal of Applied Radiation and Isotopes, 17, 595 (1966b). K. Ueno, F. Williarns, Ko. Hayashi and S. Okamura, Transactions of the Faraday Society, 63, 1478 (1967). K. Ueno, Ko. Hayashi and S. Okamura, Journal of Macromolecular Science, A2, 209 (1968). J-P. Vairon, A. Rives and C. Bunel, Makromolekulare Chemie, Macromolecular Symposia, 60, 97 (1992). M. Villesange, G. Sauvet, J-P. Vairon and P. Sigwalt, Journal of Macromolecular Science, Chemistry, A11, 391 (1977). M. Villesange, G. Sauvet, J-P. Vairon and P. Sigwalt, Polymer Bulletin, 2, 131 (1980). M. Villesange, A. Rives, C. Bunel, J-P. Vairon, M. Froeyen, M. van Beylen and A. Persoons, Makromolekulare Chemie, Macromolecular Symposia, 47, 271 (1991). Y. Wang and L. M. Dorfman, Macromolecules, 13, 63 (1980). F. Williams, K. Hayashi, K. Ueno, K. Hayashi and S. Okamura, Transactions of the Faraday Society, 63, 1501 (1967). F. Williams in Fundamental Processes in Radiation Chemistry, Ed., P. Ausloos, Interscience Publishers, Chapter 8, p.515 (1968).

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5.8

Rate Constants of Cationic Polymerisations and Mayr’s Rate † Constants, Reconciled (2001) P. H. Plesch

This paper was first published in Macromolecules, 2001, 34, 5, 1143-1147. Reproduced with permission from the American Chemical Society, copyright 2001.

Prologue The reconciliation mentioned in the title of this work is, fundamentally, one of an unreal conflict arising from a lack of understanding. Despite this author’s attempts over several decades (which are the subject of Chapter 5) to show that in the context of cationoid polymerisations the concept of rate constant must be used with great care, many colleagues were dismayed by the discrepancy implicit in the title. It seems that most chemists cling to the idea that what appear to be similar reactions must have similar rate constants, without examining whether the apparent similarity reflects reality. In the present context the reality is defined by the electro-chemical situations of the ions which are very different in the two sets of reaction conditions with which the controversy is concerned, namely ‘high’ and ‘low’ alkene concentrations. Because of this undiscriminating attitude, several attempts were made to ‘explain away’ the discrepancy in terms of vague concepts invented ad hoc, but no other attempts at explanation in terms of conventional physical chemistry are known to this author. He is greatly encouraged by the fact that his theory which had been devised to account for quite different phenomena (Section 4.9, Polymerisations by Ionising Radiations) has served so well in dealing with the present problem, especially as no new assumptions, but only conventional physico-chemical concepts, are involved. He is reminded of Marlene Dietrich’s famous saying: ‘It is not that my legs are so good - it’s just that I know what to do with them.’ In order to appreciate the cogency of the argument developed here, the reader will find it useful to read first at least the introduction of the Section 5.9. †

Part XII: P. H. Plesch, European Polymer Journal, 1993, 29, 2/3, 121.

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Commercial rubbers

Developments in the Theory of Cationoid Polymerisations

Abstract The rate constants k2 for the attack of carbenium ions on an alkene determined by Mayr for nonpolymerising systems, are ca. 4 orders of magnitude greater than the + kp for the propagation of cationic polymerisations, which involve ostensibly the same reaction. This discrepancy is explained here as due to the different monomer concentrations [M] used in the two types of experiment. The argument starts from the fact that the planar, trigonal carbenium ion has two principal complexing sites, one on each side of the ion. These positions are competed for by all the constituents of the reaction mixture, which include the monomer, and therefore the characteristics of the ion are determined by the nature of its solvators. At high [M], the carbenium ions are predominantly solvated by the monomer, and they are less reactive than those complexed by the polar, but bulky solvent when [M] is low. The reason is that solvation by the π-donor monomer on both sides reduces the charge density at the carbenium ion so much that the covalent bond formation to monomer, the propagation, requires a considerable activation energy. However, solvation by the + solvent has a so much smaller effect on the charge density at the C atom, that the cation solvated only by solvent can polarise the incoming monomer sufficiently for the mutual potential energy between ion and molecule to lead to bond formation with little activation energy. Therefore, since the [M] in Mayr’s experiments are smaller than those in the polymerisations, the cations in the two types of experiments are essentially different species, and therefore their kinetic constants are different. Mayr’s rate constants are essentially the propagation rate constants extrapolated to [M] = 0, and they are likely to be all very similar for the same classes of monomers. + + The long quest for the ‘real’ kp has therefore been ended and the meaning of the kp values selected by the present author has been established.

1 The problem This paper is concerned with the resolution of a discrepancy between a set of kinetic constants for cationic polymerisations selected by the present author as the most reliable recorded in the literature [1] and the rate constants for ostensibly similar reactions measured by Mayr, who has emphasised the urgent need to resolve the disagreements [2]. No other adequate theoretical attempts to do so are known to this author.

1.1 Preamble The rate constants kp+ for the propagation of cationic polymerisations were long believed to be single quantities characteristic for each monomer which could be defined precisely

578

Rate Constants of Cationic Polymerisations and Mayr’s Rate Constants (2001) and unambiguously, like those of other types of polymerisation. Then the present author showed that in any cationic polymerisation there might be more than one species propagating the reaction, from which it follows that the nature and relative proportions of the different chain-carriers must depend on the physicochemical circumstances prevailing during the reaction, and that therefore the measured rate constants may be composite [1, 3, 4] and for that reason cannot properly be called ‘constants’. Moreover, the relative concentration of the different kinds of chain carriers must change during the lifetime of the polymerisation, in any case, because of the consumption of the monomer, and possibly also for other reasons. Such polymerisations, in which more than one species consumes the monomer, were termed ‘enieidic’ [3-5]. Among the possible propagators present simultaneously in a polymerising solution, he recognised that the solvation by solvent and by monomer would produce distinct species of cations, each of which could be unpaired or paired, and the differently solvated cations would + ± have different kp and kp and the ion pairs would have different dissociation constants KD. As a result of his detailed analysis of most of the relevant claims, he compiled a list + of what he regarded as reliable rate constants kp for the attack on an alkenic monomer molecule by an unpaired carbenium ion, solvated mainly by the monomer which is being polymerised [1]. At about the same time, Mayr measured the rate of attack of various types of carbenium ions on alkenes by new and ingenious methods. His rate constants k2 for tertiary carbenium ions are ca. 4 orders of magnitude greater than the kp+ values recommended by this author [1]. Despite detailed discussions between Mayr and the present writer, involving also a detailed examination of Mayr’s methods, a reason for the discrepancy could not be discovered in the mid-1990s [2]. The purpose of the present paper is to suggest one, and thus to explain the discrepancy.

1.2 Summary of Mayr’s findings Mayr’s work had shown that several features which could have been responsible for the discrepancy in fact only had minor effects on the order of magnitude of his rate 9 -1 -1 constants, k2, which are close to that of binary collisions, i.e., ca. 10 l mol s . The findings for secondary and tertiary carbenium ions were very similar. Mayr found k2 to be almost independent (i.e., changed by less than a factor of ca. 4) of the length of the molecule carrying the charge or of the chain attached to the double bond. Also, the k2 were not much affected by a change of solvent from hexane to CH2Cl 2. Therefore there seemed to be few variables left that could be responsible for the discrepancy.

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2 The solution

2.1 Origin of the discrepancy We need to re-examine the basic assumptions underlying the interpretation of the reaction + under discussion, which is the attack of an organic cation R on an alkene, M, to give + another cation, RM : +

R + M → RM

+

Its rate constant k2 is therefore defined by the following equation: observed rate = k2[alkenel[attacking ion] To explain the fact that in different types of experiments very different rate constants were found for ostensibly the same reaction, we have (at least) the following options: (1) The observed rates are not those of the same processes. (2) The alkene is not the same species. (3) The concentration of the attacking ion is not what one thinks it is, either (a) because in one or the other type of experiment the measured quantity is not equal to the concentration of the ions or (b) because in fact the attacking ions are not the same species in the two types of experiment. Options 1 and 2 can be dismissed as highly unlikely. Option 3a can be set aside just + because the kp in question which should be, but are not, the same as the k2, were selected as those (very few) which had been derived from reactions for which the concentration of propagating carbenium ions was deemed to have been well-established and which were clearly first-order with respect to the monomer. The much-quoted rate constants for radiation-induced polymerisations of bulk monomers, which are internally of zero order, were not included (see Plesch [1] for details). This leaves option 3b to be scrutinised closely. When the present writer did this, he realised that his puzzlement had arisen because he like others, had fallen into the trap of which he had frequently warned his students and which he has emphasised in his writings: it is a serious error to attempt to understand electrochemical phenomena by thinking of ions in isolation, because this puts them putatively into a vacuum. But the ions of concern to us do not exist in a vacuum. Ions would not leave their positions of low energy in a crystal lattice to go into solution or be formed from neutral molecules by the transfer of a charged fragment from one molecule to another if those processes were not made exo-energetic by the interaction of the ions with polar or polarisable species in their environment, most commonly the solvent. For that reason, one should always think, and indeed talk, about

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Rate Constants of Cationic Polymerisations and Mayr’s Rate Constants (2001) an ion-in-solution. The properties of an ion, including its reactivity, depend critically upon the nature of its solvation shell [6]. We can make an apt comparison with humans: when people are naked, their attributes and capabilities are very similar, but these are very different when a person is wearing a wet suit, a spacesuit, or a ball gown. The discrepancy with which we are concerned arises from assuming that the active species, i.e., the carbenium ions, are the same in Mayr’s work as those which propagate the polymerisations. The message here is that they are not. The main source of the difference is the solvation of the carbenium ions by the monomer. This phenomenon has been mentioned by this writer in many of his publications from the late 1960s onward [3, 79] and by others, and it soon became a generally accepted part of the theory of cationic polymerisations [10]. The ideas involved were given precision and elaborated [11], and they were used to explain in detail and for the first time the phenomenology of the polymerisations initiated by ionising radiations [12]. It will be shown here that they have a further application in explaining the mystery of the rate constants, i.e., that the reason for the discrepancy lies in the complexing of the monomer with the carbenium ion.

2.2 Cation-monomer complex Although, as has been pointed out, many authors adopted the idea that the carbenium ions can be solvated by monomer, no one before the present author has attempted to explain why in certain situations a monomer molecule could form a stable complex with the carbenium ion instead of reacting with it [12]. In other words, the conditions under which a monomer molecule can act as a solvator to a carbenium ion instead of reacting with it have not been explained hitherto. From a different point of view, we need to find out what it is that may inhibit the addition of such a cation to an alkene when they first meet. Our starting point is that for two naked ions of opposite charge the mutual potential energy decreases as they approach each other until a bond or an ion pair is formed or an electron or a proton is transferred and the assembly becomes stable, and the same holds for an encounter of a naked ion with a reactive molecule, such as an alkene, which is polarised by the approaching cation. For any one of these possible events not to take place, the ion needs to be not naked; in other words, its electrical potential must be reduced by a dispersal or attenuation of the charge. Consider first the tertiary carbenium ions, such as those derived from isobutene which, in the absence of any steric constraints, are trigonal and planar. These have two positions of minimum potential energy, one on each side of the plane. These are the sites for an anion or for the negative end of a dipole or for an n- or a π-donor monomer. However, as soon as one of these positions is occupied, the resulting electrical distortion weakens the electrical potential on the other side; put

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Developments in the Theory of Cationoid Polymerisations another way, when there is an ion or a dipole on each side of the carbenium ion, each one is held less strongly, or sits in a shallower potential trough, than if it were the only one. This simple model served well to explain hitherto unexplained features of the polymerisations by ionising radiations [12], and it will help us to resolve the mystery of the rate constants, and other puzzles as well. In particular, it enables us to resolve the question at the start of this section thus: in any solution of interest in the present context, there are several species competing for the prime solvation sites, the positions of minimum potential energy on either side of the cation. These competitors include the solvent, the monomer, and anions of various kinds and possibly metal halides. The success of these competitors, that is, the proportion of the complexing sites occupied by each one of the competing species, depends on their concentration through the Law of Mass Action. The equilibrium constants for the complexations are determined by the standard free energy ΔG° of the relevant interaction; this in turn is governed by the steric constraints and by the effective electrostatic attraction, which is the resultant of the charge or dipole moment and the polarisability of all the species involved. From these considerations, we conclude that if the carbenium ion is strongly complexed on one side, e.g., by being paired with an anion, then the residual positive charge on the side opposite to that occupied by the strong complexor is not strong enough to polarise the approaching double bond sufficiently to produce the monotonically decreasing mutual potential energy which is needed for bond formation to take place without (or with a very low) activation energy. Therefore the monomer molecule settles in a potential well and is a π-donor-solvator if it is an alkene and an n-donor-solvator if it contains a heteroatom, such as O or N.

2.3 Propagation The ternary complex consisting of the carbenium ion with an anion and a monomer molecule can isomerise with incorporation of the previously complexed monomer molecule into the chain and a shift of the positive charge to the new chain end. This is a unimolecular propagation reaction of zero order with respect to the monomer concentration. It occurs in polymerisations of bulk monomer and in nonpolar solvents, and at relatively high monomer concentrations in polar solvents. It is appropriate to point out here just why it is not valid to assume (as is commonly done) that throughout the propagation step a paired cation will remain paired and that the resulting newly formed carbenium ion will therefore start its life paired (see, e.g., Mayr et al. [13]). On the contrary, if we follow the assumption made by the founders of Transition State Theory that the transition state can be treated as a thermodynamically stable species, it follows that because in the transition state the positive charge is less concentrated than in the ground state and because therefore the Coulombic force holding

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Rate Constants of Cationic Polymerisations and Mayr’s Rate Constants (2001) the anion is less than in the ground state, the (quasi-) dissociation constant of an ion pair of which the cation is in the transition state must be greater than the dissociation constant of an ion pair whose cation is in the ground state. Therefore, the probability of the newly formed cation being paired is less than that for a cation which is in the ground state. Any carbenium ions which are not paired have both their complexation sites occupied by the most polar or polarisable species available, which can be the solvent or the monomer, according to their relative polarities, polarisabilities, and concentrations; for paired cations, the picture applies to their other, still vacant, site. Such a situation will generally prevail in nonpolar solvents because in these the concentration of paired cations is dominant. In a polar solvent, both sites at an unpaired cation can be occupied by solvent, or one by solvent and one by monomer, or both by monomer. In the radiation polymerisations, one sees clearly that as the monomer concentration is reduced from bulk monomer, the kinetics change and they eventually become first order in monomer, whatever the solvent; the critical monomer concentration at which this happens depends on the polarity of the solvent [12]. If we now compare Mayr’s experiments with those of conventional polymer chemistry, including the radiation-induced polymerisations, we find that the single greatest difference is the monomer concentration which in most of Mayr’s experiments is much lower than in most conventional polymerisations. This means that in Mayr’s experiments there are relatively few alkenes in the solvation shell of the carbenium ions, or put more precisely, few of the propagating carbenium ions have even one monomer molecule in their solvation shell. Hence we conclude that Mayr’s k2 for the equivalent of a propagation step are so big because the displacement of the loosely held solvating solvent molecules requires only a very small activation energy, as indeed reported by Mayr. From the opposite point of view, we can see that what makes the conventional kp+ so much smaller than Mayr’s k2 is the energy needed to shift the firmly bound solvating monomer molecules around into the configuration of the transition state, so that the incorporation of such a monomer molecule and the relocation of a solvating monomer molecule on the newly formed cation can occur. In his examination of the effects of monomers cornplexing with the propagating carbenium + ions [11], this author pointed out that the comparison of the kp for various monomers obtained under normal conditions would not be very informative because the relative + magnitudes of the kp would be those of the various carbenium ions, each one solvated at + least partly by its own monomer. Therefore a meaningful comparison of the kp could only be made between the values obtained by an extrapolation to [M] = 0, and it is that extrapolated value which Mayr has measured. The irony of the situation is that at the end of the long + quest for the ‘real’ kp , these turn out to be all approximately the same, namely, the rate

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Developments in the Theory of Cationoid Polymerisations constants for diffusion-controlled reactions (neglecting relatively minor differences due to differences in charge density and steric hindrance in cations of different structure). I am strongly reminded of Peer Gynt’s onion! When, at the centre of the onion which symbolises his life’s quest, he finds - nothing, he realises the irony and can only exclaim: ‘How witty!’

3 Some consequences and suggestions 3.1 A very detailed explanation of the nature of the different propagating species will be found elsewhere [12], as well as a discussion of the factors affecting their relative abundances, as these vary with the concentration of the monomer and the nature of the solvent. In considering the present thesis that a change of monomer concentration can bring about a 10,000-fold change of rate constant by changing the relative abundance of chain carriers of different reactivity, one must also consider the concurrent effects of the changes in the dielectric constant of the reaction medium. These can be dramatic for ionic reactions because KD depends exponentially on the dielectric constant. For all these reasons, to clarify the subject further, it would be most useful to do conventional kinetic experiments with diminishing [M] and Mayr-type experiments with increasing [M] with the aim of obtaining an overlap of the ranges of [M] for the two types of experiment, and for fairly obvious reasons these experiments should be done in the same polar solvent at fixed dielectric constant with compensation by, say, n-butane. Mayr et al. claim that they have done this experiment by increasing [M] up to 0.6 mol/l, and that the reaction was still first-order in monomer and that the rate constant was unchanged. However, in reference [12] evidence is presented showing that the change of kinetic order, signalling a change in the nature of the dominant propagating species, only starts at much higher monomer concentrations. In Figures 9 and 10 of reference [12], it is seen that for the polymerisation of isobutene the variation of the rate with [M] indicates that for the solvents CS2, CHCl3, and CH2Cl2 significant kinetic changes start around [M] = 4 mol/l, and the variation of the DP of the polymers with [M] indicates clearly a change of order in the region of 5–10 mol/l (Figure 15 of reference [12]). It follows that the correctly designed critical experiments remain to be done. A referee has suggested that if the gradual replacement of monomer by solvent leads to an increase in the proportion of more reactive ions, as is proposed here, then a reduction of [M] should accelerate the polymerisation of isobutene. This is so, as shown in the figures of reference [12] quoted above where the rate is seen to go through a marked maximum at around 4 mol/l.

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Rate Constants of Cationic Polymerisations and Mayr’s Rate Constants (2001) +

4

8

-1

-1

It does seem curious that no kp between the extremes of ca. 10 and 10 l mol s have been reported for chemically initiated polymerisations. The most likely reason is the sheer technical difficulty of measuring polymerisation rates for such systems with [M] in the range of 4–8 mol/l and of determining reliably the nature and the concentration of the propagating species and the ratio of unpaired to paired ions. This the more so, since nothing less than the high-vacuum techniques used by Sigwalt, Pepper, Plesch, et al. [4] which have fallen into disuse would be required for such an enterprise. 3.2 The effect of monomers on the KD of ion pairs can be tested by experiments similar to those of Bos and Treloar [15]. They found that the addition of styrene to a solution of – + trityl HgCl3 increased the KD. More detailed information could be obtained from analogous conductometric experiments with salts of a variety of stable cations with a – – – – variety of unreactive anions of various sizes, such as BF4 , BCl4 , SbF6 , and tetra-aryl B . These salt solutions could be titrated with 2-methylbutene-1 and other alkenes and with n-donor monomers such as alkyl vinyl ethers and N-vinylcarbazole. Some guidance in – + this area is provided by the conductometric titration of Et3O PF6 with Et2O in CH2Cl2, which showed clearly the increase in the dissociation constant KD of that salt due to the progressive solvation of the oxonium ion by the ether [16]. 3.3 The author’s theory which has been used here was developed in detail to explain the polymerisations by ionising radiations of some alkyl vinyl ethers, the polymerisations of which proceed by secondary ions. Although it was shown that the theory is also perfectly serviceable for the tertiary carbenium ions considered here, it must be realised that there is a fundamental difference between these two types of carbenium ions. When one of the bonds of the carbenium ion is a C—H bond, the solvators, especially of course an ion, can get much closer to the positive centre, and they are therefore correspondingly more firmly held; to which effect is added that of a smaller steric hindrance. The most researched monomer propagating by secondary cations, apart from the alkyl vinyl ethers, is, of course, styrene. Thus, Mayr’s many studies with diaryl methylium cations are directly relevant to the polymerisation of styrene. This difference between secondary and tertiary carbenium ions is strictly analogous to that between tertiary and quaternary ammonium ions: the ion pairs involving the former have much lower dissociation constants [17]. It is this difference which most probably accounts also (at least partly) for the great phenomenological differences between the behaviours of styrene and isobutene. This is attested by numerous scattered papers going back to the earliest times, but a systematic and detailed comparison is to be found only in the work of this author’s group on isobutene [4] and on styrene [18] in methylene chloride with initiation by TiCl4 and water over a wide range of temperature.

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Developments in the Theory of Cationoid Polymerisations

4 Related phenomena 4.1

Ideas very similar to those presented here were developed by Litt and Wellinghoff [19] with regard to the formation of D—A complexes and the involvement of competition of donors (D) and solvents in the solvation shell of the acceptors (A) and of the complexes. Their theory was used successfully to account for deviations from the Benesi-Hildebrand equation [20].

4.2

It follows from the present argument that the ideas of the intimate and solvent-separated ion pairs, which are useful in the context of anionic polymerisations, are not relevant for cationic polymerisations. The reason is that in contrast to the carbenium ions, the carbanions are tetrahedral, the fourth ‘valency’ being the lobe of the electron pair. Therefore, a solvent molecule can find a potential well between the anion and the cation, but there is no suitable site on the opposite side of the anion.

4.3

Since this manuscript was completed, Faust and his collaborators [21] have reported + 9 -1 -1 a kp of ca. 10 L mol s for the polymerisation of isobutene in 60/40 (v/v) hexane/ MeCl at –80 °C with [M] from 1 to 2.5 mol/L. This agrees with Mayr’s findings as was to be expected on the basis of the present paper.

An explanatory theory has fulfilled its purpose when it has been proved inadequate and has generated a more successful successor. The present author looks forward to that development.

Acknowledgement The author thanks Professor H. Mayr and two other referees for useful criticism and suggestions.

References and notes 1.

Plesch, P. H. Prog. React. Kinet., 1993, 18, 1.

2.

This point is made explicitly by Mayr et al., see: Mayr, H.; Roth, M.; Lang, G. in Cationic Polymerization; Faust, R., Shaffer, T. D., Eds.; American Chemical Society: Washington, DC, 1997, where detailed references to Mayr’s work are given.

3.

Plesch, P. H. in Progress in High Polymers, Vol. 2; Robb, J. C.; Peaker, F. W., Eds.; Iliffe Books, London, 1968, p.137. Note that the symbols used in that review were rather ineptly chosen and have since been changed.

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Rate Constants of Cationic Polymerisations and Mayr’s Rate Constants (2001) 4.

Biddulph, R. H.; Plesch, P. H.; Rutherford, P. P., J. Chem. Soc., 1965, 275.

5.

Plesch, P. H. Brit. Polym. J., 1973, 5, 1.

6.

Plesch, P. H. J. Polym. Sci. Symp., 1977, 56, 373.

7.

Plesch, P. H. Adv. Polym. Sci., 1971, 8, 137.

8.

Plesch, P. H. in Cationic Polymerization and Related Processes; Goethals, E. J., Ed.; Associated Press, London, 1984; p 1.

9.

Plesch, P. H. Brit. Polym. J., 1989, 25, 875.

10. Pepper, D. C. J. Polym. Sci., Symp., 1975, 50, 51. 11. Plesch, P. H. Makromol. Chem., Macromol. Symp., 1990, 32, 299. In this paper + the last two sentences of section 3, concerning kp in nitrobenzene, are wrong as shown in Ref 1 of the present paper. 12. Plesch, P. H. Philos. Trans. R. Soc., 1993, A342, 469. 13. Mayr, H.; Schneider, R.; Schade, C.; Bartl, J.; Bederke, R. J. Am. Chem. Soc., 1990, 112, 4446. See the last three sentences of Section V.1 on p.4449. 14. Plesch, P. H. High Vacuum Techniques for Chemical Syntheses and Measurements, Cambridge University Press, Cambridge, UK, 1989. 15. Bos, S. S.; Treloar, F. E. Australian J. Chem. 1978, 31, 2445. See also this author’s treatment of Bos and Treloar’s results in ref. 11. 16. Jones, F. R.; Plesch, P. H. Chem. Commun. 1970, 1018. 17. Kraus, C. A. J. Phys. Chem. 1956, 69, 129. 18. Longworth, W. R.; Panton, C. J. Plesch, P. H. J. Chem. Soc. 1965, 5579. 19. Litt, M. H.; Wellinghoff, J. J. Phys. Chem. 1977, 81, 2644. 20. Benesi, H. A.; Hildebrand, J. H. J. Am. Chem. Soc. 1949, 71, 2703. 21. Schlaad, H.; Kwon, Y.; Sipos, L.; Faust, R.; Charleux, B. Macromolecules, 2000, 33, 8225.

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6

Pseudocationic Polymerisation, Renamed ca. 1998 ‘Cationoid Insertion Polymerisation’

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Developments in the Theory of Cationoid Polymerisations

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6.1

The Interaction Between Perchloric Acid and Styrene in Methylene Dichloride (1964) A. Gandini and P. H. Plesch

This paper was first published in the Proceedings of the Chemical Society, 1964, July, 240. Reproduced with permission from the the Royal Society of Chemistry, copyright 1964.

Prologue This Chapter contains most of the papers on pseudocationic polymerisations from the writer’s research group and, because the experimental evidence plays such an important part in this story, it includes, exceptionally, the experimental papers which led Professor Gandini and the writer to devise the pseudocationic theory in the 1960s. Also, because of numerous misunderstandings, it is appropriate to include here an account of the circumstances surrounding the origin and fate of the pseudocationic theory of polymerisation. Around 1962, this author recognised that the polymerisation of styrene by many ‘cationic’ initiators differed in several respects from that of isobutene, and he had begun to assemble the experimental facts from the Literature with a view to devising an explanation. Also, in an attempt to clarify this difference experimentally, he had undertaken a comparative study of the polymerisations of isobutene and of styrene by TiCl4 [4, 7, 12, 15-17, 38, 40, 54, 59]. At that time several groups were working on what we will call here the ‘cationoid’ polymerisation of styrene and related monomers. These groups included one in Kyoto, led successively by Okamura, Higashimura, and Sawamoto and Overberger at Brooklyn Polytechnic, and in Europe the most original work was being done by Pepper in Dublin. The present writer had done and had supervised a total of approximately. 6 man-years of work in his laboratory on the polymerisation of styrene by TiCl4, when Pepper’s work on its polymerisation by anhydrous perchloric acid appeared (A). With a new research student, Gandini, he repeated Pepper’s experiments, but using the more rigorous and versatile reaction calorimeter and vacuum techniques developed at Keele. They obtained essentially the same rate-constants and DPs as Pepper’s group, but observed new

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Developments in the Theory of Cationoid Polymerisations phenomena involving colour and electrical conductivity of the reaction mixtures. From these results, and in disagreement with Pepper, Gandini and Plesch concluded that this polymerisation does not involve carbenium ions. Since, however, the phenomenology was similar in many respects to that of cationic polymerisations, they called the mechanism ‘pseudocationic’ (Ψ-Cat). The Kyoto workers, also using styrene, but with other acids as initiators, realised that their results were incompatible with a propagation by cations, and they invented, but never defined clearly, an ‘invisible species’ (meaning that it had no UV-vis absorption) which they described in terms virtually identical to those used by the supporters of the pseudocationic theory, e.g., Giusti (working with the I2 + HI system), to describe the propagation by esters, but they refused to acknowledge that their views were indistinguishable from ours and to recognise the Keele group’s priority. The essence of the chemical dispute which ensued from our proposal is the nature of the propagating species. In the cationic polymerisations this is held to be a carbenium ion derived from the alkene by the addition to it of a proton from an initiating acid, HA, or of some other cation from a non-protonic initiator:

(HA)2 + CH 2 : CHPh → CH 3CH + Ph + HA 2− In contrast to this, according to the Ψ-Cat mechanism, the initiator forms an ester with the alkene which incorporates the next monomer molecule by means of an insertion reaction involving a 6-membered cyclic transition state. The ester mechanism also explains well Gandini’s and Plesch’s observations on the dehydration of aromatic carbinols by acids [60], and it is actually an old item in the stock-cupboard of organic reaction mechanisms which has proved useful in explaining numerous organic reactions. This respectable antiquity and usefulness seem to have done nothing to make it more acceptable to many polymer chemists. The impact which was made by the writer’s revival of the old ester mechanism in the context of polymerisations is attested by the number of polymer chemists who set about examining the validity of the theory experimentally. For example, Bywater in Canada confirmed that during the progress of a polymerisation of styrene by perchloric acid the acid could not be distilled out of the reaction mixture, but after exhaustion of the monomer it could be. This regeneration of the initiating acid after the consumption of the monomer is an often attested characteristic of pseudocationic polymerisations with many different protonic acids; it is most simply explained by the decomposition of the ester to an alkene and the acid, i.e., a reversal of the initiation, when the monomer has been consumed. Enikolopian in the USSR found that the effect of pressure on the rate of polymerisation in the same system was not compatible with the propagation step involving an ion, and

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The Interaction Between Perchloric Acid and Styrene in Methylene Dichloride (1964) he therefore supported the Ψ-Cat theory. These researchers were amongst the earliest supporting the Ψ-Cat theory. None-the-less, the opponents of our ideas, although lacking any convincing evidence or a plausible, logically consistent, alternative theory, prevailed to the extent that our views are omitted entirely from recent text books. A comprehensive summary of the evidence and arguments was given by this writer in 1987 at the Eighth International Symposium on Cationic Polymerisation [135], (B), see Section 6.6. One obvious test of the Ψ-Cat theory was to try to synthesise the perchlorate ester of styrene and to find out whether it will act as a polymerisation initiator; however, the ester is stable only in the presence of an excess of styrene. This proved to be the first instance of the stabilisation of a ‘hyperactive’ ester by an electron donor to give a species which is sufficiently long-lived to be an effective propagator (C). Some time later it was found by Gandini and others that esters of some weak acids which are inert towards monomers could be activated by protons and other electron acceptors. Then, from the 1970s onwards, living cationoid polymerisations of isobutene, styrene, and alkyl vinyl ethers were discovered, and it was found that some ‘hyperactive’ initiator systems could be moderated and some sluggish systems could be activated by certain additives. Setting out to explain what it is that gives ‘life’ to living polymerisations, the present writer recognised eventually that all of these effects could be given a common mechanistic explanation in terms of the ester mechanism, and he gave a detailed account of this unifying theory in the first part of the final paper in this group [143]. It is shown there how the theory also explained many other features of living cationoid systems, including those which had been attributed to a common ion effect on an ionic reaction. Moreover, it also proved to be easily adaptable for explaining the cationoid polymerisations in nitrobenzene which have a character all their own (see Chapter 5.6 [145]). The generalisation of the Ψ-Cat theory to embrace the steadily expanding area of living cationoid and group-transfer polymerisations also met with opposition. This originated partly from the fact that the best known alkene and acid system, namely Pepper’s styrene and perchloric acid, gave polymerisations which under some conditions yielded low polymers because of effective transfer reactions. Some workers accepted that these polymerisations are Ψ-Cat reactions and concluded thence – erroneously – that all Ψ-Cat polymerisations would be transfer-dominated, and that therefore the living polymerisations could not be of the Ψ-Cat type. They were unaware of the fact that Pepper had actually obtained one of the earliest living polymerisations with just that system under special conditions. A further prejudice that inhibited the acceptance of the Ψ-Cat mechanism was the belief that esters, admitted to exist, but called ‘dormant species’, were in equilibrium with conventional propagating carbenium ions. This belief persisted despite the fact that no

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Developments in the Theory of Cationoid Polymerisations such equilibrium had been shown to exist in any system remotely similar to those concerned in polymerisations, and despite the existence of much evidence for the progressive, irreversible decomposition of such esters to ions, and eventually regenerating the initiating protonic acid. In the second part of the paper 6.10 [143] this writer generalises his new kinetic treatment of living polymerisations [134]. By applying it to data from the literature, he shows how this treatment can reveal which one of the components of a binary syncatalytic system (e.g. I2 and organic iodide) determines the concentration of the propagating species and, much more important, how the rate-constant of propagation can be calculated from readily available data. There remains here a rich mine of information to be exploited by others. In this group there are also two reviews from the earliest days of the theory of Ψ-Cat polymerisation. Although much of what they contain is presented again later, they are included here because they show in greater detail how the new theory fits into the contemporary framework of thinking at that time. The paper 6.5 [63] is particularly interesting historically, because the writer mentions explicitly that the esters involved in the propagation may be (or need to be) activated or deactivated. As we have seen, this idea was not developed to fruition until some 30 years later. Other useful features in that paper are the examination of the evidence for the ionic nature of the propagators in the cationic polymerisations, and explanations of how difficult it was for polymer chemists to shake off the ideas taken over from the familiar radical polymerisations and to adapt their thinking to ionic processes.

Notes A Some of the most interesting and informative experiments in this field were done by Pepper’s group and then at Keele and elsewhere with anhydrous perchloric acid as the initiator. It is therefore historically important that in the present super-cautious, safety conscious era, few, if any, workers are ever likely to follow Pepper’s pioneering work with this hazardous material, to test the reproducibility of these classical findings. The same applies of course to our studies on the polymerisation of various 1,3-dioxacycloalkanes, most of which were also done with anhydrous HClO4, see Chapter 7. There is no substitute for it, as every acid behaves differently and in particular the lazy worker’s substitute aq. HClO4 + acetic anydride, is a very different initiator system. B One of the main critics of the Ψ-Cat theory, K. Matyjaszewski, submitted a series of Comments on this lecture to the Editor of the proceedings of that Symposium who

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The Interaction Between Perchloric Acid and Styrene in Methylene Dichloride (1964) agreed to publish them together with a reply by the present writer. These are to be found following the paper by this writer [135] on pages 389–392 and 393–395, respectively, of the symposium papers but are not reproduced here. C Several different pieces of kinetic evidence from this writer’s laboratory were thought to indicate that for the styrene + perchloric acid system the ester is stabilised by four molecules of styrene (48, 67). This feature seemed so unlikely that it helped to create opposition to the whole idea of the pseudocationic polymerisation by an ester, although that improbable solvation pattern is in no way essential to the theory nor logically connected with it. At this point it is necessary to introduce an important new insight which came to the writer whilst assembling this Prologue (ca. 30 years too late!). It is strange, but true, that he and other physical chemists, fell into a logical trap, in company with the referees of those papers. Plesch and Gandini had concluded that because under the conditions of their experiments the polystyryl perchlorate ester began to ionise rapidly whenever the styrene concentration fell below a critical value, Mc which was ca four times the acid concentration (assumed to be equal to that of the propagating ester), therefore each ester molecule was stabilised by the co-ordination of four molecules of styrene. This is a non sequitur, because the ratio 1:4 is simply determined by the entire character of the solvation equilibrium. Therefore several factors, whose magnitude is unknown, are involved. The most important of these are of course, n (the number of styrene molecules which are involved), and the equlibrium constant(s), K, involved in the solvation. Therefore a single observation, the value of Mc/[ester] = ca. 4, is not sufficient to determine n. The most desirable conclusion of this argument would be a full algebraic analysis, but unfortunately that enterprise is frustrated by the extremely complicated chemistry of these systems. Inevitably, most of the papers dealing with the Ψ-Cat polymerisations contain some reference to the alleged solvation of the polystyryl perchlorate ester by four styrene molecules. However this feature must now be ignored, but its omission does not affect any of the arguments. A full explanation of this error has been submitted to the Journal of Polymer Science.

595

Developments in the Theory of Cationoid Polymerisations In order to ascertain the nature of the propagating species in the polymerisation of styrene catalysed by perchloric acid in methylene dichloride we have investigated the behaviour of this system by (a) calorimetric, (b) spectroscopic, and (c) conductimetric techniques. All experiments were carried out in high-vacuum apparatus, with highly purified and dried reagents which were mixed by breaking phials or break-seals magnetically. a) The polymerisation of styrene (0.1–0.4 M) catalysed by perchloric acid (10-4 – 8 x 10-3 M) was followed in an adiabatic calorimcter at 19 ºC, 0 ºC, and –19 ºC (20 runs) [1]. The reactions went to completion. The polymers formed at 19 ºC had DP ≈ 4, independent of [HClO4]. In agreement with Pepper and Reilly’s findings [2] the reactions were of first order up to 90–95% conversion, and the rate constant is directly proportional to the acid concentration; k2 = 10.7 l mole-1 s-1 at 19 ºC, E = 12 kcal/mole. During the polymerisation the solution remained colourless even at the highest acid concentration, but after the heat evolution (polymerisation) had ceased, the solution became yellow and the intensity of the colour became constant after a few minutes. Addition of styrene at this stage caused instantaneous disappearance of the colour, and polymerisation proceeded with a rate constant identical to that of the first reaction; at the end the yellow colour reappeared. This cycle could be reproduced several times. b) The spectroscopic investigation ([styrene] = 10-2 – 3 x 10-1 M, [HClO4] = 4 x 10-4 – 2 x 10-3 M; 25 runs) was carried out at 18–20 ºC with a UNICAM SP 700 recording spectrophotometer. By scanning at fixed wavelength (λ = 424 mμ) against time from about 30 seconds after the mixing, it was found that no carbonium ion could be detected for several minutes. The reciprocal of this period was approximately proportional to [HClO4], and it is evident from the calorimetric experiments that this is the period during which the polymerisation takes place (Figure 1b). Since, for styryl and polystyryl ions, ε 3.86 x 103 at λmax. 424–427 mμ in methylene dichloride [3], the minimum concentration of these ions which we could detect with certainty was about 3 x 10-6 M. In no experiment did the D424 exceed 0.0087 (the experimental error for D = 0.000) during this period, but once this was over, the typical peak at 424 mμ began to appear, and its growth followed a second-order curve (Figure lb). Addition of styrene when D424 had become constant caused immediate total disappearance of the peak for several minutes (polymerisation), and subsequently new formation of ions in roughly the same way as before, but with higher final D424. Water did not aftect the polymerisation, but destroyed an equivalent of carbonium ions, so that if [H2O] > [HClO4] no ions were detectable after the polymerisation (spectroscopic and calorimetric experiments). c) Measurements of the electrical conductivity at 15 ºC of solutions containing the two reactants in concentrations equivalent to those employed in the spectroscopic experiments, showed (10 runs) that when styrene is added to perchloric acid the conductivity remained

596

The Interaction Between Perchloric Acid and Styrene in Methylene Dichloride (1964) at the level characteristic of the acid solution (κ << 10-7 mho/cm) for a period which depended on the conditions of the run, but which was obviously equivalent to the duration of polymerisation. There followed a progressive increase in conductivity (accompanied by colour formation) which, as Figure 1c shows, closely resembled the corresponding increase in optical density at λ 424 mμ; the maximum values of κ were (1–8) x 10-6 mho/ cm depending on concentrations. When a second portion of styrene was added, κ fell instantaneously to its initial values, then increased again, and reached a maximum higher than the previous one, after the second polymerisation. These results indicate that in the polymerisation of styrene by perchloric acid the propagating species is not a carbonium ion (either free or paired), but a complex between acid and monomer. Our results indicate that this has the composition HClO4, 4C8H8 and that it participates in the equilibrium

2(HClO 4 , 4 Pn ) ↔ m(HPn+ ClO 4− ) + (8 – m)Pn + (2 – m)HClO 4 where Pn is either monomer or unsaturated polymer and m = 1 or, more probably, 2. The nature of the propagating complex and of the propagation reaction are obscure. The kp values reported by Pepper and Reilly [2] cannot now be regarded as those of cationic polymerisations.

Figure 1 Typical reaction curves obtained with the following concentrations

a) Calorimetry b) Spectroscopy c) Electrical conductivity

[Styrene] (mole/l) 0.334 8.1 x 10-2 7.5 x 10-2

[HClO4] (mole/l) 6.72 x 10-4 1.0 x 10-3 2.5 x 10-3

T °C 19 18 15

597

Developments in the Theory of Cationoid Polymerisations

References 1.

Biddulph and Plesch, Chem. and Ind., 1959, 1482.

2.

Pepper and Reilly, J. Polymer Sci., 1962, 58, 639.

3.

Gandini and Plesch, unpublished. This value is much greater than that given by Jordan and Treloar [4] for reasons which will be discussed elsewhere.

4.

Jordan and Treloar, J. Chem. Soc., 1961, 729.

598

6.2

Pseudocationic and True Cationic Polymerisation of Styrene with Various Catalysts (1965) A. Gandini and P. H. Plesch

This paper was first published in The Journal of Polymer Science, Polymer Letters, 1965, 3, 2, 127-129. Reproduced with permission from John Wiley, copyright 1965. The polymerisation of styrene by anhydrous perchloric acid in methylene dichloride was shown not to be an ionic reaction (1) and we have now found further examples of what we propose to call ‘pseudocationic’ reactions and have formulated a tentative mechanism for these. This involves as chain-carrier an ester which, if it is a perchlorate, is stabilised in solution by coordination of at least three molecules of monomer (or possibly unsaturated oligomer): C8H8

(C8 H 8O)3 ClOCHPhCH 3 → (C8 H 8O)3 ClOCHPhCH 2 CHPhCH 3 Whether the molecule of styrene participating in the propagation reaction is free, or one of those coordinated to the perchlorate part of the ester, is not clear at present. (In all the experiments to be described, all operations were carried out in vacuum apparatus, and the solvent was methylene dichloride, unless otherwise stated.) We tested the ester theory by using the ester as catalyst. However, since pure 1-phenylethyl perchlorate is not stable at room temperature, we prepared it in situ, thus: in an adiabatic vacuum calorimeter (2) we dissolved ca., 1 mmole of AgClO4 in 100 ml of a 0.25 M solution of styrene at 0 ºC. When a phial containing 0.5 mmole of 1-phenylethyl bromide in 0.6 ml of CH2Cl2 was broken into this solution, polymerisation started immediately, with concurrent formation of colloidal AgBr, and was complete in 3 minutes; the reaction trace was sigmoid. The solution was colourless until the end of the reaction when it became yellow. This showed that, just as with catalysis by perchloric acid (1), the chain-carriers were not ionic, but ions were formed at the end of the polymerisation. We presume that the initiating species was the 1-phenylethyl perchlorate ester formed by double decomposition, and stabilised by styrene. A smaller concentration of ester gave a correspondingly lower rate of polymerisation. The product from the reaction of AgClO4 and 1-phenylethyl bromide in concentrated solution is deep brown and spectroscopic examination (of a diluted solution) shows the presence of 1-phenylethyl ions and of allylic ions derived from polystyrene. Addition of excess styrene to this dilute solution at room temperature decolourised it instantaneously, polymerisation proceeded rapidly (warming of the solution), and at the

599

Commercial rubbers

Developments in the Theory of Cationoid Polymerisations end the colour was reformed. Thus, as with perchloric acid, presence of excess styrene shifts the equilibrium from salt to ester by stabilizing this. The visible spectra of the solution before and after the polymerisation had the same peaks, at 424 and ca., 460 mμ. The molecular weight of the polymers obtained by these reactions closely agreed with that of polystyrenes obtained by perchloric acid catalysis (1). Other catalytic systems, studied by the spectroscopic technique described (1), showed the following features (room temperature): a) Addition of styrene (to give a 0.8–0.9 M solution) to 3–5 x 10-3 M solutions of sulphuric acid gave a very low yield of polymer and no detectable absorption near 424 mμ even after 24 h, i.e., no 1-phenylethyl or related ions were formed; the same result was obtained with wet solvent. b) When styrene was added to an excess of trifluoroacetic acid, there was rapid polymerisation (3), but no absorption near 424 mμ. Several hours later the solution became yellow-brown and its spectrum showed peaks at 425 and 460 mμ. c) Many experiments with styrene (3 x 10-3 – 0.5 M) and stannic chloride (10-2 – 0.25 M) in which scanning started 20–30 seconds after mixing of the reagents, showed no absorption at 424 mμ during the polymerisation, but after several hours a broad peak at 420–430 mμ developed. In the presence of deliberately added traces of water, the polymerisation was much faster, but there was no sign of ions until many hours after the end of the reaction. In all these experiments the complex between styrene and stannic chloride (λmax. ≈ 305 mμ) was detectable spectroscopically, and its concentration diminished as polymerisation progressed. d) In ethylene dichloride solution with perchloric acid and styrene, results very similar to those reported for methylene dichloride were obtained (1). We conclude that in these systems the chain-carriers are not ions, and the ester mechanism suggested will serve to explain them all. However, we believe that we have also been able to diagnose true cationic polymerisations of styrene, but only under special conditions: in calorimeter experiments with relatively large quantities of perchloric acid, especially at low temperature, down to –90 ºC, it was found that when the phial of acid was broken in such a way that the mixing of acid with the solution was relatively slow, the solution turned yellow for a fraction of a second, near the broken phial, and there was an abnormally fast polymerisation which settled down after a few seconds to the rate appropriate to the pseudocationic reaction. The rate of these very fast reactions was much greater than could be accounted for by the high local concentration of acid if the reactions had been of the normal pseudocationic type, and we believe them to betray the transient presence of, and polymerisation by, true ions.

