Frank Matthews Leslie - ePrints Soton€¦ · Web viewFrank Matthews Leslie. 8 March 1935 – 15 June 2000. Elected F.R.S. 1995. R.J. ATKIN. School of Mathematics and Statistics,

Biographical Memoir F.M. Leslie

Frank Matthews Leslie

8 March 1935 – 15 June 2000

Elected F.R.S. 1995

R.J. ATKINSchool of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH

and

T.J. SLUCKINSchool of Mathematics, University of Southampton, Southampton SO17 1BJ

Frank Leslie was a distinguished applied mathematician, who was above all foremost in creating the modern continuum theory of nematic liquid crystals in the late 1960s. This theory is now known as the Ericksen-Leslie theory, and the crucial elements in it as Leslie coefficients. After developing the hydrodynamic theory of nematic liquid crystals, he went on to perform a similar task in the 1990s for smectic liquid crystals. He also actively collaborated with experimentalists and engineers involved in liquid crystal applications, and his work has been extremely influential in the development of liquid crystal display device technology.

Biographical Memoirs of the Royal Society 49¸ 315-33 (2003) 1



F.M. Leslie in 1995


EARLY LIFE

Frank Matthews Leslie was born in Dundee, Scotland on March 8, 1935. There was little in his family pedigree to herald a distinguished scientific or mathematical career. As far back as records go, the family hailed from Dundee. Frank’s paternal great-grandfather, William Ogilvy Leslie (1849-1938), worked as a labourer and fruit porter. His son, Frank’s paternal grandfather, also named William (1871-1947), was listed in the 1891 census as an apprentice reedmaker, and his later profession was given as reedmaker. He is known to have spent some time in India with the Jute trade, which flourished in Dundee. He and his wife, née Jane Burgess (1873-1950) had four children, of which Frank’s father (also William Ogilvy), born in Bankfoot, Perthshire in 1895, was the second. This William Leslie worked as a factory clerk with Wm. Fergusson & Sons in their Dudhope Works in Dundee. He then served as a private in the Black Watch in France in World War I, and was medically discharged in 1916 following a shrapnel wound to the right elbow. He married Frank’s mother Catherine Pitkethly Matthews in 1933.

Catherine’s father Frank Rollo Matthews (1860-1921) was a blacksmith in the Dundee Jute industry, as well as being a pipe major who taught piping in his home. He was also, and this may be of relevance to his grandson’s future illustrious career, a great lover of books, which reputedly consumed the greater part of his disposable income. The books were transmitted through his daughter into the Leslie household, thereby apparently infecting Catherine’s husband with some of her father’s affection for the written word. Indeed, many of the volumes of the elder Matthews’s library remain till this day in the hands of the extended Leslie family. Thus the young Frank was born into a home which, although without a history of scholarship, nevertheless possessed a large book collection, as well as a strong tradition of hard work; surely two important foundation stones in Frank’s later academic vocation.

William and Catherine Leslie’s marriage gave rise to three children. A son, William McLeish Leslie (known as Bill) was born in November 1933, followed within 18 months by Frank himself, named after his bibliophilic grandfather. Some six years later, in 1941, a younger daughter, Norma, was born. Both sons attended Hawkshill junior school, where they both did well, sufficiently so that when the time came to move on they were entered for Harris Academy, the premier academic high school in Dundee. Frank Leslie’s impressive academic reputation at Hawkshill seems to have lasted a considerable time, for when his younger sister Norma attended the same school some years later, much was expected from her.

When Leslie was only eleven years old, in 1946, disaster struck the family. His father was taken into hospital for an operation to cure a chronic duodenal ulcer. However, the operation was unsuccessful, and shortly afterwards he died, at the rather young age of 50. His mother was left with three children, the youngest still under five years old, to bring the family up alone. This affected Leslie’s elder brother’s choice of employment. Bill was concerned about the financial health of the family. On leaving school, rather than continuing his studies at university, he sought a stable and reliable job — at the British Linen Bank (later the Bank of Scotland) — which would help support his mother and younger siblings.

