Les vertus des défauts: The scientific works of the late Mr Maurice Kleman analysed, discussed and placed in historical context, with particular stress on dislocation, disclination and other manner of local material disbehaviour

ABSTRACT

In memory of Maurice Kleman: Over the last half century, Maurice Kleman was the High Priest of the science of defects in condensed matter. I discuss some aspects of the history of dislocations, disclinations, and defects in liquid crystals, together with some of Maurice's other work. In so doing, I combine intellectual strands coming from pure and applied mathematics, physics, material science, and biology.

GRAPHICAL ABSTRACT

KEYWORDS:

• Liquid crystals
• Kleman
• defects
• disclination
• dislocation
• topology
• homotopy

Acknowledgments

I would like first of all to thank the editors of this issue, Oleg Lavrentovich, Randy Kamien and Corrie Imrie, for inviting me to write this paper. I had long been an admirer of Maurice Kleman. The task of summarising his work has only increased this admiration. I hope that in this essay I have been able to do him justice, both as a scientist and as a human being.

Over and above the issue editors, I first thank the late Maurice Kleman, the subject of this essay. The biographical sketch in Section 2 owes much to Maurice's autobiography Chronologie d'un physicien [14]. The autobiography, which gives insight into both Maurice's intellectual and his emotional life, well repays the read, although unfortunately it is not available in English. My biographical reading was significantly augmented by discussions with colleagues, and by my own memories of discussions with Maurice. I am particularly grateful for the significant and patient assistance from Maurice's son Jean-Philippe, and from Maurice's partner Madeleine Veyssié. In addition, I would like to single out Claire Meyer, who was kind enough to provide me with a detailed list of Maurice's publications.

Some forty years ago, before we were personally acquainted in any meaningful sense, Maurice's writings were the first to arouse in me an interest in liquid crystal defects. Over the years we enjoyed long discussions on this subject, its history, the history of science in general, and in fact other subjects of common intellectual and emotional interest. His 1977 text on Points, Lines and Walls [191], in the original French (rather ragged by now, but not doing so badly, all things considered) has accompanied me across Europe and back, and continues to be an inspiration. In a scientific context it was Nils Schopohl who persuaded me that he could transfer experience in superconductivity to enable us to think more fruitfully about defects in liquid crystals.

I owe my interest in Vito Volterra to the historian of science Judith Goodstein. Parts of this article have been extracted (and much edited) from a longer (eventually unpublished) article on Volterra's scientific work originally intended to accompany her magnificent biography of Volterra [24]. The present article contains reworked versions of parts of: (a) a semi-popular article in Mathematics Today [308], (b) an article celebrating Claudio Zannoni's 70th birthday celebration [89]. I apologise to readers for repetition in the pursuit of a self-contained text.

My interest in liquid crystals first emerged from a study of molecular fluids at interfaces, at which simple fluids, isotropic in the bulk, nevertheless exhibit nematic ordering. It was nurtured by discussions in Bristol with Charles Frank, and in Southampton in particular with Geoffrey Luckhurst. I owe a particular debt of gratitude to David Dunmur, who has shared much of my journey through liquid crystal history. David encouraged me to think about the history of the subject when, as editor of ‘Liquid Crystals Today’, he asked me to write an afterword (although I now think it rather imperfect) to Charles Frank's career following his death in 1998. David savaged an earlier version of this essay. I am sure he will not be satisfied by the final version either. However, notwithstanding our differences over this particular issue, his advice has remained essential.

In writing this paper, I have needed considerable help in understanding or revising concepts in pure mathematics, theoretical physics and biology. I have also sought memories from key players in the development of important ideas in the theory of defects, as well as from members of their families. In so doing I have benefited from helpful correspondence and conversation with: Amit Acharya, Gareth Alexander, John Chad, David Chillingworth, Mark Dennis, Jean Friedel, Philip Greulich, Roger Horn, Randy Kamien, Efim Kats, Claire Meyer, Oleg Lavrentovich, Thomas Machon, Vladimir Mineev, Graham Niblo, Pawel Pieranski, Valentin Poénaru, Victor Reshetnyak, Chuck Rosenblatt, Doug Ross, Tyler Shendruk and Grigoriy Volovik. I also acknowledge (older) correspondence with distinguished colleagues no longer with us, in particular Yves Bouligand, Charles Frank, Jacques Friedel, George Gray, Frank Leslie and Misha Monastyrsky. Finally, I apologise particularly to some close colleagues of Maurice Kleman, and to many others who played a role in this story, all of whom I should have consulted but was not able to as a result of time constraints.

Disclosure statement

No potential conflict of interest was reported by the author.