600

Pseudocationic and True Cationic Polymerisation of Styrene with Various Catalysts... The same idea will explain an experiment in which a styrene phial (20 mmole) was broken at –10 ºC into 100 ml of a 6 x 10-3 M solution (ClO4- content) of the coloured ionic reaction product between AgClO4 and 1-phenylethyl bromide (see above). Because of the rather slow initial mixing, the colour of the solution was not completely discharged by the styrene, and a violent polymerisation ensued, at least 100 times faster than the reaction catalysed by an equivalent amount of perchloric acid would have been. Other evidence indicating true ionic polymerisation was found in some reactions in which, because of the relatively low molar ratio [styrene]/[HClO4], the styrene sequestered by complexing with the ester was a considerable fraction of the total [styrene], and therefore the colour developed while there was still an appreciable concentration of monomer. In these experiments the reaction curves showed a marked kink, corresponding to a spectacular increase in rate, just at the instant of color formation, and the previously very slow polymerisation was brought to completion in a few seconds from this time. These experiments and similar ones with other monomers, to be described elsewhere, show that the explanation of the allegedly cationic polymerisations of aromatic monomers in terms of ions must be revised drastically, and that the interpretation of the rate-constants reported must be treated with the greatest circumspection.

Acknowledgements We thank the US Rubber Co. for a Studentship (AG) and for other financial help.

References 1.

A. Gandini and P. H. Plesch, Proc. Chem. Soc., 1964, 240.

2.

R. H. Biddulph and P. H. Plesch, Chem. Ind. (London), 1959, 1482.

3.

J. J. Throssell, S. P. Sood, M. Szwarc and V. Stannett, J. Am. Chem. Soc., 78, 1122 (1956).

601

Developments in the Theory of Cationoid Polymerisations

602

6.3

Cationic and Pseudocationic Polymerisation of Aromatic Olefins Part I. Kinetics and Mechanism of the Pseudocationic Polymerisation of Styrene by Perchloric Acid (1965) A. Gandini and P. H. Plesch

This paper was first published in the Journal of the Chemical Society, 1965, 4826-4830. Reproduced with permission from the Royal Society of Chemistry, copyright 1965. The kinetics of the polymerising system styrene-perchloric acid-methylene dichloride have been studied in the temperature range +19 ºC to –19 ºC, by a calorimetric technique. The propagation is pseudocationic, its rate constant at 19 ºC is kp = 10.6 l mole-1 s-1, and Ep = 11.6 kcal mole-1. The elementary reactions are interpreted in detail by a mechanism involving an ester as chain carrier. We have reported [1, 2] that the polymerisation of styrene catalysed by perchloric acid in methylene dichloride and 1,2-dichloroethane proceeds normally in absence of carbonium ions (free or paired) and that the chain carriers are 1-phenylethyl perchlorate and the analogous oligomeric esters; this newly discovered kind of polymerisation we called ‘pseudocationic’ [2]. Subsequently, we investigated a series of polymerisation systems in order to ascertain whether they belong to the class of cationic polymerisations as previously suggested by other authors, i.e., whether carbonium ions propagate the polymerisation, or whether they represent further examples of pseudocationic polymerisation. The present paper is the first of a series in which we will report on the behaviour of a wide range of polymerising systems in an attempt to map out the conditions under which cationic and pseudocationic reactions occur. Pepper and Reilly [3] studied in detail the kinetics of the polymerisation of styrene by perchloric acid in 1,2-dichloroethane and in mixtures of 1,2-dichloroethane and carbon tetrachloride. Our investigation of the spectroscopic and conductimetric behaviour of this monomer-catalyst pair was carried out in methylene dichloride [1]. Since the evidence obtained from our work was in conflict with Pepper and Reilly’s interpretation of the chemistry of the system, we decided to supplement our results by kinetic studies with methylene dichloride instead of 1,2-dichloroethane, so that mechanistic conclusions could be drawn from a self-consistent group of results, without any assumptions about the similarity of the solvents.

603

Commercial rubbers

Developments in the Theory of Cationoid Polymerisations

Experimental

Techniques Reactions were followed in an adiabatic calorimeter [4] according to the procedure described [5]. At the end of the polymerisations, the reaction mixture was quenched with ethanolic ammonium hydroxide and evaporated to constant weight in a vacuum oven at 40 ºC.

Materials Methylene dichloride [6] and perchloric acid [7] were purified and dosed as described. Silver perchlorate (BDH) was treated in vacuo for a few hours before use. 1-Phenylethyl bromide (Eastman-Kodak) was fractionally distilled under high vacuum and the middle fraction was collected into breakable phials; since this compound undergoes a slow decomposition, yielding hydrogen bromide and styrene, when kept in bulk, solutions of it in methylene dichloride were prepared from the original phials by the tipping technique [7]. Styrene was purified [8], dried, and stored [9] as described. Shortly before use it was vacuum-distilled into breakable phials from a microburette.

Determination of molecular weight Owing to the very low degree of polymerisation of the polymers obtained, molecular weights (Mn) were determined with a MECROLAB Vapour Pressure Osmometer, model 301 A with benzene as solvent. For values of Mn ranging between 400 and 2000 the reproducibility was ± 30 units.

Results

Catalysis by perchloric acid All reactions at 19 ºC, 0 ºC, and –19 ºC were of the first order internally, up to at least 90% conversion, and all went to completion. Details are given in Tables 1–3. The firstorder rate constant, k1, is directly proportional to the acid concentration as shown by the constancy of the values of kp = k1/[HClO 4]0. The Arrhenius plot for kp gave

604

Cationic and Pseudocationic Polymerisation of Aromatic Olefins, Part I... Ep = 11.6 ± 0.2 kcal mole-1 and Ap = 8.9 x 109 l mole-1 s-1. Addition of further monomer at the end of the first polymerisation reaction resulted in a second polymerisation which had the same absolute rate constant (Experiment SGP11, Table 2).

Table 1 Reaction data for experiments at 19 ºC ± 0.5 ºC Expt.

[HClO4]o (104 M)

k1 (103 s-1)

Mn

kp (l·mole-1 s-1)

SGP3

4.30

4.53

540

10.53

SGP4

6.72

7.17

550

10.67

SGP6 *

13.2

14.0

580

10.61

SGP8

18.0

19.3

690

10.72

SGP7 †

18.0

10.0

590

-

Av. 590

10.63

[Styrene] = 0.334 M * Wet solvent (vessel pumped out for only a few minutes) † The acid phial contained approximately 50% of HClO4, H2O (white crystals) and 50% HClO4; the actual [HClO4]o is therefore ca. 9 x 10-4M

Table 2 Reaction data for experiments at 0 ºC ± 0.5 ºC Expt.

[Styrene] (M)

[HClO4]o (104 M)

k2 (103 s-1)

Mn

kp (l·mole-1 s-1)

SGP9

0.334

17.2

4.60

790

2.67

SGP10

0.334

31.0

8.25

830

2.66

SGP11

0.134

55.5

14.7

SGP11 *

0.132

54.9

14.2

2.65 710

2.59

* Second addition of styrene

Table 3 Reaction data for experiments at –19 ºC ± 0.5 ºC [Styrene] (M)

[HClO4]o (104 M)

k2 (103 s-1)

Mn

kp (l·mole-1 s-1)

SGP19

0.226

23.0

1.38

1340

0.600

SGP14

0.264

73.0

4.4

1140

0.603

SGP17

0.236

91.5

5.5

1000

0.601

Expt.

605

Developments in the Theory of Cationoid Polymerisations Water present in the monomer solution before the addition of perchloric acid did not affect the rate of polymerisation (Experiment SGP6, Table 1), but if water was added to the catalyst solution before the polymerisation, with consequent formation of HClO4, H2O, which is insoluble in methylene dichloride, only the anhydrous acid was found to be an active catalyst (Experiment SGP7, Table 1). During virtually the whole of the polymerisation the solutions remained colourless. A yellow colour always developed towards the end of the polymerisation; its origin and phenomenology will be discussed in the next paper of this series. No colour formation was observed if water was present at a concentration higher than that of the perchloric acid.

Discussion

Mechanism We have shown [1, 2] that, in the polymerisation of styrene by perchloric acid under the conditions reported here, the initiation reaction does not produce carbonium ions and that the monomer is polymerised by non-ionic chain carriers. Since the most likely nonionic reaction product formed from perchloric acid and styrene is the ester 1-phenylethyl perchlorate we attempted its preparation in order to try it as catalyst for the polymerisation of styrene. However, we found this ester to be unstable in methylene dichloride solution. It forms styrene oligomers, polystyryl ions, and perchloric acid, and the preparative technique and the mechanism of the reactions involved will be discussed in a paper dealing with the spectroscopic behaviour of polymerising and polymerised systems. Since we could not prepare a stable solution of the ester, we attempted its preparation in the styrene solution to be polymerised. Silver perchlorate was dissolved in this and the reaction was started by the crushing of a phial containing 1-phenylethyl bromide (under our conditions styrene was not polymerised by the silver perchlorate alone). The solutions became cloudy because of the formation of colloidal silver bromide, but no colour formation could be observed until the end of the polymerisation; then the solutions became yellow, very like the reaction mixtures in which perchloric acid had been used as catalyst. The ester was found to be as effective a catalyst as anhydrous perchloric acid. Equal concentrations of the ester and the acid produced very similar polymerisations as shown in the Figure. The accelerating parts of the curves obtained with the ester as catalyst are readily explained by the fact that the reaction between silver perchlorate and 1-phenylethyl bromide is not instantaneous and therefore a steady increase in catalyst concentration characterises the first part of the polymerisation.

606

Cationic and Pseudocationic Polymerisation of Aromatic Olefins, Part I...

Figure 1 A comparison between a perchloric acid-catalysed polymerisation (SGP11, Table 2) and one catalysed by an equivalent amount of 1-phenylethyl perchlorate (SGP21). For SGP21: [Styrene] = 0.158 M, [CH3CHPhBr] = 5.55 x 10-3 M, [AgClO4] ca. 1 x 10-2 M, T = 0 ºC a indicates the crushing of the acid phial (SGP11) and of the 1-phenylethyl bromide phial (SGP21); b and b´ indicate the time at which the colour appeared in the reaction mixtures.

The DP of the polymers obtained from these experiments were the same as those of the polymers from the corresponding acid-catalysed reactions. The above evidence strongly suggests that the pseudocationic reactions involve the ester 1-phenylethyl perchlorate and its oligomeric homologues as catalyst. It also shows that the ester is only stable when an excess of styrene is present in the reaction mixture. Spectroscopic and conductimetric studies on the present system confirmed this interpretation and indicated that at least four molecules of styrene are required for the stabilisation of one molecule of ester. Details of the experiments carried out to investigate the stoicheiometry of ester stabilisation will be given in a later paper. The mode of this stabilisation is not clear at present and we do not known the location of the four styrene molecules with respect to the ester. For the system styrene-perchloric acid-methylene dichloride we can now write the following reactions on the basis of what has just been discussed and of our findings on the state of perchloric acid in methylene dichloride solutions [9]: i) Initiation

ki 5C8H8 + (HClO4)4/4 → (CH3·CHPh·O·ClO3) – 4C8H8

607

Developments in the Theory of Cationoid Polymerisations ii) Propagation

kp

(CH3·CHPh·O·ClO3) – 4C8H8 + C8H8

→

(CH3·CHPh·CH2·CHPh·O·ClO3) – 4C8H8

The transfer reactions, undoubtedly important because of the low DP, were not studied in detail, but both double bonds and indanyl end-groups were detected from the ultraviolet and infrared spectra of the polymers. Most probably the two types of transfer studied by Pepper and Reilly [10] are responsible for these groups: one dependent on monomer concentration, giving indanyl end-groups, and one which they termed spontaneous transfer, giving terminal double bonds. Since these authors’ method could not distinguish between a truly unimolecular chain-breaking reaction and one which, though independent of monomer concentration, involved an unknown transfer agent, we prefer to call this second reaction noncommittally ‘monomer-independent’. We formulate these chainbreaking reactions as follows: iii) Monomer transfer ktm

(CH3·CHPh·[CH2·CHPh·]n·CH2·CHPh·O·ClO3) – 4C8H8 + C8H8

→ CH3·CHPh·[CH2·CHPh]n·CH2·CH —CH2

→ CH

8 8

+ (CH3·CHPh·O·ClO3)–4C8H8

CHPh

iv) Monomer-independent transfer

(CH3·CHPh·[CH2CHPh]n·CH2·CHPh·O·ClO3) – 4C8H8

k

→t

C8H8

→ CH3·CHPh·[CH2·CHPh]n·CH:CHPh + (CH3·CHPh·O·ClO3)–4C8H8 This mechanism applies equally well, as we have shown [2], to the system styrene perchloric acid-1,2-dichloroethane, studied by Pepper and Reilly [3] and therefore replaces their interpretation based on carbonium ions. We propose to explain the mechanism of the propagation and transfer reactions in terms of even-membered cyclic transition states such as structure (I) for the propagation step (ii), structure (II) for reaction (iii), and structure (III) for reaction (iv).

608

Cationic and Pseudocationic Polymerisation of Aromatic Olefins, Part I...

An analogous structural interpretation was recently advocated by us to explain the mode of catalytic dehydration of aromatic carbinols by acids [7].

The effect of added water The observation that traces of water do not influence the rate of polymerisation if the water is present in the reaction medium before the acid is added (Experiment SGP6, Table 2), indicated that: (a) The reaction leading to the formation of an ester is much faster than the addition of water to HClO4; (b) the ester is fairly insensitive to quantities of water up to about 10 times its concentration [3], i.e., hydrolysis under these conditions is negligible. On the other hand, if H3O+ClO4- is already present when the polymerisation is started, this is found to have no catalytic activity, most probably because it is insoluble in methylene dichloride (Experiment SGP7, Table 2). The destructive effect of water upon the carbonium ions formed at the end of the polymerisations will be discussed in a future paper.

Kinetics The facts that (a) the polymerisation reactions are of the first order internally, (b) their first-order rate constant is directly proportional to the initial acid concentration, and (c) a second addition of styrene results in a second polymerisation with the same absolute rate constant of propagation, clearly suggests that we are dealing with stationary-state conditions. These facts, however, do not indicate whether this is of the first kind (rate of initiation equal to rate of termination), or of the second kind (rapid and complete initiation, no termination). We have collected during the present work evidence which points unambiguously towards a stationary state of the second kind. Complete initiation is suggested by the twin experiments typified in the Figure; equal starting concentrations of ester and acid produce ‘carbon copy’ polymerisations, i.e., all the acid added reacts with styrene and an equivalent amount of 1-phenylethyl perchlorate is formed. After one experiment, the polymerised mixture was shaken with aqueous ammonia, and the perchlorate-ion concentration in the water layer was determined gravimetrically; 85% of the initial acid could be accounted for. Tests for chloride and chlorate ions were negative.

609

Developments in the Theory of Cationoid Polymerisations Because of the small quantities involved (1 mmole of acid was used) and the absence of the possible degradation products, we concluded that virtually all the perchlorate ion was still present at the end of the polymerisation and that this rules out termination reactions involving destruction of the perchlorate moiety. The kinetic equations for reactions (i)-(iv) can therefore be written as follows:

Ri = ki [HClO 4 ]10/ 4 [M]5 , fast and complete

(1)

Rp = kp [HClO 4 ]0 [M] = k1[M]

(2)

Rt = kt [HClO 4 ]0

(3)

Rtm = ktm [HClO 4 ]0 [M]

(4)

where [M] indicates the styrene concentration and [HClO4]o is both the initial acid and the stationary ester concentration. Our kinetic results agree both qualitatively and quantitatively with Pepper and Reilly’s [3], if the comparison is made between solutions having the same dielectric constant; thus for runs at 0 ºC, the value of kp predicted by Pepper and Reilly for our conditions (1/ε = 0.117) is 2.6 l. mole-1 s-1 which agrees with our results in Table 2. Since, however, we have disproved the chemical interpretation in terms of ions proposed by these authors we can conclude that the values for the rate constants and for the corresponding activation energies do not refer to cationic but to pseudocationic polymerisations. This distinction is most fundamental not only because of its chemical significance, but also because the two chain carriers, i.e., the carbonium ions and the ester molecules, exhibit a vast difference in activity, the former giving reaction rate constants several powers of ten higher than the latter [2]. The true cationic polymerisation of styrene will receive our attention in a later paper of this series.

Acknowledgements We thank the US Rubber Company for a studentship to AG and for other financial help.

610

Cationic and Pseudocationic Polymerisation of Aromatic Olefins, Part I...

References 1.

A. Gandini and P. H. Plesch, Proc. Chem. Soc., 1964, 240.

2.

A. Gandini and P. H. Plesch, J. Polymer Sci., Part B, Polymer Letters, 1965, 3, 127.

3.

D. C. Pepper and P. J. Reilly, J. Polymer. Sci., 1962, 58, 638.

4.

R. H. Biddulph and P. H. Plesch, Chem. and Ind., 1959, 1482.

5.

R. H. Biddulph, P. H. Plesch and P. P. Rutherford, J. Chem. Soc., 1965, 275.

6.

W. R. Longworth, P. H. Plesch and M. Rigbi, J. Chem. Soc., 1958, 451.

7.

A. Gandini and P. H. Plesch, J.Chem. Soc., 1965, in the press.

8.

R. O. Colclough and F. S. Dainton, Trans. Faraday Soc., 1958, 54, 886.

9.

A. Gandini and P. H. Plesch, J. Chem. Soc., 1965.

10. D. C. Pepper and P. J. Reilly, Proc. Chem. Soc., 1961, 460.

611

Developments in the Theory of Cationoid Polymerisations

612

6.4

New Views on Cationic Polymerisation (1966) P. H. Plesch and A. Gandini

This paper was first published in the Society of the Chemical Industry Monograph, No.20, 1966, 107-114. Reproduced with permission from the SCI, copyright 1966.

Introduction The polymerisations catalysed by conventional acids or by metal halides in conjunction with a co-catalyst have been recognised as a distinct species of polymerisation for more than 20 years. It thus seems strange that there should still be room for ‘new views’ on essentials concerning these reactions. There are many reasons why this subject still appears somewhat chaotic in comparison with related fields. Some are accidental, others are intrinsic to the subject; among these is the great difficulty of obtaining reliable and reproducible results. This makes many studies carried out by insufficiently rigorous methods of doubtful value. Another reason is our great ignorance concerning the chemistry of the catalysts, especially their detailed interactions with monomers and solvents. And finally, and basically, there is the very great reactivity of positive organic ions, and of strongly dipolar molecules in which the positive moiety is organic, and the large gradation in their reactivity with changes in the character of the parent monomer. The subject has been very thoroughly reviewed [1-3], but certain fundamental aspects can profitably be reconsidered in the light of some recent developments [4-6]. Certainly the most startling of these is the discovery that under conventional conditions the polymerisation of styrene by perchloric and other acids, and by the syncatalytic system stannic chloride-water, is not an ionic process. These polymerisations have been named ‘pseudocationic’. This finding is in direct contradiction to the beliefs held previously about this and related reactions. Hence a new survey of the whole field has become necessary which must start with an enumeration of those systems for which the nature of the polymerisation reaction has been established with reasonable certainty. From these ‘boreholes’ one can then try to assess the nature of the intervening territory and to decide where further detailed exploration would be most profitable. 613

Developments in the Theory of Cationoid Polymerisations

Systems for which the reaction mechanism is established

a) Pseudocationic systems The systems for which the polymerisation has been shown definitely to be pseudocationic are listed in Table 1. From this evidence and the similarities in kinetic behaviour, it follows that probably almost all the polymerisations of styrene and of some related monomers by conventional acids and by stannic chloride in hydrocarbons and chlorinated hydrocarbons are of this type. An interesting feature of pseudocationic polymerisations is that they are relatively insensitive to water which may be without effect on the kinetics even in concentrations up to ten times greater than that of the catalyst. This is of great diagnostic value since the carbonium ions derived from polymerisable olefins are instantly destroyed by water if the ionogenic catalyst is a conventional acid. If it is a metal halide, water may form a catalytic hydrate and its effect on rate and degree of polymerisation (DP) will depend on its concentration relative to the catalyst, and other factors. The pseudocationic polymerisations are tentatively explained in terms of an ester as the active species. For the styrene-perchloric acid system it is known that this ester is only stable in the presence of an at least four-fold excess of styrene. When, at the end of a polymerisation, the styrene concentration has fallen to this level, the ester ionises. When styrene is mixed with an excess of acid in dilute solution, protonation is the only reaction [5-7]. The ester hypothesis is supported by experiments in which the ester was formed in situ by the reaction of 1-phenylethyl bromide with silver perchlorate in the presence of styrene. These gave results in close agreement with those obtained with perchloric acid [6]. Propagation by the ester is envisaged as addition of the two parts of the ester across the double bond of the monomer; in modern terminology this is an ‘insertion’.

(O 3Cl ⋅ O ⋅ CHPh ⋅ CH 3 )solv + C 8 H 8 (styrene) → (O 3Cl ⋅ O ⋅ CHPh ⋅ CH 2 ⋅ CHPh ⋅ CH 3 )solv The subscript solv. signifies stabilisation by four molecules of monomer.

b) Cationic systems Just as there are but few systems for which it has been shown definitely that the chaincarriers are not ionic, so there are only very few for which one can be reasonably sure that they are ionic. These are listed in Tables 2–4. Whereas the non-participation of ions

614

New Views on Cationic Polymerisation (1966)

Table 1 Pseudocationic systems Monomer

Catalyst

Solvent

Reference

Styrene

HCl O 4

CH2Cl2

5

Styrene

HCl O 4

(CH2Cl)2

6

(a)

Styrene

HCl O 4

EtNO2

7

(a)

Styrene

HCl O 4

EtNO2 + (CH2Cl)2

7

(a)

Styrene

CF3·CO2H

CH2Cl2

6

(b)

Styrene

SnCl4 + H2O

CH2Cl2

6

Styrene

AgClO4 + CH3·CHBrPh

CH2Cl2

6

CF3·CO2H

CH2Cl2

7

Acenaphthylene

HCl O 4

CH2Cl2

7

Acenaphthylene

H2SO4

CH2Cl2

7

N-Vinylcarbazole

HCl O 4

CH2Cl2

7

N-Vinylcarbazole

H2SO4

CH2Cl2

7

1,1-Di-p-methoxyethylene

CCl3·CO2H

C6H6

12

(c), (d)

1,1-Diphenylethylene

SbCl3 + HCl

C6H6

13

(c)

p-Methoxystyrene

Note

(a) Gandini and Plesch’s results are in complete agreement with those of Pepper and Reilly [10], but these authors did not recognise the non-ionic nature of the reaction they were studying (b) The results of Gandini and Plesch are in essential agreement with those of Throssell et al., [11] Their finding that the reaction is unaffected by small quantities of water supports the view that it is pseudocationic (c) The observations of Evans and his collaborators concerning colour and its absence in the reacting systems provide the essential clues, but they did not recognise its significance (d) With relatively low concentrations of acid, colour was developed only towards the end of the reaction, but with high concentrations it developed immediately [12b] so that in this case the system probably belongs in Table II

can be shown quite clearly if ions cannot be detected, the proof that ions are the chaincarriers is much more difficult, for, ideally, ions must be detected, and it must then be established that they are actually concerned in the polymerisation. Whilst this has been accomplished for only a few systems, most of which involve aromatic monomers, other,

615

Developments in the Theory of Cationoid Polymerisations

Table 2 Cationic systems: Aromatic hydrocarbon monomers Monomer

Catalyst

Solvent

Diagnosis

Reference

Styrene

HClO4

CH2Cl2, (CH2Cl)2

Kinetic and spectroscopy

[6]

Styrene

R+ClO4-

CH2Cl2

Kinetic and spectroscopy

[6]

Styrene

H2SO4

CH2Cl2, (CH2Cl)2

Kinetic and spectroscopy

[6, 7]

p-Methoxystyrene

HClO4

CH2Cl2

Rate, colour, conduct

[7]

p-Methoxystyrene

AgClO4+CH3· CHPhBr

CH2Cl2

Rate, colour, conduct

[7]

p-Methoxystyrene

Ph3C+ClO4-

CH2Cl2

Rate, colour, conduct

[7]

1,1-Diphenylethylene

CCl3·CO2H

C6H6

Kinetic and colour

[14]

1,1-Diphenylethylene

CCl3·CO2H

C2H5·NO2

Kinetic and colour

[12a]

1,1-Diphenylethylene

SnCl4+H2O

C6H6

Kinetic and spectroscopy

[15a]

1,1-Diphenylethylene

SnCl4+HCl

C6H6

Kinetic and spectroscopy

[15b]

1-Phenyl-1-p-methoxyphenylethylene

CCl3·CO2H

C6H6

Kinetic and colour

[12a]

1,1-Di-p-tolylethylene

CCl3·CO2H

C6H6

Kinetic and colour

[12a]

more circumstantial, evidence has established at least a very strong case for cationic propagation in some aliphatic systems.

i) Aromatic hydrocarbon monomers At the head of Table 2 stands what appears to be the same system as one quoted in Table 1; superficially it is, and the differences are subtle. During the work on the pseudocationic polymerisation of styrene by perchloric acid it was found that under special conditions a quite different type of reaction occurred which had all the

616

New Views on Cationic Polymerisation (1966) characteristics to be expected of a true cationic polymerisation [6]. This happened when either the concentration of monomer was small compared with that of the acid, (e.g., at the end of a pseudocationic polymerisation), or when the phial containing the acid solution was broken into the monomer solution in such a way that a transient, high, local concentration of acid was produced, or when the monomer was introduced into a solution already containing organic ions, namely, those resulting from the reaction of 1-phenylethyl bromide with silver perchlorate before addition of the styrene. The reactions occurring under these conditions are at least a hundred times faster than the pseudocationic polymerisations and are very fast even at –90 °C, at which temperature the pseudocationic polymerisation is exceedingly slow. The system styrene-sulphuric acid merits some special discussion. Gandini and Plesch [6, 7] were unable to reproduce the results of Pepper and his collaborators [8]. When a phial containing styrene was broken into a solution of sulphuric acid in methylene or ethylene dichloride at ~20 °C only traces of polymer were obtained, apparently very rapidly, and thereafter no further polymerisation and no colour developed. These results are in essential agreement with those of Tsuda [9] who also found the polymerisation to be inhibited by water. When some methylene dichloride containing a suspension of sulphuric acid was added to bulk styrene there was instantaneous development of colour and fast, complete polymerisation [7]. It thus appears that sulphuric acid can, under some conditions, cause a cationic, but not a pseudocationic, polymerisation, but the matter is not yet entirely clear. Probably the largest body of systematic evidence concerning the occurrence of cationic and pseudocationic reactions is that of Evans and his co-workers [12-15]. It indicates that 1,1-diphenylethylene and its derivatives are very suitable for an exploration of the conditions under which these reaction modes may occur. It is worth noting that even for those systems, in which the dimerisation takes place in the absence of ions, these are formed at the end of the reaction; this same behaviour is found in the pseudocationic polymerisation of styrene by perchloric acid [5].

ii) Aliphatic hydrocarbon monomers Strictly, there is no direct evidence concerning the presence of ions for any aliphatic hydrocarbon monomers. The spectroscopic studies which are of such great diagnostic value for aromatic systems are at present useless for those involving aliphatic monomers and therefore such information as we have for these (Table 3) consists of measurements of electrical conductivity and other, more circumstantial, evidence. It is not claimed that the evidence assembled in these Tables is complete and as far as Table 3, especially, is concerned, its content depends obviously on what one considers to be satisfactory evidence for the participation of ions.

617

Developments in the Theory of Cationoid Polymerisations

Table 3 Cationic systems: Aliphatic hydrocarbon monomers Monomer

Catalyst

Co-catalyst

Solvent

Diagnosis

Reference

Isobutene

AlCl3

?

EtCl

Conduct. and DP

[16]

Isobutene

TiCl4

H2O

CH2Cl2

Kinetic

[18]

Isobutene

SnCl4

H2O

EtCl

Kinetic

[19]

3-Methylbutene-1

AlCl4

?

Various

Structural

[21]

and related monomers

AlBr3

?

Various

Structural

[21]

For the polymerisation of isobutene by aluminium chloride in ethyl chloride at –78 °C in the presence of various polar compounds, Vesely and his collaborators [16] showed that the DP of the polymers was inversely related to the conductivity of the catalyst solutions before addition of the monomer. This suggests very strongly that the propagating species is ionic [17]. Detailed study [18] of the system isobutene-titanium tetrachloride-water-methylene dichloride showed it to be highly complex, but the kinetics and the temperaturedependence of rate and DP could be explained, at least qualitatively, on the hypotheses that the chain-carriers are ions, that paired and free cations have appreciably different reactivities, and that the degree of dissociation of the ion-pairs increases with decreasing temperature. In a similar way the kinetics of the polymerisation of isobutene by stannic chloride and water in ethyl chloride at –78 °C are most simply explained in terms of propagation by free cations [19, 21, 22]. The next entry in Table 3 concerns the observations of Kennedy and his collaborators [20] on the polymerisation of 3-methylbutene-1 and related monomers by aluminium chloride or bromide in various solvents. The essential point is that, at temperatures below approximately –100 °C, the polymer has the repeat unit — + (CH2)2⋅CMe2— which is formed by isomerisation of the ion —CH2⋅C H⋅CHMe2. This indicates that the isomerisation is faster than the propagation. At higher temperatures the propagation is too fast for this isomerisation to take place and the polymer has the normal structure. There is a great weight of organic-chemical evidence that such isomerisations only take place when an ion is formed. If this is accepted as valid and relevant, then the case for an ionic propagation is proved. Furthermore, it follows that all other polymerisations in which isomerisation accompanies polymerisation are also ionic; the polymerisation of β-pinene is perhaps the most familiar example, but there are many others.

618

New Views on Cationic Polymerisation (1966)

Table 4 Cationic systems: Oxygen-containing monomers Monomer

Catalyst

Solvent

Diagnosis

Reference

1,3-Dioxolan

HClO4

CH2Cl2

Conduct.

[23]

I2

Various

Kinetic and spectroscopy

[24, 25]

Various vinyl ethers

iii) Oxygen-containing monomers The scanty information relevant to oxygen-containing monomers is in Table 4. Studies of the kinetics of the polymerisation of 1,3-dioxolan and of the depolymerisation of its polymer by perchloric acid in methylene dichloride have been accompanied by measurements of the electrical conductivity of the reaction mixtures [23]. These have shown that ions are present during the reactions and the evidence strongly suggests that they are essentially concerned in these. This is one of the very few direct demonstrations of the participation of ions. The work of Eley’s school [24, 25] on the polymerisation of alkyl vinyl ethers by iodine and iodine chloride and bromide in various solvents has shown a relatively simple, selfconsistent reaction pattern. Its interpretation in terms of initiation by I+ and propagation + by carboxonium ions R1.CH2⋅CH⋅O⋅R is so much in agreement with general chemical expectation, and any alternative mechanism at present so difficult to visualise, that the kinetic evidence seems almost strong enough to sustain the case. Unfortunately, spectroscopic work [24] has not provided any strong support, owing to overlapping of spectra, but does not appear to be in conflict. In view of recent results, made available to us in advance of publication by Dr. P. Giusti, on the essential role of HI in the polymerisations of styrene and acenaphthylene by iodine, all polymerisations apparently initiated by this catalyst require most careful scrutiny.

Conclusion It is considered that Tables 1–4 contain most of those systems for which it has been definitely established whether the chaincarriers are ionic or non-ionic; if any have been overlooked, they cannot be numerous. The operative word here is ‘definitely’. No doubt, ideas as to what constitutes proof in this domain vary from one worker to another, and also with time. There are very many systems for which an ionic chain-carrier seems at present the only reasonable hypothesis, but in this context it is essential to recall that not very long ago the only ‘reasonable’ reaction between perchloric acid and styrene appeared to be protonation of the olefin!

619

Developments in the Theory of Cationoid Polymerisations At this stage one of the most urgent tasks is a re-investigation of a wide range of systems by other than kinetic methods, especially by spectroscopy and conductivity measurements. It may be useful to point out here that, if more investigators had taken an old-fashioned natural historian’s view of their experimental material and had noted and recorded the presence or absence of colours in reacting systems, and followed up these clues, the present situation might never have arisen.

References 1.

‘Chemistry of Cationic Polymerisation’, Ed., P. H. Plesch, 1963 (London: Pergamon Press).

2.

Kennedy, J. P., and Langer, A. W., Advanc. Polym. Sci., 1964, 3, 508.

3.

Plesch, P. H., ‘Progress in High Polymers’, Vol. 2. (J. C. Robb and F. W. Peaker, eds.) (London: Heywood and Co. Ltd.).

4.

Gandini, A., and Plesch, P. H., Proc. Chem. Soc. Lond., 1964, p. 113.

5.

Gandini, A., and Plesch, P. H., Proc. Chem. Soc. Lond., 1964, p. 246.

6.

Gandini, A., and Plesch, P. H., J. Polym. Sci., (B), 1965, 3, 127.

7.

Gandini, A., and Plesch, P. H., unpublished; Gandini, A., Thesis, Univ. of Keele, 1965; papers submitted to J. Chem. Soc.

8.

Pepper, D. C., et al., Proc. Roy. Soc., [A], 1961, 263, 58, 63, 75, 82.

9.

Tsuda, Y., Makromol. Chem., 1960, 36, 102.

10. Pepper, D. C., and Reilly, P. J., Proc. Chem. Soc., 1961, p. 200; J. Polym. Sci., 1962, 58, 639. 11. Throssell, J. J., Sood, S. P., Szwarc, M., and Stannett, V., J. Amer. Chem. Soc., 1956, 78, 1122. 12. a. Evans, A. G., Jones, N., Jones, P. M. S., and Thomas, J. H., J. Chem. Soc., 1956, p. 2757. b. Evans, A. G., Jones, P. M. S., and Thomas, J. H., ibid., 1957, p. 104. 13. Evans, A. G., James, E. A., and Owen, E. D., J. Chem. Soc., 1961, p. 3532. 14. Evans, A. G., Jones, N., and Thomas, J. H., J. Chem. Soc., 1955, p. 1824.

620

New Views on Cationic Polymerisation (1966) 15. Evans, A. G., and Lewis, J., J. Chem. Soc., (a), 1957, p. 2975; (b) ibid., 1959, p. 1946. 16. a. Zlamal, Z., Ambroz, L., and Vesely, K., J. Polym. Sci., 1957, 24, 285; b. Vesely, K., ibid., 1958, 30, 375; c. Ambroz, L., and Zlamal, Z., ibid., 1958, 30, 381; d. idem., ibid., 1958, 29, 595; e. Zlamal, Z., Symposium on Macromolecules, (Wiesbaden), 1959, Paper III. A 14; f. Zlamal, Z., Ambroz, J., and Ambroz, L., Chem. Listy, 1955, 49, 1606; g. Zlamal, Z., and Kazda, A., Symposium on Macromolecules, (Moscow), 1960. 17. Plesch, P. H., J. Chem. Soc., 1964, p. 104; also as reference 1, p. 171. 18. Biddulph, R. H., Plesch, P. H., and Rutherford, P. P., J. Chem. Soc., 1965, p. 275. 19. Norrish, R. G. W., and Russell, K. E., Trans. Faraday Soc., 1952, 48, 91. 20. Kennedy, J. P., and Thomas, R. M., Makromol Chem , 1962, 53, 28; 1963, 64, 1; Kennedy, J. P., Minckler, L. S., Wanless, G. G., and Thomas, R. M., J. Polym. Sci., (A), 1964, 2,1441, 2093; (C), No. 4, p. 289; Kennedy, J. P., Minckler, L. S., and Thomas, R. M., ibid., (A), 1964, 2, 367, 381; Kennedy, J. P., Elliott, J. J., and Groten, B., Makromol. Chem., 1964, 77, 26. 21. Biddulph, R. H., and Plesch, P. H., J. Chem. Soc., 1960, p. 3913. 22. As reference 1, p. 178. 23. Plesch, P. H., and Westermann, P. H., unpublished; Gandini, A., Giusti, P., Plesch, P. H., and Westermann, P. H., Chem. and Ind., 1965, 1225. 24. Eley, D. D., and Seabrooke, A., J. Chem. Soc., 1964, p. 2226. 25. Eley, D. D. et al., J. Chem. Soc., 1954, p. 1677 and earlier papers.

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Developments in the Theory of Cationoid Polymerisations

622

6.5

Reaction Mechanism in Cationic and Pseudocationic Polymerisations (1966) P. H. Plesch

This paper was first published in Pure and Applied Chemistry, 1966, 12, 117-125, Reproduced with permission from Butterworths, copyright 1966.

Introduction The polymerisations of olefinic and cyclic compounds catalysed by conventional acids and by syncatalytic systems comprising a metal halide and a co-catalyst have been reviewed from several points of view [1-6]. These reactions are unusual in that the ideas used in their interpretation have changed frequently and the theoretical position is still somewhat confused. I shall examine here some of the reasons for this situation and attempt to clarify the picture by an historical approach. I will also give an account of some recent work leading to a revival of the old ‘ester’ theory and indicate some of its implications and connections.

Co-catalysis Since the 1930s it has been recognised that polymerisations catalysed by metal halides are in many essential respects different from those induced by radicals, and it was generally agreed by the early 1940s that the chain-carriers, or active species, are highly polar and, possibly, cationic. The discovery in the late 1940s of co-catalysis in isomerisations, alkylations, and polymerisations catalysed by metal halides appeared to bring some uniformity to the subject, because many of the syncatalysts (metal halide and co-catalyst) could plausibly be considered to act in the same way as conventional acids. Thus the reactions catalysed by them were open to interpretation by the Whitmore carbonium ion mechanism. Whilst this view was widely accepted as explaining many of the observations, a few workers retained for some time a modified version of Hunter and Yohé’s ‘direct’ initiation mechanism to explain a limited range of phenomena. The point at issue is whether the polymerisation of an olefinic hydrocarbon can be initiated by a metal halide alone, without the participation of a co-catalyst, which might be water, a hydroxylic impurity, or a

623

Developments in the Theory of Cationoid Polymerisations solvent alkyl halide. This whole problem is extremely difficult and complicated, and it has been analysed in some detail [2, 6]. It is difficult because the definitive answers must come from quantitative experiments with extremely pure materials under the most rigorous conditions, and such are very rare. It is complicated because of the great diversity of behaviour which is shown by different metal halides and monomers, and because we are still very ignorant of the chemistry of metal halides. The interpretation of reactions catalysed by metal halides was complicated and confused further by the formation of π-complexes between these catalysts and olefins, and the unfortunate fact that many of these complexes formed from aromatic olefins have a colour which to the unaided eye is indistinguishable from that of the triphenylmethyl and related cations. There is no evidence that these complexes are catalytic, and quite a lot that they are not. Recent work has shown that in some systems in which polymerisation was believed to occur without co-catalyst, a co-catalyst is in fact required [7, 8, 11]. But it has also been shown that in others [12, 13] the addition of water has no effect on the rate and, therefore, there is evidently no need for a co-catalyst of this type. Since ‘direct’ initiation by metal halide alone seemed very unlikely, an explanation in terms of co-catalysis by the solvent was suggested for lack of any more plausible theory [12]. Whilst ‘direct’ initiation by the Hunter-Yohé mechanism remains implausible [6], a different form of ‘direct’ initiation has been suggested and must be considered; it is analogous to initiation of anionic polymerisation by sodium naphthyl, and involves formation of a cation-radical by oxidation. This reaction is limited to reducible catalysts and its details (if it occurs at all!) remain to be explored. Scott, Miller and Labes [14] have suggested such a reaction for the initiation of N-vinylcarbazole polymerisation by organic catalysts with marked electron-acceptor character; Bawn, Fitzsimmons and Ledwith [15] suggested it for initiation by the tropylium ion; Chi-Hua Wang [15a] put forward the idea with respect to initiation by reducible metal ions, but emphasised the radical reaction which might ensue therefrom; and Bawn, Ledwith and Yang Shih-Lin [15b] reported polymerisation of N-vinylcarbazole by sodium chloroaurate involving reduction of the Au (III). I would like to suggest here that the mechanism could be generalised to metal halide catalyst. One might represent it as involving the metal halide molecule, or the cation formed from this by the self-dissociation of metal halides in suitable solvents [16]:

2TiCl4 + RCH:CH2 + • TiCl3 + TiCl-5 + RCH·CH2

TiCl3+ + TiCl-5 + RCH:CH2 624

Reaction Mechanism in Cationic and Pseudocationic Polymerisations (1966) The formation of the easily identifiable lower halides should facilitate diagnosis of this type of reaction.

Influence of views derived from radical chemistry The mode of action of catalysts and the mechanism of initiation are inseparable from the problems concerning the nature of the chain-carriers. From the discovery of co-catalysis it was generally believed that the chain-carriers are ions, but we can now see that this theory was neither firmly based, nor thoroughly worked out in its consequences. It has been shown that there was, until recently, extraordinarily little evidence for ions being the reactive species [6]. Seeking the reasons for this, one can now see that in the 1940s and 1950s workers refrained from conductivity measurements, or ignored negative or equivocal results of such studies, probably for two reasons: the electrochemistry of nonaqueous solutions, especially those of metal halides, was still largely unexplored and beset by great experimental difficulties; and, perhaps more important, most workers still looked upon all addition polymerisations from the point of view of radical reactions, which implied that the concentration of chain-carriers is too small to be measured directly. The ‘radical’ point of view had several other consequences which retarded the development of an adequate conceptual framework for the acid and metal halide catalysed reactions. Among these was the practice of studying only initial rates and ignoring the complete reaction curves as important evidence concerning the nature of the reactions; the prejudice that these reactions could all be treated in terms of a steady state of the First Kind; and the (usually implicit) assumptions that for all systems the chain-carrier is fundamentally the same, (i.e., a carbonium ion), and that in any one system there is only one kind of active species. The electrochemically and thermodynamically obvious implication of any ionic theory, that the presence of ions implies necessarily the simultaneous existence of ion-pairs and free ions, was largely ignored, or circumvented by guesswork. A detailed analysis of this problem has only been given very recently [6, 17]. The somewhat wayward development of the theory of acid and metal halide catalysed polymerisations is in great measure due to the slowness with which ideas taken over from radical chemistry were re-examined and, when found inappropriate, discarded. During the last fifteen years an adequate theory has grown up-but it is still far from complete. In the light of our present knowledge, the logical steps in the elucidation of reaction mechanism must include these: i) To decide whether the propagation is a first or second order process it is necessary to construct a First Mayo Plot for polymer formed at low conversion. If 1/DP against 1/m

625

Developments in the Theory of Cationoid Polymerisations gives a straight line, Vp = kpmm* (m = monomer concentration, m* = concentration of active centres); if 1/DP against m gives a straight line, Vp = k′pm*. (For a detailed discussion see Reference [6]). ii) Kinetic analysis of whole reaction curves. If the order of reaction is constant, m* = constant (except for the unlikely situation in which dm*/dt = -dm/dt), and the reaction is stationary - at least over that part for which the order is constant. iii) Whether stationary reactions are of the first kind (Vi = Vt ≠ 0) or of the second kind (Vi = Vt = 0) cannot be decided by any generally applicable procedure. The only unambiguous method is to determine, (e.g., spectroscopically or conductimetrically), the concentration of growing chains, and its relation to initial catalyst concentration. iv) Identification of chain-breaking reactions by end-group analysis and Mayo plots.