It was around this time that Leslie entered Harris Academy, where he continued to excel, particularly in mathematics, but also in other academic subjects. A contemporary was R.P. Ferrier FRSE, later professor of physics in the University of Glasgow, who recalls in addition his performances on the cricket field. Given his outstanding academic talents and the financial cushion provided by his elder brother, it was now possible for Leslie to think about studying at university. He would be the first in his family to do so. Bright young people from Dundee were often tempted to pursue the big city bright lights at the Universities of Glasgow or Edinburgh, but Harris Academy had strong links with the local University College in Dundee, which at that time formed a college — Queen’s College — of the ancient University of St. Andrews.

Thus it was that in the spring of 1953, Leslie was a candidate in the Entrance Scholarship Examination in mathematics for University College, Dundee. The examination was both set and marked by the newly arrived professor in mathematics, Murray Macbeath. He recalls that Leslie’s Biographical Memoirs of the Royal Society 49¸ 315-33 (2003) 3


performance stood head and shoulders above that of other candidates. At Queen’s College, Leslie swept all before him. His outstanding performances won him the Myles Bursary and the Spence Bursary. During this period he began to concentrate on applied mathematics, much to the disappointment of Professor Macbeath, who had hoped to direct the energies of bright students in the direction of pure mathematics. This initial period of his life came to a close in 1957, when he was awarded a B.Sc. with 1st class honours in mathematics from what was still at that time the University of St. Andrews.

EARLY ACADEMIC CAREER

Following his graduation, Leslie headed south across the border, to the University of Manchester, to begin doctoral study in continuum mechanics.. His work at Manchester was partly supported by a Sir James Caird Scholarship; Sir James (1864-1954) was a philanthropic Dundee Jute Baron. At this time, as a result of the influence of Leslie’s supervisor, the still relatively young Professor (later Sir) James Lighthill (F.R.S. 1953), the Manchester Mathematics Department was a very exciting and stimulating place. He was set the problem of extending Lighthill’s work on so-called thermosyphons. However, after one term Lighthill took a rare period of study leave, and Leslie was passed onto Lighthill’s younger colleague B.R. Morton.

But in fact, Leslie’s progress seems to have been rapid, for by 1959, he was appointed to an assistant lectureship in mathematics by the University. In the end his Ph.D. work was very much conducted under his own steam and without real supervision, while at the same time performing the not inconsiderable duties of an assistant lecturer. His Ph.D., with a thesis entitled Problems of flow in the open thermosyphon and viscoelasticity of liquids, was awarded in 1961. The thesis work gave rise to three papers. Two of these were concerned with the thermosyphon, and one was concerned with viscoelastic fluids. Here we begin for the first time to see a hint of Leslie’s main life work. In the 1950s interest was growing in the formulation of constitutive theories for viscoeleastic materials. Leslie’s work developed aspects of J.G. Oldroyd’s models (1950, 1958) for viscoelastic fluids, making Oldroyd a natural choice of external examiner for Leslie’s Ph.D.

What is noticeable even at this early stage of Leslie’s career, is that of the three papers resulting from his Ph.D. work, none was written in collaboration with a mathematical colleague. On the other hand, two of the three papers were written with the active collaboration of experimental colleagues. His first paper [1], entitled “Laminar flow in the open thermosyphon, with special reference to small Prandtl numbers”, appeared, perhaps inauspiciously for an classical applied mathematician, in the Journal of Mechanical Engineering Science, and was co-authored by B.W. Martin of the Mechanical Engineering Department of Imperial College, London, and contained both theoretical and experimental results. Likewise his third paper [2], entitled “Slow flow of a visco-elastic fluid past a sphere”, which appeared in the mathematically much more orthodox Quarterly Journal of Mechanics and Applied Maths, although singly-authored, contained an appendix by his colleague Roger Tanner (F.R.S. 2001) of the Manchester Department of Mechanical Engineering.