Discovery of pseudocationic polymerisation The chemical and kinetic complexity of systems involving metal halides led to a search for simple catalysts, such as conventional acids. However, since these were generally believed to give much lower DPs than syncatalysts (and with aliphatic monomers, especially, gave not even oligomers under many conditions) they were eschewed by polymer chemists who were more interested in making high polymers with any catalytic system that would serve, than in the elucidation of reaction mechanism. Moreover, such attempts as were made in this direction seemed to show that ‘simple’ catalysts gave reactions which were hardly less complex than those catalysed by syncatalysts [18-27]. The first to succeed in devising a truly simple system in which oligomers higher than dimer are formed, were Pepper and Reilly [28]. They found that the polymerisation of styrene by anhydrous perchloric acid in ethylene dichloride obeyed very simple kinetics over a reasonable range of temperature and they interpreted these in terms of a very fast initiation with complete consumption of catalyst, leading to a stationary system of the Second Kind, so that the second order rate constant is kp. In conformity with then current ideas they considered the initiation to consist of protonation of the styrene, and the propagating species to be the polystyryl ion. Although there are at least three features of the results which seem hard to reconcile with this interpretation, any other theory would have seemed quixotic at that time. These features are the high activation energy for propagation, Ep ca., 10 kcal mole-l; that water, even in ten-fold excess over the acid, does not affect kp; and the fact that over a wide range of concentrations and temperatures the plots of the first-order rate constant against the concentration of perchloric acid gave accurately straight lines; this has the unlikely implication [6] that the kp for free ions and ion-pairs are equal to within a factor of 10 or less.

626

Reaction Mechanism in Cationic and Pseudocationic Polymerisations (1966) Pepper and Reilly’s views on the mechanism of this polymerisation implied that with the concentrations of perchloric acid used by them, it should be possible to estimate the concentration of polystyryl ions spectrophotometrically and so to test whether initiation did indeed give carbonium ions in concentration equal to that of the acid. When Gandini and Plesch [5, 29-31] carried out the appropriate measurements, they found from spectroscopic, conductimetric and kinetic studies that no ions were present during the polymerisations, but that they were formed once the styrene concentration had been reduced by polymerisation to less than four times the concentration of acid. Addition of more styrene instantly removed the ions, which reappeared once again when polymerisation had reduced the styrene concentration sufficiently. This formation of ions after polymerisation had misled some workers into concluding that they were also present during that reaction. Detailed studies led Gandini and Plesch to formulate the concept of pseudocationic polymerisations. These are reactions which show many of the characteristics of cationic polymerisations, but do not involve ions. Since they could see no other alternative compatible with general chemical knowledge, they formulated the reactive species as an ester, and they were able to support this view by direct experiments (formation of the ester in the styrene solution by metathesis). The evidence indicates that in the system styrene, perchloric acid, methylene dichloride, the poly(styryl perchlorate) ester requires four molecules of styrene for its stabilisation. When these are no longer available, the ester ionises, and the residual styrene is consumed by a very fast, truly cationic polymerisation; ionisation of the ester is a complicated reaction which has been only partly elucidated. The initiation and propagation of the pseudocationic polymerisation can be represented thus:

(1/4)(HClO4)4 + 5C8H8 → (CH3CHPh·O·ClO3)4C

8

H8

C8H8

{H(CH2CHPh)n·O·ClO3}4C 8H 8 The formation of the ester is very fast and the propagation is rate-determining. The chain-breaking reactions (which do not include a termination) are essentially those characterised by Pepper and Reilly [32]. The (very few) systems in which the character of the reaction has been definitely established as cationic or pseudocationic have been listed [5]; one of the most urgent current tasks is to extend this list by exploring a range of monomers, catalysts, solvents and temperatures so that the type-determining factors may be quantified.

627

Developments in the Theory of Cationoid Polymerisations

Esters as chain-propagating species It is now opportune to examine the status and implications of the ester theory. Historically, esters are the oldest of the ‘active species’ which have been adduced to account for the reactions of olefins in the presence of acids. A most perspicacious comparison of theories concerning interaction of olefins and acids has been given by Schmerling and lpatieff in which they include various forms of ester theory [33]. They found that whilst there was then little experimental evidence for preferring one theory to another for the (conventional) acid catalysed reactions of olefins, the carbonium ion theory provided greater insight into the detailed processes. Since that time all forms of ‘ester theory’ have lost popularity, but it now seems that the pendulum of fashion has swung too far in favour of carbonium ions; this is in no small measure due to the increasing amount of information concerning the properties of carbonium ions which has become available [34-36]. When we now reconsider the ester theory we can do no better than to start by quoting Whitmore [37]: ‘Esters are often assumed as intermediates in various processes of the types in which we are interested. It should be noted, however, that any use of a pure neutral ester is naturally ineffective since the ester by itself probably has no more tendency to give ions than does water by itself or hydrogen chloride by itself. On the other hand, the ester in the presence of a suitable donor of protons can form carbonium ions.’ and Schmerling and Ipatieff [33]: ‘It should be remembered, of course, that in the carbonium theory the word ‘ion’ has a different connotation than it does in inorganic chemistry; the degree to which the ester is dissociated may actually lie somewhere between the undissociated ester as in the ester mechanism and the free ions as usually written (although actually believed to be very short-lived) in the carbonium ion mechanism.’ Whilst today we can no longer accept either of these statements as literally and universally valid, they contain two very important and closely related ideas which have been proved useful. The first of these is that a normal, stable ester may become activated by interaction with another species; a natural corollary of this is that esters can also be deactivated, or stabilised, by such interaction. The other idea is that in a series of esters gradations of polarity may be found, or that the polarity of any one ester, in particular the reactivity of the bond linking the potentially anionic and cationic moieties, may change according to the environment in which the ester finds itself. The two ideas are thus closely linked. One serious point in which I find myself in disagreement with Schmerling and Ipatieff and some contemporary writers is that, with respect to identifiable reaction intermediates,

628

Reaction Mechanism in Cationic and Pseudocationic Polymerisations (1966) I consider there to be a sharp distinction between the most polar form of a molecule and its ionically dissociated form. The reason for this is empirical: An ion is defined as a species carrying a charge equal to an integral multiple of the electronic charge, and this definition implies that it will have a characteristic predictable electronic spectrum and, under suitable conditions, mobility in an electric field. There is so far no evidence which would compel one to abandon this definition, and I think it is important to distinguish clearly in this context between reaction intermediates (chain carriers, active species) of finite life-time, and transition states. Whilst the kinetics, and probably the mechanism of pseudocationic polymerisations are simple, those of the reactions following polymerisation are not. Since generalisations are dangerous in this field, I will confine the discussion here to the system which we have explored and hope that others will find useful analogies in systems well known to them. Our findings on the ionogenic reaction which follows polymerisation in the system styrene, perchloric acid, methylene dichloride and other related evidence can be summarised tentatively by the following scheme [31]:

(IV) –4st (RCH2CHPhA)4st +4st

(I) RCH2CHPhA

(II) Tertiary ions

(III) RCH:CHPh + HA A = ClO4 R = Oligostyryl

Oligostyrene with indanyl end-groups

+HA Allylic ions

Experiment shows that when polymerisation has consumed so much styrene that its concentration is only four times that of the perchloric acid, ions1 are formed suddenly, but their concentration is less than that of the acid and their formation is accompanied by the formation of double bonds. When more styrene is added to the system, the ions disappear instantaneously because a new species (IV) is formed and its formation shifts all the equilibria. We can say that the ester (I) is stabilised by being specifically solvated by four molecules of styrene (it is not known yet whether other compounds can fulfil this function); in other words, the specific solvation reduces the polarity of the C—O bond and gives the ester a stability which the pure ester does not possess: attempts to prepare it at room temperature result in a mixture containing species (II), (III) and others. 1

Note added in proof - It now seems certain that the ion absorbing near 309 and 424 mμ, which is readily observed in these systems, is not the 1-phenylethyl ion; its exact nature is still uncertain.

629

Developments in the Theory of Cationoid Polymerisations The reactivity of the ions (in terms of rate constants) is at least two orders of magnitude greater than that of the stabilised ester, but it can only show itself under special conditions: when a high concentration of acid is formed locally in a solution, especially at low temperatures, or when ions such as (II) are introduced into a styrene solution, or at the end of a ‘normal’ ester polymerisation when the remaining four molecules of styrene per acid molecule are polymerised with great speed. Under the first two of these conditions the exceedingly fast ionic polymerisations can consume all the monomer before the ions are removed through the reactions (II) → (I) → (IV). Under the same conditions which with styrene give pseudocationic polymerisation (perchloric acid, methylene dichloride), the much more basic p-methoxystyrene does give a cationic polymerisation, but with the weaker trifluoroacetic acid it polymerises pseudocationically. The opposite of the stabilisation of an ester is its activation. If we include in the concept ester the alkyl halides, their Friedel-Crafts reactions provide familiar examples of this phenomenon. An unusual example especially relevant to our present considerations is provided by some results made available to me in advance of publication by Giusti and Andruzzi. Their results [38] on the polymerisation of styrene by iodine and hydrogen iodide can be interpreted in terms of an organic iodide derived from styrene, probably 1-phenylethyl iodide, being activated by the co-ordination of one or two molecules of iodine. This process appears to polarise the C—I bond to such an extent that the normally stable ester becomes activated to a chain-propagating species and induces a pseudocationic polymerisation:

CH3CHPhI, (I2)n + C8H8 → CH3CHPhCH2CHPhI(I2)n n = 1 or 2

Conclusion It now remains to place the concept of an ester as an active species into a wider chemical context, with special reference to polymerisation catalysts. Sinn and Patat [39] have emphasised the distinction between monofunctional and bifunctional catalytic systems† and this distinction is obviously and necessarily related to the idea, explained above, that there is a difference in kind between polarised molecules and the ions which can be formed from them. Whereas the carbonium and other cations as reactive species are monofunctional, the esters evidently belong to the class of bifunctional catalysts; their mode of action - the addition of their constituent parts across a double bond - is, in modern terminology, an insertion reaction. In this context, we must note the important † The term ‘bifunctional’ as used by these authors is not to be confused with its use by Keulemans and Schuit who give it a quite different meaning [40].

630

Reaction Mechanism in Cationic and Pseudocationic Polymerisations (1966) role of labile esters, (e.g., 1-alkoxyvinyl esters), in synthetic organic chemistry, and that of enzyme-activated esters in biochemical processes. Many authors [41] have noted that one could find in the vast range of more or less complex polymerisation catalysts evidence that changing composition was accompanied by a change in type of catalytic activity - from pure cationic to pure anionic - and that certain catalysts could show cationic or anionic characteristics according to the type of monomer offered to them. Whilst such speculations are always attractive to the scientist searching for unifying principles, and whilst they were well founded at the anionic end in the metal alkyls, no cationically acting species was known which, whilst bifunctional, is a well-defined chemical species. Our discovery of the pseudocationic reactions catalysed by esters has now completed the range; by analogy we would call the polymerisations catalysed by covalent metal alkyls pseudoanionic. Moreover, it seems to me that the complementary ideas of activation and stabilisation of a potentially reactive species may be useful in thinking about the modes of action of many complex catalytic systems.

References 1.

Cationic Polymerisation and Related Complexes (Ed. P. H. Plesch) Heffer and Sons, Cambridge (1953).

2.

Chemistry of Cationic Polymerisation (Ed. by P. H. Plesch) Pergamon Press, London (1963).

3.

D. C. Pepper. ‘Cationic Polymerisation’, Chapter in Friedel-Crafts and Related Reactions (Ed. G. A. Olah) Interscience, New York, 1964.

4.

J. P. Kennedy and A. W. Langer., Adv. Polymer Sci. 3, 508 (1964).

5.

A. Gandini and P. H. Plesch, S.C.I. Monograph No. 20, The Chemistry of Polymerisation Processes, London, 1966, 107.

6.

P. H. Plesch. ‘Cationic Polymerisation’, Chapter in Progress in High Polymers, Vol. II (Ed. J. C. Robb and F. W. Peaker), Iliffe Books Ltd., London, 1968, p.137.

7.

D. O. Jordan and F. E. Treloar, J. Chem. Soc., 1961, 737.

8.

W. R. Longworth, P. H. Plesch and P. P. Rutherford., Dokl. Akad. Nauk. USSR, 127, 97 (1959).

9.

W. R. Longworth, P. H. Plesch and P. P. Rutherford., Proc. Chem. Soc., 1960, 68.

631

Developments in the Theory of Cationoid Polymerisations 10. a. D. D. Eley and Anne Seabrooke., J. Chem. Soc., 1964, 2231. b. D. D. Eley and A. F. Johnson., J. Chem. Soc., 1964, 2238. 11. E. B. Lyudwig, A. R. Gantmakher, and S. S. Medvedev., This Symposium., Abstract No. A 494. 12. a. J. H. Beard, P. H. Plesch and P. P. Rutherford., J. Chem. Soc., 1954, 2566. b. W. R. Longworth, C. J. Panton and P. H. Plesch., J. Chem. Soc., 1965, 5579. 13. M. Chmelir, M. Marek, and O. Wichterle., This Symposium., Abstract No. AS 1. 14. H. Scott, G. A. Miller and M. M. Labes., Tetrahedron Letters, 1963, 1073. 15. C. E. H. Bawn, C. Fitzsimmons and A. Ledwith., Proc. Chem. Soc., 1964, 391. 15. a. Chi-Hua Wang., Chem. and Ind., 1964, 751. b. C. E. H. Bawn, A. Ledwith and Yang Shih-lin., Chem. and Ind., 1965, 769. 16. W. R. Longworth and P. H. Plesch., J. Chem. Soc., 1959, 1887. 17. R. H. Biddulph, P. H. Plesch and P. P. Rutherford, J. Chem. Soc., 1965, 275. 18. R. G. Heiligmann, J. Polymer Sci., 6, 155 (1950). 19. J. Throssell, S. P. Sood, M. Szwarc and V. Stannett, J. Am. Chem. Soc., 78, 1122 (1956). 20. C. P. Brown and A. R. Mathieson, J. Chem. Soc., 1957, 3608; 3612; 3620; 3625; 3631; 1958, 3445, 3507. 21. Y. Tsuda, Makromol. Chem., 36, 102 (1960). 22. D. C. Pepper et al., Proc. Roy. Soc., A263, 58, 63, 75, 82 (1961). 23. R. Rothe, G. Reinisch, W. Jaeger and I. Schopov., Makromol. Chem., 54, 183 (1962). 24. V. Jaacks and W. Kern., Makromol. Chem., 62, 1 (1963). 25. R. C. Schulz and A. Banihaschemi, Makromol. Chem., 64, 140 (1963). 26. M. Rothe, H. Boenisch and W. Kern, Makromol. Chem., 67, 90 (1963). 27. J. Upadhyay, P. Gaston, A. A. Levy and A. Wassermann, J. Chem. Soc., 1965, 3252 and preceding papers.

632

Reaction Mechanism in Cationic and Pseudocationic Polymerisations (1966) 28. D. C. Pepper and P. J. Reilly, J. Polymer Sci., 58, 639 (1962). 29. A. Gandini and P. H. Plesch, Proc. Chem. Soc., 1964, 240. 30. A. Gandini and P. H. Plesch, J. Polymer Sci. B. Polymer Letters, 3, 127 (1965). 31. A. Gandini and P. H. Plesch, J. Chem. Soc., 1965, 4765, 4826; Also work to be published. 32. D. C. Pepper and P. J. Reilly, Proc. Chem. Soc., 1961, 460. 33. L. Schmerling and V. N. Ipatieff, Adv. Catalysis, 2, 21 (1950). 34. Ref. 2, Chapters 1 and 2. 35. N. C. Deno, Chem. Eng. News., 42, 88 (1964) and many papers in J. Am. Chem. Soc. 36. G. A. Oláh et al. many papers in J. Am. Chem. Soc. 37. F. C. Whitmore, Chem. Eng. News, 26, 668 (1948). 38. P. Giusti and F. Andruzzi, This Symposium, Paper A275. 39. H. Sinn and F. Patat, Angew. Chem., 75, 805 (1963). 40. A. I. M. Keulemans and G. C. A. Schuit, In The Mechanism of Heterogeneous Catalysis, (Ed. by I. H. De Boer et al.), Elsevier, Amsterdam (1960). 41. See e.g. M. Roha, Adv. Polymer Sci., 4, 353 (1965); and references therein.

633

Developments in the Theory of Cationoid Polymerisations

634

6.6

Cationic and Pseudocationic Polymerisation of Aromatic Olefins-II. The Reactions Following Polymerisation of Styrene by Perchloric Acid (1968) A. Gandini and P. H. Plesch

This paper was first published in European Polymer Journal, 1968, 4, 55-74. Reprinted with permission from Pergamon Press, copyright 1968.

Abstract We report spectroscopic and conductimetric studies on the reactions of styrene in the presence of perchloric acid (most in methylene dichloride but some in ethylene dichloride), both during and after the polymerisation. During polymerisation no ions are detectable, but at the end aralkyl (and subsequently allylic) ions are formed. Quantitative results show that ion formation sets in when the styrene concentration has fallen to four times the acid concentration; we interpret this finding as showing that the ester (oligo-)styryl perchlorate requires four molecules of styrene for stabilisation in solution. The ionogenic reaction which follows polymerisation, changes its kinetics from second to first order. It is completely inhibited if the solution contains more water than acid, though this does not affect the polymerisation itself. At the end of the polymerisation, the ionogenic reaction sets up an equilibrium which involves many components and which is slowly shifted by formation of stable species; the position of equilibrium can be driven back towards predominance of non-ionic compounds by addition of fresh monomer. The relation between our work and that of other authors is discussed in detail.

635

Commercial rubbers

Developments in the Theory of Cationoid Polymerisations

Introduction In the first paper of this series[1] we reported on the kinetics of the polymerisation of styrene by perchloric acid in methylene dichloride. Some of the other features of this reaction and the reasons for describing it as ‘pseudocationic‘ have also been reported briefly [2, 3] and have been discussed in a wider context [4-6]. The present paper deals specifically with the formation and destruction of ions during and after the polymerisation. Although these results have been available for some time, we could not interpret them with confidence until the nature of the ions concerned had been clarified. Now that the complicated ionogenic reactions of styrene with an excess of perchloric acid have been unravelled [7], the ionogenic reactions following its polymerisation have also become much more intelligible.

Experimental

Materials Styrene [8], perchloric acid [9], methylene dichloride [10] and 1,2-dichloroethane [10] were purified, stored and dosed as described. Phials containing known quantities of water were prepared as described [11]. The products of all the polymerisations mentioned in this work were oligomers of DP between 3 and 8.

Techniques All the spectroscopic experiments were carried out in the all-glass high-vacuum device described [12], provided with a 1 cm Pyrex or silica cell; solutions were made up by vacuum distillation of styrene, solvent and, when needed, water, into the device which had been previously charged with a phial of perchloric acid solution. Reactions were started by crushing the phial of acid in the olefin solution; scanning could be started about 20 seconds after the mixing. Additions of styrene at the end of the first reaction were accomplished through magnetic break-seals mounted on the device. All this work was performed at room temperature (20–23 °C) with a UNICAM SP700 recording spectrophotometer. Because of the relatively high styrene concentrations, it was impossible to obtain spectroscopic information at wave lengths below about 350 mμ in most experiments. Conductivity measurements were carried out in a high vacuum cell in the shape of an inverted cone provided with a phial breaking device [13] and with bright platinum

636

Cationic and Pseudocationic Polymerisation of Aromatic Olefins... electrodes fixed near the apex supported by tungsten leads. The cell contents were stirred magnetically. With a perchloric acid phial in the breaking device, the cell was pumped out for a few hours. The solvent and the styrene solution were then dosed into the cell from dispensing burettes through all-metal taps [14]. The reactions were started by crushing the acid phial in the well-stirred, thermostatted (oil bath) olefin solution. The changes in conductivity were followed by readings taken every 5–10 seconds on a WayneKerr B221 Universal Bridge. The cell constant, computed by Fuoss’s method [15], was 0.110 cm-1.

Conductivity of materials The specific conductivity of the styrene solutions in ethylene dichloride was (1 to 2) x 10-9 mho/cm; that of a 4.0 x 10-2 M solution of perchloric acid was 9 x 10-8 mho/cm. The conductivity of the acid solutions increased very slowly, and linearly, with time, but this change was so small that it did not cause any ambiguity in our results. It is due to a slow attack of the acid on the tungsten leads carrying the Pt electrodes. A plot of the spectroscopically computed maximum ionic concentrations [SD ions]m (sum of free ions and ion-pairs) at the end of the reactions (m denotes maximum values throughout this paper, the subscript 0 denotes initial values) against the final values of the specific conductivity κm. for the equivalent runs (Tables 1 and 2) gave a straight line through the origin, showing that virtually only free ions were present in our systems; if there had been important quantities of ion-pairs, this plot would have been markedly curved.

Reproducibility and errors In nominally identical experiments the differences between rates, maximum optical densities and conductivities were never greater than could be accounted for by instrument errors or by errors arising from computation of concentrations. No inexplicable irreproducibilities were found.

Qualitative results Like all earlier authors, we assigned [16] the absorption near 309 and 421 mμ, observed when styrene reacts with an excess of perchloric acid and also in many related systems, to the 1-phenylethyl ion. We now know that this assignment is incorrect [7].

637

Developments in the Theory of Cationoid Polymerisations This absorption is in fact due to the ions derived from 1-methyl-3-phenylindane (the cyclic dimer of styrene) and its higher homologues (oligostyrenes with indanyl end groups). There can be no doubt that the ions formed at the end of the polymerisation of styrene belong to the same families of compounds (indanyl and various phenyl alkyl carbonium ions [7]). Our evidence showed that the 1-phenylethyl cation is absent from the ions formed from styrene by excess of acid; its dimeric homologue, the 1,3-diphenyl-n-butyl cation, is a minor component of the ion mixture. We refer to this mixture of ions formed rapidly from styrene by excess acid, or at the end of a styrene polymerisation, as SD (styrene-derived) ions. In order to study the variation of the concentration of ions during and after polymerisation, we scanned the solutions at 424 mμ against time. We found that, in addition to the SD ions, several other species giving peaks in the visible were formed at the end of the polymerisation. Therefore the kinetic study on the formation of the SD ions had to be supplemented by repeated scannings of the full visible and UV spectra. Some of the experiments carried out in the spectroscopic device were repeated in the conductivity cell. In view of the rather complicated behaviour of the system after the end of the polymerisation, we shall first give a chronological account of the phenomena, and then discuss their quantitative aspects. Figure 1 illustrates the different phases of the reaction from a spectroscopic point of view. 1 The latency period Provided that the ratio [styrenel/[HClO4] was higher than about 4, D424 did not exceed 0.0087 (experimental error for 0.000) for some time after the mixing of the reactants. This indicated that if ions with ε424 equal to about 4 x 103 had been formed at all, their concentration was lower than about 10-6 M. No other absorption band could be detected in the visible spectrum of the solutions. The only change in conductivity during this first phase of the reaction was a slow and linear increase, independent of working conditions, due to attack on the tungsten leads. This period of complete visible transparency and absence of organic ions we name the latency period (t′). It is a well-defined and reproducible feature which comes to an abrupt end with the onset of ion-formation. We ascertained that, at the end of the latency period, the polymerisation itself is almost complete; this was done by calculations involving the rate constant determined from kinetic experiments, by ‘killing’ the reaction mixture at this stage and isolating the polymer and, for experiments with very low monomer concentration, by observing disappearance of monomer spectroscopically. Thus the reactions following the latency period cannot involve the monomer.

638

Cationic and Pseudocationic Polymerisation of Aromatic Olefins...

Figure 1 A typical sequence of visible spectra for a spectroscopic experiment. a: At the end of the ion formation (only SD ions). b: Some 10–20 min later (mixture of SD and allylic ions). c: About 1 h later (more allylic ions). d: A few hours later (dienic polymer molecules + allylic ions). e: 20–30 h later (more dienic polymer molecules and less allylic ions). f: Same as ‘e‘ after addition of a few drops of ethanol (only dienic polymer molecules)

639

640

2.6

3.3

3.3

6.2

6.7

8.1

28.6

29.0

SGU18

SGU14

SGC9

SGU16

SGC8

SGU15

SGU13

SGC7

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

460

375

245

240

225

175

175

140

75

t′′ (s)

530

450

330

300

295

200

200

180

105

tm (s)

3.44

3.19

2.72

2.02

1.68

0.98

-1

-1

(10 M min )*

5

0.89

0.57

0.43

(μ μmho cm-1 min-1)

Rm

–

12.38

10.18

3.96

3.44

1.35

[SD ions]m (105 M)*

4.21

1.82

0.895 (1.12†)

κm

(μ μmho cm-1)

2. 4

–

5. 1

7.3

7.3

10.2

13.2

14.0

16.0

S2 (103 s-1)

5. 0

–

10.2

13.3

11.6

10.5

11.5

10.5

11.3

S1 (104 s-1)

* The maximum concentration of SD ions, and their rate of formation were calculated from the extinction coefficient ε424 = 3.8 x 103 which was obtained under the same standard conditions (see Reference [16]) † Value of κ at 0 °C m S2 and S1 are the slopes of the second and first order plots for the ionogenic reactions, respectively (see Figure 7)

1.0

[HClO4]0 [St]0 (102 M) (103 M)

SGU25

Exp. no.

Table 1 Spectroscopic (SGU) and conductimetric (SGC) experiments at fixed initial acid concentration in CH2Cl2 at room temperature

Developments in the Theory of Cationoid Polymerisations

6.1

6.1

6.2

6.1

6.2

6.7

6.1

33.0

35.0

34.0

SGU21

SGC10

SGU23

SGC11

SGU16

SGC8

SGU22

SGU12

SGU10

SGU11

12.0

8.7

4.3

20.0

10.0

10.0

8.0

8.0

5.0

5.0

[HClO4]0 (104 M)

120

30 0

300

400

380

700

840

tm (s)

450

700 540

800

1260 1350

85

24 0

225

320

310

600

630

t′′ (s)

3.37

2.10

0.31

9.07

2.72

1.45

0.54

-1

-1

(10 M min )*

5 -1

-1

0.57

0.33

0.117

(μ μmho cm min )

Rm

–

–

–

11.86

10.18

7.51

4.66

[SD ions]m (105 M)*

1.82

1.22 (1.54†)

0.87

κm

(μ μmho cm-1)

–

–

– –

–

20.7

13.3

11.6

9.7

9.4

5.3

5.0

S1 (104 s-1)

–

14.3

7.3

7.3

6.1

4.6

2.8

2.9

S2 (103 s-1)

* The maximum concentration of SD ions, and their rate of formation were calculated from the extinction coefficient ε424 = 3.8 x 103 which was obtained under the same standard conditions (see Reference [16]) † Value of κ at 0 °C m S2 and S1 are the slopes of the second and first order plots for the ionogenic reactions, respectively (see Figure 7)

[St]0 (102 M)

Exp. no.

Table 2 Spectroscopic (SGU) and conductimetric (SGC) experiments at fixed initial styrene concentration in CH2Cl2 at room temperature Cationic and Pseudocationic Polymerisation of Aromatic Olefins...

641

Developments in the Theory of Cationoid Polymerisations 2 The formation of an unstable intermediate At the end of the latency period, the reacting solutions became pinkish-red and a peak appeared at 510 mμ. The lifetime of this peak lay between 5 and 30 seconds, according to the working conditions, but a detailed study of its origin could not be made because of its transitory nature. 3 The formation of the SD ions The vanishing of the peak at 510 mμ left a yellow solution with a single peak at 424 mμ in the visible region of the spectrum. D424 and the specific conductivity of the solutions increased with time, as shown in Figure 2. The curves representing this production of ions were S-shaped, but the accelerating part was always very short compared with the rest of the curve.

Figure 2 A typical pair of curves for the formation of SD ions; SGU14, spectroscopic; SGC9 by conductivity (see Table 1); A is the cell constant

4 The formation of indanyl end-groups If the reaction mixture was left under vacuum for several hours after the end of the ionogenic reaction described in Section 3, the polymer no longer contained double-bonds (UV spectrum), indicating that the formation of indanyl end-groups went to completion. At the same time D424 fell to zero and the conductivity decreased to the background level due to impurities.

642

Cationic and Pseudocationic Polymerisation of Aromatic Olefins... 5 The formation of allylic ions Towards, or after, the end of the reaction leading to the formation of the SD ions, the spectra of the solutions slowly developed a rather broad peak around 450 mμ (Figure 1). We attribute this peak to allylic carbonium ions formed by hydride ion abstraction from an unsaturated polymer molecule by an SD ion X+:

– CHPh ⋅ CH 2 ⋅ CHPh ⋅ CH : CHPh + X + + ClO −4 → – XH + – CHPh ⋅ CH 2 – (CPhLCHLCHPh )+ + ClO −4 This conclusion is based on a study of allylic ions [17], on the recovery of polyunsaturated oligomers with conjugated double bonds (see Section 6), on analogous observations in aliphatic systems [18, 19], and on the occurrence of analogous processes in anionic systems [20]. Inoue and Mima [21] have reported that, when gaseous styrene was bubbled through 98 % sulphuric acid, a yellow solution, absorbing at 450 mμ was obtained. They attributed this rather broad peak to the 1-phenylethyl carbonium ion, but it is clear now that allylic ions were formed in their system following the partial oligomerisation of the monomer. 6 The formation of polyunsaturated oligomers On long standing under vacuum, the reacting solutions became fluorescent and their visible spectra exhibited a pair of peaks at 390 and 410 mμ whilst the 450 mμ peak was reduced: these peaks were not destroyed by neutralisation of the solution and were present in spectra of solutions obtained by redissolving the recovered polymer in methylene dichloride. We attribute these twin peaks to oligomers containing at least two conjugated double bonds and formed by proton abstraction from an allylic ion by some more basic species, such as a highly conjugated system: –H+

– CHPh ⋅ CH 2 (CPhLCHLCHPh )+ → — CHPh — CH == CPh — CH == CHPh This attribution is based on the fact that diphenylpolyenes absorb with a strong twin peak at wavelengths which increase as the number of double bonds is raised (the compound Ph(CH=CH)4Ph absorbs at 385 mμ and 405 mμ). Polystyrenes with conjugated double bonds, having a phenyl group on alternate carbon atoms of the chain, would possess a higher degree of conjugation than the diphenylpolyenes, so that one can estimate the number of conjugated double bonds in our oligostyrenes to be two or three. By using the extinction coefficient of the diphenyl polyenes, we can estimate the concentration of these groups of conjugated double bonds to be between 10 and 25

643

Developments in the Theory of Cationoid Polymerisations per million oligostyrene chains of DP about 5. Despite their very small number, these groups impart to the polymer solutions a strong fluorescence which slowly disappears if the solutions are left exposed to air and light, because of oxidation. The concentration of allylic-type ions was presumably about the same as that of the groups of conjugated double bonds. However, since the extinction coefficient of such ions is probably as high as ∼105, i.e., about twenty times greater than that of the SD ions, the resulting D450 was of the same order of magnitude as D424. 7 The effect of further monomer additions At any stage after the end of the polymerisation of the first portion of styrene, (i.e., after the latency period t ′), addition of a further quantity of monomer induced complete decolouration of the solution (except for the fluorescence given by the polyunsaturated oligomers), with a corresponding reduction in conductivity. After a second latency period, during which the monomer was polymerised, colour and conductivity reappeared. The formation of ions followed a pattern similar to that encountered at the end of the first polymerisation: the position of the broad peak, which slowly replaces the initial peak, was found to be variable depending on the polymer chain concentration in the reaction mixture. Thus for Experiment SGU11, in which three successive additions of styrene were made (Table 3), the λmax was 450–453 mμ at the end of the first reaction, 462–463 mμ at the end of the second and 475–479 mμ at the end of the third. This effect is probably due to progressive formation of more highly conjugated systems.

Table 3 The effect of succesive styrene additions on the spectroscopic behaviour of the system HClO4-styrene-CH2Cl2 Experiment SGU11 102[St]0,N (M)

104[HClO4]0,N (M)

t′′N (s)

[D450-480]m

[D410]m

1

34.0

12.0

450

1.1 (452 mμ)

0.25

2*

37.9

11.8

480

1.3 (462 mμ)

0.41

3†

25.5

11.4

470

1.4 (477 mμ)

0.64

Addition N

* 30 h after beginning † 50 h after beginning NB D450-480 went to 0 after each addition

644

Cationic and Pseudocationic Polymerisation of Aromatic Olefins... Figure 3 illustrates a conductivity experiment with four successive additions of styrene: whenever more styrene was added, the equivalent conductance (referred to the total perchloric acid concentration) fell abruptly, but not quite down to its original value during the first latency period. This is not because some carbonium ions remained after the styrene addition, but because the free acid present after the end of the polymerisation reacted with the tungsten leads, as mentioned above. This was confirmed by a blank experiment without styrene which gave the dotted base-line in Figure 3.

Figure 3 The effect of successive styrene additions on the conductivity of the reacting solutions (See Table 4)

Table 4 The effect of succesive styrene additions on the spectroscopic behaviour of the system HClO4-styrene-CH2Cl2 Experiment SGC11 102[St]0,N (M)

104[HClO4]0,N (M)

t′′N (s)

κm (μ μmho cm-1)

1

6.1

8.0

320

1.2 2

2

8.3

6.67

450

2.2 9

3

10.6

5.24

700

2.5 7

4

13.5

3.75

1000

2.3 0

Addition N

645

Developments in the Theory of Cationoid Polymerisations Table 4 gives details for the experiment illustrated in Figure 3. Similar features were obtained in spectroscopic experiments involving further styrene additions. Table 3 refers to one of these: the plot of D424 against time was strictly equivalent to that shown in Figure 3. 8 The influence of added water The influence of added water upon the ionogenic reaction was studied only spectroscopically: the results obtained are given in Table 5. When sufficient water was added to make [H2O] ≈ 5[HClO4]0, no carbonium ions at all were formed at the end of the polymerisation (run SGU17): this shows once again the strongly poisonous effect of water on these ions. When [H2O] ≈ 1/3 [HClO4]0, both the rate of ion formation and the final ionic concentration were considerably lower than those obtained for a ‘dry’ run (compare SGU9 and SGU20, Table 5). These results indicate that, at the end of the polymerisation when free acid is regenerated (see below), the water which was present in solution and which did not affect the actual polymerisation, reacts with an equivalent amount of perchloric acid to form H3O+ClO4which is too weak to cause ionisation. If [H2O] < [HClO4]0, the rate of formation of SD ions and their maximum concentration, both of which depend on [HClO4], are reduced because the active acid concentration is only [HClO4]0– [H2O]. Our evidence concerning the effect of water on carbonium ions shows convincingly that, since the rate of polymerisation is not affected by relatively large quantities of water [22], it is most improbable that carbonium ions present during the polymerisation, at concentrations too low to be detected by our spectroscopic technique, could be responsible for the propagation. If that had been so, no polymerisation would have been obtained with [H2O] > [HClO4].

Table 5 The influence of water upon the spectroscopic behaviour of the system HClO4-styrene-CH2Cl2 [St]0 (102 M)

[HClO4]0 (104 M)

[H2O] (104 M)

t′′ (s)

Rm (105 M-1 min-1)*

[SD ions]m (105 M)*

SGU8

7.1

6.3

-

475

0.725

5.96

SGUI7

7.5

6.3

32.0

-

none

none

SGU9

18.0

18.0

-

180

11.09

37.6

SGU20

20.0

17.0

7.4

240

7.17

29.5

Experiment no.

* See the footnote to Table 1

646

Cationic and Pseudocationic Polymerisation of Aromatic Olefins... 9 The reactions in 1,2-dichloroethane Five reactions in 1,2-dichloroethane were performed to discover whether the interaction of styrene with perchloric acid in this solvent, used by Pepper and Reilly, [22] produced a pattern of behaviour similar to that encountered with methylene dichloride. A latency period was noticed in all the reactions, but it was always shorter than the corresponding one in methylene dichloride. The absorption peak growing at the end of this period was centred around 395 mμ; the maximum D395 was always lower than the corresponding D424 in methylene dichloride. The third phase in the reaction produced a broad peak at about 450 mμ, which slowly grew while the 395 mμ peak correspondingly declined. Several hours after the mixing, the usual pair of peaks at 390 m and 410 mμ had formed, while the peak around 450 mμ was still present. Ethanol discharged the latter peak but not the former ones. The fact that the latency times were shorter than in methylene dichloride is readily explained because the polymerisation in 1,2-dichloroethane is faster, for the same working conditions [22]. The only substantial differences between the behaviour in the two solvents is the absence of the SD ions in runs conducted in 1,2-dichloroethane; we were never able to detect a peak at 424 mμ in these spectra. The nature of the ions, produced at the end of the polymerisations and absorbing at 395 mμ, is still obscure. The rate of formation of ions after the polymerisation in 1,2-dichloroethane was very similar to that obtained for the equivalent experiments in methylene dichloride. On the basis of these findings and of those reported by Pepper and Reilly, we conclude that the polymerisation of styrene, catalysed by perchloric acid in 1,2-dichloroethane, is very similar to the reaction in methylene dichloride, but the reactions following polymerisation are different. 10 Attempts to isolate 1-phenylethylperchlorate The reactions to be described were carried out in an all-glass high vacuum device consisting of a reaction tube connected through a sintered-glass filter plate to the tipping device described [9]. When a phial of 1-phenylethyl bromide was crushed in a silver perchlorate suspension in methylene dichloride, reaction started immediately; the suspension turned orange-yellow and its colour deepened considerably within a few minutes while silver bromide was precipitated. After about 1 h, the mixture was filtered off into the tipping device and phials of the reaction product were sealed off. The visible spectrum of the solution had a major peak at ~470 mμ. Analysis of the organic part of the reaction product showed it to consist mainly of oligostyrenes with absorption at 390 and 410 mμ. Addition of a large excess of styrene to a solution of the reaction product made the colour disappear and the solution became hot. After about 2 minutes the colour began to reappear:

647

Developments in the Theory of Cationoid Polymerisations the spectrum showed a peak at 424 mμ, which in a few minutes was shifted to a broad peak centred at about 475 mμ. The final value of D475 was higher than that obtained from the original solution. The polymer obtained from this run had DP = 6. The situation can be summarised as follows: (a) The reaction of silver perchlorate with 1-phenylethyl bromide gives SD ions at first which, with their anions, form perchloric acid and styrene which is then polymerised. The ultimate result of this series of reactions closely resembles the state of affairs at the end of a styrene polymerisation catalysed by perchloric acid: a twin peak in the near visible portion of the spectrum and the broad peak at about 470 mμ. (b) Addition of styrene to the ionic solution obtained from the reaction suppresses the ions whilst the added monomer polymerises in the same way as when a second addition of styrene is made to a polymerised, coloured solution after a ‘normal’ polymerisation experiment. The colour re-emerges at the end of the polymerisation and its final intensity is, as in the ‘normal’ spectroscopic experiments (Table 3), higher than it was before the styrene addition.

Quantitative results and discussion The following discussion is based on our earlier conclusion that the propagating species in these polymerisations is oligostyryl perchlorate ester, which is stabilised in solution by excess styrene. One question arising concerns the number of molecules of styrene per ester molecule required for this stabilisation; another concerns the kinetics and mechanism of the ionogenic reactions which ensue once the styrene concentration has been reduced by polymerisation to such a low level that the quantity of styrene no longer suffices to stabilise the ester.

The number of styrene molecules required to stabilise the ester Three series of experiments were carried out; one involved constant [HClO4]0 and variable [St]o (Table 1), and two involved fixed [St]o and variable [HClO4]0 (Table 2). The values of t′ for both conductivity and spectroscopic experiments are given in Tables 1 and 2; the agreement between them was always very close. Since we know the kinetics of the polymerisation under the present conditions [1], we can relate the latency period to the extent to which the polymerisation had proceeded during that time. The disappearance of styrene follows the rate equation:

– d[St ]/ dt = kp [St ][HClO 4 ]o It follows that

log[St ]0 – log[St ]t = kp [HClO 4 ]0 t / 2 ⋅ 3

648

(1)

Cationic and Pseudocationic Polymerisation of Aromatic Olefins... If one assumes that at the end of the latency period, i.e., at t = t′, the number of styrene molecules remaining is a multiple n of the number of chain carriers which is in turn equal to the number of acid molecules introduced [1], i.e., that [St]t’ = n [HClO4]0, Equation 1 takes the form:

log[St ]0 – log n – log[HClO 4 ]0 = kp [HClO 4 ]0 t ′ / 2 ⋅ 3

(2)

Equation 2 can be used in two ways to obtain values of n. For runs at constant [St]o, a plot of log [HClO4]0 against [HClO4]0t′ should give a straight line with slope –kp/2.3 and intercept log [St]o – log n. For runs at constant [HClO4]0, a plot of log [St]o against t′ should again give a straight line with slope kp [HClO4]0/2.3 and intercept log [St]t’ = log [HClO4]0 + log n. Straight lines were in fact obtained (Figure 4) from the slopes of which we computed values of kp (11.8 and 11.7 l mole-1 s-1, respectively). These agree with the value of 11.7 obtained from the kinetic results [1] for 22 °C and thus confirm the validity of the procedure. The values of n obtained from the intercepts are 4.2 and 4.0, respectively. Our results thus show that at least four molecules of styrene are needed for the stabilisation of one molecule of ester.

Figure 4 Determination of the quantity of styrene remaining at the end of the latency period t′ by means of Equation 2. o-Spectroscopic experiments. •-Conductimetric experiments

649

Developments in the Theory of Cationoid Polymerisations

Figure 5 Polymerisation curve for a reaction carried out in the calorimeter (see Ref. [1], Experiment SGP 14). T0 = - 19 °C, [St]0 = 0.264, [HClO4]0 =7.3 x 10-3 M. When the colour appears and the rapid reaction sets in, [St] =~ 2.7 x 10-2 M Another, necessarily much less precise, method for determining n is available from the kinetic experiments [1]. At the end of these reactions, at the precise instant at which the reaction mixtures turned yellow, a very fast reaction took place (Figure 5). This represents the polymerisation of the residual styrene by a true cationic reaction caused by the ions formed from the ester at the point where the styrene concentration was reduced to a level no longer sufficient to stabilise the ester. From the very small temperature rise during this final fast reaction, the number of styrene molecules polymerised could be calculated; it was always about four times the initial concentration of perchloric acid. This phenomenon was particularly evident in the reactions carried out at –19 °C in which relatively high acid concentrations were used so as to obtain reasonably fast polymerisations [1]. Our interpretation of these phenomena is as follows: the ester styryl perchlorate is not stable alone in solution, but this ester and its oligomeric homologues do exist in the presence of excess styrene, consequently the styrene must stabilise the ester. Presumably it does this by being co-ordinated (probably to the oxygen atoms) and thus reduces the polarity of the ester carbon-oxygen bond. It is not known yet whether any other compounds can exert the same effect.

The ionogenic reaction The ionogenic reaction which sets in abruptly at t = t′ (see Section 1 above) was followed spectroscopically by scanning at 424 mμ against time and by following the change of

650

Cationic and Pseudocationic Polymerisation of Aromatic Olefins... conductivity. The results from both methods were always in complete agreement. The kinetic information thus obtained cannot yet be interpreted in detail. One consistent feature was that the maximum rate (at tm, the end of the acceleration) was proportional to [HClO4]2 (Figure 6) and most of the reaction curve thereafter obeyed second order kinetics (equal initial concentrations, with respect to the final concentration of ions) (Figure 7). This means that the ions are formed by some species reacting with its own kind; in view of the fact that at t = t′ the nominal, (i.e., initial), concentration of acid, [HClO4]0, is in fact the concentration of ester, it means that the ions are formed by reaction of two ester molecules. If, for simplicity, we show only the principal component of the SD ion mixture (the 1-aralkyl-3-phenylindanyl cation) the stoichiometry of the reaction is this:

where R= oligostyryl.

Figure 6 The dependence of the maximum rate of ion formation, Rm, on the initial acid concentration (Table 2). Spectroscopic experiments: o-scales A and D, •-scales B and E. Conductimetric experiments: ❑ -scales C and F

651

Developments in the Theory of Cationoid Polymerisations

Figure 7 Kinetic analysis of a typical ionogenic reaction (Experiment SGC 9) by means of first and second order plots. p is the ratio [SD ions]t/[SD ions]m. The change of order occurs at about 300 s when p = ~ 70%. The mechanism of the reaction is still obscure but our results are probably compatible with those of Pepper and Barton [23] who found that the rate of disappearance of unsaturation, when 1,3-diphenyl butene-1 (distyrene) reacted with perchloric acid, was of second order in olefin and in acid. Unfortunately they did not investigate whether any saturated products other than the cyclised dimer were formed, although they found some higher oligomers. The final part of the ionogenic reaction is of first order with respect to the ionogenic species (Figure 7) and the rate constant k1 is proportional to [HClO4]0 (Figure 8). This may indicate that when the concentration of ester becomes small, and that of free acid large, the dominant ionogenic reaction is the acid-catalysed ionisation of the ester. When the conductivity and optical density had attained their maximum values, the spectra showed that double bonds were still present. The acid released by the decomposition of the ester catalyses the subsequent slow cyclisation whereby these terminal double bonds form indanyl end groups [23]. The situation at the end of the ionogenic reaction (maximum conductivity and D424) is complicated, in that the reaction mixture then contains ester, saturated and unsaturated

652

Cationic and Pseudocationic Polymerisation of Aromatic Olefins...

Figure 8 The dependence of k1on the initial acid concentration. k1 = 2.303S1 where S1, is the slope of the plot for the first-order part of the ionogenic reaction (Figure 7). o-Spectroscopic experiments. • - Conductimetric experiments. oligomers, and SD and allylic ions. That all these are in a quasi-equilibrium (which is slowly shifted by the progressive cyclisation and formation of multiple unsaturation) is shown by the following observations: i) The concentration of SD ions is always much lower than the initial concentration of acid. ii) The conductivity increases considerably when the temperature is reduced from 23 °C to 0 °C, and returns to its initial value when the system regains the original temperature (Tables 1 and 2). iii) When the concentration of double bonds is increased by addition of more monomer the ions disappear completely. The scheme shown in Figure 9 indicates the reactions involved. The scheme expresses most of what is known about the system; some parts of it are less certain than others and it may need some detailed modification in the light of further work, but it is a useful model whereby this system can be understood.

653

Developments in the Theory of Cationoid Polymerisations The species IA, IB, IC represent the chain-propagating ester molecules, stabilised by styrene, and they are equivalent from the point of view of the polymerisation. At the end of the polymerisation, the now unstabilised ester II reacts with its own kind to give the indanyl ion III and a saturated linear polymer IV. It is also in equilibrium with unsaturated polymer V, and it reacts with acid and/or V to give the polymer with indanyl end groups VI. This is equivalent to the transfer reaction with monomer which gives the indanyl end groups [23]. The oligostyryl ion VII can only be present in very small concentration, as it is much less stable than the other SD ions which co-exist with ion III [7]; these other SD ions have been omitted from the scheme so as not to complicate it unnecessarily. The equilibrium VI–VII requires some comment. We reported originally [16] that the indane dimer of styrene (VI, R = CH3) did not react with strong acids. Subsequent experiments [7, 24] have shown that it does react to give the ions III, VII, and others. (We have been unable to discover the reasons for our erroneous result.) In sulphuric acid the ion VII is formed as a minor constituent of the mixture of ions but we were unable to find it in experiments with perchloric acid in methylene dichloride [7]. None the less, it seems likely that minute amounts of it are formed at the end of the polymerisation when the perchloric acid is set free. The main reason for introducing the oligostyryl ion VII into the scheme is that we believe it to be responsible for the very fast polymerisation of the last styrene molecules (Figure 5) and also the fast, abnormal polymerisation, especially obvious at low temperatures, which occurs when a high local concentration of acid is introduced into a styrene solution. It seems reasonable, therefore, to suppose that these ions are also important in the ionogenic reactions following the normal polymerisation but they do not affect the endproducts directly. These consist essentially of polymer of types VI and VIII, whose formation is a slow draining of the system of equilibria. At the end of the polymerisation, when species IA has disappeared and ions are present, the addition of styrene makes the ions vanish instantaneously and they remain absent whilst polymerisation proceeds. Moreover, this polymerisation has the same rate constant as the first. This means that it cannot have been initiated only by the acid that was free at that time and that the acid bound as ions must also have become available. These facts are represented by the reaction paths leading to esters IB and IC, which complete the cycle whereby eventually ions are formed again, and can be destroyed again by addition of more monomer. Of course, reaction of the freshly added monomer with the then free acid leads to formation of ester IA. The maximum concentration of carbonium ions increases after each addition because of the increasing double bond concentration, as the polymer concentration increases. Thus the final value of the equivalent conductance and

654

Cationic and Pseudocationic Polymerisation of Aromatic Olefins... of D424 are higher after each addition, and they depend upon the actual concentrations of double bonds and of acid.

Figure 9 Comprehensive reaction scheme

655

Developments in the Theory of Cationoid Polymerisations The bathochromic shifts with increasing chain concentration are compatible with the mechanism proposed above, since an increase in the concentration of unsaturated chains will favour hydride abstraction and will therefore give allylic ions with higher degrees of conjugation, which will absorb at wavelengths greater than 450 mμ. The only serious chemical (as opposed to mechanistic) uncertainty in this scheme is whether route III→ IB or III → IC, or both, or perhaps some other process, adequately represent the removal of the ions by addition of monomer. Some reaction path of this kind seems to exist since there is no evidence that either route II → III or route II → VI is reversible.

Comparison with results of other workers Bywater and Worsfold [25] studied essentially the same system; where our results overlap, they agree. These authors established that during polymerisation there is no absorption down to about 305 mμ; this we have confirmed [26]. They also showed that during, but not after, the polymerisation, the acid cannot be distilled out of the reaction mixture. This supports our view of ester formation, and release of acid during the ionogenic reactions following the polymerisations. They also showed very clearly the rise and fall of the concentration of unsaturated endgroups during and after polymerisation. However, we cannot agree with their suggested reaction scheme. In particular, their penultimate equation in which a free proton appears to be released from an oligostyryl cation is implausible. It might be combined with their last equation, in which the free proton is shown reacting with perchlorate anion, but then the resulting reaction orders would be incompatible with observation. The central question at issue is still whether pseudocationic polymerisation, propagated by a large concentration of activated ester, is a real phenomenon sui generis or whether all these reactions can be explained in terms of very fast propagation by a very small concentration of conventional carbonium ions. The results of Enikolopyan and co-workers [27, 28] on the polymerisation of styrene by perchloric acid at high pressures shed some new light on the problem. Essentially their kinetic results agree with those of Pepper and Reilly and of ourselves. The important feature of their findings is that the extent of acceleration by pressure is merely that which can be attributed to increase of dielectric constant of the solvent. There was no effect which could be attributed to increasing abundance of free ions by increased dissociation of ion-pairs. This means that, if the propagating species are ions, then they are all free ions even at normal pressure (which is reasonable), or the propagating species is non-ionic.

656

Cationic and Pseudocationic Polymerisation of Aromatic Olefins... Bywater and Worsfold’s [25] and our own [26] results show that for the SD ions the optical density and conductivity are linearly related (methylene dichloride solution, concentration 10-5–10-3 M) showing that under these conditions ion-pairing is unimportant. It follows, a fortiori, that if the pseudocationic polymerisations were indeed propagated by ions at concentration less than 10-6 M these would be entirely free ions. Therefore any alleged explanation of these reactions which involves ion-pairs is now ruled out. We emphasise that the strongest single argument against the view that the pseudocationic reactions are propagated by ions is the nil-effect of water on the rate. The strongly inhibiting effect of water on radiation-induced true cationic polymerisations is too well known to require further elaboration here. Other arguments in favour of the reality of pseudocationic polymerisation, based on activation energies, co-polymerisation ratios, electric field effects, etc., have been given [6] and will be elaborated elsewhere. Higashimura, Kanoh, and Okamura [29] drew attention to the fact that we, like all previous authors, had misinterpreted the spectrum given by styrene in presence of acids; this matter, like some of the queries raised in their paper, has now been resolved. However, they are mistaken in their criticism of our pseudocationic theory on the grounds that we had misinterpreted the spectra. The two questions are in no way logically related. Similarly, the paper of Gantmakher and Medvedev [30] confuses the two issues and adds nothing which clarifies the position.

Conclusion Our studies have confirmed that the oligomerisation of styrene by perchloric acid is both chemically and kinetically simple. However, the reactions which follow completion of the polymerisation, and during which carbonium ions are formed and destroyed, are complicated. They can be rationalised in terms of equilibria involving ions, acid, double bonds, and esters; cyclisation of olefinic oligomers and formation of polyenes by way of allylic ions add further complications. We have thus shown in some detail just why such systems must be treated with the greatest circumspection if they are to yield valid information.

Acknowledgements We wish to thank the US Rubber Company for a studentship (to AG) and for other financial help, and the SRC for a grant for equipment.

657

Developments in the Theory of Cationoid Polymerisations

References 1.

A. Gandini and P. H. Plesch, J. Chem. Soc. 4826 (1965). (Part I).

2.

A. Gandini and P. H. Plesch, Proc. Chem. Soc. 240 (1964).

3.

A. Gandini and P. H. Plesch, J. Polym. Sci. Part B, Polym. Lett. 3, 127 (1965).

4.

A. Gandini and P. H. Plesch, SCI Monograph, No. 20, Chemistry of Polymerisation Processes, SCI, London (1966).

5.

P. H. Plesch, Pure Appl. Chem. 12, 117 (1966).

6.

P. H. Plesch, Polymer Preprints, ACS Meeting, September (1966).

7.

V. Bertoli and P. H. Plesch, Chem. Commun. 625 (1966).

8.

R. O. Colclough and F. S. Dainton, Trans. Faraday Soc. 54, 886 (1958).

9.

A. Gandini and P. H. Plesch, J. Chem. Soc. 6019 (1965).

10. W. R. Longworth, P. H. Plesch and M. Rigbi, J. Chem. Soc. 451 (1958). 11. R. H. Biddulph, P. H. Plesch and P. P. Rutherford, J. Chem. Soc. 275 (1965). 12. A. Gandini, P. Giusti, P. H. Plesch and P. H. Westermann, Chem. Ind., 1225 (1965). 13. R. H. Biddulph and P. H. Plesch, Chemy Ind. 1482 (1959). 14. BiPl valves, obtainable from Polymer Consultants Ltd., High Church St., New Basford, Nottingham, England. 15. J. R. Lind, J. J. Zwolenik and R. M. Fuoss, J. Am. Chem. Soc. 81, 1557 (1959). 16. A. Gandini and P. H. Plesch, J. Chem. Soc. 4765 (1965). 17. K. Hofner and H. Pelster, Angew. Chem. 73, 342 (1961). 18. C. M. Fontana and G. A. Kidder, J. Am. Chem. Soc. 70, 3745 (1948). 19. P. V. French, L. Roubinek and A. Wassermann, J. Chem. Soc. 1953 (1961). 20. C. Spach, M. Levi and M. Szwarc, J. Chem. Soc. 355 (1962).

658

Cationic and Pseudocationic Polymerisation of Aromatic Olefins... 21. T. Inoue and S. Mima, Chem. High Polym. 14, 402 (1957). 22. D. C. Pepper and P. J. Reilly, J. Polym. Sci. 58, 638 (1962). 23. J. M. Barton and D. C. Pepper, J. Chem. Soc. 1573 (1964). 24. S. Bywater, private communication. 25. S. Bywater and D. J. Worsfold, Can. J. Chem. 44, 1671 (1966). 26. V. Bertoli, Thesis, Keele (1967). 27. A. A. Zharov, A. A. Berlin and N. S. Enikolopyan, Int. Symp. Macromols., Prague, P 272 (1965). 28. A. A. Zharov, V. V. Tatarintsev and N. S. Enikolopyan, Vysokomolek. Soyedin., 7, 1863 (1965); Translated in Polym. Sci. USSR, 7, 2044 (1965). 29. T. Higashimura, N. Kanoh and S. Okamura, J. Macromol. Chem., 1, 109 (1966). 30. A. R. Gantmakher and S. S. Medvedev, Vysokomolek. Soyedin. 8, 955 (1966).

659

Developments in the Theory of Cationoid Polymerisations

660

6.7

Cationic and Pseudocationic Polymerisation of Aromatic Olefins - III [la, b]. A Re-investigation of the Polymerisation of Styrene by Perchloric Acid in Methylene Dichloride (1976) D. J. Dunn, E. Mathias and P. H. Plesch

This paper was first published in European Polymer Journal, 1976, 12, 1, 1-4. Reprinted with permission from Pergamon Press, copyright 1976.

Abstract A reinvestigation of the polymerisation of styrene by perchloric acid in methylene dichloride at 0 °C with improved techniques has shown that the polymerisations are not of first order throughout; after the first half-life, the reaction accelerates and the electrical conductivity of the reaction mixture increases concurrently. These phenomena are ascribed to the slow ionisation of the propagating polystyrylperchlorate ester to much more rapidly propagating polystyryl ions present in very low concentrations, and in equilibrium with a much larger concentration of non-propagating polystyrylindanyl ions. Our observations, together with those of other authors on the bimodal DP distribution of polystyrenes formed under similar conditions, confirm that the pseudocationic polymerisation propagated by the polystyryl perchlorate ester is indeed a distinct form of reaction.

Introduction There has been considerable argument over the mechanism of the polymerisation of styrene by perchloric acid in halogenated solvents in the temperature range ca. 30 °C to ca. –20 °C [1-11]. By spectroscopic and conductance measurements, Gandini and Plesch [1] could not detect any carbenium ions during the polymerisation; this and other evidence led them to conclude that the dominant propagating species is the ester, polystyryl perchlorate (I), which is stabilised by an excess of styrene.

661

Developments in the Theory of Cationoid Polymerisations

They envisaged the propagation as monomer insertion into the C–O bond of the ester via a four- or six-membered cyclic transition state (II).

The term ‘pseudocationic’ was used to describe this mode of propagation [1d]. The arguments for pseudocationic polymerisation have been set out in detail [1b, 12-14]. Most other contemporary authors have contended that the propagating species is some kind of ion-pair [2-4] or a π-complex [6, 10], although the electrochemical arguments against ion-pairs playing an important kinetic part were set out in some detail [15]. In the course of further studies of this problem, we have re-investigated this reaction in methylene dichloride at 0 °C using improved techniques. We found new phenomena reported here which shed fresh light on the mechanism.

Experimental Materials Styrene [16] and methylene dichloride [17, 18] were purified and dosed under high vacuum; solutions of perchloric acid in methylene dichloride were prepared by standard techniques [19]. The styrene and the solutions of perchloric acid in methylene dichloride were then transferred into phials with a tipping device [19, 20].

662

Cationic and Pseudocationic Polymerisation of Aromatic Olefins - III...

Polymerisation The kinetics were studied by adiabatic calorimetry [18] and high vacuum isothermal dilatometry [21, 22]. The calorimeter and the dilatometers were fitted with electrodes [21] for measuring the conductivity of the reaction mixtures.

Characterisation of products The reaction products were precipitated in methanol containing 0.880 ammonia. The precipitated polymer was filtered off and dried at 50 °C in a vacuum oven. Evaporation of the filtrate yielded the oligomers. For molecular weight determinations, the two fractions were dissolved together in CCl4. Molecular weights were determined with a vapourpressure osmometer.

Results A summary of the results (calorimetric and dilatometric) is given in Table 1. Figure 1 shows typical first-order plots (log m versus time) for the reaction at 0 °C. The plots are curved towards the time-axis, indicating an acceleration. This acceleration only becomes evident at, or sometime after, the first half-life. The first-order rate-constants k1 in Table 1 correspond to the slopes of the rectilinear portion of the first-order plots. The k1, is directly proportional to the initial concentration of the acid, as shown in Figure 2. The slope of this plot gives the second-order rate constant k2 in the rate expression:

– dm / dt = k1m = k2 [HClO 4 ]m

(1)

a least squares analysis gives k2= 2.76 dm3 mol-1 s-1 correlation coefficient = 0.984 (literature [1b]: 2.66 dm3 mol-1 s-1). The conductivity remained constant between about 15 s after the initiation and the end of the first half-life of the reactions and was approximately equal to the conductivity of the monomer solution alone (ca. 10-8 Ω-1 cm-1) and variable from one experiment to another; the reaction mixtures were completely colourless. At or shortly after the end of the first half-life, the conductivity began to increase slowly at first; when the reaction was almost complete, it rose quickly and then became constant. At this stage the solution was yellow.

663

Developments in the Theory of Cationoid Polymerisations

Table 1 The polymerisation of styrene by perchloric acid at 0 °C [Styrene] (mol dm-3)

104 [HClO4] (mol dm-3)

103k1 (s-1)

DP

12C

0.331

9.90

2.76

13. 8

2C

0.336

6.05

1.85

–

1C

0.335

5.15

1.67

–

27D

0.319

8.5 5

2.10

12. 3

24D

0.326

5.50

1.31

19. 0

23D

0.322

5.50

1.38

17. 7

21D

0.342

5.25

1.36

17.6

225D

0.332

4.1 9

1.27

20.6

221D

0.346

4.18

1.16

19. 9

222D

0.340

4.17

0.98

26. 7

223D

0.335

3.1 1

0.95

22. 8

224D

0.340

3.1 1

0.84

23. 1

217D

0.336

2.33

0.61

21. 5

216D

0.337

2.26

0.63

20. 2

229D

0.338

2.2 0

0.52

17. 0

230D

0.335

2.19

0.50

21. 8

215D

0.342

2.07

0.61

–

220D

0.343

1.88

0.44

32. 3

218D

0.354

1.3 1

0.32

20. 2

219D

0.337

1.13

0.25

17. 3

227D

0.345

0.79

0.14

20. 4

228D

0.348

0.78

0.14

24. 4

Experiment no.

k1 First-order rate-constant C Calorimetric experiments D Dilatometric experiments

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Cationic and Pseudocationic Polymerisation of Aromatic Olefins - III...

Figure 1 First-order plots of typical calorimetric and dilatometric experiments o - 2C , • - 217D

In the calorimetric studies, the kinetic acceleration only became apparent when the calorimeter was stabilised to a constant temperature, rather than to a constant pre-cooling rate as had been the practice in the earlier work; this improvement in technique had revealed the acceleration. However, the acceleration and the corresponding increase in conductivity were also observed in the isothermal dilatometric studies so that they cannot have been caused simply by the increase in temperature during the adiabatic reactions in the calorimeter. As is well-known [1a] with this system, the degree of polymerisation of the polymer increases slightly as the concentration of the initiator is lowered (Table 1).

665

Developments in the Theory of Cationoid Polymerisations

Figure 2 The dependence of k1 on the concentration of perchloric acid

Discussion The new features shown up by this study are the increase in rate and the concurrent increase in conductivity during the greater part of the polymerisations. We attribute the increase in conductivity during the polymerisation to the formation of at least two types of free ions, namely, the polystyryl ion and the polystyrylindanyl ion, the relation between which has been explained before [1b].

The ‘bistyryl’ ion, namely, the 1,3-diphenyl-n-butyl ion (IV) and its higher homologues have been identified by Bertoli and Plesch [23]. It is known [23] that ion (IV) can abstract

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Cationic and Pseudocationic Polymerisation of Aromatic Olefins - III... a hydride ion from 1,3-diphenylindane to give the 1,3-diphenylindanyl ion analagous to (III). During the polymerisation of styrene by perchloric acid ion (IV) and the corresponding polystyryl carbenium ions are probably formed by the dissociation of the growing ester, oligostyryl perchlorate. They in turn can either propagate or react with polystyrylindane(V) (which is formed slowly by transfer reactions [la, 24] to give the stable polystyrylindanyl ion (VI) analogous to (III).

Since the polystyryl carbenium ion has a very high propagation rate-constant, the slow formation of even very low concentrations of these is an adequate explanation of the acceleration; and since they are in equilibrium with a much larger concentration of the non-propagating indanyl ions (VI) the concurrent rise in conductivity follows as a corollary. From Figure 1 we can estimate the concentration of propagating ions, assuming simultaneous propagation by both ester and free ions. The rate equation takes the form:

– dm / dt = k2′[ E]m + k2′′[ Pn+ ]m

(2)

where [E] and [P+n] are the concentrations of ester and free ions, respectively. Hence ln m1 / m2 = (k2′ [E ] + k2′′ [Pn+ ])(t1 – t2 )

(3)

Towards the end of the polymerisations, the reactions tend towards first-order behaviour and thus we can make the reasonable assumption that [E] and [Pn+] are constant. With the further assumptions that [E] = [HClO4]0, k2′ = k2 and k2′′ =105 dm3 mol-1 s-1, [Pn+] can be calculated from the conversion curves in Figure 1 and is found to be of the order of 10-8 mol dm3 towards the end of the polymerisations. This concentration is too small to account for the rise in conductivity but, as mentioned above, this is due to the much larger concentration of indanyl ions with which the propagating ions are in equilibrium.

667

Developments in the Theory of Cationoid Polymerisations

Comparison with the results of other workers The principal difference between these and earlier results [1-4] lies in the acceleration and the conductivity rise. Despite this, the early, non-accelerated phase of our reactions can be seen to correspond to what was observed previously because of the near identity of the rate constants, namely, 2.76 (this work) and 2.66 dm3 mol-1 s-1 [1b]. We offer the following explanation for the acceleration. Since the ester is relatively insensitive to water (and probably other similar impurities [la, 2b, c]) but the propagating ions are excessively so [1b, 28] we think that in the earlier work the ions formed by the slow dissociation of the styrene-solvated ester were inactivated as quickly as they were formed; ions became evident as chain-carriers only when the depletion of monomer removed the stabilising coordinated monomer molecules from the ester and this then ionised very rapidly, producing the final very fast ‘reaction-kick’ observed by Gandini and Plesch [1]. The different behaviour reported here is ascribed to the much improved purity of monomer and especially solvent; consequently the ion-inactivating impurities become sufficiently depleted relatively early during the reaction so that the increasing number of surviving ions can manifest their presence kinetically. Higashimura and co-workers have studied the polymerisation of styrene in methylene dichloride initiated by acetyl perchlorate [25, 26] and by perchloric acid [26]; they found bimodal molecular weight distributions with both initiators. This important observation led Pepper [27] to carry out a systematic GPC study of the perchloric acid initiated polymerisation at 0 °C. Over a wide range of experimental conditions the distribution was bimodal, showing two clearly defined peaks, one near molecular weight 2 x 103, insensitive to conditions of preparation, and the other at varying molecular weight in the region 2 x 103 to 1.5 x 104. The high molecular weight peak is undoubtedly produced by an ionic propagating species, since its weight fraction is reduced in the presence of a perchlorate salt or water. These results indicate [26, 27] simultaneous propagation by two independent species (one of which is free ions) which are not in rapid equilibrium and this is exactly what one would expect on the basis of a slow dissociation of the perchlorate ester to give free ions. The second species is certainly the ester, because ion pairs or higher aggregates would be expected to be in rapid equilibrium with free ions, and their effect would be to produce a broadened unimodal molecular weight distribution. Indeed, Pepper [27] concludes that the low molecular weight fraction (which contains the vast majority of chains) is formed by propagation from an ester-monomer complex, in agreement with the original

668

Cationic and Pseudocationic Polymerisation of Aromatic Olefins - III... postulate of Gandini and Plesch [1], and thus the reactions can be called ‘essentially pseudo-ionic’ [27]. We conclude that the polymerisation of styrene by perchloric acid in methylene dichloride at 0 °C involves at least two types of independent propagating species. Rate studies and conductivity measurements, in conjunction with an independent study of molecular weight distributions [26, 27], indicate that these species include the perchlorate ester and the free polystyryl carbenium ion and that the term ‘pseudocationic’ is a very appropriate description of what is a distinctive form of organic reaction.

Acknowledgements We thank the Science Research Council for an equipment grant.

References 1.

A. Gandini and P. H. Plesch, (a) Part I, J. Chem. Soc. 4826 (1965); (b) Part II, Europ. Polym. J. 4. 55 (1968); (c) Proc. Chem. Soc. 240 (1964); (d) J. Polym. Sci. Polym. Lett. B3, 127 (1965).

2.

P. J. Reilly and D. C. Pepper, (a) Proc. Chem. Soc 200 (1961); (b) Proc. R. Soc. A, 291, 41 (1966); (c) J. Polym. Sci. 58, 639 (1962).

3.

L. E. Darcy, W. Millrine and D. C. Pepper, Chem. Commun. 1441 (1968).

4.

B. McCarthy, W. P. Millrine and D. C. Pepper, Chem. Commun. 1442 (1968).

5.

A. A. Zharov, V. V. Tatarintsev and N. S. Enikolopyan, Polym. Sci. USSR 7. 2044 (1965), Vysokomolek. Soedin. 7(11), 1863 (1965).

6.

S. Bywater and D. J. Worsfold, Can. J. Chem. 44, 1671 (1966).

7.

A. A. Zharov, A. A. Berlin and N. S. Enikolopyan, J. Polym. Sci. C16, 2313 (1967).

8.

F. S. D’yachkovskii, G. A. Kazaryan and N. S. Enikolopyan, Polym. Sci. USSR 11, 928 (1969).

9.

T. Higashimura, N. Kanoh and S. Okamura, J. Macromol. Sci. 1, 109 (1966).

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Developments in the Theory of Cationoid Polymerisations 10. S. D. Hamann, A. J. Murphy, D. H. Solomon and R. I. Willing, J. Macromol. Sci. - Chem. A6 (4), 771 (1972). 11. A. R. Gantmakher and S. S. Medvedev, Polym. Sci. USSR 8, 1052 (1966). 12. D. J. Dunn, M.Sc. Dissertation, University of Bradford (1970). 13. P. H. Plesch, Pure Appl. Chem. 12, 117 (1966). 14. A. Gandini and P. H. Plesch, SCI Monograph, No. 20, Chemistry of Polymerisation Processes, SCI, London (1966). 15. P. H. Plesch, Fortschr. Hochpolym. Forsch. 8, 137 (1971). 16. A. Gandini and P. H. Plesch, J. Chem. Soc. 4765 (1965). 17. W. R. Longworth, P. H. Plesch and M. Rigbi, J. Chem. Soc. 451 (1958). 18. R. H. Biddulph and P. H. Plesch, Chem. Ind. 1482 (1959). 19. P. H. Plesch and E. Mathias, Chem. Ind. 1043 (1971). 20. A. Gandini and P. H. Plesch, J. Chem. Soc. 6019 (1965). 21. A. Gandini, P. Giusti, P. H. Plesch and P. H. Westermann, Chem. Ind. 1225 (1965). 22. M. A. Hamid, M. Nowakowska and P. H. Plesch, Makromolek. Chem. 132, 1 (1970). 23. V. Bertoli and P. H. Plesch, (a) Chem. Commun. 265 (1966); (b) J. Chem. Soc. (B) 1500 (1968). 24. D. C. Pepper and P. J. Reilly, Proc. Chem. Soc. 460 (1961). 25. T. Masuda and T. Higashimura, J. Polym. Sci. Polym. Lett. B9, 783 (1971). 26. T. Higashimura and O. Kishiro, J. Polym. Sci. 12, 967 k 1974). 27. D. C. Pepper, Makromolek. Chem. 175, 1077 (1974). 28. K. Hayashi, K. Hayashi and S. Okamura, Polym. J. 4 (4), 426 (1973).

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6.8

Pseudo-Cationic Polymerisation After 24 Years (1988) P. H. Plesch

This paper was first published in Makromolekulare Chemie, Macromolecular Symposia, 1988, 13/14, 375-387. Reproduced with permission from Huthig & Wepf Verlag, Copyright 1988.

Abstract It is shown that the theory of pseudo-cationic polymerisation is now well established. This is because it can account for old and new observations, including the living polymerisations initiated by Giusti’s syncatalytic system (I2 + HI); and because attempts at disproving it have been unsuccessful. The theory’s essential part is that in certain cationoid polymerisations the propagating species is an ester (which may be stabilised or activated), and that the propagation step involves the insertion of the monomer into a polarised covalent bond. It is made clear that the pseudo-cationic theory is merely a generalisation of reaction mechanisms which are well known and uncontroversial in conventional organic chemistry. Ten experimental facts are analysed to show the relevance and plausibility of the pseudo-cationic theory. The two main versions of the ‘ions-at-any-price’ rival theories, namely the ‘large concentration of invisible ions’ view and the ‘minute concentration of conventional carbenium ions’ view are both shown to be incompatible with all the facts. It is emphasised that many industrial cationoid oligomerisations and polymerisations are pseudo-cationic.

1 Introduction It gives me great pleasure to report that the theory of pseudo-cationic polymerisation, which Professor Gandini and I developed from 1963 [1-10], is alive and well and living now in several text-books and reviews [11-13]. Many new pseudo-cationic systems have been identified, and several systems known for many years are now recognised as being (mainly) pseudo-cationic. The scope of the theory has thereby been extended considerably.

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Commercial rubbers

Developments in the Theory of Cationoid Polymerisations A most promising advance is that many of the living cationic systems are now seen clearly to belong to this category, which fact was first recognised by Pepper [14]. However, the Kyoto group, who claim to have first discovered the living cationic polymerisations, found it necessary to reinvent the pseudo-cationic theory, but gave it strange names. Whilst straining the bounds of chemical language to avoid using the word ‘ester’ [15] they proposed (recte revived) a mechanism for the polymerisations of alkenes by iodine + RI (R = H or alkyl) which involves the ‘insertion of the monomer into a C-I bond activated by iodine’ [16, 17]. This is completely identical with Giusti’s views (and indeed his description) of the mechanism [18] of what is now considered to be a typical pseudo-cationic polymerisation. When the Kyoto workers denied that activated esters could be active species, they ignored the fact that alkyl iodides are esters of HI. Their attitude was hardly helpful, because a well-developed science like chemistry generally progresses by discovering the unity of phenomena, not by maintaining unreal differences artificially and arbitrarily. Also notable for their strange beliefs are the members of a fraternity whose motto is ‘ions-at-any-price’, which we will analyse later. They are foremost amongst those who complain that the pseudo-cationic theory has not been ‘proved’ and they thus show themselves ignorant of an important principle in the philosophy of science. This is that no theory can ever be proved to be the true explanation of a set of observations. It is only possible to disprove a theory by showing it to be incompatible with certain facts [19]. This has not happened so far to the pseudo-cationic theory. Most allegations to this effect, mainly found in Higashimura’s papers, centre around the observation that some esters, by themselves, do not initiate polymerisation. However, this is not really relevant, because the pseudo-cationic theory merely says that the propagation occurs by the insertion of a monomer molecule into a covalent species, an ester, which may need to be stabilised or activated according to circumstances. It is true that one implication of the theory is that there may be a few special systems in which the ester alone can propagate (whatever ‘alone’ may mean in this context); but the discovery of such systems is in no way a critical test for the validity of the theory. We wish to emphasise that the formation of esters (E) from alkenes (M) and acids (HA), the catalysis of the reactions of E by HA or MtXn, and the activation of E, such as organic chlorides, by the co-ordination of a Lewis acid, such as AlCl3, are all very familiar chapters in conventional organic chemistry. It follows that the pseudo-cationic theory is nothing more than a generalisation of conventional organic-chemical ideas and a revival of some pre-Whitmore interpretations which had become occulted by the usefulness and novelty of the carbenium ion concept. From the fundamental reaction-mechanistic point of view, the essential difference between the cationic and the pseudo-cationic mechanisms is this: the attack of an ion on the double bond of an alkene to form a carbenium ion generally involves a 3-centred transition state in

672

Pseudo-Cationic Polymerisation After 24 Years (1988) which the ‘second half’ of the double bond is broken whilst a new covalent bond is made. In contrast to this, the mechanism of propagation by an ester involves a cyclic transition state in which the simultaneous making and breaking of more than two bonds is involved.

2 Some facts and explanations relating to the theory of pseudocationic polymerisation 2.1 Outline of the theory In many polymerisations of alkenes initiated by what are generally classed as ‘cationic’ + + initiators, i.e., acids HA, salts Q A , metal halides MtXn, metal salts Mt A , iodine I2, + and some others, the chain-carriers can be of at least three kinds: unpaired cations, R or + + + + Pn paired cations (R or Pn with A or MtX n+1) and esters PnA, where R is any kind of + organic cation and Pn is a cationated monomer or polymer. The esters E, which may need to be stabilised in order not to dissociate to ions too rapidly, (e.g., CH3CHPh+ OClO3), or to be activated by a Lewis acid, such as H , I2, AlCl3, are an important propagating species, and reactions propagated by them are known as pseudo-cationic. As prototype examples we may choose: +

-

i) Styrene and related monomers with HClO4, MeCO ClO4 or sulphonic acids in solvents of low or moderate dielectric constant ε [11]. ii) Isobutyl vinyl ether polymerised by CF3CO2H in (CH2Cl)2 [20] or by picric acid in CH2Cl2 [21]. iii) Many aliphatic and aromatic alkenes + I2 + HI in solvents of low or moderate ε [15, 16, 22, 23 and many intervening papers]. Few cationic polymerisations are monoeidic, i.e., carried by one kind of chain-carrier only and, contrary to earlier beliefs, the participation of paired cations is uncommon, + but dieidic polymerisations, in which E and Pn coexist, are very common. However, these two species are not in equilibrium but, on the contrary, the progressive formation + of Pn from E seems to be a frequent feature of such systems. Also, in many typical pseudo-cationic polymerisation systems the complete exhaustion of the monomer is followed by regeneration of the acid HA, which initiated the reaction; this also happens if the initiator was a salt or a mixed anhydride comprising the anionoid fragment A. In all cationoid systems the character of the polymerisations is determined by the extent to which the different kinds of chain-carriers participate; this can be illustrated with respect to the rate which, if the polymerisation is trieidic, is given by the equation

673

Developments in the Theory of Cationoid Polymerisations

– dm / dt = ( kp+ [ Pn+ ] + kp± [ Pn+ A −} + kpE [ E ])m where the symbols have their usual meaning [24]. The magnitude of the rate-constants and the relative magnitude of the concentration terms, which together determine the character of the reactions, depend upon the exact nature of the system: i) Nature of the monomer, e.g., the type of ring-substitution in styrene. ii) Nature and polarity (ε) of the solvent. iii) Purity. iv) Temperature. The factors (i) and (ii) are conventional and need no comment here. However, point (iii) is special to our systems, and (iv) also requires comment. To (iii): Since the esters are very insensitive to destruction by polar impurities, especially + water, but the Pn react with these very rapidly, it may happen that in an insufficiently + pure system the Pn generated by the slow decomposition of the ester are all consumed by the impurities and thus cannot contribute to the polymerisation, which is then carried entirely by the ester. (See 2.2.1). With regard to (iv), the whole pattern of the polymerisations initiated by HA changes drastically with temperature, a feature which has been explored and explained very lucidly by Pepper [14]. The end-product of the reactions is of course the polymer, and the greatest body of systematic studies of various influences on the products, as assessed by their DPD (and occasionally by other tests) was accumulated by Higashimura’s group; it is ironic that this great effort also generated (unintentionally) the most cogent evidence in favour of the pseudo-cationic theory [25, 26]. [The abbreviation DPD is used here in preference to the more usual MWD because it is more general].

2.2 Some facts and their explanations in terms of the pseudocationic theory

2.2.1 The polymerisation of styrene by HClO4 in CH2Cl2 at ambient temperature is internally of first order (rate-constant k1) if the system is ‘reasonably’ pure [3, 27], but shows marked acceleration if it is extremely pure (9).

674

Pseudo-Cationic Polymerisation After 24 Years (1988) In both types of experiment the reaction mixture is colourless but suddenly becomes yellow at the end of the reaction, at which point the electrical conductivity also increases markedly. If the [H2O] > [HClO4]0, the k1 is unaffected, but at the end there is no colour and no conductivity. In the dry systems the addition of M, when the first dose has been consumed, removes the colour and the conductivity and the ensuing polymerisation has the same k1. Explanation: The ester polystyryl perchlorate is stabilised by M, but it decomposes slowly + + to Pn . In the ‘moderately’ pure system the [Pn ] are consumed by impurities, mainly + water, and only when depletion of M leads to fast decomposition of E are enough Pn formed to give colour and conductivity. In the very pure system the scavenging of water, + etc., by the ions is completed before all the M has been consumed, so that the Pn formed thereafter contribute to the rate. At the end of a typical polymerisation of this type the + -7 -1 [Pn ] is ca. 10 mol l . If [H2O] > [HClO4]0, the k1 is unaffected because the rate of reaction of E with H2O in CH2Cl2 is much smaller than the rate of polymerisation, but + the Pn and/or the HClO4 are hydrated so that no colour or conductivity appears. The visible and conducting ions are not polystyryl carbenium ions, but a ‘cocktail’ of others in which the substituted indanyl ion is the most abundant [28]. Sigwalt [29] has attempted to show by a calculation that the insensitivity to water could be compatible with propagation by a minute concentration of ions. This calculation is based on three premises which are in direct conflict with well established experimental facts: (i) ‘...water does not seem to be consumed...’; there is much evidence to the contrary [30]. (ii) That the systems were in any case not really dry, which is contradicted by internal evidence, for example the ‘impurity intercept’ on a plot of k1 against [HClO4]0 which is much smaller than the [HClO4]0, used [9]. And (iii) that the hydrated acid can initiate; actually it is effectively insoluble in the usual solvents and has been shown repeatedly not to be an initiator.

2.2.2 In some pseudo-cationic systems, e.g., styrene + H2SO4, polymerisation ceases when the yield, Y, is less than 100%, but it can be restarted by the addition of a very small quantity of trichloroacetic acid [31]. Explanation: In this system the formation of the E, styryl hydrogen sulphate, is relatively slow. When eventually all the acid has been consumed in this way, none is left to activate the E, and therefore the polymerisation stops; but a low concentration of a much weaker acid, incapable of initiating polymerisation on its own, is sufficient to activate the ester of the stronger initiating acid.

675

Developments in the Theory of Cationoid Polymerisations

2.2.3 The character of a polymerisation initiated by HClO4 or AcClO4 can be changed from pseudo-cationic to cationic by the addition of AgSbF6 to the reaction mixture [32]. Explanation: The ester ends react with the salt and AgClO4 is precipitated, with the formation of a propagating carbenium salt of SbF6-, which cannot form an ester.

2.2.4 With the syncatalytic system HI + I2 and a wide variety of monomers, living polymerisations can be obtained, especially at low temperatures and in solvents of moderate or low polarity, including toluene [22, 23 and earlier papers]. Explanation: The increase of both Y and DP with time implies a growing species of long life, which is characteristic of esters but not of carbenium ions, and an absence of transfer reactions. The suppression of all kinds of transfer reactions seems to require some very special features in the anionoid moiety of the ester which are not yet understood fully but which, by hypothesis, cannot affect the reaction pattern of an isolated, unpaired cation. The fact that living polymerisations can occur in toluene is a convincing demonstration that these reactions cannot involve carbenium ions, because growing cations alkylate toluene [33-37], a process which produces low DPs, independent of Y.

2.2.5 The rate-constants, kp, calculated for polymerisations by H2SO4 and HClO4 from R = kpmc0, (with c0 = [initiator], m = [monomer], R = rate) are very similar, but much smaller than the kp+ for polymerisations by radiation or some metal halides; hence kp = R/m[HA]0 is actually the kpE [3, 9, 27, 38].

2.2.6 The activation energy, Ep, for polymerisations by HA (40–100 kJ/mol) is too great for an E + (R + M) reaction, but appropriate for an (E + M) reaction, and is therefore Ep [39, 40].

2.2.7 The effect of the dielectric constant of the solvent, ε: For pseudo-cationic polymerisations dE/ -1 + dε is positive, as is expected for an (E + M) reaction, but not for an (R + M) reaction [40].

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Pseudo-Cationic Polymerisation After 24 Years (1988)

2.2.8 The copolymerisation ratios for styrene and 4-chlorostyrene by HClO4 [41], H2SO4 [38], or I2 [42] all give r1r2 ≈ 1. This indicates that the sequence of reactivities of the propagating ends is the same as that of the corresponding monomers. All the authors concerned point out that this is the opposite of what one would expect for the attack of an ion on a molecule, and one can conclude therefore that the active species is not ionic. Some preliminary results [43] obtained with EtAlCl2, which gives cationic polymerisations, have given r1 and r2 both < 1, and this is what one expects for propagation by ions, the ranking of whose reactivities must be the reverse of that of their parent monomers.

2.2.9 Under ‘intermediate’, i.e., not extreme, conditions of monomer reactivity and solvent polarity the polymers formed from styrenes and some other monomers by HA have a bimodal DPD. A change to a less reactive M or to a solvent of lower polarity leads to an increase in the fraction of the product of lower DP, and vice versa [44]. Explanation: During the polymerisation two types of growing chain-ends coexisted, which are not rapidly interconvertible. These are the ester and the carbenium ion. The E forms the low polymer, the carbenium ions the high polymer.

2.2.10 If the ε of a two-component solvent mixture is increased progressively, the character of the polystyrenes formed in it by various HA changes abruptly near ε, ca. 6, from a polymer of low DP with a monomodal DPD to one with a bimodal DPD containing an appreciable fraction of high polymer [45]. Explanation: The abruptness of the change is most likely due to the concurrence of two related effects: The increase in ε, achieved by raising the ratio [(CH2Cl)2]/[C6H6], (a) accelerates the formation of ions from the ester, and (b) increases the effective size of the ions, by their selective solvation by the more polar component. The effect of (a) is that the solution is cleaned up more rapidly by the ions scavenging the chain-breaking impurities, which leads to the formation of more and longer chains by the ionic mechanism. The effect of (b) is to reduce the rate of chain-breaking by the reaction of the propagating cations with the anions. The abruptness of the increase of DP over a narrow range of ε also makes it very unlikely that the species producing the high polymer in solvent mixtures of ε > 6 played any part in the formation of the low polymer in solvent mixtures of ε < 6. This matter has been discussed penetratingly in Reference [11].

677

Developments in the Theory of Cationoid Polymerisations Some authors have claimed that a bimodal DPD could be explained by a dieidic polymerisation involving unpaired cations and ion-pairs whose life-time is of the same order as that of the growing ‘low DP’ chains. Apart from the intrinsic improbability of such a model from a physico-chemical standpoint, the proponents of this view have not explained why the very common dieidic anionic polymerisations have not yielded polymers with bimodal DPDs. The second paragraph of Section 2.3.1 applies with equal force in the present context.

2.3 The ‘ions-at-any-price’ theories Those who wish to preserve at all costs the ionic interpretation of the reactions which we have been discussing, mostly take one of two distinct views:

2.3.1 One opinion is that the polymerisations are propagated by carbenium ions which are paired, but in some special way in which they do not have the normal absorption spectrum of such ions and are therefore ‘invisible’; their concentration is supposed to be of the same order of magnitude as, or equal to, that of the initiator. It cannot be emphasised too strongly that this entirely new hypothetical species lacks the essential feature of a scientific theory, namely that the newly invented species should have well-defined properties so that its existence can be tested by experiment; moreover, it offends against Occam’s Razor (‘hypotheses must not be multiplied unnecessarily’). In fact, the only species known to chemistry (apart from acid and alkene) which can be formed from anionoid and cationoid fragments of the type which are of interest here are (i) radicals (which are ruled out because of the low temperatures involved), and (ii) the ester, which is the essential part of the pseudo-cationic theory. The ideas criticised here were expressed in a great variety of ways over the last 20 years, mainly by Higashimura’s group, but on at least two occasions they admitted the possible validity of the pseudo-cationic view [46, 47].