This commitment to collaboration with experimentalists continued throughout Leslie’s academic life. It is particularly important in view of the fact that many of his experimental colleagues needed, at least to begin with, some convincing that a collaboration with


Leslie at his Ph.D graduation, Manchester 1961


Leslie would be fruitful. One colleague later noted that Leslie was “fluent in tensor calculus”, but by contrast, did not seem to develop the pictorial and visual images which many physical scientists use to organise their understanding. It was all the more impressive, therefore, that even at this early stage in his career, Leslie’s mathematical facility was producing results which interested his experimentalist colleagues.

After his period in Manchester, Leslie was lucky enough to obtain a fellowship to spend a year at M.I.T. In order to economise, he searched for the cheapest method of transport to the United States. Finally he found a whisky cargo boat, leaving, as luck would have it, from Glasgow, but he had to stand by to see whether space was available. When he finally was able to make the rather Spartan journey, it took 12 days. Once in America, he continued to work on viscoelastic fluids, writing a further paper [3] in this area. It was also during this period that his attention was first drawn to the work on anisotropic fluids by J.L. Ericksen at Johns Hopkins University in Baltimore, Maryland. Leslie’s interest was sufficient to impel him to write to Ericksen for reprints.

On his return to the UK after his year in America, Leslie was appointed by Professor A.E. Green (F.R.S. 1958) to the staff of the Mathematics Department at the newly created University of Newcastle. The department was undergoing a rapid expansion, enabling Green to attract young researchers and build up one of the strongest centres of research in continuum mechanics in the UK. Leslie’s previous work in viscoelastic theory made him an ideal member of this group. It was Green’s suggestion that he should concentrate on the anisotropic fluid theory developed by Ericksen. There followed two papers on aspects of the flow of these fluids. The first of these treated Hamel (converging) flow [4] and the second Couette (essentially shear) flow [5]. We should note that at this stage the identification of Ericksen’s anisotropic fluids and liquid crystals was far from being definitive. When Ericksen first started to work in this area he had not been aware of liquid crystals at all. Later he had been concerned to strengthen this identification, but had not yet solved the problem. We shall deal with some of the scientific issues in more detail again when we discuss Leslie’s scientific work in more detail..

Then, in 1965, Leslie returned to the more fundamental problem of the foundations of the theory of anisotropic fluids. Green and Rivlin (1964a) had used the invariance of an appropriate energy equation under superposed rigid motions to show that it was possible to derive the balance of mass, the balance of linear momentum, and the consequences from the balance of angular momentum (symmetry of stress in the classical case). They then (Green and Rivlin 1964b) developed their theory for multipolar materials. Leslie applied this technique to anisotropic fluids. In doing so he introduced an additional vector, or director, at each point of the continuum, and used an energy equation proposed earlier by Ericksen. This included contributions to the rate of working from couple stresses and generalised body forces. The paper also included thermal effects and introduced a Clausius-Duhem inequality, deducing restrictions from this inequality using an approach proposed by Coleman and Noll (1963). The effect was to rederive, under appropriate restrictions, Ericksen’s earlier theory; one important difference was the elimination of a term in the stress, which now reduced to a hydrostatic pressure, thus simplifying the predictions for viscometric flows.

The result, submitted in December 1965, was a classic paper [6] on the road to a continuum theory of liquid crystals. The abstract states:

The theory of a continuum with a director is considered and constitutive equations relevant to a class of anisotropic fluids is discussed. Some exact solutions for simple shear, Poiseuille and Couette flow are given.

This abstract emphasises one of Leslie’s strengths. He had gone back to the foundations of the subject (as do many), but, in addition, some examples are given. This was a typical feature of Leslie’s work, always to give some examples, by contrast with others who might have tried to be more ambitious with the theory, but failed to find applications for the theory which might enable it to be subjected to empirical test.