2.3.2 The second version of ‘ions-at-any-price’ is that the active species are the normal carbenium ions, but that they are present in very low concentrations and are in equilibrium with the ester which is regarded as inactive and inactivatable [29, 48].

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Pseudo-Cationic Polymerisation After 24 Years (1988) Most of the facts in Sections 2.2.1 to 2.2.10 are actually sufficient to dispose of this view and, taken together, they form an array of concordant and compatible observations which are all incompatible with it. In addition, it must be noted that amongst reagents of the type which interest us here, equilibria between ions and esters are unknown, and that attempts to prepare some of the active esters, e.g., styryl triflate, in the absence of a stabilising agent, always produce intractable mixtures [49]. The ‘minute concentration of ions’ has gained some credence amongst those who are unaware of all the facts to be explained; a contributory source of confusion is that unfortunately many chemists have not been taught to distinguish between a reaction intermediate of finite lifetime, in principle detectable, and a transition state with a lifetime -13 of one molecular vibration, i.e., 10 s.

3 Conclusions The demonstration that neither of the ‘ions-at-any-price’ views, the main rivals of the pseudo-cationic theory, is compatible with the facts does not, of course, prove the ester theory. As I pointed out in my introduction, it is not possible to prove any scientific theory. What has been demonstrated, however, is that the ester theory will account for most of the established facts; it has the advantage of being based in conventional organic chemistry, and it provides interesting guide-lines for future research and innovation. This line of thought prompts me to point out that the economically important aspect, the ‘industrial dimension’, of cationic polymerisation has actually been mainly concerned with pseudo-cationic oligomerisations and polymerisations. Here we must include the enormous tonnages of high-octane fuels made over catalysts derived from phosphoric acids, the coumarone-indene and terpene resins made with sulphuric acid, and many related products. We must also include the synthetically so very useful dimerisations of aromatic alkenes by protonic acids, which have been known for a very long time. In more recent times, Higashimura’s group have worked also in this field [15, 50, 51], as have others, but the most interesting example of a pseudo-cationic oligomerisation in optima forma is that catalysed by diphenylphosphoric acid which is a catalyst in the true sense, being continuously regenerated [52]. The exploration of the mechanistic details [22] and synthetic potential [23] of living polymerisations proceeding by the Giusti insertion mechanism also promises to have important economic consequences. These are areas in which much more fundamental work needs to be done, and it promises to be rewarding. It is quite clear, to me at least, that whilst we now have a useful theoretical basis for approaching cationoid polymerisations, we certainly do not yet understand all the strange phenomena occurring in such reactions; moreover there is great scope for theoretical and experimental

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Developments in the Theory of Cationoid Polymerisations innovation. Our subject has entered a very exciting phase, and so I look forward with pleasure to hearing the relevant progress report in another 24 years - in 2012.

4 Acknowledgements My thanks are due to the Leverhulme Trust for funds which helped me in the production of this paper and to Professor A. Gandini for some very useful discussions.

References 1.

A. Gandini and P. H. Plesch, Proc. Chem. Soc., 240 (1964).

2.

A. Gandini and P. H. Plesch, J. Polym. Sci., B, 127 (1965).

3.

A. Gandini and P. H. Plesch, J. Chem. Soc., 4826 (1965).

4.

A. Gandini and P. H. Plesch, ‘The Chemistry of Polymerisation Processes’, Society of the Chemical Industry Monograph No. 20, London (1966).

5.

P. H. Plesch, Pure and Applied Chem., 12, 117 (1966).

6.

A. Gandini and P. H. Plesch, Europ. Polym. J., 4, 55 (1968).

7.

P. H. Plesch, Adv. Polym. Soc., 8, 137 (1971).

8.

P. H. Plesch, Brit. Polym. J., 5, 1 (1973).

9.

D. J. Dunn, E. Mathias and P. H. Plesch, Europ. Polym. J., 12, 1 (1976).

10. W. Obrecht and P. H. Plesch, Makromol. Chem., 182, 1459 (1981). 11. A. Gandini and H. Cheradame, Adv. Polym. Sci., 34/35 (1980). 12. A. Gandini, Rolduc Conference (1987). 13. D. J. Dunn in Developments in Polymerisation - 1, Ed., R. N. Haward, Applied Science Publishers Ltd., Barking, UK, (1979) p. 45. 14. D. C. Pepper, Makromol. Chem., 175, 1099 (1974). 15. T. Higashimura and M. Sawamoto, Adv. Polym. Sci., 62, 49 (1984). 16. T. Higashimura, M. Miyamoto and M. Sawamoto, Macromolecules, 18, 611 (1985).

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Pseudo-Cationic Polymerisation After 24 Years (1988) 17. T. Higashimura and M. Sawamoto, Makromol. Chem. Suppl., 12, 153 (1984). 18. P. Giusti and F. Andruzzi, La Chimica e l’Industria (Milano) 48, 442 (1966) see especially the Conclusions. 19. K. R. Popper, The Logic of Scientific Discovery, Hutchinson, London (1972). 20. F. Bolza and F. E. Treloar, Makromol. Chem., 181, 839 (1980). 21. G. Heublein and S. Spange, Makromol. Chem. Macromol. Symp., 3, 65 (1986). 22. M. Sawamoto and T. Higashimura, Makromol. Chem. Macromol. Symp., 3, 83 (1986). 23. T. Higashimura, S. Aoshima and M. Sawamoto, Makromol. Chem., 386, Macromol. Symp., 3, 99 (1986). 24. P. H. Plesch in Cationic Polymerisation and Related Processes, Ed., E. J. Goethals, Academic Press (1984), p.1. 25. M. Sawamoto, T. Masuda and T. Higashimura, Makromol. Chem., 178, 1497 (1977) and the four preceding papers of the series. 26. T. Higashimura and T. Masuda, Polymer J., 5, 278 (1973); T. Higashimura and O. Kishiro, J. Polym. Sci. Polym. Chem. Ed., 12, 967 (1974) and very many subsequent papers. 27. P. J. Reilly and D. C. Pepper, Proc. Roy. Soc. Ser. A, 291, 41 (1966). 28. P. H. Plesch and V. Bertoli, J. Chem. Soc., (B), 1500 (1968); Spectrochimica Acta, 25A, 447 (1969). 29. P. Sigwalt, Polymer J., 17, 57 (1985). 30. There is a vast amount of evidence from radiation and polymer work that carbenium ions react irreversibly with water. 31. C. Peniche and A. Gandini, Rev. CENIC (Cuba) 4, 59 (1973), C. A., 84, 5472 (1976). Quoted in Ref. 11. 32. O. F. Olaj, H. Rhemann and J. W. Breitenbach, Monatshefte f. Chemie, 110, 1029 (1979). 33. D. S. Brackman and P. H. Plesch, J. Chem. Soc., 1289 (1952). 34. D. S. Brackman and P. H. Plesch, Chem. and Ind., (London), 255 (1955).

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Developments in the Theory of Cationoid Polymerisations 35. P. H. Plesch, J. Chem. Soc., 1659 (1953). 36. K. Ikeda, T. Higashimura and S. Okamura, Kobunshi Kagaku, 26, 369 (1969). 37. K. Hatada, T. Kitayama and H. Yuki, Polymer Bulletin, 2, 15 (1980). 38. K. Ikeda, T. Higashimura and S. Okamura, Kobunshi Kagaku, 26, 364 (1969). 39. M. J. Hayes and D. C. Pepper, Proc. Roy. Soc., A263, 63 (1961). 40. D. C. Pepper and P. J. Reilly, J. Polym. Sci., 58, 639 (1962). 41. G. R. Brown and D. C. Pepper, Polymer, 6, 497 (1965). 42. N. Kanoh, A. Gotoh., T. Higashimura and S. Okamura, Makromol. Chem., 63, 106 (1963). 43. P. H. Plesch, unpublished. 44. T. Higashimura, J. Polym. Sci., Polymer Symposia, 56, 71 (1976). 45. M. Sawamoto, T. Masuda and T. Higashimura, J. Polym. Sci., Polym. Chem. Ed., 16, 2675 (1978). 46. T. Higashimura, O. Kishiru and T. Takeda, J. Polym. Sci., Polym. Chem. Ed., 14, 1089 (1976). 47. M. Sawamoto, T. Masuda and T. Higashimura, Makromol. Chem., 177, 2995 (1976). 48. K. Matyjaszewski, private communication, to be published. 49. K. Matyjaszewski and P. Sigwalt, Makromol. Chem., 187, 2299 (1986), and earlier similar attempts by others. 50. M. Hiza, H. Hasegawa and T. Higashimura, 6th International Symposium on Cationic Polymerisation, Kyoto (1980). Preprint 17A07, p.98. 51. H. Hasegawa and T Higashimura, 6th International Symposium on Cationic Polymerisation, Kyoto (1980). Preprint 17A08, p.100. 52. N. Yamazaki, S. Nakahama, K. Yamaguchi and H. Kasai, 6th International Symposium on Cationic Polymerisation, Kyoto (1980). Preprint 17A06, p.96.

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Reply by P. H. Plesch to K. Matyjasewski’s Comments on ‘Pseudocationic Polymerisation after 24 years’. This response was first published in Makromolekulare Chemie, Macromolecular Symposia, 1988, 13/14, 393-395. Reproduced with permission from Huthig & Wepf Verlag, Copyright 1988. The Commentator’s arguments can be answered summarily by scrutinising their basis, which is, in his own words, ‘minute amounts of reactive carbenium ions being in equilibrium with covalent esters’. The Commentator has produced no evidence of any kind for the existence of an equilibrium between ions and esters in the systems of interest here. Thus all his subsequent arguments are based on an hypothesis which is unsupported by any evidence, but which is in clear and direct conflict with experimental evidence obtained by several investigators (including himself). Many attempts have been made to prepare model esters, such as styryl perchlorate or triflate. In all systems which have been studied in sufficient detail to reveal the presence of small concentrations of ions, i.e., by spectroscopy and/or conductimetry, the formation of ions is progressive without any sign of reaching an equilibrium and is usually accompanied by chaotic reactions yielding a mixture of products. Under polymerisation conditions, when the monomer is exhausted, the active end, regarded by this author as the ester, decomposes progressively to alkene and acid, and the acid ionises, so that there is a steady formation of ions with no sign of an equilibrium. In his comments on Section 2.3.2, the Commentator writes: ‘…the equilibria between ions and esters are well known…’, but the reference [10] which he cites is almost entirely concerned with the ionisation of trityl compounds in highly polar media and is thus no help whatever. The Commentator refers repeatedly to the pseudocationic theory as being ‘new’ and thus ignores this author’s explicit contention that it is merely the extension of a wellknown organic reaction mechanism into a new field. A further weakness of the Commentator’s protestations is that he is attempting to apply conclusions drawn from one system, e.g., trifluoracetic acid, to others involving other acids and even metal halides. It cannot be emphasised too strongly that because of the steep gradations in the reactivities of both the different cations and the different anions and their corresponding acids, it is most unwise to generalise. Further the Commentator ignores this author’s view that pure pseudocationic polymerisations are comparatively rare, that a polymerisation may start by being purely pseudocationic and later in the life of the reaction, when impurities have been consumed, become dieidic with a cationic

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Developments in the Theory of Cationoid Polymerisations component whose extent of participation in monomer consumption increases with time. Because of the involvement of impurities, this phenomenon will be of differing importance in different laboratories. It would be both unnecessary and tedious to take issue with each of the arguments advanced against the ‘ten points’ of the original paper, but a few obvious weaknesses need to be pointed out. In support of his arguments relating to the points 2.2.4 and 2.2.9 the Commentator cites information produced by Professor Lenz during this Symposium. Since the methods used to obtain that confusingly large mass of results were not presented in sufficient detail, their significance and their relevance, if any, of the points under discussion cannot be assessed at present, at any rate by this author. But the citations seem to be further examples of the Commentator’s tendency to confuse different types of systems. To the first sentence of the comment on 2.2.9 the reply is ‘how does anyone know?’ because no conductivity measurements have been reported. To 2.2.6: the statement is true but it would only be relevant if the ΔH° of the ionisation of the esters were positive, which is unproven and seems unlikely. To 2.2.8: the Commentator’s second sentence is not true. In an aromatic system p-X-C6H4-CH=CH2, any changes in X which make the double bond more reactive than it is with X=H, will have the same effect on the reactivity of any derived covalent species, such as an ester, but it will have the opposite effect on the reactivity of the derived + carbenium ion p-X-C6H4-C HCH3. This is one of the most cogent arguments against the Commentator’s views. The Commentator’s much cited Reference [8] is indeed an interesting and valuable paper, but it contains numerous unsupported assumptions and highly speculative arguments, so that its evidential value is rather doubtful. This author is pleased to repeat that his views on the role of esters as propagating species in cationoid polymerisations are surely open to improvement and refinement, but that they are a more useful guide to the interpretation of phenomena and the planning of experiments, than the views of the Commentator. The criterion of a successful scientific theory is heuristic utility.

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6.9

Kinetics of Living Polymerisations (1988) P. H. Plesch

This paper was first published in Polymer Bulletin, 1988, 19, 2, 145-148. Reproduced with permission from Springer Verlag, copyright 1988.

Summary By means of a simple kinetic analysis of living polymerisations it is shown how both the concentration of growing ends and the rate-constant of propagation can be determined, provided that both the yield and the degree of polymerisation are given as functions of time.

Introduction Since Pepper (1974) first identified explicitly the polymerisation of styrene by perchloric acid in methylene dichloride at –73 °C and –45 °C as a living cationoid polymerisation, many more reports of such systems have appeared. Although of course the kinetics of living anionic polymerisations have been explored extensively since Szwarc first identified and named this category of reactions, it seems appropriate to put together the relevant equations in a manner which is new and more useful for cationoid (cationic and pseudocationic) polymerisations, although no novel principle is involved, see especially Boehm et al., (1972). The main reason for doing this is that in most earlier treatments the timeelement was rather neglected, and that most of the results of recent researches are presented in the form of the dependence of molecular weight on conversion or yield. This form of presentation eliminates the independent variable, time, and thus immediately curtails the scope and usefulness of the study. The reason can be made clear very easily: In the general rate-equation (1) below, there are two unknowns: the rate-constant and the concentration of growing centres. In order to measure these, we need two dependent variables to measure, and in the studies with which we are concerned these are the yield as a function of time and the molecular weight as a function of time. One purpose of this paper is to show that, given this information, the kinetic problem can be solved completely. However, if the time is eliminated, the problem is not soluble; so a second purpose of this paper is to plead that in all studies on living polymerisations both conversion and molecular weight should be reported as time-dependent variables.

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Commercial rubbers

Developments in the Theory of Cationoid Polymerisations

Algebraic treatment Consider a polymerisation without transfer and termination with a stationary state of the Second Kind, i.e., one in which ki = kt = 0 throughout the reaction after its instantaneous start. Assume further that the rate of propagation is of order z with respect to the monomer concentration at any time, and that z ≥ 0. z * Then − dm/dt = kx m [Pn ]

(1)

where [Pn*] is the concentration of growing chains, which is constant, kx is the experimental rate-constant. Under the assumed conditions, the Degree of Polymerisation (DP), n, will be the ideal DP, so that n = (mo − m) /[Pn* ]

(2)

Therefore the variation of n with time is given by

dn / dt = (−dm / dt) /[Pn* ]

(3)

From (1) and (3):

dn / dt = k x m z

(4)

and if Y = (mo - m)/mo and therefore dY/dt = - (dm/dt)/mo, then from (3): dn / dY = mo /[Pn* ]

(5)

Consequences 1. Most results on allegedly living polymerisations are presented as plots of n against Y. The Equation (5) shows i)

why many of these plots are rectilinear: [Pn*] is constant;

ii) that when the plots start to curve, at least one of the underlying assumptions ceases to be valid; iii) that the all-important concentration of growing chains, [Pn*] can be calculated from the slope of the n versus Y plot; and iv) that this is valid, whatever may be the value of z.

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Kinetics of Living Polymerisations (1988) 2. If z = 1, kx = kp* which can be obtained from a plot according to Equation (4). This method of obtaining kp* is unambiguous. It is, however, obvious that this kp* cannot be assigned to any particular mode of propagation without further chemical information about the system. If, for example, one has a dieidic polymerisation carried by paired and unpaired cations, the rate-equation takes the form

− dm / dt = ( k +p [ Pn+ ] + k p± [ Pn+ A − ])m

(6)

The kp* is a weighted mean of kp+ and kp±, and of course the [Pn*] determined as indicated above is a weighted mean of [Pn+] and [Pn+A-]. Additional evidence from experiments with common-ion salts, from the dependence of the DPD on the reaction conditions, etc., is required to resolve such ambiguities. Nevertheless, the order of magnitude of the kp* obtained and the manner in which it varies with reaction conditions, e.g., the dielectric constant of the medium, can give useful clues as to whether one is dealing with an enieidic or monoeidic system, and if monoeidic whether it is, for example, cationic or pseudocationic. 3. If z = 1, Equation (1) can be rewritten as −dln m / dt = kp+ [Pn* ]

(7)

The corresponding plot has slope kp*[Pn*], and this should agree with the product of the values of kp* and [Pn*] obtained separately as indicated above. 4. If z ≠ 1, a more useful form of Equation (4) is Equation (8):

ln(dn / dt ) = ln k x + z ln m

(8)

Both z and kx can be found from the plot of ln(dn/dt) against ln m. Actually, many published polymerisations appear to be of zero order with respect to m, so that z = 0, and for such systems the plot of n against t is also rectilinear and its slope is kx. The simplest interpretation (though not the only one) of a zero-order polymerisation is in terms of the Fontana-Kidder mechanism (Fontana 1948) in which the growing centre is a partner in an associative equilibrium with the monomer, and the ratedetermining propagation step is the isomerisation of the resultant complex: Pn* + M ↔ Pn* ⋅ M, K

(9)

Pn* ⋅ M → Pn +1*, k x

(10)

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Developments in the Theory of Cationoid Polymerisations The rate equation for such a reaction is −dm / dt = k x Km([Pn* ] + [Pn* ⋅ M]) /(1 + Km)

(11)

This is, of course, a well-known type of kinetic equation. If dt/dm is plotted against 1/m, a straight line is obtained with slope S and intercept I, where S = 1 / k x K ([Pn* ] + [Pn* ⋅ M])

(12)

I = 1 / k x ([Pn*l + [Pn* ⋅ M])

(13)

so that K = I/S

(14)

Since kx can be obtained as shown earlier in this section, values of [Pn*] + [Pn*·M] can be found from both I and S. At very low m, the order of the reaction should change from zero to first with respect to m. 5. It is evident from our treatment and discussion, that it would be of great advantage if in all future publications on allegedly living systems both the Y and the DP were to be reported as functions of time and the values of kx and [Pn*] derived from them were given. This cannot entail any extra work, since in all such researches the time must be known at which samples are taken for analysis; the gain in information, however, would be considerable.

Acknowledgements My thanks are due to Prof. D. C. Pepper and Dr. S. Bywater for helpful discussions and to the Leverhulme Foundation for help with the production of this paper.

References Boehm, L. L., Chmelir, M., Loehr, G., Schmidt, B. J. and Schulz, G. V., Adv. in Polymer Sci., 9, 1 (1972). Fontana, C. M. and Kidder, G. A., J. Amer. Chem. Soc., 70, 3745 (1948). Pepper, D. C., Makromol. Chem., 175, 1077 (1974).

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6.10

Cationoid Living Polymerisations 1 (1992) P. H. Plesch

This paper was first published in Makromolekulare Chemie, Macromolecular Symposia, 1992, 60, 11-35. Reproduced with permission by Huthig & Wepf Verlag, Copyright 1992.

Prologue The new treatment of kinetic data described here is generalised in this paper and used to calculate rate constants.

Abstract The cationoid living polymerisations have many of the characteristics of pseudocationic (Ψ-cat) polymerisations and none of those of cationic polymerisations. In contrast to the ψ-cat polymerisations by protonic acids, which are transferdominated, those giving living polymerisations are propagated by esters which are part of a donor-acceptor complex involving a ‘third reagent’. There are three types: The first is exemplified by an ester which is activated by a metal halide, e.g., HMI (from monomer M + HI) + ZnBr2, or oligoisobutyl acetate + BCl3. The second type is exemplified by a polymer triflate complexed by a dialkyl sulphide. The reagents which change the reactivity of the ester are termed ‘modifiers’. The acceptors, e.g., ZnBr2, which co-ordinate to a donor group on the polymer, are positive modifiers (or activators). The donors, such as R2S, which co-ordinate onto an acceptor group at the end of the polymer, e.g., the acidic β-H, are negative modifiers (or moderators). The propagation by both types of modified ester probably involves a 6-centred cyclic transition state. The same applies to a third type of ψ-cat propagation, in which a polymeric ester reacts with a D–A complex formed from M + I2. The formation of unwanted non-living polymers of high degree of polymerisation (DP) and/or broad DPD, together with those resulting from living polymerisations, 1

This is Part X of ‘Developments in the Theory of Cationic Polymerisations’. For Part IX see Ref [36]; for Part XI see Ref. [46].

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Developments in the Theory of Cationoid Polymerisations happens because the metal halides used in these reactions not only form the ψ-cat propagating centres, but also react with ionogenic impurities to initiate concurrent, short-lived cationic polymerisations. These parasitic reactions can be suppressed by an excess of base, e.g., an ester or halide ions, which scavenge protons and carbenium ions. This phenomenon indicates that, whatever else is propagating the living polymerisations, it is unlikely to be carbenium ions. The kinetic equations for the living polymerisations, developed here, make it possible to calculate propagation rate-constants from rate and DP data; such calculations are shown for a variety of published results.

1 Acknowledgements The author thanks the Editor for giving him the opportunity to revise the original version of this paper in the light of the discussions and some of the other papers presented during the 10th Symposium on Cationic Polymerisation. He thanks Professor J. P. Kennedy and Dr. M. Sawamoto for making their lectures available to him before publication, and Professors B. A. Feit and A. Gandini for stimulating comments.

2 The nature of living cationoid polymerisations The subject of this paper is the group of polymerisations which have living character in the sense defined by Penczek et al., [1]. The term ‘cationoid’ comprises both the cationic and the pseudo-cationic (ψ-cat) polymerisations; however, it is a principal contention of this paper that none of the living polymerisations which have been adequately characterised actually show any of the characteristics of cationic polymerisations, but that they all show important features of the ψ-cat polymerisations [2, 3]. The converse of this proposition is not true: not all ψ-cat polymerisations are living. Before proceeding further, we must define our terms: In cationic polymerisations the reaction is propagated by unpaired and paired carbenium ions. These are in equilibrium, and the ratio of their concentrations is determined by the usual physical parameters, such as the charge and size of the ions and the dielectric constant of the solvent. They can proceed rapidly at very low temperatures; the rate-constants kp+ are in the range 104 to at least 106 l mol-1 s-1, depending on the monomer and the solvent, and they decrease with increasing polarity of the solvent [4]; these polymerisations are effectively inhibited by water and other bases; in most systems the DP of the polymers is dominated by various transfer reactions, the distribution of the DP of the polymers is unimodal, and the ratio of weight-average DP/number average DP, DPW/DPN is usually > 1.5.

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Cationoid Living Polymerisations (1992) Pseudo-cationic polymerisations are reactions in which an alkene is inserted between the positive carbon atom and the negative heteroatom of a polar bond at the growing end of a polymer chain, without the formation of a carbenium ion; they do not differ essentially from the well-known additions of esters to alkenes. The theory of these reactions was devised by Gandini and Plesch [2] and has been brought up to date by Plesch [3]. It will be shown below that the theory of ψ-cat polymerisations provides a self-consistent, widely applicable, and heuristically useful interpretation of the living polymerisations. An alternative theory, proposed by Matyjaszewski and Sigwalt [5-7], is applied to the living cationoid polymerisations by Matyjaszewski and several other contributors to this Symposium. Much confusion can be avoided if it is realised that at any one time more than one type of reaction can be going on in the same solution. This means that a living polymerisation may be accompanied by a ‘normal’ cationic polymerisation. The evidence for this is that changes in the composition of the reaction mixture, e.g., the addition of a base, may effect a narrowing of the DPD or may remove a peak from a gel-permeation (GP) chromatogram, which means that a cationic polymerisation, previously concurrent with the ψ-cat polymerisation, has been suppressed by the added base. The existence of such dieidic polymerisations and the suppression of their cationic component by bases which scavenge protons and carbenium ions now seems to be widely recognised [8, 9]. However, Faust [8] failed to draw the obvious conclusion, that these very experiments make it very unlikely that the living polymerisations which they are studying are propagated by ions. In their contribution to this Symposium, Sawamoto and Higashimura describe the effects of adding quaternary ammonium halides (R4NX) to polymerisation mixes containing a monomer, M [4-methoxystyrene (4-MeOSt) or styrene or isobutyl vinyl ether (IBVE)] and the product HMX of the reaction of M with HX, and ZnX2 or SnCl4 (MtXn), in toluene or in CH2Cl2 (X = halogen). The observations need not be repeated here; suffice it to say that the addition of R4NX to any mix in which a non-living component of high DP is formed, suppresses this completely. The simple explanation of very similar observations from the same research group [9] is equally applicable to these results: in the inadequately dried and purified systems involving CH2Cl2 solvent, the MtXn together with one or more adventitious ionogens (especially water) initiate cationic polymerisations which accompany the ψ-cat living polymerisations, and the added X- simply converts the Pn+ to PnX, which then reacts with the excess of MtXn to give more ψ-cat living centres. In Reference [9] the correct conclusion is finally drawn that these living centres cannot be ionic. That the cationoid living polymerisations are pseudocationic is also evident from three of their common characteristics [3]: 1. Their insensitivity to water [10]. This is in contrast to the cationic polymerisations which are inhibited by very small concentrations of water.

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Developments in the Theory of Cationoid Polymerisations 2. The finding by many investigators that they can be done in toluene solvent. Cationoid living polymerisations in that solvent cannot involve carbenium ions, because at temperatures down to ca. –15°C cationic polymerisations in toluene generally yield products of low DP with p-tolyl end-groups by a normal Friedel-Crafts alkylation, giving polystyryl-C6H4Me from styrene [11], which is, from the polymer kinetics point of view, a proton transfer involving solvent. These reactions can be represented generally as:

Pn+ + ArH → Pn – ArH + + M → Pn – Ar + HM +

(i)

They were explored in some detail by Overberger’s and Okamura’s groups in the 1950s and 1960s. Miyamoto et al. [12] have shown very clearly that for various alkyl vinyl ethers the cationic polymerisation by BF3·Et2O (due to H+ from adventitious water [13, 14]) gives a much lower DP in toluene than in hexane, presumably because of the reaction shown above; and in toluene the same initiator gives a polymerisation producing polymers with a wide DPD (because it is cationic), whereas HI + I2 gives a product with a narrow DPD, in our view because it is a living ψ-cat reaction. 3. The effect of changing the polarity of the solvent is further evidence in favour of the ψcat nature of living polymerisations. For example, Schappacher et al. [16], reported that the polymerisation of chloroethyl vinyl ether by H-halide + Zn-halide ‘in CH2Cl2 proceeds 3–5 times faster than in toluene’, and they allege - contrary to the accepted transition state theory - that this ‘ ... tend(s) to support an ionic mechanism’. Their observation actually indicates that the rate-determining step involves two dipoles, in agreement with our view, not an ion and a dipole. Another particularly informative example is offered by Sawamoto and Higashimura [16] who wrote: ‘As expected, the polymerisation (of alkyl vinyl ethers by I2 + HI) was faster in CH2Cl2 than in hexane, otherwise under the same conditions’. The ‘As expected ...’ and indeed many other passages in their papers imply, or state explicitly, that this Kyoto group also now believes these living polymerisations to be ψ-cat, because only for a reaction between two dipoles would one expect the rate-constant to increase with increasing polarity of the solvent. Many research groups still seem to be committed to some form of ionic interpretation of their living polymerisations, despite the well-known phenomena which indicate that carbenium ions are very unlikely to be involved. We think it unprofitable to attempt here a detailed analysis of the shifting and ill-defined views of Kennedy’s group and some others, but one important point must be emphasised: it is, that one cannot make progress in understanding reaction mechanisms by confusing transition states which, by definition, have a life-time of 10-13 s, with reaction intermediates of a longer life-time. Unfortunately, in many papers these two concepts are not distinguished clearly. It is useful to note in this context that the much-quoted Winstein distinguished clearly the reactions between dipolar

692

Cationoid Living Polymerisations (1992) molecules which involve strongly polar transition states from those involving ions of finite life-time. Any author implicating in his mechanism an ionic species of finite lifetime, e.g., the ion-pairs of Nuyken et al. [17, 18], must explain why these ions do not give cationic polymerisations producing polymers of DP and DPD different from those formed by the living polymerisation. As mentioned above, the experiments with ion-scavengers, and indeed all living polymerisations in the presence of an excess of a base, tell their own story, namely that the involvement of carbenium ions as the chain-carriers is very unlikely. Schappacher and Deffieux [15] considered propagation both by an insertion involving a 6-centred transition state [like that favoured by us [2c]] and by an ionic mechanism involving ion-pairs, and considered the latter more likely, thereby ignoring the evidence discussed here. If, however, an author specifies a mechanism in which bonds become more strongly polarised in the transition state and the monomer becomes inserted into one of these, then he is in fact formulating a mechanism which contains the essential feature of our insertion mechanism. It is of the very nature of a transition state in this kind of reaction that it involves bonds more polarised than in the ground state. And in that case it seems heuristically unprofitable to maintain that there is any fundamental difference between that view and our ψ-cat theory of the living polymerisations and to use a different terminology. Theoretical understanding is served better by seeking the underlying common features of diverse phenomena, than by particularising unnecessarily. The only group we know of who has eschewed ions in their mechanism is that of McGrath [19]; they write unequivocally in terms of insertions into covalent bonds and generally hold mechanistic views very close to ours. Once it is understood that the evidence is in favour of the living polymerisations being ψcat, the belief that all ψ-cat polymerisations are necessarily transfer-dominated will be seen as an unfounded prejudice. In the next sections we will show what it is that differentiates the living from the transfer-dominated ψ-cat polymerisations.

3 The activation of the esters A second misunderstanding concerns the nature of the propagating species in the pseudocationic polymerisations. The essential feature of these reactions is that the propagation involves the insertion of the alkene monomer into the heteroatomic bond of an ester, which in many instances needs to be activated in order to become sufficiently labile for the insertion. In a short discussion of pseudo-cationic polymerisations contained in a very comprehensive review [20], the statement was made: ‘Plesch did not realise, however, the necessity of activating the end-group which seems to be imperative to allow for the

693

Developments in the Theory of Cationoid Polymerisations growth, as is evident from the above two examples’. The two examples referred to are the initiation of living polymerisations of various hydrocarbons and alkyl vinyl ethers by BCl3 + an ester and by I2 or ZnI2 + HI. Van Beylen et al. [20], had overlooked that from the beginning of the theory of pseudo-cationic polymerisation it has been emphasised by Plesch and others [2, 21, 22] that in most systems the activation of the ester (formed from an alkene and an acid) is an essential feature without which propagation by the insertion of the monomer into the ester bond cannot take place; this had been stressed by Whitmore [23] and by Schmerling and Ipatieff [24] in their discussions of the reactions which were subsequently called ‘pseudocationic’ by Plesch and his co-workers. The well-known addition of tert-butyl chloride to ethylene by means of AlCl3 without skeletal rearrangement is simply another example of the initiation step of a ψ-cat polymerisation, involving the insertion of the alkene into an ester, namely the C–Cl bond, which is activated by the AlCl3, via a six-centred transition state (I), as shown in equation (ii):

(ii)

The lack of isomerisation indicates that a non-ionic process is involved. The reaction does not continue to give a polymerisation of ethylene, because in contrast to the tertiary C–Cl bond which is broken, the primary C–Cl bond which is formed is too strong to be activated sufficiently by the AlCl3. For the polymerisations involving an organic (monomer) halide and a metal halide, such as ZnBr2, it seems reasonable to represent the insertion also as occurring via a 6-membered cyclic transition state (II):

The important features here are the activation of the C-I bond and the steric constraints in the species (II) which inhibit the transfer of a proton from the β-carbon of the growing

694

Cationoid Living Polymerisations (1992) chains to the CH2 = group of the monomer, which would break the chain; therefore the original physical chain continues to grow and the polymerisation is living. The clearing up of the misunderstanding concerning the need for activation of the ester puts the record straight, and it provides a logical introduction of the critical role which the activator of the ester plays in determining the character of the pseudo-cationic polymerisation. We will show that it is the nature of the activator which determines whether a pseudo-cationic polymerisation is ‘ordinary’, i.e., transfer-dominated, or living.

4 What gives ‘life’ to a ψ-cat polymerisation ? It is the nature of the activator that holds the answer to the inherent question: If the polymerisations initiated by protonic acids, e.g., CF3SO3H, and by syncatalytic systems, such as that consisting of the same acid + thiolan [25] or Me2S [26] are both pseudocationic, why does the one yield a product whose DP is determined by proton transfer to monomer, whilst the other produces a living system? A review of the facts shows a simple phenomenological distinction, from which a mechanistic explanation can be deduced. The distinction is this: The transfer-dominated ψ-cat polymerisations involve propagating ester groups which are either so unstable that they ionise unless they are stabilised by the co-ordination of monomer (the best documented, but certainly not the only, such system is styrene + HClO4), or the ester is inert unless activated by protonation, e.g., styrene + CF3CO2H [27]. The high kinetic orders with respect to acid, which are found in many systems involving protonic acids, are evidence for this [28]. The proton transfer to the monomer [reaction (iii)] (or some other base) which constitutes the chain-breaking event, can originate either from the β-carbon at the growing end, which experiment shows to be stabilised by 4 molecules of M

–CH2CHPh ⋅ O ⋅ ClO3) 4 M + M → –CH = CHPh + HMOClO3) 4 M

(iii)

or from the protonated ester group (IV) [reaction (iv)]: –CH2CHPhOClO3H + ) 4 M ClO−4 + nM → –CH = CHPh + HM nOClO3H + ) 4 M ClO−4 (iv)

The anions A2H– may also be involved. The two forms of propagating centre, (III) and (IV), may well co-exist, their relative kinetic importance depending upon solvent, temperature, concentrations, age of the reaction and - in the general case - the nature of the acid. The transition states for both the reactions (iii) and (iv) can best be visualised as cyclic and 6-centred [2c, 7a, 29].

695

Developments in the Theory of Cationoid Polymerisations In contrast to the transfer-dominated ψ-cat systems, the living systems comprise an ester and a third component, which hitherto has been called the ‘activator’. This term, however, is inadequate, because a survey of the field shows that in many systems the third component does not increase the reactivity of an ester, but diminishes it, or it may even convert a highly reactive cationic system to a more inert Ψ-cat system giving living polymerisations. This distinction of the two types of ‘third components’, although implicit in the evidence, has not been made explicitly heretofore in our terminology. However, priority in this line of thought must be accorded to Faust et al. [8]. They realised that because in some systems an excess of base inhibits polymerisation, whereas in others an excess of base is necessary, two different reaction intermediates must be involved; but they did not develop this theme. The new understanding requires the devising of a new generic term to designate both compounds which reduce and compounds which enhance the reactivity of a potential reagent which is either too reactive or too inert in the absence of the third component; the most suitable term to occur to this author is ‘modifier’. We will refer to compounds which accelerate inert systems as positive modifiers and use this term as synonymous with activator; and we will refer to stabilising compounds as negative modifiers and also as moderators. The essential feature of the modifiers is either to activate an inert chain-end so that it can insert a monomer molecule, but in such a way that the chain-breaking β-proton transfer is prevented; or to reduce the reactivity of a propagating species and in particular to prevent the transfer of an acidic β-proton from the growing end of the chain [30]. The positive modifiers are exemplified by Higashimura’s system of monomer + HX (equivalent to HMX) + ZnX2, where the C–X bond of the ester (organic halide) is activated by the metal halide. The transition state (II) for this reaction has been given above. Evidently, the active species PnX.ZnX2 is a reversibly formed donor (PnX) - acceptor (ZnX2) complex. From amongst the numerous systems cited by Kennedy and his collaborators which give living polymerisations, we select here the one consisting of 2,4,4-trimethylpentyl acetate + BCl3 which is stated not to give polymers with Cl end-groups [8]. In our view, the activity of this syncatalytic system can be interpreted in terms of a positive modification of the ester by the BCl3. The propagation involves the insertion of the monomer into the ester bond, with a 6-centred cyclic transition state as shown in (V), and with the BCl3 changing its attachment from the erstwhile carbonyl to the nascent carbonyl oxygen:

(v)

696

Cationoid Living Polymerisations (1992) Once again the modification involves a donor-acceptor equilibrium. The group-transfer polymerisation of a silyl vinyl ether by benzaldehyde and ZnBr2, as described by Boettcher [31], in which the ZnBr2 is transferred from an original to a nascent carbonyl group, appears to be cationoid, as is pointed out (though not with this terminology) in a very useful review by Sawamoto [32]; and in our view it is ψ-cat, with ZnBr2 being a positive modifier. Good examples of the effects of negative modifiers are provided by the systems of Goethals et al. [25], and Cho et al. [26]; in these an alkyl sulphide converts a transfer-dominated ψ-cat polymerisation into a living polymerisation. It seems likely that in the active species the electron donor sulphide is co-ordinated to the acidic β-protons and that in the transition state (VI) it migrates from the erstwhile β-CH2 group to the nascent β-CH2 group on the monomer molecule which is being incorporated, thus:

Once again the active species is an associative D–A complex =CH2·SR2 of donor-acceptor type, but - in contrast to the positive modifiers - the negative modifiers are the donors, and the acceptor (the acidic CH2) is part of the polymer end-group. In some of their publications Higashimura’s group, and others using the same terminology, are close to our view when they write about the modifiers ‘reducing the reactivity of the carbocation’. However, since in our view there is no carbenium ion to be stabilised, we see these donors as reducing the polarity of the ester bond and the reactivity of the βprotons, and they obstruct physically the transfer of a β-proton to the monomer or to any other base. So the answer to the question which heads this section is that an adequately polar complexor is required to convert a transfer-dominated ψ-cat polymerisation into a living one, or to activate an inert mixture so that a living polymerisation ensues.

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Developments in the Theory of Cationoid Polymerisations

5 Mechanisms and kinetics 5.1 Polymerisations of first order with respect to monomer Our ideas can be represented in generalised form by Scheme 1, in which D is the anionoid moiety of the ester, A is the acceptor, i.e., a positive modifier, and PnD.A is the propagating species, which, as before, we denote by Pn*. As the algebra for negative modifiers, i.e., donor complexors, is essentially the same, it will not be shown here. jM

Scheme 1:

Pn D + A ↔ Pn D ⋅ A → Pn + jD + A

The dissociation of PnD.A → PnD + A is equivalent to what some authors have called ‘reversible termination’, and the activatable ester PnD is what has been called a ‘dormant’ species. In the simplest reactions conforming to Scheme 1 the formation of P1D, (e.g., HMI from HI and a monomer) goes to completion, so that if [M] = m > [D]o, then [PnD]o = [D]o; and the formation of PnD.A also goes to completion, so that if

[A]o > [D]o , [ Pn D ⋅ A]o = [D]o

(5.1)

and if [A]O < [D]o, then

[ Pn D ⋅ A]o = [A]o

(5.2)

The rate, R, is given by

– dm / dt = R = kp* ⋅ [ Pn D ⋅ A]o ⋅ m = kp* ⋅ [ Pn* ] ⋅ m

(5.3)

The DP is given by

ΔDP = Δm /[ Pn* ]

(5.4)

where ΔDP is the increment of the DP accompanying the reduction of the initial m, mo, by Δm. When all the monomer has been consumed Δm = mo, DP = DPf (DPf = final DP) and

DPf = mo /[Pn* ]

(5.5)

It follows that

dDP / dt = (– dm / dt ) /[ Pn* ]

698

(5.6)

Cationoid Living Polymerisations (1992) If the yield Y is defined as

Y = ( mo – m) / mo

(5.7)

dY / dt = (– dm / dt ) / mo

(5.8)

dDP / dY = mo /[ Pn* ]

(5.9)

and

This means that for these systems the value of [Pn*], obtained from the plot of Y against DP, can be used to find kp* from Equation (5.3). If the rate is not of first order with respect to m, but is given by

– dm / dt = R = kpz* ⋅ m z ⋅ [ Pn* ]

(5.10)

where usually 0 < z < 1, Equation (5.9) is still valid so that [Pn*] can be found even if z = 1. So far we have followed essentially Plesch’s treatment [33], which we now generalise by considering the formation of PnD·A as an equilibrium reaction (viii)

Pn D + A ↔ Pn D ⋅ A, KDA

(viii)

so that

KDA = [ Pn* ]/([Pn D] ⋅ [ A])

(5.11)

The material-balance equations are (5.12) and (5.13):

[D]o = [ Pn D]o = [ Pn D] + [ Pn* ]

(5.12)

[A]o = [A] + [ Pn* ]

(5.13)

Therefore the rate is given by

R = kp* ⋅ [ Pn* ] ⋅ m = kp* ⋅ K DA ⋅ [ Pn D] ⋅ [A ] ⋅ m

= kp* ⋅ KDA ⋅ ([Pn D]o – [ Pn* ]) ⋅ ([A]o – [ Pn* ]) ⋅ m

(5.14) (5.15)

699

Developments in the Theory of Cationoid Polymerisations Hence

R /( kp* ⋅ K DA ⋅ m) = [ Pn* ]2 – [ Pn* ]([ Pn D]o + [ A ]o ]) + [ Pn D]o ⋅ [ A]o

(5.16)

Since for these systems the DP is determined by the totality of actually and potentially growing centres, ΔDP = Δm /([PnD] + [ Pn* ])

(5.17)

it is more difficult to determine [Pn*] and thus kp*. One way of resolving the problem is to work with such an excess of one of the reagents, say PnD, that effectively [Pn*l = [A]o, so that one can then find kp* from Equation (5.3). Alternatively, if [PnD]o >> [Pn*l, Equation (5.16) takes the form R /(kp* ⋅ KDA ⋅ m) = [ PnD]o ⋅ [A]o – [ PnD]o [ Pn* ] so that

R /( m ⋅ [ Pn D]o ⋅ [ A]0 ) = kp* ⋅ K DA – kp* ⋅ K DA ⋅ [ Pn* ] /[ A]o

(5.18)

From appropriate plots the product kp*·KDA and [Pn*l can be obtained, so that from Equation (5.14) kp* and hence KDA can be found. It follows from Equation (5.14) that the apparent activation energy, E R, of the polymerisation rate, is given by o ER = ΔHDA + Ep*

Since for most D–A reactions the standard enthalpy of complexation, ΔH° DA, corresponding to KDA, is negative, and the activation energy of propagation Ep*, is necessarily positive, ER will be positive or negative according to the relative magnitude of these two quantities, so if ⏐ΔH°DA⏐ > Ep* then ER is negative, and the rate increases with decreasing temperature. It is therefore evident that a negative ER is not, as has been alleged, an indication that the reaction concerned is cationic.

5.2 Polymerisations of zero order with respect to monomer Many polymerisations are known for which the rate is internally of zero order with respect to m, i.e., the plot of Y against t is rectilinear up to (almost) Y = 1 (100%

700

Cationoid Living Polymerisations (1992) conversion); most of these involve I2. In the context of polymer chemistry there are two favourite theoretical models which can account for R being independent of m. One of these is the Fontana-Kidder model [34, 35] In this the propagating species forms a πbond with the monomer reversibly, and the rate-determining step is the isomerisation of this complex with the incorporation of the previously π-complexed molecule into the chain; this has been discussed extensively by the present writer [36]. Since the ester is an electron donor and the monomers of concern here are also electron donors, this model is implausible in the present context and can therefore be dismissed. Kojima et al., also considered and rejected this mechanism, but for a different reason [37]. The second model involves the reversible formation of a complex between the iodine and the monomer, and in this context it is unimportant whether the iodine forms an n-complex, e.g., with the O-atom of a vinyl ether, or a π-complex with a double-bond or an aromatic ring of the monomer (styrene, N-vinylcarbazole); the only important point is that the complexed monomer is very much more reactive with the propagating ester group than the uncomplexed monomer, and that its formation is an equilibrium reaction. [Very detailed studies of the reactions of iodine with styrene [38] and with butyl vinyl ether (nBVE) [39, 40] have been reported in which the formation of various complexes is discussed.] The idea of the preferential reaction of a complexed monomer is quite old and in the context of cationoid polymerisations it has been used by Choh and MacGrath [19], Kojima et al., [37] and Héroguez et al., [41, 42] in a manner which forms the basis of the following exposition: The first stage of the polymerisation is again the formation of the ester P1D with complete consumption of D such that [P1D] = [D]o, e.g., CH3CHI·O·R from HI + alkyl vinyl ether, and the complexation of the monomer M by the acceptor A:

M + A ↔ MA, K M

(ix)

[MA] = K M ⋅ m ⋅ [ A]

(5.19)

[ A ]o = [A ] + [MA]

(5.20)

[MA] = K M ⋅ m ⋅ [ A]o /(1 + K M ⋅ m)

(5.21)

Since

The propagation results from the encounter of P1D with MA:

P1D + MA → P2 D + A

(x)

701

Developments in the Theory of Cationoid Polymerisations and it can be envisaged as occurring once again via a 6-centred transition state as shown in structure (VII) of Equation (xi):

(xi)

The rate is given by

– dm / dt = R = kpo* ⋅ [ Pn D] ⋅ [MA]

= kpo* ⋅ K M ⋅ m ⋅ [ Pn D] ⋅ [ A]o /(1 + K M ⋅ m)

(5.22) (5.23)

Evidently, over the range of m over which R is independent of m, KM·m >>1, and

R = kpo* ⋅ [ Pn D] ⋅ [ A]o

(5.24)

The slope of the Y – t plot gives kpo*·[PnD]·[A]o, whence kpo* can be found, [A]o being known and the [PnD] being equated to [D]o. For this kind of polymerisation the DP is given by

ΔDP = Δm /[ Pn D]

(5.25)

so that one can test whether in fact, as assumed, the concentration of growing centres, [PnD], equals [D]o. If one wishes to explore the reaction at high m, where the dependence of R on t is no longer rectilinear, the conventional inversion of Equation (5.23) to give Equation (5.26): * * 1 / R = 1 /( kpo ⋅ K M ⋅ m ⋅ [ Pn D] ⋅ [ A]o ) + 1 /( kpo ⋅ [ Pn D] ⋅ [ A]o )

(5.26)

enables one to find kpo*·and KM. We will show below how the general equations deduced here can be used to calculate the propagation rate-constants.

702

Cationoid Living Polymerisations (1992)

6 Rate-constants 6.1 The use of our equations will be illustrated by applying them to a few systems from the literature showing simple kinetic behaviour. However, before starting the calculations we must ascertain how reliable the literature data are. There seems little reason to doubt the soundness of the rate data, but almost all the DP data, essential for the calculation of [Pn*], are suspect because in most researches the DP is obtained by GP chromatography (GPC) with a polystyrene (PSt) calibration. The extent of the uncertainty is revealed by two sets of measurements: Cho and McGrath [19] found that for poly(nBVE)(PnBVE) the DP determined by vapour pressure osmometry (VPO), which one would favour as closest to the ‘real’ DPn, is related to that found by GPC, DP(PSt), as

DP(VPO) = 0.72 × DP( PSt ) Another similar comparison by Nuyken et al. [18], involving GPC measurements on poly(IBVE) with PSt and PIBVE standards gave

DP( PIPVE) = 1.1 × DP( PSt ) That this is not a trivial matter becomes evident when one examines the results of Heroguez [41, 42] (Figure 2 in the first publication, Figure 3 in the second publication) for the polymerisation of chloroethyl vinyl ether (CEVE) by HI and I2. In our notation, they found that Δm/ΔDP = (2.8 ± 0.2) x 10-2 mol·l-1 (depending on what line one draws through their points), and by hypothesis this is equal to the total concentration of actually and potentially growing chains. However, [HI]o = 1.7 x 10-2 and [I2]o = 0.32 x 10-2 mol·l-1. So, even if the iodine had participated in the formation of growing centres, one would still have a concentration of these which is lower than that indicated by the ratio Δm/ΔDP. A simple way out of the difficulty would be to suppose that for this system the determination of the DP by GPC with a PSt standard has given results which are substantially too high. It is useful to note that in most of their very numerous results the Higashimura group found close agreement between [HI]o (or its equivalent) and Δm/ΔDP.

6.2 Systems with z = 1 6.2.1 Kojima et al. [37], reported on the kinetics of the system IBVE in toluene at –40 °C, mo = 0.38 mol·l-1, giving the rate as

703

Developments in the Theory of Cationoid Polymerisations R = k3 ⋅ m ⋅ [HI]o ⋅ [ZnBr2 ]o = k1 ⋅ m k1 = k3 ⋅ [HI]o ⋅ [ZnBr2 ]o They show plots of k1 against [HI]o and [ZnBr2]o (their Figure 8) but they did not calculate k3. We find from their diagrams: [HI]o variable 5 x 10-3 mol·l-1

[ZnBr2]o 2 x 10-4 mol·l-1 variable

k3/(l2·mol-2·s-1) 6 x 102 7 x 102

The above equation is actually an approximation to our Equation (5.15) for the case that [PnD]o >> [A]o which is equivalent to [HI]o >> [ZnBr2]o. The k3 of the original authors is equivalent to our kp*·KDA. If one treats these results by the simplified equation (5.3) and puts [Pn*] = [HI]o, which in fact is indicated by their Figure 9, one obtains

R = kp* ⋅ m ⋅ [ HI]o kp* ⋅ [ HI]o = k1 = k3[ HI]o [ZnBr2 ]o kp* = k3[ZnBr2 ]o = 2 × 10 −4 × 6 × 102 = 0.12 l ⋅ mol −1 ⋅ s −1 Since

k3 = kp* ⋅ K DA , K DA = 5 × 10 3 l ⋅ mol −1 The original authors did not indicate that their k 3 is composite, involving an equilibrium constant.

6.2.2 Kinetic information provided by Higashimura et al. [43], on the polymerisation of 4MeOSt by HI and ZnI2 in toluene at –15 °C enables us to calculate a rate-constant thus: From information on other systems it appears that the rate is likely to be of first order with respect to [HI]o (= 10-2 mol·l-1); the kinetic curves indicate z = 1, so that

R = kp* ⋅ [HI ]o ⋅ m = k1 ⋅ m From the half-life of the polymerisation we get k1 = 7.6 x 10-4 s-1, giving kp* = 7.6 x 10-2, and from the initial rate kp* = 9 x 10-2, giving an average kp* = (8 ± 1) x 10-2 l·mol-1·s-1.

704

Cationoid Living Polymerisations (1992) For the same initiating system, solvent, and concentrations at –15 °C and +25 °C, Higashimura et al. [44], give rate and DP data for 4-tert-butoxystyrene (4-t-BuOSt) from which we calculated T/K kp*/(l·mol-1·s-1)

298 6.4 x 10-2

258 6.4 x 10-3

whence we obtain an activation energy Ep* = 37 kJ mol-1.

6.2.3 The polymerisation of IBVE in CH2Cl2 and other solvents at various temperatures by HMI (from M + HI) and perchlorate salts is reported by Nuyken and Kroener [17] in sufficient detail, so that kinetic calculations to supplement their own can be made. From their Table 1(a), experiments at –40 °C with mo = 0.4 mol·l-1, we find ΔY = 0.11, ΔDP = 17. The equation (5.9) gives [Pn*] = mo/(dDP/dY) = 2.6 x 10-2 mol·l-1. This corresponds closely to the 2.5 mol·l-1 which is the concentration of both HMI and Bu4NClO4, so that we cannot say which of these reagents determines [Pn*]. However, their Table 1(b) containing the results for mo = 1 mol·l-1, T = –25 °C, [HMI]o 5 x 10-3, [Bu4NClO4] = 10-3 mol·l-1, gives ΔDP/ΔY = 200, whence [Pn*] = 5 x 10-3 mol·l-1, i.e., exactly [HMI]o, so that this settles which of the two reagents determines [Pn*]. From their Table 1(a) we can construct a plot of DP versus mt·t (Equation (4) of Reference [33]) which is linear and its slope is kp* = ΔDP/Δ(mt·t) = 2.4 x 10-2 l·mol-1·s-1. These rate-constants are collected in Table 1.

6.3 Systems with z = 0 6.3.1 Higashimura et al., [45] reported on the system CEVE, toluene, –15 °C, mo = 0.5, [I2]o = 10-2, [HI]o = 10-2 mol·l-1. From their Figures 6 and 7 we obtained R = 3.2 mol·l-1·s-1, Δm/ ΔDP = 1.25 x 10-2 mol·L-1. As R was found to be independent of m, our Equation (5.24) applies, in the form

kpo* = R /([ Pn D]o ⋅ [ A]o ) = R /([HI]o ⋅ [I 2 ]o ) giving kpo* = 3.2 x 10-2 mol·l-1.s-1. we have taken [PnD]o = [HI]o rather than = Δm/ΔDP for the reason given in Section 6.1.

705

Developments in the Theory of Cationoid Polymerisations

6.3.2 Cho and McGrath [19] calculated rate-constants kpo* (kpzn in their notation) for the polymerisations of nBVE and ethyl vinyl ether (EVE) in hexane and CCl4 at various temperatures for initiation by HI + I2. The polymerisations had z = 0 and were of first order with respect to [HI]o and [I2]o- so that

R = kpo* ⋅ [HI ]o ⋅ [I 2 ]o The rate-constants are collected in Table 1. For nBVE in hexane they found Epo* = 38 kJ·mol-1.

Table 1 Systems with z = 1 kp*/ (l·mol-1·s-1)

No

Ref.

M

T, °C

1

[37]

IBVE

–40

toluene

ZnBr2

0.12

2

[43]

4-MeOSt

–15

toluene

ZnI2

(8±1) x 10-2

3

[44]

4-t-BuOSt

–15

toluene

ZnI2

6.4 x 10-3

4

[44]

4-t-BuOSt

+2 5

toluene

ZnI2

6.4 x 10-2

5

[17]

IBVE

–40

CH2Cl2

Bu4NClO4

2.4 x 10-2

Solvent A

In the systems 1–4 HI was introduced into the reaction mixtures and formed the donor HMI very rapidly; in No. 5 HMI was used

Table 2 Systems with z = 0 Ref.

M

T, °C

Solvent A

kpo*/(L·mol-1·s-1)

[45]

CEVE

–15

toluene

0.032

[19]

nBVE

–16

hexane

1.2

[19]

nBVE

–25

hexane

0.87

[19]

nBVE

–35

hexane

0.35

[19]

nBVE

–45

hexane

0.13

[19]

nBVE

–16

CCl4

2.3

[19]

EVE

–16

CCl4

4.5

For all systems D = HI and A = I2

706

Cationoid Living Polymerisations (1992)

6.4 The rate-constants of both kinds calculated here for the ψ-cat living polymerisations are of course only a small sample of those which can be extracted from the published and unpublished information on these reactions. We hope that colleagues active in this field will now evaluate the measurements languishing in their filing cabinets and give us many more rate-constants for many more systems. Since these will be based on independent measurements of the concentration of growing centres, they will be sound, and they can therefore be used with confidence for the calculation of activation energies, and for appropriate systems it will then be possible to calculate the formation constants of the complexes involved. A particularly interesting area which now becomes accessible is the effect of the nature of the solvent on kp* and kpo* and KDA for a variety of systems. Some data for such calculations are already available (see for example Nuyken et al., [18]), but we have refrained from entering this area, because an adequate treatment would go beyond the limits which we have set for the present work.

7 Summary and conclusions 7.1 Since living cationoid polymerisations do not show any of the characteristics of cationic polymerisations, but have many features in common with the previously defined transferdominated pseudo-cationic polymerisations, it is concluded that they, too, are pseudo-cationic.

7.2 Like the transfer-dominated pseudo-cationic polymerisations, the living polymerisations are propagated by the insertion of the monomer double-bond into a polar ester bond at the growing end of the polymer.

7.3 The living polymerisations differ from the transfer-dominated ones in that the latter are mostly initiated by oxo-acids only, whereas to achieve living character, the ester needs to form a donor-acceptor complex with a third component, the ‘modifier’. One function of the modifiers is to prevent the chain-breaking transfer of a β-proton from the growing end to a base, such as the monomer or solvent.

707

Developments in the Theory of Cationoid Polymerisations

7.4 Esters, such as alkyl halides, which are too inert to propagate, require a positive modifier (acceptor), e.g., a metal halide, to activate them by forming a D–A complex.

7.5 Esters which are unstable and/or too reactive, such as those of CF3SO3H, require a negative modifier (donor), e.g., a dialkyl sulphide, to give living systems; such modifiers form a D–A complex with an acceptor centre, e.g., the acidic protons, at the growing end.

7.6 The modifiers required to produce living polymerisations depend critically upon temperature and solvent.

7.7 The living polymerisations by an alkyl halide and I2 are a third category of living cationoid polymerisations; they are propagated by a polymer iodide reacting with a D–A complex between the monomer and I2.

7.8 The parasitic formation of polymers of high DP and/or broad DPD in the same reaction mixture as the living polymers is due to cationic polymerisations initiated by adventitious impurities; it can be prevented by cation scavengers such as halide ions and other bases.

7.9 By means of these simple ideas one can rationalise most of the many published examples of cationoid living polymerisations, and they should provide guidance for the design of new systems.

708

Cationoid Living Polymerisations (1992)

7.10 If use is made of the time-dependence of both yield and DP, the resulting kinetic equations make possible the calculation of propagation rate-constants and D–A complexation constants. Some examples of such calculations are given.

7.11 In an area containing numerous very active researchers thinking about similar problems it is difficult to keep abreast of developments and to attribute innovations correctly. Therefore this author apologises in advance to any colleagues whose contributions he may have overlooked or under-rated, and for any incorrect attributions of priorities.

References 1.

S. Penczek, P. Kubisa, and R. Szymanski, Makromol. Chem. Rapid Comm., 12, 77 (1991).

2.

A. Gandini and P. H. Plesch, (a) Proc. Chem. Soc., 240 (1964); (b) J. Polym. Sci. B, Polym. Lett. 3, 127 (1965); (c) J. Chem. Soc., 4826 (1965); (d) ‘The Chemistry of Polymerisation Processes’, Soc. Chem. Ind. (London) Monograph No.20, p. 107 (1966).

3.

P. H. Plesch, Makromol. Chem., Macromol. Symp., 13/14, 375 and 393 (1988).

4.

P. H. Plesch, Progr. in Reaction Kinetics., Sept. 1992.

5.

K. Matyjaszewski and P. Sigwalt, Makromol. Chem., 187, 2299 (1986).

6.

K. Matyjaszewski and P. Sigwalt, Macromolecules , 20, 2679 (1987).

7.

K. Matyjaszewski, Makromol. Chem., Macromol Symp.,(a) 13/14, 433 (1988); (b) 13/14, 389 (1988).

8.

R. Faust, B. Ivan and J.P. Kennedy, J. Macromol. Sci., Chem.-A28, 1 (1991).

9.

K. Kojima, T. Higashimura and M. Sawamoto, Macromolecules , 23, 948 (1990).

10. R. Faust and J. P. Kennedy, J. Polym. Sci., 25, 1847 (1987).

709

Developments in the Theory of Cationoid Polymerisations 11. P. H. Plesch, J. Chem. Soc., 1659 (1953). 12. M. Miyamoto, M. Sawamoto, and T. Higashimura, Macromolecules., 17, 265 and 2228 (1984). 13. J. M. Moulis, J. Collomb, A. Gandini, and H. Cheradame, Polymer Bull., 3, 197 (1980). 14. A. Gandini and A. Martinez, Makromol. Chem., Macromol. Symp., 13/14, 211 (1988). 15. M. Schappacher and A. Deffieux, Macromolecules, 24, 4221 (1991). 16. M. Sawamoto and T. Higashimura, Makromol. Chem., Macromol. Symp., 3, 83 (1986). 17. O. Nuyken and H. Kroener, Makromol. Chem., 191, 1 (1990). 18. O. Nuyken, H. Kroener, and S. Aechtner, Makromol. Chem. Macromol. Symp., 32, 181 (1990). 19. C. G. Cho and J.E. McGrath, J. Macromol. Sci., A25, 499 (1988). 20. M. Van Beylen, S. Bywater, G. Smets, M. Szwarc and D. J. Worsfold, Adv. Polym. Sci., 86, 87 (1988). 21. P. H. Plesch, Pure Appld. Chem., 12, 117 (1966). 22. A. Gandini and H. Cheradame, Adv. in Polym. Sci., 34/35, 41-84 (1980), esp. pp. 84-92. 23. F. C. Whitmore, Ind. Eng. News, 26, 668 (1948). 24. L. Schmerling and V. N. Ipatieff, Adv. Catal., 2, 21 (1950). 25. E. J. Goethals, N. H. Haucourt, A. M. Verheyen, and J. Habimana, Makromol. Chem, Rapid Commun., 11, 623 (1990). 26. C. G. Cho, B. A. Feit and W. O. Webster, Macromolecules, 23, 1918 (1990). 27. W. Obrecht and P. H. Plesch, Makromol. Chem., 182, 1459 (1981). 28. The most comprehensive discussion of the polymerisations by protonic acids is in Ref. 22. See. also Refs. (5) and (6). 29. D. J. Dunn, E. Mathias, and P. H. Plesch, Europ. Polym. J., 12, 1 (1975).

710

Cationoid Living Polymerisations (1992) 30. Note on terminology: Many authors write ‘stable’ when they mean ‘unreactive’ or ‘inert’; but ‘stable’ is the opposite of ‘unstable’, and the opposite of ‘reactive’ is ‘unreactive’ or ‘inert’. Methyl radicals are very stable, but very reactive; hexaphenyl ethane is unstable, but very inert. 31. F. P. Boettcher, Makromol. Chem., Macromol. Symp., 13/14, 193 (1988). 32. M. Sawamoto, Progr. in Polymer Sci., 16, 111 (1991). 33. P. H. Plesch, Polymer Bull., 19, 145 (1988). 34. C. M. Fontana and G. A. Kidder, J. Amer. Chem. Soc., 70, 3745 (1948). 35. C. M. Fontana, G. A. Kidder, and R. J. Herold, Ind. Eng. Chem., 44, 1688 (1952). 36. P. H. Plesch, Makromol. Chem., Macromol. Symp., 32, 299 (1990). 37. K. Kojima, M. Sawamoto, and T. Higashimura, Macromolecules , 22, 1552 (1989). 38. D. S. Trifan and P. D. Bartlett, J. Amer. Chem. Soc., 81, 5573 and 5582 (1959). 39. D. D. Eley and A. Seabrooke, J. Chem. Soc., 2226 (1964). 40. D. D. Eley, F. L. Isack, and C. H. Rochester, J. Chem. Soc. A., 1651 (1968). 41. V. Héroguez, A. Deffieux, and M. Fontanille, Polymer Bull., 18, 287 (1987). 42. V. Héroguez, A. Deffieux, and M. Fontanille. Makromol. Chem., Macromol. Symp., 32, 199 (1990). 43. T. Higashimura, K. Kojima, and M. Sawamoto, Polymer Bull., 19, 7 (1988). 44. T. Higashimura, K. Kojima and M. Sawamoto, Makromol. Chem., Suppl., 15, 127 (1989). 45. T. Higashimura, Y.-M. Law, and M. Sawamoto, Polym. J., 16, 401 (1984). 46. P. H. Plesch, Phil. Trans. Roy. Soc., A342, 469.

711

Developments in the Theory of Cationoid Polymerisations

712

7

The Polymerisation of 1,3-Dioxacycloalkanes

Prologue 7.1

The Mechanism of the Polymerisation of Cyclic Formals, P.H. Plesch, IUPAC International Symposium on Macromolecular Chemistry, 1969, Plenary and Main Lectures, Budapest, 1971, 213-221.

7.2

The Propagating Species in the Polymerisation of 1,3-Dioxacycloalkanes by Perchloric Acid, Y. Firat, F. R. Jones, P. H. Plesch and P. H. Westermann, Die Makromolekulare Chemie, 1975, Supplement 1, 203-216.

7.3

Some Aspects of the Polymerisation of 1,3-Dioxacycloalkanes, P. H. Plesch, Pure and Applied Chemistry, 1976, 48, 287-293.

In 1964 this writer’s research group at Keele had become well established and the work on hydrocarbons, especially isobutene and styrene, was going well, attracting good students and producing interesting results. He therefore thought it time to branch out into another area of cationic polymerisation. Just then he saw in Japan some work on the cyclic formal 1,3-dioxolan, one of the general class of 1,3-dioxacycloalkanes, DCA for short. There seemed to be interesting problems concerning the mechanism of the polymerisation and the DP of the polymers, and the fact that the polymerisation is an equilibrium reaction made it rather a novelty at that time. Also, the polymerisation of dioxolan was being studied in various industrial laboratories because of its relation to the formation of polyformaldehyde from trioxan which at that time was a very hot topic. Several firms, including Hoechst in Germany, DuPont and Celanese in the USA and British Industrial Plastics (BIP) in Britain were heavily involved. The last of these agreed to pay for a research student in the author’s group at Keele to investigate the polymerisation of DCA. Thus the Keele Polymer Group became one of the very few worldwide, in which the polymerisations of both alkenes and of oxacyclics were being studied, and only the Keele work included electrochemical studies on the properties of organic cations. The first holder of the BIP studentship was Peter H. Westermann. He thoroughly enjoyed starting up a new project, and very soon he had produced his own mystery: He had found no difficulty in manipulating anhydrous perchloric acid as initiator and in making the polymers by the high vacuum techniques which had become the speciality of the

713

Developments in the Theory of Cationoid Polymerisations Keele Polymer Group, and their PMR-spectrum agreed with that in the literature. What puzzled us was that he could find no end-groups by any of the conventional methods. We were encouraged, however, by a DuPont patent for the preparation of poly-1,3dioxolan, in which the inventor had recorded that no end-groups could be found in the polymers. This absence of end-groups in our polymers was the principal problem that determined the direction of our researches {70, 72, 73}. The essential and new feature proposed by us to explain the absence of end-groups from the reaction mixtures is the ring expansion mechanism involving a cyclic transition state. This is the central theme of the three papers reproduced here which deal largely with the mechanism of the polymerisation of the DCA and provide explanations of why the polymers produced by others under less strictly anhydrous conditions contain OH endgroups. Once again the difference between our results and those of others was found to be due to a difference in purity of reagents and rigour of experimental procedure; see for example {115}. Further, because there had been so little work on the physical chemistry of the oxonium ions involved, it seemed appropriate to also study other aspects of their chemistry. These episodic and mainly practical researches are not presented here, but they included a direct demonstration by conductivity measurements of the solvation of the Et3O+ ion by Et2O and DCA and the effect of this on the dissociation constant of Et3O+ salts {77}. Also, because of the frequent use of theses salts as polymerisation initiators by others, we made a detailed study of their spontaneous decomposition in solution which had been known since their discovery by Meerwein {74, 110}. The major enterprise in this field, oxonium ion chemistry, was something entirely new. In view of the success of the concurrent studies in the writer’s laboratory on the polarographic characterisation of carbenium ions, it was an obvious step to try the polarography of oxonium ions. This was unexplored territory, with monsters, phantoms and mirages as found in the best adventure stories {101, 113, 121}. The outcome, however was that the polarography of oxonium ions appeared to be a promising enterprise, and polarography also proved useful for investigating the hydride transfer between trityl ion and various oxacyclic compounds {108}. However, as these studies have no direct relation to polymer science (yet?), they are not included here. Note to Chapter 7.2 The captions to the Tables 1 and 2 in Chapter 7.2 have been corrected so that where in the original there was [tert-Ox.Ion] it now reads: +

([t-Ox ] + [HmFm]), where HmFm = hemiformal.

714

7.1

The Mechanism of the Polymerisation of Cyclic Formals (1971) P. H. Plesch

This paper was first published in the IUPAC International Symposium on Macromolecular Chemistry, Budapest, 1969, 213-221. Reproduced with permission from IUPAC, copyright 1969.

Introduction There are many studies of the mechanism and kinetics of the polymerisation of cyclic oxygen compounds, but only relatively few of these are concerned with cyclic formals. In the present paper I will review this field, and I hope to show that formals have some special characteristics which distinguish their polymerisations from those of other cyclic oxygen compounds. Since it is not possible to deal with all aspects of this group of reactions in one lecture, I will concentrate attention on questions of chemistry and mechanism, and I will not deal with other aspects, such as the thermodynamics and kinetics of these polymerisations. Most of the published work has been done with 1,3dioxolan (I) and there are only very few papers on any other cyclic formals, although the patent literature on the homo- and copolymerisation of (I) and other cyclic formals is quite extensive. The polymerisation of (I) has been studied over a wide temperature range, in bulk and in solution, and with several different catalysts. All these are protonic acids, or metal halides, or carbonium, carboxonium, or oxonium compounds. None of the cyclic formals tested can be polymerised by radicals or anions. It is generally believed that cyclic formals substituted in the 2- and/or in other positions do not polymerise for thermodynamic reasons, although there is little reliable information on this. (Cyclic formals with methylene or other unsaturated groups will not be considered here.) However, there is no evidence that this generalisation applies to rings of more than seven members; in fact, consideration of Dainton, Devlin, and Small’s [1] famous ΔGlc – x curve (x = number of atoms in the ring) and of Yamashita’s [2] curve relating experimental heats of polymerisation to x, suggests that some larger rings carrying one or more substituents should be polymerisable. It is less well known, but not unexpected, that it is possible to polymerise some substituted dioxolans which are part of another ring-system, because this type of substitution may increase the ring-strain. The work of Korshak et al.

715

Commercial rubbers

Developments in the Theory of Cationoid Polymerisations [3], and of Schuerch’s group [4] on the polymerisation of 1,6-β-D-gluco- and -mannopyranose derivatives is especially significant in this context, because these compounds are bridged 1,3-dioxolans.

The structure of the polymers The first systematic study of the structure of polydioxolan by Okada, Yamashita, and Ishii [5] proved that the polymer formed by bulk polymerisation with various catalysts at 0 °C had a completely regular structure resulting from the breaking of the O–1–C–2 link: –O–CH2–O–(CH2)2–O–CH2–O–(CH2)2–. In polymers made with aqueous perchloric acid and acetic anhydride they identified acetoxy and hydroxyl end-groups. The next structural study of polydioxolans of DP ranging from 7 to 70 by Plesch and Westermann [6] confirmed the regular structure of the polymer. It was also shown that when a polydioxolan was formed and then depolymerised in solution by perchloric acid, the only product was monomer. This is apparently in conflict with the findings of Miki, Higashimura, and Okamura [7] who reported that a reaction mixture, in which dioxolan had been polymerised for 3 hours at 35 °C by BF3·Et2O, contained 1,3,5-trioxepan, 1,4dioxane, trioxane, and other compounds. Most probably the difference is at least partly due to the long reaction time and the use of boronfluoride, which is well known to produce more side-reactions than protonic acids. Studies of 1,3-dioxepan by Plesch and Westermann [8] showed that its polymers, produced by perchloric acid catalysis, also have a completely regular structure similar to that of the polydioxolans, and that depolymerisation produces no product other than the rnonomer. A study by Weichert [9] of the structure of poly-1,3,6-trioxocane (diethyleneglycol formal) showed that these polymers also have a regular structure resulting from fission of the O–1–C–2 bond of the monomer. The polymers of (I) and of 1,3-dioxepan made with perchloric acid under anhydrous conditions were found to contain virtually no end-groups [6-8]. The only detectable endgroup was –OH and its concentration was always extremely low and much lower than the concentration of polymer molecules. Plesch and Westermann therefore concluded that the polymers must be cyclic. This same conclusion, with respect to poly-dioxolan, had been formed by Gresham [10] many years previously, but had been largely ignored. In experiments with quantities of water of the same order of magnitude as the perchloric acid concentration, Plesch and Westermann found two hydroxyl end-groups for each water molecule, but again it was obvious from the DP that most of the polymer molecules did not have these - or any other - end-groups.

716

The Mechanism of the Polymerisation of Cyclic Formals (1971) Subsequent experiments by Jones and Plesch [11] showed that polymers of (I) and of 1,3dioxepan made with various triethyloxonium salts as catalysts, were also almost devoid of end-groups and therefore the great majority of the molecules must also be cyclic.

The propagation mechanism Before entering upon a detailed discussion of the propagation mechanism it is important to emphasise four points: 1. In order to form definite conclusions about the propagation mechanism, it is essential to have accurate information on initial and terminal groups. 2. As mentioned above, the only quantitative information of this kind which is available relates to polymers made with perchloric acid or triethyloxonium salts. 3. The nature of any terminal groups depends also on the reagent which is used for stopping the reaction. 4. Under most conditions the number of polymer molecules is vastly greater than the + number of catalyst molecules, at least with HClO4 and Et3O salts as catalysts.

The carboxonium ion theory The first suggestions concerning the mechanism, whereby polymers of cyclic formals are produced by protonic acids came independently from Weichert [12] and from Okada et al., [5]. They suggested that the propagating species is a carboxonium ion R·O(CH2)2·O+·CH2 (II); this is analogous to Kern and Jaacks’s mechanism for the polymerisation of trioxan. It is evident that a propagating species of this kind can only yield polymers free from end-groups if there is a 100% efficient end-to-end ring-closure reaction of the terminal group with the initial group; this, of course, is extremely improbable anyway. Furthermore, such a ring-closure reaction could only take place with a reactive initial group, such as OH, and this could only be formed from a protonic acid catalyst; initiation by tertiary oxonium salts would give an initial alkoxy group which could not take part in an end-to-end ring-closure reaction. Thus the formation exclusively of ringpolymers under the influence of trialkyloxonium salts cannot be explained by end-to-end cyclisation of a growing carboxonium ion (II). Another possibility is that the ion (II) reacts with an oxygen of the main chain to give a tertiary oxonium ion which is part of a macrocycle, and that the linear fragment forming part of this tertiary oxonium ion is then transferred as a new ion of type (II) to a monomer molecule.

717

Developments in the Theory of Cationoid Polymerisations The formation of rings by this back-biting mechanism implies that when the reaction mixture is neutralised, there should be a number of linear fragments corresponding to the number of catalyst molecules. Careful examination of the reaction mixtures has shown that if such linear fragments are present, their concentration is very much lower than that of the initiator [13] This, therefore, appears to exclude this and any other kind of ring formation by back-biting; this question will be discussed in more detail later. The most cogent argument against propagation by (II) is the demonstration by Jaacks et al., [14] that methoxymethyl perchlorate reacts with (I) to give dimethyl ether and dioxolenium perchlorate (III) (Reaction (A)).

CH3•OCH2+ClO4- + O

O

(CH3)2O + O

C H

O

ClO4-

(A)

(III)

Since the organic part of methoxymethyl perchlorate is a very close analogue of the ion (II), propagation by (II) is effectively ruled out, since, if these ions were formed, they would react with monomer to give (III). This conclusion is in conflict with the contention of Berman et al., [15] that (II) is the propagating species in the polymerisation of (I) by Et3O+SbCl6 - (IV). These authors observed that a solution of (IV) in ethyl chloride absorbs at 272 nm, that a reaction mixture containing (I) and (IV) absorbs at 228 nm, and that a solution of n-butylvinyl ether and (IV) absorbs at 231 nm. Since they assumed that the absorption of the polymerising n-butylvinyl ether is due to the –CH2–CH+–O–C4H9 ion and that the absorption of (IV) at 272 nm is due to the Et3O+ ion, they concluded that the absorption at 228 nm which they found when (I) was polymerised by (IV), is due to the ion (II) which is closely related to the carboxonium ion derived from the alkylvinyl ether. However, there is no independent evidence that trialkyloxonium ions absorb near 270 nm, or that carboxonium ions absorb near 230 nm; in fact we have found that Et3O+ClO-4 and Et3O+BF-4 do not absorb above 220 nm [13]. On the other hand Penczek has shown that SBCl5 and SbCl6- absorb at 272 nm in methylene dichloride, and SbCl3 and SbCl6- at 235 nm [16]. Therefore the argument of Berman et al., is at present quite unconvincing.

The ‘Keele’ and ‘Mainz’ theories Since the carboxonium ion has been eliminated as a possible propagating species, one is left with two alternatives which we may call the ‘Keele’ and the ‘Mainz’ theories. Plesch and Westermann [6, 8] have suggested that the cyclic formals polymerise by a ringexpansion mechanism, in which no free end is ever formed. This is illustrated in Reaction (B), where Y = H if the initiator is a protonic acid, and Y = Et if the initiator is a

718

The Mechanism of the Polymerisation of Cyclic Formals (1971) triethyloxonium salt; thus when reaction is initiated by a protonic acid, the propagating species (V) or (VI) is a secondary oxonium ion. The depolymerisation is a pinching-off of monomer units from the ring-polymer.

(B)

The ring expansion mechanism is of course only a special case of the well-known mechanism by which dioxolan reacts with non-cyclic formals; e.g., (I) and CH2–(OMe)2 give (MeOCH2OCH2-)2 in this way. It also accounts in a simple manner for the cleanness of the monomer-polymer equilibrium and for the high yields of cyclic dimer (without any detectable linear fragments) which are obtainable from 1,3-dioxane and 1,3-dioxepan [8]. Jaacks and co-workers [17], however, maintain that in these polymerisations the propagating species is a tertiary oxonium ion (VII), and they consider the propagation to be essentially the same as in the polymerisation of tetrahydrofuran, as is shown in Reaction (C).

OH•(CH2)2OCH2• O

O

+ O

O

HO•(CH2)2OCH2O(CH2)2OCH2

O

O

(C)

When one considers how cyclic polymers could be formed from propagating species (VII) one is faced with exactly the same problem as with the carboxonium ion theory: either there must be a 100% efficient end-to-end ring-closure (which in any case would be confined to polymers with an initial hydroxyl group); or there must be ‘back-biting’ and the formation of linear fragments, as illustrated by Jaacks [17a]. To distinguish between the Mainz and Keele mechanisms it is necessary to do the following studies on strictly anhydrous polymerisation mixtures in which the initiator is a protonic acid: 1. One must determine hydroxyl groups quantitatively. If the Mainz theory is right, then there should be one hydroxyl group for every molecule of acid, if the initiator

719

Developments in the Theory of Cationoid Polymerisations is 100% efficient. Although there is some uncertainty about the rate at which protonated monomer and oligomer are formed, kinetic and electrochemical studies indicate that at least during the final, first-order stage of the polymerisation of dioxolan the concentration of growing species is equal to the initial concentration of perchloric acid, and this point is not in dispute [13, 17a]. +

2. One must treat a reaction mixture with the sodium salt RO–Na of an alcohol or phenol, and search for compounds of the type H–[O(CH2)2OCH2]n–OR, which would be formed from homologues of (VII) (Mainz theory), but not from secondary oxonium ions such as (V) or (VI) (Y = H) (Keele theory), which would form ROH. We have examined very carefully reaction mixtures of (I) in methylene dichloride with perchloric acid. Under our best anhydrous conditions, when the reaction mixtures were neutralised with anhydrous triethylamine, the concentration of hydroxyl groups was between 2 x 10-3 and 10-2 M, which corresponds to between 2 and 5% of the perchloric acid concentration [18]. These small concentrations of hydroxyl groups are difficult to determine accurately, and they probably correspond to the residual water concentration. Thus this line of evidence favours the Keele mechanism. The test (b) we carried out typically as follows: but we have also used many variations of this procedure [18]. We used an assembly of connected reaction tubes attached to the vacuum line. In one tube we polymerised (I) by perchloric acid in methylene dichloride. Reaction was stopped by adding sodium phenate, and any phenol formed from secondary oxonium ions was neutralised with sodium hydride. The volatile compounds were distilled into a second tube where the same experiment was repeated. This technique is based on that of Saegusa and Matsumoto [19]; phenol and phenyl ethers can be estimated separately by their UV spectra. In the first tube we found a (so far unidentified) phenyl ether; its concentration -2 increased with the initial monomer concentration and corresponded to about 10 M in the monomer, and it was independent of, and much smaller than the acid concentration. In the second tube we also found phenyl ether, whose concentration was also much smaller than that of the perchloric acid. Although this work is still incomplete, it shows that some tertiary oxonium ions are formed in the reaction, but that by far the greater part of the active species are secondary oxonium ions. The origin of the tertiary oxonium ions, which yield the involatile phenyl ether by reaction with C6H5O–, is not at all clear at present. Some may be formed from an impurity in the monomer and others may arise from a slow side-reaction.

720

The Mechanism of the Polymerisation of Cyclic Formals (1971) Jaacks and his colleagues [17] have claimed that when they terminated dioxolan polymerisations with sodium ethylate, they could detect ethyl ethers. It seems to us that these results may very well be due to the same kind of impurity and/or sidereaction that gave us the involatile phenylether, and therefore this evidence alone cannot at present be taken as proof of their mechanism.

Evidence from copolymerisation with styrene A quite different phenomenon, which helps to elucidate the propagation mechanism, is the copolymerisation of dioxolan with styrene [20]. It is well known that the triphenylmethyl cation reacts with (I) by hydride abstraction, giving triphenyl-methane and the dioxolenium ion (III) [21]. It follows, a fortiori, that if the much more reactive styryl ion were formed at any stage during the copolymerisation, it would react in the same way, and thus there could not be any copolymerisation. Moreover styrene cannot be polymerised cationically in the presence of ethers or other oxygen compounds, since these are much more basic than the olefin. Therefore the propagation step, by which styrene is incorporated in the polymer, must take place without the formation of a carbonium ion. An obvious alternative mechanism involves the insertion of the double bond into one branch of the oxonium ion. According to the Mainz theory one might represent this by Reaction (D1) or (D2):

(D1)

(D2)

The oxonium ion resulting from Reaction (D1) is a derivative of a dioxacyloheptane. A further styrene unit could be incorporated into its near branch by a reaction analogous to route (D2). The product of Reaction (D2) could incorporate a styrene unit into the ring by route (D1). According to the Keele theory the incorporation of styrene would be represented by Reaction (E). Since Yamashita’s experiments were done with the catalyst boron fluoride etherate, whose mode of action is still quite obscure, we denote the activating group derived from the catalyst by Y (which may be Et).

721

Developments in the Theory of Cationoid Polymerisations

(E)

The Y-group (like the linear branches of the oxonium ions in Reactions (D1) and (D2)) is mobile over all the oxygen atoms in the system. Thus further styrene units can be incorporated by Reaction (E) until all the formal oxygens have been converted into ether oxygens, and an alternating copolymer is obtained. Reactions (D1) and (D2) could also only give copolymers with not more than 50% of styrene. Experiment [20], however, shows that when a great excess of styrene is used, sequences of up to four styrene units can be formed, although the formation of styrene sequences is under all conditions much less probable than the formation of dioxolan sequences. Thus both reaction mechanisms require a reaction step such as (F) whereby sequences of styrene units can be formed:

CH2

CH2 —0(CH2)3CHØ–O+

+ CH2:CHØ → —(CH2)3CHØCH2CHØ –O+

CH2

(F)

CH2

It would be useful to have direct evidence on this from model reactions. The remarkably high molecular weights of copolymers of dioxolan and styrene, which were achieved by Yamashita, are also easily intelligible in terms of the insertion mechanisms shown in schemes (D) and (E): the fact that cationically produced polystyrenes have low molecular weights is mainly due to proton transfer to monomer from the β-carbon at the growing end of a chain. If there is no growing end but a cyclic oxonium ion, this reaction cannot occur, and thus the principal chainbreaking reaction is frustrated. It remains to be seen whether these copolymers are cyclic and if so, whether they are wholly so, or whether they contain also linear fragments; thus we could distinguish between the Mainz and Keele theories as applied to this copolymerisation.

Conclusion From the foregoing discussion it appears that the mechanism of polymerisation of cyclic formals may differ considerably from that by which cyclic ethers polymerise,

722

The Mechanism of the Polymerisation of Cyclic Formals (1971) and our recognition of this difference should stimulate studies on other cyclic compounds. Of course, even for the cyclic formals there are still unresolved problems, especially the mechanism by which metal halides initiate their polymerisation [16]. Once again it has become evident that attention to impurity effects and side-reactions is of paramount importance if the conclusions from chemical studies of catalytic reactions are to be valid. I cannot conclude without referring to the numerous papers dealing with the kinetics of cyclic formal polymerisations. Some of these show considerable mathematical virtuosity in interpreting the kinetic results, but very regrettably they contribute relatively little to our understanding, because the mechanisms used are completely unsubstantiated by any chemical evidence and the nature and concentration of growing centres is unknown. We see here again that kinetics without chemistry is little more than a mathematical exercise. We must also remember that so far only one single cyclic formal has been studied in detail. It seems to me very likely that this class of compounds, which are so easily prepared from cheap materials, will eventually repay a much more extensive study.

References 1.

F. S. Dainton, T. R. E. Devlin, P. A. Small, Trans. Faraday Soc., 51, 1710 (1955).

2.

Y. Yamashita, M. Okada, K. Suyama, H. Kasahara, Makromol. Chem., 114, 146 (1968).

3.

V. V. Korshak, O. P. Golowa, V. A. Sergew, N. M. Merlies, R. Y. Sneer, Vysokomol. Soyed., 3, 477 (1961).

4.

a. C. C. Tu, C. Schuerch, Polymer Letters, 1, 163 (1963); b. E. R. Ruckel, C. Schuerch, J. Amer. Chem. Soc., 88, 2605 (1966); c. E. R. Ruckel, C. Schuerch, J. Org. Chem., 31, 2233 (1966); d. E. R. Ruckel, C. Schuerch, Biopolymers, 5, 515 (1967); e. J. Zachoval, C. Schuerch, J. Amer. Chem. Soc., 91, 1165 (1969); f. J. Frechet, C. Schuerch, J. Amer. Chem. Soc., 91, 1161 (1969).

5.

M. Okada, Y. Yamashita, Y. lshii, Makromol. Chem., 80, 196 (1964).

6.

a. P. H. Plesch, P. H. Westermann, Symp. on Macromolecules, Prague, 1965, Preprint 506. b. P. H. Plesch, P. H. Westermann, J. Polymer Sci., C16, 3837 (1968).

723

Developments in the Theory of Cationoid Polymerisations 7.

T. Miki, T. Higashimura, S. Okamura, Polymer Letters, 5, 583 (1967).

8.

P. H. Plesch, P. H. Westermann, Polymer, 10, 105 (1969).

9.

D. Weichert, Symp. on Macromolecules, Prague, 1965, Preprint 323. J. Polymer Sci., C16, 2701 (1967).

10. W. F. Gresham, USPatent 2,394,910. 11. F. R. Jones, P. H. Plesch, Chem. Comm., 1969, 1230. 12. D. Weichert, Plaste und Kautschuk, 10, 12 (1963). 13. F. R. Jones, P. H. Plesch, P. H. Westermann, unpublished. 14. V. Jaacks, H. Frank, E. Gruenberger, W. Kern, Makromol. Chem., 115, 290 (1968). 15. E. L. Berman, E. L. Ludwig, V. A. Ponomarenko, S. S. Medvedev, Vysokomol. Soyed., 10, 476 (1968). 16. S. Penczek, A. Stolanczyk, S. Slomkowski, P. Kubisa, S. Penczek, 23rd IUPAC Congress Boston, 1971, Macromol. Preprints, p. 178. 17. a. V. Jaacks, K. Boehlke, E. Eberius, Makromol. Chem., 118, 354 (1968); b. V. Jaacks, K. Boehlke, H. Frank, P. Weyland, Symp. on Macromolecules, Budapest 1969, Abstract 2/10. 18. F. R. Jones, P. H. Plesch, to be published. 19. T. Saegusa, S. Matsumoto, J. Polymer Sci., A-1, 6, 1559 (1968). 20. a. M. Okada, Y. Yamashita, Y. Ishii, Makromol. Chem., 94, 181 (1966); b. Y. Yamashita, M. Okada, M. Hirota, Makromol. Chem., 122, 284 (1969). 21. S. Slomkowski,, S. Penczek, Chem. Comm., 1970, 1347.