Nevertheless, it is important to stress that this paper was only a milestone. At the end of the introduction, Leslie writes:

The theory described in this paper allows a fluid to have a preferred direction at each point……. Materials called liquid crystals possess such preferred directions. However, since the present theory does not reduce to Frank’s hydrostatic theory of liquid crystals, it would appear that it is inadequate to describe these materials.

According to tradition, in fact, this paragraph was only inserted at the request of a referee. Whether the tradition is true is impossible to verify, as we know that Leslie had been familiar with Ericksen’s work on anisotropic fluids from the time he had spent at M.I.T, and in his later work Ericksen was already referring to liquid crystals. At this stage, however, Leslie was really still exploring general theories of hydrodynamics. The application to liquid crystals was not yet central to his study, and so the lack of application of his theory to liquid crystals was no great disappointment.

At this time Leslie’s life was going through important phases, both personally and professionally. After his year at M.I.T., in the summer of 1962, he had returned to Dundee for a holiday to see his family. At a Church of Scotland youth fellowship walking group he met Ellen Reoch. The relationship flourished, and in 1965 they were married. On the professional side, prompted by a colleague and encouraged by Ellen, he successfully applied to spend a sabbatical year in Jerald Ericksen’s group in Baltimore. He served as visiting assistant professor, and additionally enjoyed some support from the Fulbright Foundation. In August 1966 he and Ellen set sail from Southampton for the United States. The voyage was in a different class from his earlier 1961 journey. This time, as befitted a newly-married up-and-coming scholar, Ellen and he travelled in H.M.S. Queen Elizabeth to New York, completing the journey by train.

SUBSEQUENT LIFE AND CAREER

We postpone the detailed story of Leslie’s period in the United States to a later part of this memoir. Suffice it to say here that it resulted in a paper which revolutionised the understanding of liquid crystals. On his return to the UK, Leslie returned to Newcastle, but now started actively seeking promotion. In early 1968 he was called to interview for senior lectureships in Sheffield and Strathclyde. Unfortunately the interviews were set for the same day. However, both he and his wife felt a strong attachment to their native Scotland, and had always set it as a long term goal to return to Scotland to live. The possible choice between Glasgow and Sheffield was no choice. Leslie only attended the Strathclyde interview, and the bet paid off. In October 1968 he and Ellen moved to Glasgow, and Leslie began work in the Department of Mathematics at Strathclyde University. He was to spend the rest of his life there.

As his career progressed, Leslie was promoted, to reader in 1971, and then to a personal chair in 1979, and finally to an established chair in 1982. As the impact of his liquid crystal work increased, he was much in demand as a speaker at conferences and as a visitor in academic institutions abroad. He revisited Baltimore as Senior Fellow in Mechanics in 1973, and then in 1978 was invited by Steve Cowin, a biophysicist at Tulane University in New Orleans, to spend a couple of months as a visiting professor of engineering in New Orleans. In 1985 he visited Hokkaido University, Sapporo, Japan, and a 1992 visit to Pisa began a long-standing interaction with Epifanio Virga. Leslie also hosted large numbers of academic guests in Glasgow, including from time to time Jerry Ericksen. The photograph included here shows Ericksen and Leslie in Glasgow some time in the mid-1970s.

Leslie’s personal life flourished at the same time as his career. His daughter Sheena was born in 1969, followed by a son Calum in 1974. His wife Ellen remembers him as “working all the time”, which is an indication of his commitment to his mathematics, but not to the exclusion of all



else. He was an active, if amateur, golf-player, and also hill-walker. Somewhat to the surprise of more secular colleagues, as a regular churchgoer, he would always carry his bible to academic conferences. In 1971 he was elected an Elder of the Church of Scotland. He was a Justice of the Peace for 15 years in Bearsden and Milngavie, sitting on the bench in judgement over his peers (and, presumably others!) three times a year.