724

7.2

The Propagating Species in the Polymerisation of 1,3-Dioxacycloalkanes by Perchloric Acid (1975) Y. Firat, F. R. Jones, P. H. Plesch and P. H. Westermann Dedicated to Herman Mark

This paper was first published in Die Makromolekulare Chemie, 1975, Supplement 1, 203-216. Reproduced with permission from Huthig & Wepf Verlag, copyright 1975.

Summary The object of the work described was to discriminate between the two principal rival theories concerning the polymerisation of 1,3-dioxacycloalkanes by anhydrous perchloric acid, the ‘Mainz theory’ and the ‘Keele theory’. By means of Jaaks’s method for determining tertiary oxonium ions we found that in polymerisations under the driest conditions the concentration of these is negligibly small. This was done with 1,3-dioxolane (1), 4-methyl-1,3-dioxolane (4), and 1,3-dioxepane (5), and the findings are supported by determinations of the content of hydroxy groups of polymers prepared and ‘killed’ under different conditions. It follows that when the water content of the reaction mixtures is less than ca. 10-4 M the propagation is principally by secondary oxonium ions, and that it must therefore go by the ring-expansion mechanism of Plesch and Westermann. Water causes the formation of tertiary oxonium ions and this probably explains why previously other workers and ourselves had reported their presence, and sometimes their dominance, in reaction mixtures prepared under much less stringent conditions. The recent theory of Penzcek, which involves co-ordinated oxy-carbenium ions, is also shown not to be applicable to the systems considered here. The heuristic value of the ring-expansion theory is illustrated briefly by reference to a new method of synthesising crown ethers from 1,3-dioxacycloalkanes, which arose from it.

725

Developments in the Theory of Cationoid Polymerisations

Introduction The polymerisations of 1,3-dioxacycloalkanes, such as 1,3-dioxolane (1), by acids, oxonium salts and related initiators are equilibrium reactions. Most workers are agreed that when these reactions are carried out under ‘reasonably’ anhydrous conditions with perchloric acid as initiator, the number of end groups detectable is very much smaller than the number of polymer molecules, and one is thus driven to the conclusion that the great majority of the molecules are cyclic. Some 1,3-dioxacycloalkanes under near-ceiling conditions can form crystalline cyclic oligomers in very high yields. The theories concerning the mechanism of these polymerisations have been reviewed by Jaaks et al., [1] and by Plesch [2]. Whereas Jaacks considered four rival theories, Plesch thought that at the time he wrote only two theories needed consideration. The first is the ‘Mainz theory’ developed by Jaacks and his associates [3] which sees the propagation in terms of tert-oxonium ions 2 reacting by ring-opening with a monomer such as 1:

(i) The ‘Mainz theory’ interprets the propagation as the opening of an O-alkylated ring at the formal bond and the attachment of the C-2 to an O-atom of the next monomer, thus reforming a tert-oxonium ion. This is strictly analogous to the growth mechanism in the polymerisation of cyclic ethers and of 1,3,5-trioxan. The formation of cyclic oligomers and polymers is explained by the ‘Mainz theory’ in terms of a ‘back-biting’ mechanism in which the growing tertiary ion 2 reacts with one of the O-atoms of a unit along the chain to form another tert-oxonium ion consisting of a linear fragment attached to an O-atom of a polymeric ring. The nature of R depends upon the initiator (for protonic acids R=H), so that when such initiators are used, the reaction mixture should contain a concentration of –OH groups of the same order of magnitude, if not equal to, the concentration of acid. This important point will be taken up in detail later. The second theory is the ‘Keele theory’ proposed by Plesch and Westermann [2, 4, 5] in which the propagation reaction is seen as a ring-expansion during which no free chainend is formed:

(ii)

726

The Propagating Species in the Polymerisation of 1,3-Dioxacycloalkanes… The group Y, derived from the initiator, is a proton if the initiator is a protonic acid, and e.g. C2H5+ if the initiator is (C2H5)3O+, etc. Since that time a further theory has been advanced by Penzek [6] which we will discuss at the end of this paper. It had been the hope of the senior author to resolve the conflict between the ‘Mainz and Keele theories’ in a very direct manner by determining the nature of the propagating ions and their concentrations by polarographic studies on polymerising solutions. Regrettably, various technical obstacles have so far frustrated this plan, though much of the background work on the half-wave potentials for the reduction of some oxonium ions at the dropping Hg electrode has been completed [7], and we hope to resume work towards this objective shortly. Our attempts [2] to determine the nature and concentration of the ions in the polymerising solutions by neutralising (‘killing’) them with sodium phenoxide, indicated that the method would require further development. We, therefore, decided to adopt the well-tried technique devised by Jaacks and his school, of determining quantitatively the concentration of tert-oxonium ions in a polymerising systems [8, 9]. The principle of the method is that the reaction is killed with sodium ethoxide. Tertiary ions are thus destroyed by the formation of linear polyformals with terminal ethoxy groups (reaction (iii)) which, after hydrolysis (reaction (iv)), are determined gas-chromatographically as ethanol. Secondary oxonium ions, such as those envisaged by the ‘Keele theory’, would form ethanol (reaction (v)) which is removed by evaporation of a solution of the polymer before the hydrolysis; in this way also any ethanol originating from surplus C2H5O- is removed.

2 + C 2 H 5O − → R – (OCH 2 CH 2 OCH 2 )n – OC 2 H 5 + 1

(iii)

3

3 + H 2 O → ROCH 2 CH 2 OH + ( n − 1)HOCH 2 CH 2 OH + nCH 2 O + C 2 H 5OH (iv) H + O H2C H2 C

H2 C

O

O CH2 CH2

O

H 2C +C2H5O–

C O H2 n

H2C

H2 C

O CH2 CH2

O

+C2H5OH

C O H2

(v) n

It is an irony which no-one would have relished more than our late friend Jaacks himself, that the very method which he devised, was in the end used by us to establish the rival theory. At this point the senior author wishes to say simply that his carrying on, to a definitive conclusion, of the controversial researches which we enjoyed together for so 727

Developments in the Theory of Cationoid Polymerisations many years, is intended to be a tribute to, and in no way a triumph over, a gentleman, a chemist, and a friend of rare distinction. In this paper we report our results obtained by Jaacks’s method, together with some earlier findings, obtained by different methods, which help to establish our case.

Experimental part General: Experiments over several years by a variety of techniques had shown us that the concentration of -OH end-groups and that of tert-oxonium ions in polymerisation mixtures initiated by anhydrous HClO4 depend critically upon the purity, especially the dryness, of solvent, monomer, and killing reagent. Our most recent techniques, described below, were developed out of this experience and we believe them to be a useful advance on those in use previously and elsewhere. Materials: 1,3-Dioxolane (1) and 1,3-dioxepane (5) were prepared and purified conventionally. Compound 1 contained no impurities detectable by GLC, but 5 contained a trace of tetrahydrofuran (THF) which could not be removed even by distillation on a Fenske column with a reflux ratio of 50:1; 4-methyl-1,3-dioxolane (4) was prepared by Astle’s method [10]. All monomers were dried preliminarily by storage over LiAlH4 in reservoirs attached to a conventional high-vacuum line fitted only with all-metal valves, and then stored with liquid Na-K alloy until used. Methylene dichloride was purified conventionally, distilled on a Normatron 1.5 m column, dried i.vac. over LiAlH4 on a conventional high-vacuum line, and then stored for 24 h over a fresh sodium film immediately before use, in a reservoir attached to the vacuum line. Note: It is very dangerous to bring CH2Cl2 into contact with a sodium film except i.vac. and after drying it very carefully. Phials of anhydrous perchloric acid in methylene dichloride were made up as described [11]. Sodium ethoxide was prepared i.vac. from purified ethanol and sodium purified by ‘cascade fusion’. Solutions of it in diethyl ether were prepared and filled into phials [11, 12] by standard techniques on a tapless, jointless high-vacuum system. These solutions were colourless, whereas those prepared i.vac. from vacuum-distilled sodium were always yellow or brown.

Apparatus and procedure: Determination of tert-oxonium ions (Carried out by Y. Firat) Polymerisation: The polymerisations were carried out in tubular reactors containing a phial of HClO4 solution in CH2Cl2 and a glass-enclosed magnetic phial-breaker; the

728

The Propagating Species in the Polymerisation of 1,3-Dioxacycloalkanes… reactors were fitted with a side-arm containing a phial of sodium ethoxide in diethyl ether. Measured quantities of solvent and monomer were distilled into the reactor which was then sealed off from the vacuum line. After thermostatting, the phial of initiator was broken, the solution was mixed well by shaking and left to react. Then the phial of the sodium ethoxide solution was dropped from the side-arm into the reactor and broken with strong agitation, at the reaction temp. The polymer solution was then evaporated in a ‘Rotavapor-R’ apparatus to remove all volatile material. Water was then added and evaporated off, and this was repeated several times in order to decompose unreacted sodium ethoxide and to remove the ethanol thus formed. Some experiments (Table 1, Experiments No. 97 and 108) were carried out in one leg of an H-shaped reactor. After the killing of the reaction, all volatiles were distilled into the other leg of the reactor which was then scaled off, and its contents were analysed by GLC for ethanol. We hoped to measure in this way the ethanol formed from the sec-oxonium ions by reaction (v), but as the results show, the recovery of ethanol was rather incomplete, presumably because much of it remained trapped in the polymer. In some experiments a phial containing a measured amount of water was broken before the initiator phial (Table 1, Experiments No. 115, 111 B, 114). As the polymerisation mixtures containing 4 were extremely viscous, a special technique had to be used with these, which has been described [14]. Hydrolysis and analysis: The purified and dried polymer (0.1 g) and 1 ml of aqueous HCl (0.1 mol l-1), together with a measured amount of acetone (as internal GLC standard), was heated for 1 h at 100 °C in a sealed tube to hydrolyse the polymer. The solution was then neutralised and the ethanol content was determined by GLC by means of a calibration graph. As polymers of 4 and 5 are strongly hydrophobic and are thus hydrolysed only very slowly in water, they were hydrolysed in aqueous dioxane.

Conductivity measurements and determinations of the –OH content (Carried out by P. H. Westermann and F. R. Jones) Most of the experiments were done either in the Biddulph-Plesch reaction calorimeter or in vacuum dilatomers, both types of device being fitted with electrodes so that the changes of electrical conductivity during the reactions could be followed [15]. The preparation and purification of monomers and solvent were essentially as described above, except that the final drying by Na-mirror (CH2Cl2) or by Na-K alloy (monomers) was not used.

729

730

1.9

1.9

1

1

1.4

111 B

114

101

102

103 3.5

2.92

3.16

4.86

4.69

5.12

8.51

3.77

4.64

3.52

–60

–30

–30

0

0

0

0

0

0

0

0

T, °C

-

-

-

4.86

2.4

1.28

-

-

-

-

-

103·[H2O] mol l-1 b

0.1

0.7

0.31

e

0.1

0.1

0.1

9

8.5

7.8

0

0.1

0.1

0.1

0.1

103·[sec-Ox.Ion]c 103·[t-Ox+]+[HmFm]d mol l-1 mol l-1

a Carried out by Y. Firat b Added water c Minimum values d Maximum values e An exceptionally small vessel and an unusually long evacuation were used for this experiment HmFm Hemiformal

1.9

115

2

105 B

2.86

1.9

108

67

1.9

66 B

2.27

[1] 103·[HClO4] -1 mol l mol l-1

1.86

a

97

Exp. no

Table 1 The content of tert-oxonium ions in poly(1,3-dioxolan)s

1.9

1.8

1.5

103·[t-Ox+]+[HmFm] [HClO4]

Developments in the Theory of Cationoid Polymerisations

The Propagating Species in the Polymerisation of 1,3-Dioxacycloalkanes… The –OH content of polymers was determined by IR spectroscopy. Calibration graphs were constructed by means of solutions of 1,4-butanediol in polydioxolane. It was ascertained that any ethylene glycol which could have been formed by hydrolysis of monomer or polymer would have been removed completely during the isolation and purification of the polymers. The smallest concentration of OH groups given here was at least twice as great as the lower detection limit.

Results and discussions Typical reaction curves for monomers 1, 4, and 5 are shown in Figures 1 a–c.

H2 C O

O H2C O

H2C

CHCH3 4

O

CH2 CH2

H2C CH2 5

Full details of the kinetics will be published in due course, but for the present it suffices to say that for 1 under the conditions which concern us here the reaction curves beyond the inflexion point are of first order, and that for 5 this applies to the whole reaction curves. As is shown in Figures 2a and b, the reactions obey the kinetic equation

– dm / dt = k1 ( m − me ) = k2 ( a – ai )( m – me ) where m = monomer concentration, me = m at equilibrium, a = [HClO4] and ai is the concentration of acid inactivated by impurities. The final conductivities κf of the reaction mixtures are shown in Figure 3. All the experiments represented in each of the graphs were done under the same conditions so that yield, DP, and, therefore, the viscosity, were the same. It follows from these that κf – κi is linearly proportional to a (κi = ‘impurity intercept’ probably mostly due to residual water). This, and the reaction pattern for the generation of ions during the reaction, makes it highly probable that the concentration of growing ions is not only proportional to, but virtually equal to that of the perchloric acid. The conductivities obtained with 4 are of the same order (Figure 1b). No full kinetic study of 4 has yet been made. We can thus conclude that for 1 and 5, and probably 4, the concentration of growing ions is very close to that of the perchloric acid.

731

Developments in the Theory of Cationoid Polymerisations

Figure 1a Simultaneous plots of temperature and electrical conductivity against time for the polymerisation of 1.22 M 1,3-dioxolane (1) with 3.9 x 10-3 M HClO4 at –22 °C (Experiment PHW 50) (Calorimeter)

Figure 1b Simultaneous plots of change of height of meniscus and of conductivity for the polymerisation of 3 M 4-methyl-1,3-dioxolane (4) with 2.3 x 10-3 M HClO4 at –51 °C (Experiment YF 26 B) (Dilatometer)

732

The Propagating Species in the Polymerisation of 1,3-Dioxacycloalkanes…

Figure 1c Simultaneous plots of temperature and electrical conductivity against time for the polymerisation of 0.6 M 1,3-dioxepane (5) with 1.6 x 10-4 M HClO4 at –40 °C (Experiment PHW 137) (Calorimeter)

Figure 2a The dependence of k1 on [HClO4] for the polymerisation of 1,3-dioxolane (1) at –22 °C. All calorimeter experiments except that at [HClO4] = 0.5 x 10-3 M which was done in a dilatometer (PHW)

733

Developments in the Theory of Cationoid Polymerisations

Figure 2b The dependence of k1 on [HClO4] for the polymerisation of 1,3-dioxepane (5) at – 40 °C. (Calorimeter experiments, PHW)

The results obtained by Jaacks’s ethoxide method, shown in Tables 1 and 2, prove that for all systems the concentrations of tert-oxonium ions are very considerably smaller than those of the perchloric acid. In view of the correlations shown above, they must also be much smaller than the concentrations of ions in the polymerising solutions. We conclude, therefore, that the principal growing ions are not tertiary, and that they must, therefore, be secondary.

Table 2 The content of tert-oxonium ions in polymers of 4-methyl-1,3dioxolane and 1,3-dioxepane (5) Monomer

[Monomer] mol l-1

104·[HClO4] mol l-1

T, °C

103·([t-Ox+]+[HmFm])a mol l-1

Y 31 B

4

3

2.89

–56

0.1

Y 32 B

4

3

2.88

–50

0.1

107

5

0.8

2.32

0

0.1

109

5

0.7

5.8

–30

0.1

112

5

0.74

3.07

–60

0.1

Experiment no.

a Maximum values

734

The Propagating Species in the Polymerisation of 1,3-Dioxacycloalkanes…

Figure 3a Dependence of the final conductivity κf on [HClO4] for the polymerisation of 1.22 M 1,3-dioxolane (1). Initial T = –22 °C, final T = –16 °C for the calorimeter experiments with [HClO4] > 10-3 M. The two experiments at the lowest [HClO4] where done in a dilatometer at –20 °C (PHW)

Figure 3b Dependence of κi on [HClO4] for the polymerisation of 0.8 M 1,3dioxepane (5) at – 20 °C. (Dilatometer, PHW)

735

Developments in the Theory of Cationoid Polymerisations Next, we consider the effect of water. The runs 115, 111 B, 114 in Table 1 show that water causes the formation of tert-oxonium ions, and our results suggest that as the amount of water increases, the number of these ions per mol of perchloric acid approaches 2. On this evidence one can conclude that the small amounts of tert-oxonium ions found by us in the absence of added water are probably due to residual water whose concentration we know to be less than ca., 10-4 M in our systems from conductivity and kinetic data. These results are supported by our earlier studies on the –OH group content of polydioxolanes formed under different conditions in systems which had a slightly higher water content (between ca. 10-4 and 10-3 M) than those used by Y. F. (Table 3). We found that when water was, or was contained in, the killing reagent, the –OH content of the polymers increased considerably, but that under the best conditions available when those experiments were done, the –OH concentration was very much smaller than that of the perchloric acid. Since it was a necessary corollary of the ‘Mainz theory’ that all the linear fragments forming part of the tert-oxonium ions would have at least one (terminal) –OH group after neutralisation, namely that formed by initiation, this discrepancy between the number of OH groups (= number of linear fragments) and the number of perchloric acid molecules (and therefore of ions) had long been one of the most potent objections to the ‘Mainz theory’. The consequences of our findings are: i) that under anhydrous conditions the polymerisation of at least three different 1,3dioxacycloalkanes initiated by perchloric acid is carried by sec-oxonium ions; ii) that therefore under these conditions the propagation must be by ring-expansion; iii) that in the presence of water, tert-oxonium ions are generated and presumably participate in the reaction. Since it is now evident that extremely rigorous drying of all reagents is essential to prevent the formation of tert-ions in these systems, all previous work done under less stringent conditions, which purported to prove that tert-oxonium ions are essential features of the polymerisation initiated by anhydrous perchloric acid, must be discounted. In other words, we see no reason to deny the existence of tert-oxonium ions in those systems in which Jaacks and his collaborators alleged that they found them; indeed, considering their experimental conditions in the light of what we have found out since then, it is entirely credible that in some of their studies the tertiary ions were dominant. For instance, Jaacks and Boehlke [16] reported that for 1 with perchloric acid in methylene dichloride at 30 °C, water caused the formation of 1,3,5-trioxepane, mol for mol, and

736

10

17

PHW 123

FJ 128

10

11

2.0

1.8

2.0

2.0

2.0

2.0

[Monomer] mol l-1

10.00

10.00

6.00

4.00

3.00

0.36

102·[HClO4] mol l-1

35

35

20

20

33

33

41

40

35

%Y

c

11

12

12

8

12

14

13

15

14

DP

0.53

0.53

0.19

0.9

2.4

0.77

1.0

1.00

0.45

102·[OH] mol l-1

a

d

d

d

d

f

(C2H5)3N(+H20)

(C2H5)3N

(C2H5)3N(+H20)

NH4OH vap

H2O

NH4OH vap

NH3 gas

NH4OH vap

NH4OH vap

Killing reagent

e

e

a The reproducibility of the results shows that the differences between [OH] obtained with different killing agents are meaningful. The last three results show that when the reaction mixtures are killed under anhydrous conditions, the [OH] is very much smaller than [HClO4] (=a) b The reaction mixtures marked A and B were divided into two portions without breaking the vacuum, and each of these was then neutralised i. vac. with a different killing agent c Yield of polymer d Vapour from conc. aq. NH4OH e Anhydrous (C2H5)3N was added to the reaction mixture i. vac., and water was added after opening the reaction vessel f The polymer was isolated without addition of water

FJ 180B

FJ 180 A

FJ 179B

FJ 179A

FJ 178B

12

15

PHW 15

FJ 178A

T, °C

Experiment no b

Table 3 Concentration of hydroxyl groups in poly(1,3-dioxolane)s

The Propagating Species in the Polymerisation of 1,3-Dioxacycloalkanes…

737

Developments in the Theory of Cationoid Polymerisations from their results they deduced that the content of adventitious water in their reaction mixtures was ca. 4 x 10-3 M, whilst the [HClO4] which they were using was 4.6 x 10-3 M. Thus, on the basis of our results a large concentration of tert-oxonium ions is to be expected in the reaction mixtures prepared by their methods. However, it must now be recognised that these tertiary oxonium ions are incidental features, originating from impurities (mainly water) and that only traces of them are to be found under the cleanest conditions. We now examine the theory recently put forward by Penczek [6]. Strictly, we would not need to concern ourselves with it, as the system to which it is said to apply does not involve initiation by perchloric acid, but by triphenylmethyl salts. None the less, it is useful to consider it briefly. Penczek believes that the propagating species in his systems is an oxy-carbenium ion stabilised by co-ordination of two oxygens from a polymer molecule, as shown in structure 6:

+ …–CH2CH2O – H2C 6

O—CH2–… CH2 O—CH2–…

We are, of course, unable to comment at present on the validity of this view for his systems, but we can say firmly that in our systems this cannot be the propagating species, because there is no doubt that 6 would react with ethoxide ions to give terminal –CH 2CH 2OCH 2OC 2H 5 groups which, on hydrolysis of the polymers would, like the tertiary ions, give the ethanol of which we found only traces. In concluding this paper dedicated to our distinguished octogenarian, it is especially appropriate to mention the heuristic practical value which our ring-expansion theory has had, since he has always been intent upon applications and practical uses. It was the ring-expansion theory which led the senior author to imagine that the acid-catalysed reactions of cyclic formals with olefins would be insertion reactions [21]. In his view they involve the insertion of an olefin into the O–1, C–2 bond of a protonated (or alkylated) 1,3-dioxacycloalkane:

738

The Propagating Species in the Polymerisation of 1,3-Dioxacycloalkanes… In this way the unstable 1,3-dioxacycloalkanes and their oligomers would be converted into stable ethers. This has been proved experimentally, and the reaction offers some exciting synthetic possibilities [17, 18]. In particular, it provides a new route to a variety of new crown ethers, such as the 1,4,7,10-tetraoxa-11,11-dimethylcyclotridecane (a 13-crown[4]-ether) from isobutene and the formal of triethylene glycol; but that is another story!

Acknowledgements We thank BIP Chemicals Ltd., for Research Studentships to PHW and FRJ, the British Council and the Turkish Cultural Ministry for support of YF, the British Science Research Council for funds for equipment and technical help, the National Research Development Corporation for support of the work on crown ethers, and Dr. D. Schlotterbeck for instructing us in the Jaacks ethoxide method. Note added in proof: J. Kops and H. Spanggard (Makromol. Chem. 176, 299, (1975) also favour the ring-expansion theory.

References 1.

K. Boehlke, P. Weyland, V. Jaacks, IUPAC 23rd Congress, Boston 1971, Symp. M 10, Macromol. Preprint, Vol. 2, p. 641.

2.

P. H. Plesch, IUPAC Internatl. Symp. Macromol., Budapest 1969, Plenary and Main Lectures, Akademiai Kiado, Budapest 1971, p. 213.

3.

Reference 1 and papers quoted therein.

4.

P. H. Plesch, P. H. Westermann, J. Polym. Sci. C16, 3837 (1968).

5.

P. H. Plesch, P. H. Westermann, Polymer 10, 105 (1969).

6.

S. Penczek, Makromol. Chem. 175, 1217 (1974).

7.

P. H. Plesch, F. G. Thomas, J. Chem. Soc., Perkin II, 1532 (1975).

8.

V. Jaacks, K. Boehlke, E. Eberius, Makromol. Chem. 118, 354 (1968).

9.

K. Boehlke, H. Frank, V. Jaacks, IUPAC Internatl. Symp. Macromol., Budapest 1969, Preprint 2/10.

739

Developments in the Theory of Cationoid Polymerisations 10. M. J. Astle, J. A. Zaslowsky, P. G. Lafyatis, Ind. Eng. Chem. 46, 787 (1954). 11. P. H. Plesch, E. Mathias, Chem. Ind. (London) 1971, 1043. 12. P. P. Rutherford, Chem. Ind. (London) 1962, 1614. 13. A. Gandini, P. H. Plesch, J. Chem. Soc. 1965, 6019. 14. Y. Firat, P. H. Plesch, Makromol. Chem. 176, 1179 (1975). 15. A. Gandini, P. Giusti, P. H. Plesch, P. H. Westermann, Chem. Ind. (London) 1965, 1225. 16. K. Boehlke, V. Jaacks, Makromol. Chem. 145, 219 (1971). 17. Brit. Pat. 59856/73 assigned to NRDC, Inv.: J. Cooper, P. H. Plesch. 18. J. Cooper, P. H. Plesch, J. Chem. Soc. Chem. Commun. 1974, 1017.

740

7.3

Some Aspects of the Polymerisation of 1,3-Dioxacycloalkanes (1976) P. H. Plesch

This paper was first published in Pure & Applied Chemistry, 1976, 48, 3, 287-293. Reproduced with permission from Pergamon Press, copyright 1976.

Abstract This paper is concerned with the evaluation of old and new evidence concerning the mechanism of polymerisation of 1,3-dioxacycloalkanes (DCA). The most recent evidence on polymerisations initiated by perchloric acid shows that in strictly anhydrous systems the propagating species is a sec.-oxonium ion, so that under these conditions the propagation must be by the ring-expansion mechanism. In the presence of water, tert.-oxonium ions are formed. A comparison of the polymerisation behaviour of DCA and tetrahydrofuran (THF) leads to the conclusion that the propagation mechanisms must be different. By comparing the activation entropy of DCA polymerisations initiated by organic cations on the one hand with that of DCA polymerisations initiated by perchloric acid, and on the other with that of the polymerisation of THF, it appears that the polymerisations of DCA initiated by organic cations are most probably also propagated by the ring-expansion mechanism. Some mechanistic suggestions by Penczek and by Okada are scrutinised and the status of the oxy-carbenium ion as a propagating species is analysed.

Introduction Our knowledge of the polymerisation of 1,3-dioxacycloalkanes (DCA) is still rather incomplete. In this paper I will point out some of those areas which now appear to be well understood and to discuss others where clarification is required. Since I did something similar in 1969, the present review can be regarded as a sequel and a progress report [1]1. As I had the privilege of revising my paper after the Jablonna Microsymposium at 1

Because of their anomolous behaviour 1,3,5-trioxan and higher polymers of formaldehyde are excluded from the present discussion, unless they are mentioned specifically.

741

Developments in the Theory of Cationoid Polymerisations which it was presented, I have taken the opportunity of including some matters which arose during our discussions there.

Initiation by protonic acids The generality of this title is misleading, since a worthwhile amount of information is only available for perchloric acid. The mechanism of the initiation and propagation in the polymerisation of DCA, especially 1,3-dioxolan (DXL), has been discussed many times [1-7], and the origin and nature of the differences of opinion on these subjects need not be explained here at length. The most important facts can be summarised as follows. When DCA are polymerised under anhydrous conditions by perchloric acid, no endgroups are detectable by a variety of analytical methods, except traces of OH groups. The more rigorous the drying of monomer, solvent and apparatus, and of the reagent used for neutralising the reaction mixtures, the smaller is the concentration of OH groups and this is always much smaller than the concentration of polymer molecules [8-10]; most workers are therefore agreed that the greater part of these are cyclic [11]. It has also been found that under clean, dry conditions the polymerisations are strictly reversible and that even after many polymerisation-depolymerisation cycles the depolymerised reaction mixtures contain no degradation products, but only solvent, monomer, and acid. The mechanisms which have been proposed for this polymerisation by perchloric acid include the Mainz mechanism due to Jaacks and his school and the Keele mechanism due to Plesch and Westermann. Although both these have been described many times, it is worth restating them here, because even now some experienced workers appear not to understand the essential points of the controversy; this was evident again during the discussions at the Jablonna Microsymposium. The Mainz theory envisages the initiation as a two-step process in which protonation of the monomer (Equation 1) to give the secondary oxonium ion (I) is followed by reaction of the resulting ion with another monomer molecule to give the tert.-oxonium ion (II):

(1)

(2)

742

Some Aspects of the Polymerisation of 1,3-Dioxacycloalkanes According to this view the macrocyclic molecules found in the reaction product are formed by a back-biting reaction (3) in which the formal CH2 group adjacent to the tert.-oxonium ion reacts with an oxygen atom along the chain, generating a macrocyclic tert.-oxonium ion:

(3)

It is not difficult to show by conductance measurements that when the polymerisation of dioxolan becomes of first order, roughly at the first half-life, all the available acid has reacted with monomer or oligomer to produce active centres [10]. Thus on the Mainz theory one would expect to find a number of OH groups of the same order of magnitude as the number of perchloric acid molecules introduced; this is evidently not so, as long as the water concentration in the system is significantly less than that of the acid [10]. For 1,3-dioxepan the protonation is very much faster than for DXL and is complete long before the first half-life of the polymerisation. According to the Keele theory the primary reaction between the perchloric acid and the monomer is also (1), but thereafter the growth is by a ring-expansion reaction (4) in which no free end is ever formed; this goes by way of a four-centred transition state and gives the cyclic product (IV):

(4)

It is evident that the main difference between the two theories is that according to the Mainz theory the propagating species is a tertiary oxonium ion, whereas according to the Keele theory it is a secondary one. A simple and useful method of distinguishing between secondary and tertiary oxonium ions is due to Jaacks’s group and consists of neutralising the reaction mixture with an alkoxide [12]. Details of the method have been described, but it is worthwhile repeating here exactly what it shows. If EtO- is added to a reaction mixture containing secondary oxonium ions, whatever their structure may be, it abstracts the proton, forms ethanol, and leaves the oxygen compound:

743

Developments in the Theory of Cationoid Polymerisations

EtO − + HOR 2+ → EtOH + R 2 O

(5)

Thus, whatever the nature of R2O, it does not contain an ethoxyl group. If the reaction mixture contains tert.-oxonium ions (V) (reactions 6a, b), or oxycarbenium ions (VI) (reaction 6c), or any other oxygen-containing cations which are stoichiometrically equivalent to these (see for example, (X) and (XI) below), the ethoxide ions combine with them and are thus incorporated in the polymer: (6a) (6b) (6c)

In the standard procedure the neutralised polymer is purified and hydrolysed and the hydrolysate is examined for ethanol. The absence of ethanol indicates that no tert.oxonium ions containing a polymeric moiety and no polymeric oxycarbenium ions could have been present in the reaction mixture. The presence of the ethanol in the hydrolysate, however, signifies not only the existence of tert.-oxonium ions in the reaction mixtures but also the presence of hemiformal groups as will be shown below: the DCA and their oligomers can react with small quantities of water in the presence of acid to give diols (strictly, hemiformal-ω-ols) which react with ethoxide ions as shown in scheme (7):

(7)

Upon hydrolysis of the product or of the analogous compounds formed from DCA oligomers, only the ethyl group attached to the formal group is released as ethanol. Thus the presence of ethanol in the hydrolysate signals the presence both of tertiary oxonium ions and of hemiformal hydroxyls. Evidently the number of tert.-oxonium ions cannot exceed the number of anions in the system, i.e., the acid concentration, but there is no

744

Some Aspects of the Polymerisation of 1,3-Dioxacycloalkanes obvious limit to the number of hemiformal hydroxyls formed from adventitious or deliberately added water. Thus, if one were to interpret the analytical results by equating the number of mols of ethanol with the number of tert.-oxonium ions, one could arrive at the absurd result that this number is greater than the number of anions in the polymerising systems2. The method of Jaacks and his co-workers was used by Firat and Plesch to study the nature of the cations present when DXL, 4-methyl-DXL, and 1,3-dioxepan (DXP) were polymerised by anhydrous perchloric acid in methylene dichloride. They showed that when these polymerisations are done under the most rigorously dry conditions, the concentration of tert.-oxonium ions in the polymerising mixtures is at most close to the limit of detection and much less than the original concentration of perchloric acid and the concentration of ions in the polymerising solution. Since most types of experimental inadequacy or incompetence produce more ethanol in the hydrolysate than could be derived from tert.-oxonium ions, one must conclude from this evidence that the propagating species is a secondary oxonium ion. It follows necessarily that the ring-expansion mechanism is the best representation of the propagation reaction, that tert.-oxonium ions do not play an essential role in the polymerisation of DCA by perchloric acid, and that therefore this part of the old controversy appears now to be settled. There remains the interesting question why in the hands of Firat and Plesch the method gave this result, whereas the workers who devised it found that in their reaction mixtures tert. oxonium ions were dominant. The answer was found when water was added deliberately to the reaction mixtures before the perchloric acid, a procedure which produced relatively large amounts of ethanol in the polymer hydrolysate [10], (Table 1). Earlier work of the Keele group had already shown that if water was present in the reaction mixtures before the perchloric acid was added, hydroxyl end-groups were found in the polymer, which also implies the existence of tert.-oxonium ions [8]. An examination of the work of the Jaacks group showed that in their reaction mixtures apparently the amount of residual water was such that the formation of relatively large amounts of tert.-oxonium ions and of hydroxyl groups, including of course hemiformal hydroxyls, would be expected. Moreover, they found that DXL in the presence of water formed 1,3,5-trioxepan in quantities which were approximately equivalent to the amount of water present, and they suggested a mechanism for this reaction [5]. It follows from these observations that when DCA are polymerised by a protonic acid under ‘ordinary’ conditions (not rigorously dry), the polymerising mixtures contain neutral This mistake was made in Table 1 of Reference 10 where the column [tert.-oxonium ion] should be labelled [tert.oxonium ion] + [-COH2OH]; this matter arose during discussion at the Jablonna Microsymposium. 2

745

Developments in the Theory of Cationoid Polymerisations

Table 1 Formation of tert.-oxonium ions and hemiformal groups from DXL (1.9 mol l-1) in CH2Cl2 at 0 °C in the presence of HClO4 and H2O (concentrations in mol l-1) [10] 103[HClO4] 103[H2O] 103([tert. ox. ions] +[-OCH2OH])

4.64

5.12

4.69

4.86

0

1.28

2.40

4.86

<0.1

7.8

8. 5

9.0

and protonated rings, rings with chains attached at a tert.-oxonium ion, tert.-oxonium ions consisting of three linear segments (alkoxy-alkylated chains), protonated chains, and neutral chains. Since each of the chains will have at least one hydroxyl end-group from reactions similar to (2), (3) and (7), the concentration of the chains will be of the same order of magnitude as that of the water, and the propagation is then mainly by tert.-oxonium ions. Whether these are alkylated monomer (II) growing by a reaction analogous to (2), or whether they are macrocyclic molecules (V) analogous to (IV) with an oxy-alkyl group in place of the proton, and growing by ring-expansion, will be discussed in the next section.

Initiation by organic cations Perchloric acid which gives polymerisations with a relatively simple behaviour pattern, is unfortunately a little troublesome to prepare as an anhydrous solution in, for example, methylene dichloride [13], and the very few other strong acids with anions of sufficiently low nucleophilicity (HSO3F, HSO3CF3) also present some technical problems. For this reason by far the greatest number of polymerisation studies have been done with initiators which can either be taken from a bottle, such as borontrifluoride etherate, or which can be prepared relatively easily, such as the various salts of Ph3C+ or Et3O+. Unfortunately most investigators have not realised that the saving in effort which they had hoped to make by using such readily available initiators was largely nullified either because they were not aware how complicated the resulting reactions are and thus analysed their systems and interpreted their results in such a very naive manner that their findings are almost useless; or they realised that they were faced with a tangle of competing and successive reactions which they then attempted to disentangle with much persistence and ingenuity; this produced some interesting new chemistry which, however, has little to do with the actual polymerisations. An extreme example of chemical naiveness in this field is found in Andrews and Semlyen’s attempts to apply the Jacobsen-Stockmayer theory to poly-DXL [14]. They assumed

746

Some Aspects of the Polymerisation of 1,3-Dioxacycloalkanes that the reaction product contained significant quantities of linear polymers without attempting to prove this, and they did not attempt to identify the end-groups. Thus they were unable to prove the existence and specify the chemistry of the ring-closure reaction, the existence of which is one of the fundamental axioms of the theory which they were attempting to apply. One of the obvious problems that has arisen from the use of a variety of initiators is whether the nature of the initiator has any influence on the nature of the propagation reaction. It is to be expected that initiators which involve, or from which can be generated, reactive anions such as SbCl6-, would produce a variety of side-reactions and by-products and generally a very complicated reaction pattern; this has been confirmed amply by the findings of Penczek’s group [15-17]; other groups using similar initiators but having a much more naive approach to these systems, remained completely unaware of these complications. However, even when one simplifies the systems by using initiators with very stable anions, such as SbF6- or ClO4-, one must take into account the possibility that initiation by Ph3C+ or Et+ (from Et3O+) or the ‘dioxolenium’ (1,3-dioxolan-2-ylium) ion (VII) would produce a species whose growth might proceed by a mechanism different from the ring-expansion of secondary oxonium ions. It was suggested by Plesch that with organic cations as initiators a tert.-oxonium ion would be formed which would grow by ring expansion, just like the ion (I) in reaction (4) [1]. What the tert.- ion is that is formed from each particular initiator is not always clear, and with some systems at least, more than one type of initiating organic cation may be formed from the ostensible initiator. Meerwein’s [18] report that Et3O+BF4- reacts with 2-substituted DXL to give ethane3 was confirmed by Jones and Plesch for DXL and Et3O+BF4-, but with Et3O+SbF6- and DXL no ethane was formed [19]; the reason for this difference is not known. This observation implies the formation of the ‘dioxolenium’ ion (VII) which can initiate polymerisation by the intermediacy of the ionic formic ester (VIII). This sequence of reactions is shown in reaction scheme (8) [15]. Actually, because of the abnormally low basicity of DXL the second stage of reaction scheme (8), i.e., the cationation of the DCA to give the ionic formate (VIII), will be slower with DXL than with its oligomers or any other DCA [17].

3

In Reference 17 Penczek alleges erroneously that Meerwein et al., [18] had reported finding no ethane by GLC. On the contrary, Reference 18 contains the explicit statement that the formation of ethane was confirmed gasometrically (GLC was not available in 1958.)

747

Developments in the Theory of Cationoid Polymerisations

(8)

Since the formation of ethane upon mixing DXL with a solution of Et3O+BF4- was very rapid and then ceased completely, it was suggested [20] that only the Et3O+ ions which were not paired at the instant of mixing took part in that reaction, and that those which were paired were rendered relatively unreactive by being solvated by the DXL. Subsequently the Et3O+.DXL unit can take part in two reactions, (9) and (10), both of which are probably slow compared to the establishment of the pairing equilibrium. Whilst unpaired, the solvated ion can rearrange itself by transfer of the ethyl cation from ether to DXL, forming the ethylated DXL (IX) which is another type of cationated monomer which can propagate. Even for DXL which is less basic than diethyl ether, this reaction is promoted by the relatively high concentration of monomer relative to diethyl ether.

(9)

During the periods in which a solvated ion is paired, it can decompose slowly to boron trifluoride, ethyl fluoride and diethyl ether: (10) This accounts for the steady formation of ethyl fluoride from triethyl oxonium salts, which is strongly accelerated by DXL [21].

Growth mechanisms Irrespective of the nature of the linear fragment which is attached initially to the monomer molecule at the tert.-oxonium ion, there are several possibilities for the growth of the polymer.

748

Some Aspects of the Polymerisation of 1,3-Dioxacycloalkanes

1 The views of Jaacks and of Plesch The Jaacks group appears to have held the view that their propagation mechanism (2) is operative, whatever may be the nature of the initiator. The present author holds the view that since the number of end-groups is always much smaller than the number of polymer molecules, a ring-expansion mechanism, analogous to reaction (4), is the most plausible. This matter will be discussed in Section 5.

2 Penczek’s theory Penczek [17] has propounded a complicated mechanism based on a species (X) whose existence depends upon the presence of oligomers or polymers in the reaction mixture:

It was difficult to criticise this concept constructively because no spectroscopic or other characterisation was given by means of which the species (X) could have been recognised. Further, there did not appear to the present author to be anything in Penczek’s results that could not be explained without the species (X). However in the course of discussions Penczek explained that the structure (X) represents a tert.-oxonium ion of short lifetime, in which two of the branches consist of alkoxymethylene groups, and which is in an environment of alkoxymethylene groups, so that by the making and breaking of formal CH2-O bonds the location of the charge can change rapidly.

3 Okada’s theory Okada et al. [22], used the unpolymerisable 1,3-dioxan as a model compound and let it react with Et3O+BF4- in CH2Cl2 at 21 °C for 24 h. On the basis of the 1H NMR spectrum of the resulting reaction mixture and its variation with time and temperature, and other evidence, they suggested that the oxycarbenium ion (XI), solvated by diethyl ether (from the Et3O+), is the propagating species:

(11)

749

Developments in the Theory of Cationoid Polymerisations The validity of this conclusion is dubious because the products formed from a DCA in the presence of the very high concentrations of Et3O+BF4- used in this work during 24 h probably comprise several compounds in considerable concentrations, which have nothing to do with the polymerisation; the work of Jones and Plesch on the decomposition of Et3O+BF4- and on the conductance changes in solutions containing DXL and that initiator, provide strong evidence for that. Second, there is no explanation of how species (XI) differs from a conventional tert.-oxonium ion, but Okada and his co-workers maintain that their 1H NMR spectra are not compatible with the existence of an appreciable concentration of tert.-oxonium ions. For these reasons we conclude that Okada’s evidence for the oxycarbenium ion as an essential and principal reagent remains unconvincing.

4 The status of the oxycarbenium ion The oxycarbenium ion was the first concept in terms of which the polymerisation of DXL was interpreted by Yamashita and Okada and they quite logically adopted and adapted it from the theories of Kern and Jaacks about the polymerisation of 1,3,5-trioxan. It was subsequently favoured by many other authors in the context of DCA polymerisations. There appears to be no need at present to re-examine the theory of the trioxan polymerisation and it is necessary to mention that the following critique of the oxycarbenium theory as applied to the polymerisation of DCA does not necessarily apply to trioxan, because both the nature of the monomer and the polymerisation conditions are generally very different from those of the DCA. The bare oxycarbenium ion –(CH2)nOCH2+(n>2) (XII) is relatively small and therefore has a high charge-density. It follows that if it is placed in an environment containing basic atoms, such as a solution of a DCA, in a solvent of moderate polarity such as methylene dichloride, it will stabilise itself by reacting with the most basic site available and in the example given it will form a tert.-oxonium ion (XIII) with the DCA, in which the charge density is less than in the original ion. One can now adopt a variety of views as to the nature of the resulting species. For instance, one can regard the DCA as being the primary solvator of the oxycarbenium ion and since all such solvations are equilibria, at least in principle, one can conclude that there must be a small but finite concentration of unsolvated oxycarbenium ions (XII):

750

Some Aspects of the Polymerisation of 1,3-Dioxacycloalkanes Or one can say that even if the equilibrium constant for the above reaction is negligibly small, the unsolvated oxycarbenium ion (XII) is a part of a relatively unimportant canonical form of the tert.-oxonium ion, which implies a certain probability that the oxycarbenium ion may react as such by detaching itself from the ether and finding some other basic site. The important point, however, is that under the normal conditions under which DCA are polymerised the attempts to distinguish experimentally between oxycarbenium ions and tert.-oxonium ions as the active species appear at present to be quite pointless. The situation would be completely different for oxycarbenium ions in a highly polar solvent such as sulphur dioxide which could compete effectively as solvating agent with the DCA and their polymers. In such systems one could envisage that both the solventsolvated oxycarbenium ions and also the solvent-solvated tert.-oxonium ions could coexist in a true equilibrium, and that each would react according to its own characteristics. This is an area which remains very largely unexplored, although Penczek has made a start in this direction and these considerations arose from discussions with him of his exploratory experiments with sulphur dioxide as solvent.