His academic colleagues the world over all knew of his commitment to the cause of Scottish independence. For 14 years he was treasurer of the Bearsden branch of the Scottish National Party, and at election time, come rain or shine, Leslie was on the campaign trail in support of SNP candidates. At conferences, when the topic turned to politics, Leslie could often be heard explaining patiently to sceptics the analogies between the political debate preceding the 1707 Act of (Anglo-Scottish) Union and the more current debate about Britain in Europe. Leslie was a “Scotland in Europe” man. What the English did, he felt, was up to them.

His fellow Scot Ian Shanks (F.R.S. 1984) relates the tale of his arrival at Kyoto airport in Japan. There was an immigration form to be filled in, which included a section on nationality. Leslie filled in his form, recording his nationality as “Scottish”. The immigration officer was having none of it. There was no such country. After further enquiry, he deleted “Scottish”, and replaced it with “English”. Leslie went ballistic. The ensuing argument lasted half an hour, while the queue behind (consisting of Scots, English, and many other nationalities besides!) steadily lengthened, and their temper steadily worsened. Finally a compromise was reached. On this occasion, and only on this occasion, Leslie was “British”.

For many years, starting in mid 1970s, Leslie spent summers working as a consultant for what was initially R.R.E (and then R.S.R.E, then D.R.A., and then D.E.R.A.) in Malvern. Malvern was the centre of the British liquid crystal device effort, which was headed by Cyril Hilsum (F.R.S. 1979). The whole family would decamp to Malvern over this period, and Leslie particularly enjoyed walking on the Malvern Hills. He often remarked on the irony of a nationalist like himself penetrating the centres of the “British” Ministry of Defence. However, when Mike Clark, one of the Malvern colleagues, moved to the G.E.C. Research centre in London, Leslie politely but firmly Biographical Memoirs of the Royal Society 49¸ 315-33 (2003) 7

Leslie with his colleague J.L. Ericksen (right), in Glasgow, sometime in the 1970s.


deflected the offer of a consultancy in London, remarking that London provided too many opportunities for spending money. (This cannot be whole story, for his c.v. records that over the period 1976-84 he was indeed a consultant for G.E.C.!).

LIQUID CRYSTALS

In order to place Leslie’s work in its proper context it is necessary first to digress slightly and discuss a little of the background to the study of liquid crystals. The term “liquid crystal” is a misnomer. The materials known as liquid crystals form phases with properties intermediate between those of a crystal and a fluid. The first observation was by the Austrian biochemist Friedrich Reinitzer (1857-1927), who in 1888 reported a double melting phenomenon in cholesteryl benzoate. The lower temperature melted phase was cloudy, but at a higher temperature the cloudiness disappeared suddenly, at what became known as the “clearing point”. The cloudy phase also exhibited some peculiar colours.

The high apostle of these materials was the German crystallographer Otto Lehmann (1855-1922), who examined them exhaustively under a polarising microscope. When viewed under a polarising microscope, the fluids in question exhibit patterns (often later called “textures”) which at first were confused with crystals. Lehmann put much intellectual effort into reconciling the phenomena of flow and crystallinity in one and the same material. The term “liquid crystal” is due to him. A longer version of this story is given by Kelker and Knoll (1989).

Whereas Lehmann had principally noted a degree of fluidity, the distinguished French crystallographer Georges Friedel identified two sharply distinct phases. These he labelled as “nematic” and “ smectic”. The nematic phase was identifiable from the thread-like lines (Greek = thread), and consisted of rod-like molecules, coherently oriented but without any crystalline solid structure. The smectic phase (Greek = soap, for many of these materials are soaps or their derivatives) also contained oriented molecules, but now they were also arranged in parallel equally-spaced layers.