5 The nature of the propagation by tert.-oxonium ions Thus, when one looks sufficiently critically at the ideas currently under discussion one finds that there appears to be no good reason for discarding the conventional tert.oxonium ion as the propagating species, and that the only clearly identifiable problem is whether propagation through these conventional tert.-oxonium ions goes by the Jaacks mechanism or by the ring-expansion mechanism. This is a difficult matter to resolve experimentally because the direct discrimination between the ‘microcyclic’ ions (II), (VIII), and (IX) on the one hand and the macrocyclic ion (V) on the other, requires subtle and sensitive techniques. Fortunately, there is evidence of a quite different kind available which at least provides a strong indication as to which mechanism is the more probable. In Table 2 are summarised the entropies of reaction (ΔS0ss) and activation (ΔS†) for the polymerisations of DXL, DXP, and THF. Four features are immediately evident: (1) The ΔS† is about the same for DXL and DXP initiated by perchloric acid; (2) the ΔS† for DXL is about the same for initiation by perchloric acid and by (VII); (3) the ΔS† for DXL and DXP are much more negative than for THF; and (4) for DXL and DXP the ΔS† are considerably more negative than the corresponding ΔS0ss. This means (i) that for the DCA the loss of degrees-of freedom in the transition state is much greater than that due to the incorporation of the monomers into the polymer, and

751

Developments in the Theory of Cationoid Polymerisations

Table 2 Entropies of reaction (ΔS0ss) and activation (ΔS†) for polymerisation of DXL, DXP, and THF in cal deg-1 mol-1 (rounded to nearest whole number)

Monomer

Initiator

–ΔS0ss DXL

DXP

SbF6-

Et3O+ BF4-

AlEt3 + H2O + epoxide

Various

19

–ΔS† Ref

8

–ΔS0ss

12

–ΔS† Ref

THF

HClO4

34

35

32

17

30 9

32

–ΔS0ss

21

–ΔS†

23

25

Ref

30

31

17–19

Various

(ii) that the propagation mechanism for reactions started by the two types of initiator are likely to be very similar. It has been shown that in reactions in which perchloric acid is the initiator, the ring-expansion mechanism is operative, for which the transition state can probably be represented most realistically as a four-centred structure (III) in which the monomer is tied down very firmly. In the propagation by the Jaacks mechanism the transition state (XIV) would resemble closely that in the polymerisation of cyclic ethers, such as THF; for this the transition state is (XV) which is evidently very similar to (XIV). It is reasonable to suppose that the ΔS† corresponding to (XIV) would have a value close to that for (XV); however, the ΔS† for (XV) shown in Table 2 is much less negative than that for the polymerisation of DXL by (VII). It is evident therefore that whatever may be the growth mechanism when initiation is by organic cations, it is very unlikely to involve the microcyclic tert.-oxonium ion growth centre of Jaacks. Thus all the evidence taken together indicates that in the

752

Some Aspects of the Polymerisation of 1,3-Dioxacycloalkanes polymerisation of DXL by organic cations the propagating centre is also a macrocyclic tert.-oxonium ion growing by ring expansion, like in the reactions initiated by protons4.

As far as the polymerisations of DCA other than DXL by non-protonic initiators are concerned, Kops and Spanggaard [11] favour the ring expansion mechanism for the dimerisation and polymerisation of the cis- and trans-7,9-dioxabicyclo[4.3.0] nonanes by phosphorus pentafluoride or triethyloxonium hexachloroantimonate, although they have not obtained any definitive evidence for it. On the other hand, Wegner’s studies [23] provide very strong evidence that polyoxymethylene crystals in contact with monomer and BF3Et2O also grow by a ring expansion reaction which is completely analogous to that proposed for DXL and 1,3dioxepan [8, 9]. It is not unlikely that this reaction also occurs in the solution polymerisation of trioxan simultaneously with the oxycarbenium ion propagation of Kern and Jaacks, and that it provides at least some of the cyclic oligomers which are found in these reaction mixtures.

Differences between DCA and cyclic ethers Two further pieces of well-known evidence need to be put into perspective, so that their bearing on the mechanistic problem may become clearer. One of these is the fact that under cationic polymerisation conditions cyclic ethers do not copolymerise with olefins, but that at best a mixture of homopolymers may be obtained. On the other hand, It was pointed out in discussion at Jablonna that our deductions from ΔS† values are hazardous for at least three reasons: (1) They require a knowledge of kp values for at least two temperatures, and this is not easy to obtain; (2) The ΔΔS† for the two mechanisms should be of the order of magnitude of the rotational entropy, but is in fact appreciably greater; (3) The ΔS† is strongly affected by the solvation of the initial and transition states, and because of the differences in charge-density between the initial and transition states for the two monomers, considerable differences in ΔS† could arise from this source. Nonetheless, it seems to us that the close similarities of the three ΔS† values for the DCA on the one hand, and of the two ΔS† values for THF on the other, are unlikely to be coincidences, and that therefore these ΔS† values, if used with adequate circumspection, can provide some pertinent evidence. 4

753

Developments in the Theory of Cationoid Polymerisations copolymerisations between DCA and olefins have been reported [24-27], and an acid catalysed insertion of olefins into DCA occurs quite readily whereby the DCA are converted into cyclic ethers [28]. The second concerns the copolymerisation of the two categories of compounds. However, the amount of evidence available is so great and much of it is so conflicting, that it is very difficult to interpret. The main trouble is that many results are of very dubious validity. One of the principal difficulties in this field is that few workers have recorded the DP of the alleged copolymers, but some have shown that in systems of this type the DP may be so low that end-effects (initial or terminal groups) may simulate copolymerisation when in fact only homopolymers, but with ends derived from the co-monomer, were obtained. It will suffice here to say that the evidence for the formation of true random copolymers from DCA and cyclic ethers looks, to say the least, rather unconvincing. This view is strongly supported by the findings of Leonard and his co-workers. They reported that the equilibrium concentrations of DXL and THF in reaction mixtures containing the polymers and initiated by Et 3O +PF 6- were such as were to be expected if no copolymerisation occurred, and they concluded that there are two concurrent homopolymerisations [29]. All this evidence taken together indicates very strongly that the two types of monomers polymerise by different mechanisms. Whilst this conclusion does not necessarily support the ring-expansion mechanism for the DCA, it makes the propagation via the microcyclic tert.-oxonium ion (XIV) appear very unlikely.

Conclusion The field which I have surveyed has become obscured by a vast amount of experimental results of very uneven reliability, by excessive concentration on too few monomers and solvents, by a multiplication of interpretative theories lacking in precision and therefore untestable. Although it is impossible to say with confidence that all the phenomena encountered in these polymerisations can be explained in terms of conventional sec. and tert.-oxonium ions as propagating species, I hope that I have shown that there does not appear to be a convincing need at present to add to these categories. What we require now in order to consolidate our understanding is more work with a variety of monomers and solvents, with the simplest possible initiator systems, aimed at obtaining the maximum amount of information on the polymerisations (rates, equilibria, conductivities, constituents of the reaction mixtures before and after neutralisation) and on the polymers (existence, nature and concentration of end-groups, DP distributions). There are unfortunately still too many who think they can base a valid theory on the determination of only one or two features of a polymerisation system.

754

Some Aspects of the Polymerisation of 1,3-Dioxacycloalkanes

Acknowledgement I acknowledge gratefully the help which I have received in developing these ideas from many co-workers and friends, but especially from Professor St. Penczek.

References 1.

P. H. Plesch, IUPAC Int. Symp. Macromol. Chem. Budapest, p.213 Main Lectures (1969).

2.

K. Boehlke, H. Frank and V. Jaacks, I.U.P.A.C Int. Symp. Macromol. Chem. Budapest Preprint 2/10 (1969).

3.

V. Jaacks, Adv. Chem. Series No. 91, p. 371. A.C.S. Washington (1969).

4.

S. Penczek, Makromol. Chem. 134, 299 (1970).

5.

K. Boehlke and V. Jaacks, Makromol. Chem. 145, 219 (1971).

6.

K. Boehlke, P. Weyland and V. Jaacks, I.U.P.A.C. 23rd Congress, Boston, Macromolecular Preprint. Vol. 2, p. 641 (1971).

7.

B. A. Rosenberg, B. A. Komarov, T. I. Ponomareva and N. S. Enikolopyan, I.U.P.A.C. Int. Symp. Makromol. Chem. Helsinki Preprint 1-124 (1972).

8.

P. H. Plesch and P. H. Westermann, J. Polym. Sci. C16, 3837 (1968).

9.

P. H. Plesch and P. H. Westermann, Polymer 10, 105 (1969).

10. Y. Firat, F. R. Jones, P. H. Plesch and P. H. Westermann, Makromol. Chem. Suppl. 1, 203 (1975). 11. J. Kops and H. Spanggaard, Makromol. Chem. 176, 299 (1975). 12. V. Jaacks, K. Boehlke and E. Eberius, Makromol. Chem. 188, 354 (1968). 13. E. Mathias and P. H. Plesch, Chem. Ind. (London) 1043 (1971). 14. J. M. Andrews and J. A. Semlyen, Polymer 13, 142 (1972). 15. P. Kubisa and S. Penczek, Makromol. Chem. 144, 169 (1971). 16. P. Kubisa and S. Penczek, Makromol. Chem. 165, 121 (1973).

755

Developments in the Theory of Cationoid Polymerisations 17. S. Penczek, Makromol. Chem. 175, 1217 (1974). 18. H. Meerwein, V. Hederich and K. Wunderlich, Archiv d.Pharmazie 291/63, 541 (1958). 19. F. R. Jones and P. H. Plesch, Chem. Comm. 1230 (1969). 20. F. R. Jones, Ph.D. Thesis, Keele (1970). 21. F. R. Jones and P. H. Plesch, Chem. Comm. 1231 (1969). 22. Y. Yokoyama, M. Okada and H. Sumitomo, Makromol. Chem. 176, 795 (1975). 23. R. Mateva, G. Wegner and G. Lieser, J. Polym. Sci. Letts. 11, 369 (1973). 24. L. Hohr, H. Cherdron and W. Kern, Makromol. Chem. 52, 59 (1962). 25. Y. Yamashita, Adv. Chem. Series, No. 91, p. 350. A.C.S. Washington (1969). 26. M. Okada and Y. Yamashita, Makromol. Chem. 126, 266 (1969). 27. M. Okada, S. Ikai, K. Chiba, M. Hirota and Y. Yamashita, Polymer J. 1, 1 (1969). 28. J. Cooper and P. H. Plesch, Chem. Comm. 1017 (1974). 29. R. Binet, P. E. Harvey and J. Leonard, Can. Inst. Chem. Meeting, Toronto Macromol. Sci. Div. Preprint 203 (1975). 30. B. A. Rozenberg, O. M. Chekhuta, Ye. B. Lyudvig, A. R. Gantmakher and S. S. Medvedev, Vysokomol. Soed. 6, 2030 (1964); Polym. Sci. U.S.S.R. 6, 2246 (1964). 31. T. Saegusa, H. Imai and S. Matsumoto, J. Polym. Sci. A1(6),459 (1968). 32. P. H. Westermann, Ph.D. Thesis, Keele (1967).

756

8

The Chemical Publications of P. H. Plesch in Chronological Order, 1946 - 2001

1.

Researches into the Catalysed Low-temperature Polymerisation of Isobutene, P.H. Plesch, Manchester, 1946. [Ph.D. Thesis].

2.

Friedel-Crafts Catalysts and Polymerisation, A.G. Evans, D. Holden, P.H. Plesch, M. Polanyi, H.A. Skinner and M. Weinberger, Nature, 1946, 157, 102-104.

3.

The Low-temperature Polymerisation of Isobutene by TiCl4, P.H. Plesch, Nature, 1947, 160, 868.

4.

The Low-temperature Polymerisation of Isobutene by Friedel-Crafts Catalysts, P.H. Plesch, M. Polanyi and H.A. Skinner, Journal of the Chemical Society, 1947, 257-266.

5.

Adsorption on to Ionogenic Surfaces, P.H. Plesch and R.H.S. Robertson, Nature, 1948, 161, 1020-1022.

6.

Friedel-Crafts Polymerisation, P.H. Plesch, Research, 1949, 2, 267-275.

7.

The Low-temperature Polymerisation of Isobutene, Part II, P.H. Plesch, Journal of the Chemical Society, 1950, 543-546.

8.

Suggestions Concerning the Ionic Polymerisation of Vinyl Ethers, S.D. Hamann, P.H. Plesch and H.A. Skinner, Scientific Proceedings of the Royal Dublin Society, 1950, 25 (N.S.) 141-144.

9.

Developments in the Theory of Cationic Polymerisation, P.H. Plesch, Applied Chemistry, 1951, 1, 269-272.

10. Some Physical Properties of cis-Stilbene, D.S. Brackman and P.H. Plesch, Journal of the Chemical Society, 1952, 2188-2190. 11. Cationic Polymerisation and Related Problems, P.H. Plesch, Nature, 1952, 169, 828-830. 12. The Low-temperature Polymerisation of Isobutene, Part III. The End-group Problem, M.St.C. Flett and P.H. Plesch, Journal of the Chemical Society, 1952, 3355-3358.

757

Developments in the Theory of Cationoid Polymerisations 13. Some Reactions of the Stilbenes in the Presence of Metal Halides, D.S. Brackman and P.H. Plesch, Journal of the Chemical Society, 1953, 1289-1292. 14. Cationic Polymerisation and Related Complexes, Ed., P.H. Plesch, W. Heffer and Sons, Cambridge, 1953. 15. The Polymerisation of Styrene by Titanic Chloride, Part I. Kinetics, P.H. Plesch, Journal of the Chemical Society, 1953, 1653-1658. 16. The Polymerisation of Styrene by Titanic Chloride, Part II. The End-groups, P.H. Plesch, Journal of the Chemical Society, 1953, 1659-1661. 17. The Polymerisation of Styrene by Titanic Chloride, Part III. Discussion, P.H. Plesch, Journal of the Chemical Society, 1953, 1662-1666. 18. Developments in the Theory of Cationic Polymerisation, Part II, P.H. Plesch, Journal of Polymer Science, 1954, 12, 481-487. 19. Identification by Syntheses of a Product from the Cationic Oligomerisation of Stilbene in Toluene, D.S. Brackman and P.H. Plesch, Chemistry and Industry, 1955, 255. 20. Developments in the Theory of Cationic Polymerisation, Part III, Some Considerations Concerning Energetics, P.H. Plesch, La Ricerca Scientifica, Supplemento Simposio Internationale di Chimica Macromoleculare, 1955, 25, 140-153. 21. Ueber den Chemismus der Kationenpolymerisation, Lecture delivered to the Deutsche Bunsen Gesellschaft, P.H. Plesch, Zeitschrift fur Elektrochemie, 1956, 60, 325-333. 22. Improvements Relating to Polymeric Substances (graft polymers by cationic catalysis), P.H. Plesch, inventor; National Research Development Corporation, assignee; BP 31652, 1955. 23. Apparatus for the Anaerobic Filling of Phials, R.H. Biddulph and P.H. Plesch, Chemistry and Industry, 1956, 567. 24. A Corrosion-Resistant High-Vacuum Valve for Liquids, R.H. Biddulph and P.H. Plesch, Chemistry and Industry, 1956, 569. 25. The Interaction of Metal Chlorides with Organic Chlorides, Part I, Freezing-point Phase Diagrams of Titanium Tetrachloride with some Alkyl Chlorides, W.R. Longworth and P.H. Plesch, Journal of the Chemical Society, 1958, 451-457.

758

Chemical Publications in Chronological Order 26. A New Class of Catalyst for Cationic Polymerisations, W.R. Longworth and P.H. Plesch, Proceedings of the Chemical Society, 1958, 117. 27. Graft-polymerisation with Cationic Catalysts, P.H. Plesch, Chemistry and Industry, 1958, 954. 28. The Cationic Oligomerisation of the Stilbenes, D.S. Brackman and P.H. Plesch, Journal of the Chemical Society, 1958, 3563-3573. 29. The Dielectric Constant of Ethyl Chloride, W.R. Longworth and P.H. Plesch, Journal of the Chemical Society, 1959, 1618. 30. The Interaction of Metal Chlorides with Organic Chlorides, Part II, Electrochemical Studies on Solutions of Titanium Tetrachloride in some Alkyl Chlorides, W.R. Longworth and P.H. Plesch, Journal of the Chemical Society, 1959, 1887-1894. 31. The Mechanism of Cationic Polymerisations Catalysed by Metal Halides, W.R. Longworth, P.H. Plesch and P.P. Rutherford, Doklady Akademii Nauk SSSR, 1959, 127, 97-99. 32. A New Versatile Apparatus for Measuring the Rates of Fast Liquid-phase Reactions, R.H. Biddulph and P.H. Plesch, Chemistry and Industry, 1959, 1482-1485. 33. Complex Formation between Isobutene and Titanium Tetrachloride, W.R. Longworth, P.H. Plesch and P.P. Rutherford, International Conference on Coordination Chemistry, 1959, Chemical Society Special Publication, 13, p.115. 34. The Polymerisation of Isobutene by Titanium Tetrachloride in Methylene Dichloride, R.H. Biddulph, P.H. Plesch and P.P. Rutherford, International Symposium on Macromolecules, Wiesbaden, 1959, Paper No.III.A.10. 35. The Polymerisation of Styrene by Titanium Tetrachloride in Methylene Dichloride, W.R. Longworth and P.H. Plesch, International Symposium on Macromolecules, Wiesbaden, 1959, Paper No.III.A.11. 36. Co-catalysis by Alkyl Halides in Cationic Polymerisations, W.R. Longworth, P.H. Plesch and P.P. Rutherford, Proceedings of the Chemical Society, 1960, 68. 37. The Heat of Polymerisation of Isobutene and of Styrene, R.H. Biddulph, W.R. Longworth, J. Penfold, P.H. Plesch and P.P. Rutherford, Polymer, 1960, 1, 521-522.

759

Developments in the Theory of Cationoid Polymerisations 38. The Low-temperature Polymerisation of Isobutene, Part IV, Exploratory Experiments, R.H. Biddulph and P.H. Plesch, Journal of the Chemical Society, 1960, 3913-3920. 39. Viscometric Studies on Polyisobutene Solutions, P.H. Plesch and P.P Rutherford, Polymer, 1960, 1, 271-273. 40. Chain-transfer by Anisole in the Cationic Polymerisation of Isobutene, J. Penfold and P.H. Plesch, Proceedings of the Chemical Society, 1961, 311. 41. Cationic Polymerisation, P.H. Plesch in Chimica delle Macromolecole, Cons. Naz. delle Ricerche, Rome, 1963, 33-48. 42. Chemistry of Cationic Polymerisation, Ed., P.H. Plesch, Pergamon, London, 1963. 43. Chapter on Comparison of Mechanisms, P.E.M. Allen and P.H. Plesch in Chemistry of Cationic Polymerisation, Ed., P.H. Plesch, Pergamon, London, 1963. 44. Chapter on Isobutene in Chemistry of Cationic Polymerisation, Ed., P.H. Plesch, Pergamon, London, 1963. 45. Chapter on Experimental Techniques by P.H. Plesch in Chemistry of Cationic Polymerisation, Ed., P.H. Plesch, Pergamon, London, 1963. 46. Developments in the Theory of Cationic Polymerisation, Part IV, A General Theory Explaining Discontinuous Variations of the Degree of Polymerisation with the Concentrations of the Reagents, by P.H. Plesch, Journal of the Chemical Society, 1964, 104-114. 47. The Catalytic Dehydration of Aromatic Carbinols by Acids, A. Gandini and P.H. Plesch, Proceedings of the Chemical Society, 1964, 113. 48. The Interaction between Perchloric Acid and Styrene in Methylene Dichloride, A. Gandini and P.H. Plesch, Proceedings of the Chemical Society, 1964, 240-241. 49. The Low-temperature Polymerisation of Isobutene, Part V, Polymerisation by Aluminium Trichloride in Methylene Dichloride, J.H. Beard, P.H. Plesch and P.P. Rutherford, Journal of the Chemical Society, 1964, 2566-2571. 50. The Fractionation of Polyisobutene by Gradient Elution, C.J. Panton, P.H. Plesch and P.P. Rutherford, Journal of the Chemical Society, 1964, 2586-2591. 51. The Rate Constant of a Quaternisation in Methylene Dichloride between 35° and –71° and the Irrelevance of Dielectric Constant in Kinetics, J.H. Beard and P.H. Plesch, Journal of the Chemical Society, 1964, 3682-3687. 760

Chemical Publications in Chronological Order 52. Conductance Minima in the System Methyltriethylammonium Iodide-Methylene Dichloride between 35° and –71°, J.H. Beard and P.H. Plesch, Journal of the Chemical Society, 1964, 4075-4076. 53. The Ionic Dissociation of Methyltriethylammonium Iodide in Methylene Dichloride between 0° and –95°, J.H. Beard and P.H. Plesch, Journal of the Chemical Society, 1964, 4879-4887. 54. The Low-temperature Polymerisation of Isobutene, Part VI. Polymerisation by Titanium Tetrachloride and Water in Methylene Dichloride, R.H. Biddulph, P.H. Plesch and P.P. Rutherford, Journal of the Chemical Society, 1965, 275-294. 55. Pseudocationic and True Cationic Polymerisation of Styrene by Various Catalysts, A. Gandini and P.H. Plesch, Journal of Polymer Science, Part B, 1965, 3, 127-129. 56. Devices for Measuring Electrical Conductance and Spectra during Polymerisation, A. Gandini, P. Giusti, P.H. Plesch and P.H. Westermann, Chemistry and Industry, 1965, 1225-1226. 57. Spectroscopic Studies on Carbonium Ions Derived from Aromatic Olefins. Part I. Styrene and Related Olefins, A. Gandini and P.H. Plesch, Journal of the Chemical Society, 1965, 4765-4769. 58. Cationic and Pseudocationic Polymerisation of Aromatic Olefins. Part I. Kinetics and Mechanism of the Pseudocationic Polymerisation of Styrene by Perchloric Acid, A. Gandini and P.H. Plesch, Journal of the Chemical Society, 1965, 4826-4830. 59. The Polymerisation of Styrene by Titanium Tetrachloride, Part IV. Kinetics of Polymerisation in Methylene Dichloride, W.R. Longworth, C.J. Panton and P.H. Plesch, Journal of the Chemical Society, 1965, 5579-5590. 60. The Dehydration of Aromatic Carbinols by Acids and its Mechanistic Implications, A. Gandini and P.H. Plesch, Journal of the Chemical Society, 1965, 6019-6024. 61. New Views on Cationic Polymerisation, A. Gandini and P.H. Plesch, The Chemistry of Polymerisation Processes, Society of Chemical Industry Monograph No. 20, 1966, 107-114. 62. Origin of the Alleged, and Position of the Real, UV Absorption of the 1,3Diphenyl-n-butyl Cation, V. Bertoli and P.H. Plesch, Chemical Communications, 1966, 625-627.

761

Developments in the Theory of Cationoid Polymerisations 63. Reaction Mechanisms in Cationic and Pseudocationic Polymerisations, P.H. Plesch, Pure and Applied Chemistry, 1966, 12, 117-125. 64. Spectroscopic Studies on Carbonium Ions derived from Aromatic Olefins. Part II. Acenaphthylene, N-Vinylcarbazole, and Tetraphenylethylene, A. Gandini and P.H. Plesch, Journal of the Chemical Society, (B), 1966, 7-10. 65. The Polymerisation of N-Vinylcarbazole by Electron Acceptors, Part I, Kinetics, Equilibria, and Structure of Oligomers - Part II, Discussion, J. Pàc and P.H. Plesch, Polymer, 1967, 237-262. 66. Polarography of Organic Cations, M.I. James and P.H. Plesch, Chemical Communications, 1967, 508-510. 67. Cationic and Pseudocationic Polymerisation of Aromatic Olefins, Part II, The Reactions following Polymerisation of Styrene by Perchloric Acid, A. Gandini and P.H. Plesch, European Polymer Journal, 1968, 11, 55-74. 68. Cationic Polymerisation, P.H. Plesch in Progress in High Polymers, Volume II, Ed., J.C. Robb and F.W. Peaker, Iliffe Books Limited, London, 1968, 137-191. 69. Spectroscopic Studies on Carbonium Ions derived from Aromatic Olefins, Part III, Ions derived from Styrene and Cognate Compounds, V. Bertoli and P.H. Plesch, Journal of the Chemical Society, (B), 1968, 1500-1516. 70. The Polymerisation of 1,3-Dioxolan, Part I, Structure of the Polymer and Thermodynamics of its Formation, P.H. Plesch and P.H. Westermann, Journal of Polymer Science, Part C, 1968, 16, 3837-3843. 71. The UV and PMR Spectra of Ten Related Diaryl Carbonium Ions, V. Bertoli and P.H. Plesch, Spectrochimica Acta, 1969, 25A, 447-465. 72. The Polymerisation of 1,3-Dioxepan, Part I, Structure of the Polymer and Thermodynamics of its Formation, and a Note on 1,3-Dioxan, P.H. Plesch and P.H. Westermann, Polymer, 1969, 10, 105-111. 73. The Polymerisation of Cyclic Formals by Triethyloxonium Tetrafluoroborate, F.R. Jones and P.H. Plesch, Chemical Communications, 1969, 1230-1231. 74. The Decomposition of Triethyloxonium Salts, F.R. Jones and P.H. Plesch, Chemical Communications, 1969, 1231-1232. 75. Polarography of Carbonium Ions in Acid Solution, Part I, The Triphenylmethyl Ion in Sulphuric Acid, P.H. Plesch and I. Sestakova, Journal of the Chemical Society, (B), 1970, 87-92.

762

Chemical Publications in Chronological Order 76. Impurity Effects in the Polymerisation of N-vinylcarbazole by Mercuric Chloride, M.A. Hamid, M. Nowakowska and P.H. Plesch, Die Makromolekulare Chemie, 1970, 132, 1-5. 77. The Association Constants of Triethyloxonium Salts and their Solvation by Diethyl Ether, F.R. Jones and P.H. Plesch, Chemical Communications, 1970, 1018-1019. 78. The Propagation Rate-Constants in Cationic Polymerisations, P.H. Plesch, Advances in Polymer Science, 1971, 8, 137-154. 79. Polarography of Organic Cations in Acid Solution, Part II, Various Aralkyl Ions in Sulphuric and Methanesulphonic Acids, P.H. Plesch and I. Sestakova, Journal of the Chemical Society, (B), 1971, 1337-1342. 80. The Propagation Rate-Constants in Cationic Polymerisations, P.H. Plesch, Proceedings of the Royal Australian Chemical Institute, 1971, March, 81-84. 81. Cathodic Reduction of the Trityl Cation in Methylene Dichloride, P.H. Plesch, A. Stasko and D. Robson, Journal of the Chemical Society, (B), 1971, 1634-37. 82. A Safe Method of Preparing Anhydrous Solutions of Perchloric Acid, P.H. Plesch and E. Mathias, Chemistry and Industry, 1971, 1043-1044. 83. Studies on the Cationic Polymerisation of o-Methylstryrene, P.L. Magagnini, P.H. Plesch and J.P. Kennedy, European Polymer Journal, 1971, 7, 1161-1165. 84. Criticisms of Claims in the Field of Isomerisation Polymerisation, Part I. Polymerisation of p-Methylstyrene, J.P. Kennedy, P.L. Magagnini, and P.H. Plesch, Journal of Polymer Science A-1, 1971, 9, 1635-1646. 85. Criticisms of Claims in the Field of Isomerisation Polymerisation, Part II. Polymerisation of o-Isopropylstyrene, J.P. Kennedy, P.L. Magagnini and P.H. Plesch, Journal of Polymer Science A-1, 1971, 9, 1647-1657. 86. Cathodic Reduction of the Tropylium Cation in Methylene Dichloride, P.H. Plesch and A. Stasko, Journal of the Chemical Society (B), 1971, 2052-2053. 87. The Mechanism of the Polymerisation of Cyclic Formals, P.H. Plesch, IUPAC International Symposium on Macromolecular Chemistry, 1969, Plenary and Main Lectures, Budapest 1971, 213-221. 88. The Nature of the Propagating Species in Cationic Polymerisations, P.H. Plesch, British Polymer Journal, 1973, 5, 1-12.

763

Developments in the Theory of Cationoid Polymerisations 89. Binary Ionogenic Equilibria exemplified by Acetyl Hexafluoroantimonate and their Implications for Cationic Polymerisations, O. Nuyken and P.H. Plesch, Chemistry and Industry, 1973, 379-380. 90. Adjustable Conductivity Electrodes for Measurements in Vacuum and Controlled Atmospheres, P.H. Plesch, Chemistry and Industry, 1973, 699-700. 91. Adjustable Depth Conductivity Electrodes, P.H. Plesch, Campus Scientifica, 1973, 1, 8-9. 92. Developments in the Theory of Cationic Polymerisation. V. A New Theory of Initiation by Aluminium Halides, P.H. Plesch, Macromolecular Chemistry - 8, Helsinki, 1972, Butterworths, London, 1973, p.305-318. 93. Approaches Towards a Comprehensive Theory of the Cationic Polymerisation of Olefins. P.H. Plesch, Die Makromolekular Chemie, 1974, 175, 1065-1076. 94. The Cationic Polymerisation of Ketene Acetals, and the Preparation and Characterisation of Poly(1,3-diketones), D.J. Dunn and P.H. Plesch, Die Makromolekular Chemie, 1974, 175, 2821-2836. 95. A New Method of Making New Crown Ethers, J. Cooper and P.H. Plesch, Chemical Communications, 1974, 1017-1018. 96. The Polymerisation of 4-Methyl-1,3-dioxolan, Y. Firat and P.H. Plesch, Die Makromolekulare Chemie, 1975, 176, 1179-1186. 97. The Propagating Species in the Polymerisation of 1,3-Dioxacycloalkanes by Perchloric Acid, Y. Firat, F.R. Jones, P.H. Plesch and P.H. Westermann, Die Makromolekulare Chemie, Supplement 1, 1975, 203-216. 98. Enthalpy of Polymerisation of Endo-2-Methyl-7-oxabicyclo [2.2.1] heptane, F. Andruzzi, D.S. Barnes and P.H. Plesch, Die Makromolekulare Chemie, 1975, 176, 2053-2057. 99. Oligomers from 2-Methyl-1,3-dioxolan, Y. Firat and P.H. Plesch, Journal of Polymer Science, Polymer Letters, 1975, 13, 135-136. 100. Ueber die Praeparative Anwendung der Katodischen Reduktion des Carboniumions. A. Stasko and P.H. Plesch, Zeitschrift fur Physikalische Chemie (Leipzig), 1975, 256, 418-420. 101. The Polarography of Some Oxonium Ions in Methylene Dichloride. Part I Experimental Techniques and Results for Two Tertiary Ions. P.H. Plesch and F.G.

764

Chemical Publications in Chronological Order Thomas, Journal of the Chemical Society, Perkin II, 1975, 1532-1535. (see important correction in [113].) 102. Cationic and Pseudocationic Polymerisation of Aromatic Olefins. Part III. A Reinvestigation of the Polymerisation of Styrene by Perchloric Acid, D.J. Dunn, E. Mathias and P.H. Plesch, European Polymer Journal, 1976, 12, 1-4. 103. Some Aspects of the Polymerisation of 1,3-Dioxacycloalkanes, P.H. Plesch, Pure and Applied Chemistry, 1976, 48, 287-293. 104. Ionisation of Aluminium Halides in Alkyl Halides. D.W. Grattan and P.H. Plesch, Journal of the Chemical Society, Dalton Transactions, 1977, 1734-1744. 105. Some Electrochemical Aspects of Cationic Polymerisation. P.H. Plesch, Journal of Polymer Science Symposium, 1976, No. 56, 373-382. 106. Enthalpy of Polymerisation of 7-Oxabicyclo[2.2.1]heptane and Exo-and Endo-2Methyl-7-Oxabicyclo[2.2.1]heptane. F. Andruzzi, G. Pilcher, Y. Virmani and P.H. Plesch, Die Makromolekulare Chemie, 1977, 178, 2367-2373. 107. Polarography of Organic Cations in Acid Solutions. Part 3. Three 1,1 Diarylethyl Ions in Sulphuric and Methanesulphonic Acids, Kabir-ud-Din and P.H. Plesch, Journal of the Chemical Society, Perkin II, 1978, 892-895. 108. Hydride Ion Transfer between Triphenylmethyl Cation and Tetrahydrofuran, 1,3Dioxolan and 1,3-Dioxepan, Kabir-ud-Din and P.H. Plesch, Journal of the Chemical Society, Perkin II, 1978, 937-938. 109. Polarography of some Protonic Acids in Methylene Chloride, Kabir-ud-Din and P.H. Plesch, Journal of Electroanalytical Chemistry, 1978, 93, 29-40. 110. The Decomposition of Triethyloxonium Salts in Solution. F.R. Jones and P.H. Plesch, Journal of the Chemical Society, Dalton Transactions, 1979, 927-932. 111. Binary Ionogenic Equilibria, D.W. Grattan and P.H. Plesch, Journal of Electroanalytical Chemistry, 1979, 103, 81-94. 112. The Initiation of Polymerizations by Aluminium Halides. D.W. Grattan and P.H. Plesch, Die Makromolekulare Chemie, 1980, 181, 751-775. 113. The Polarography of Oxonium Ions, Part II. The Half-wave Potentials of Five Tertiary Ions. G.E. Holdcroft, Kabir-ud-Din, and P.H. Plesch, Journal of Chemical Research, 1980, 390-391.

765

Developments in the Theory of Cationoid Polymerisations 114. The Non-polymerizability of Some Cyclic Sulphones, S.B. Kingston and P.H. Plesch, Die Makromolekulare Chemie, Rapid Communications, 1980, 1, 749-751. 115. The Polymerization of Styrene by Trifluoroacetic Acid, W. Obrecht and P.H. Plesch, Die Makromolekulare Chemie, 1981, 182, 1459-1473. 116. The Polymerization of Acenaphthylene by Carbocation Salts in Nitrobenzene, S.D. Pask, P.H. Plesch, and S.B. Kingston, Die Makromolekulare Chemie, 1981, 182, 3031-3039. 117. An Improved Vacuum Reaction Calorimeter, S.D. Pask and P.H. Plesch, Chemistry and Industry (London), 1981, 331-333. 118. A Tube Cutter for Use in the Mid-point Method of Filling Phials in Vacuo, S.D. Pask, P.H. Plesch, and M.DiMaina, Chemistry and Industry (London), 1981, 329-330. 119. Developments in the Theory of Cationic Polymerization VII. Theoretical Attempts at Improving Initiators for Cationic Polymerization of Alkenes, S.D. Pask and P.H. Plesch. European Polymer Journal, 1982, 18, 839-846. 120. Spectroscopic Studies on Carbenium Ions derived from Aromatic Olefins V. Experimental and Theoretical Studies of the Cations derived from Acenaphthylene, S.D. Pask and P.H. Plesch, European Polymer Journal, 1982, 18, 939-943. 121. Polarography of Oxonium Ions III. Ions derived from Mono- and Di-Oxacycloalkanes, G.E. Holdcroft, Kabir-ud-Din, A.A. Khan, and P.H. Plesch, Journal of Electroanalytical Chemistry, 1982, 139, 157-165. 122. Ion-Formation from α-Chloroethyl Ethyl Ether and Antimony Pentachloride, P.H. Plesch and V.T. Stannett, Journal of Macromolecular Science Chemistry, 1982, A18, 425-430. 123. Essay Review of ‘Carbocationic Polymerisation’, by J.P. Kennedy and E. Maréchal (Wiley Interscience, N.Y. 1982), P.H. Plesch, Journal of Polymer Science, Polymer Letters, 1983, 21, 304-306. 124. Operational Amplifier-Based Resistance Thermometer for Calorimetry, P.K. Grannell, S.D. Pask, P.H. Plesch and G.E. Holdcroft, Chemistry and Industry (London), 1983, 441-444. 125. The Propagation Rate-Constants for the Cationic Polymerisation of Acenaphthylene and Styrene in Nitrobenzene, G.E. Holdcroft and P.H. Plesch, Die Makromolekulare Chemie, 1984, 185, 27-35.

766

Chemical Publications in Chronological Order 126. The Propagation Rate-Constants for the Cationic Polymerisation of Alkenes, P.H. Plesch in Cationic Polymerisation and Related Processes, Ed., E.J. Goethals, Academic Press, 1984, p.l. 127. Binary Ionogenic Equilibria between Phenols and Bases, G.E. Holdcroft and P.H. Plesch, Journal of Chemical Research, (S) 1985, 36-37; (M) 1985, 0401-0450. 128. Dilatometry and Dilatometers, P.H. Plesch, International Laboratory, October 1986, p.18-29. 129. Finding the DPn of Oligomers from PMR Signals, L.P. Nethsinghe, P.H. Plesch and D.J. Hodge, European Polymer Journal, 1986, 22, 643-645. 130. The Projects that Never Were (A Lecture to the Polymer Discussion Group), P.H. Plesch, European Polymer Journal, 1986, 22, 775-781. 131. Synthesis and Properties of Compounds related to Stilbazole, L.P. Nethsinghe, P.H. Plesch and D.J. Hodge, Die Angewandte Makromolekulare Chemie, 1987, 148, 161-193. 132. Ionisation and Dissociation of Diarylmethyl Chlorides in BCl3/CH2Cl2 Solution: Spectroscopic Evidence for Carbenium Ion Pairs, R. Schneider, H. Mayr, and P.H. Plesch, Berichte der Bunsengesellschaft fur Physikalische Chemie, 1987, 91, 1369-1374. 133. The 8th International Symposium on Cationic Polymerisation and Related Processes, Munich, 1987, P.H. Plesch, Macro Group UK Bulletin, 1988, January, p.23-26. 134. Kinetics of Living Cationic Polymerisations, P.H. Plesch, Polymer Bulletin, 1988, 19, 145-148. 135. Pseudo-Cationic Polymerisation after 24 years. Die Makromolekulare Chemie, Macromolecular Symposia, 1988, 13/14, 375-387 and 393-395. 136. High Vacuum Techniques for Chemical Syntheses and Measurements, P.H. Plesch, Cambridge University Press, 1989. 137. Relation between Reduction Potentials and Solvation Energies for some Aryl Methylium Ions, P.H. Plesch, Journal of the Chemical Society, Perkin Transactions II, 1989, 1139-1142. 138. Binary lonogenic Equilibria, P.H. Plesch, Education in Chemistry, 1990, 27, 75-76.

767

Developments in the Theory of Cationoid Polymerisations 139. An Account of the Propagating Species in Cationic Polymerisations, P.H. Plesch, European Polymer Journal, 1989, 25, 875-877. 140. Adventures in Cationic Polymerisation, P.H. Plesch, Current Contents, 1989, 29, 16 (Citation Classic). 141. Developments in the Theory of Cationic Polymerisation IX. Some Effects of the Complex Formation between Cations and Monomers. P.H. Plesch, Die Makromolekulare Chemie, Macromolecular Symposia, 1990, 32, 299-306. 142. The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes - Part III. Indene, two Vinyl Ethers, and General Discussion, P. H. Plesch and S.H. Shamlian, European Polymer Journal, 1990, 26, 1113-1120. 143. Cationoid Living Polymerisations, (Developments in the Theory of Cationic Polymerisation, Part X). P.H. Plesch, Makromoleculare Chemie, Macromolecular Symposia, 1992, 60, 11-35. 144. The Propagation Rate-Constants of the Cationic Polymerisation of Alkenes, P.H. Plesch, Progress in Reaction Kinetics, 1993, 18, 1-62. 145. The Propagation Rate-Constants of the Cationic Polymerisation of some Alkenes in Nitrobenzene - Part IV. Not the Real kp+, (Developments in the Theory of Cationic Polymerisation, Part XII), P.H. Plesch, European Polymer Journal, 1993, 29, 121-124. 146. New Views on the Cationic Polymerisations initiated by Ionising Radiations, (Developments in the Theory of Cationic Polymerisation, Part XI), P. H. Plesch, Philosophical Transactions of the Royal Society of London, 1993, A342, 469-504. 147. The Eleventh Symposium on Cationic Polymerization and Related Ionic Processes, Borovets, 1993, P.H. Plesch, Macro Group UK Bulletin, 1994, January, p.30-33. 148. Developments in the Cationic Polymerization of Alkenes - A Personal View, P.H. Plesch, Macromolecular Symposia, 1994, 85, 1-31. 149. High Vacuum Techniques for Chemical Syntheses and Measurements, P.H. Plesch, Mir Publishers, Moscow, 1994, [in Russian]. 150. Baekeland Lecture: Of Alginates and Rubbers and Catalysts and Rings. P.H. Plesch, SCI Lecture Papers Series, No. 0064, 1994, (Published 1996).

768

Chemical Publications in Chronological Order 151. Symposium on Friedel-Crafts Catalysts and Polymerization, 15 September 1945. M. Polanyi and P.H. Plesch, Notes and Records of the Royal Society, London, 1999, 53, 135-141. 152. On the Distinctness of Chemistry, P.H. Plesch, Foundations of Chemistry, 1999, 1, 7-16. 153. Review of ‘Cationic Polymerisation’, ACS Symposium Series No. 665, Eds., R. Faust and T.D. Schaffer, Polymer International, 1999, 48, 12, 1288-1289. 154. The Rate Constants of Cationic Polymerisations and Mayr’s Rate-Constants Reconciled, P.H. Plesch, Macromolecules, 2001, 34, 1143-1147.

769

Developments in the Theory of Cationoid Polymerisations

770

Abbreviations and Acronyms

4MEOST

4-Methoxystyrene

A

Acceptor

ACN

Acenaphthylene

BCMO

Bis-chloromethyl oxetan

BDE

Bond dissociation enthalpy

BIE

Binary ionogenic equilibria

bp

Boiling point

Cb

Chain-breaking

CEVE

2-Chloroethyl vinyl ether

CEViE

2-chloroethyl vinyl ether

CHVE

Cyclohexyl vinyl ether

CM

Cyanomethane

CP

Cationic polymerisation

CT

Charge-transfer

D

Donor

DA

Donor-acceptor

DC

Dielectric constant

DC

Disassociation constant

DCA

1,3-Dioxacycloalkanes

DCM

Dichloromethane

DIB

Di-isobutene

DP

Degree of Polymerisation

DPD

Degree of polymerisation distribution

DXL

1,3-Dioxolan

DXP

1,3-Dioxepan

EA

Electron acceptor

ED

Electron donor

EMF

Electromotive force

771

Commercial rubbers

Developments in the Theory of Cationoid Polymerisations EVE

Ethyl vinyl ether

fp

Freezing point

glc

Gas liquid chromatography

GPC

Gel permeation chromatography

HC

Hydrocarbons

HY-MG

Hunter-Yohé and Medvedev-Gantmakher mechanism

IB

Isobutene

IBVE

Isobutyl vinyl ether

ICI

Imperial Chemical Industries

IPVE

Isopropyl vinyl ether

IR

Infra red

MEVE

Methyl vinyl ether

MSA

Methanesulphonic acid

MVE

Methyl vinyl ether

MW

Molecular weight

MWD

Molecular weight distribution

NBD

2,5-Norbornadiene

NBVE

N-butyl vinyl ether

NE3VC

N-ethyl, 3-vinyl carbazole

NMR

Nuclear magnetic resonance

NVC

N-vinylcarbazole

PhVE

Phenyl vinyl ether

PIB

Polyisobutylene

PMR

Proton magnetic resonance

PS/PST

Polystyrene

SCE

Standard calomel electrode

ST

Styrene

TBVE

t-Butyl vinyl ether

THF

Tetrahydrofuran

TrStC

Transition State Complex

VE

Vinyl ether (s)

VPO

Vapour pressure osmometry

ZAV

Zlamal, Ambroz and Veseley effect

ZK

Bimetallic catalysts

772

ISBN: 1-85957-270-7

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