The major pioneer in the theory of nematic liquid crystals was the distinguished Swedish theoretical physicist Carl Wilhelm Oseen (1879-1944). In a long series of papers in the 1920s and 1930s, Oseen developed what we now recognise as the elastic theory of nematic liquid crystals. The only exposition of Oseen’s work in English was in a symposium organised by J.D. Bernal (F.R.S. 1937) for the Faraday Society in 1933, but being in English this paper is more accessible than his other work and it has become canonised. Oseen’s 1933 paper also includes a brief description of some unpublished work by his doctoral student Adolf Anzelius (1894-1979), who had made what turned out to be a not entirely successful attempt to construct a dynamical theory of nematic liquid crystals. Here experimental progress was more rapid, for just before the outbreak of the second world war the Polish physicist Marian Mięsowicz (1907-92) made observations showing that nematic liquid crystals exhibited at least three viscosities, depending on the mutual orientation of the flow and the average molecular orientation (which later became the director).

A further renewal of interest in liquid crystals occurred in the mid-1950s, driven in the UK at least, by F.C. Frank in Bristol on the theory side and by the experimental work of G.W. Gray (F.R.S. 1983) in Hull. A paper by Frank in 1958 was particularly important. This recapitulated Oseen’s 1933 work, concentrating on the formulation of the elastic energy as a function of director curvature in nematic liquid crystals, and also (because that was Frank’s particular expertise) on defect structure. This paper was immensely influential in the burgeoning interest in liquid crystal theory in the 1970s and 1980s. However, because the elastostatics was derived from a quadratic free energy functional involving four elasticities, at that stage it was not obvious how it might be generalised to include director rotation and fluid motion.

This problem was addressed in 1961 by Ericksen, who had been puzzling as to how to reconcile Frank theory with the hydrodynamics of anisotropic fluids. He observed that previous work on liquid crystals had focussed on energy rather than on force, and that from the point of view of continuum mechanics it would be necessary to represent body forces (and not merely energies), Biographical Memoirs of the Royal Society 49¸ 315-33 (2003) 8


requiring calculation of a stress tensor. Moreover, unusually, the liquid crystal stress tensor is asymmetric, signalling the presence of body couples, which are neglected in many conventional continuum theories.

ERICKSEN-LESLIE THEORY

Leslie arrived in Baltimore in August of 1966. The intellectual environment was stimulating. More often than not, by the end of coffee break, a stream of paper napkins with equations scrawled over them could be found all over the floor. There were postdoctoral colleagues with whom to share that coffee time, at least one of whom, Ingo Müller, was to remain a lifetime friend. And there was the regular Tuesday Research Meeting, at which progress on research was reported, and more formal aspects of Rational Mechanics were examined.

Leslie first spent some time discussing with Ericksen about the form the full theory of liquid crystals should take. Ericksen then lent him his copy of Anzelius’s doctoral thesis on the dynamical theory of nematics. Although Anzelius was Swedish, according to the custom of the time the thesis was in German. The library, however, owned a comprehensive German dictionary. Leslie spent the whole of the next month in the library. With thesis in one hand and dictionary in the other, progress was painfully slow. The final form of the theory [7], only submitted after Leslie’s return to the UK (and published in 1968), was modestly entitled “Some constitutive equations for liquid crystals”. It builds on his 1966 paper, but adds elastic contributions to the stress tensor to the dissipative terms already included. The result is a theory which now does reduce to the Frank theory in the hydrostatic limit, and also (as it is designed to be) to the Navier-Stokes equations in the absence of anisotropy.

Leslie, acknowledging his strong intellectual debt to Ericksen, did suggest that his name be included as an author. It was Ericksen’s rather generous practice, however, not to include his name on papers written by his graduate students and postdoctoral workers. So the paper appeared under Leslie’s by-line alone. Nevertheless, to Ericksen’s surprise, the theory came to be called the Ericksen-Leslie theory, and given the background, the historical judgment is not unfair.

We may summarise the important elements of Leslie’s 1968 paper in modern language. The derivation of the balance laws followed his 1966 paper. However, by contrast with 1966, this time he included in addition director gradients in the constitutive theory. This led to an elastic contribution to the stress, which supplemented the dissipative stress and the non-zero couple stress. Roughly speaking , the theory welded together the Frank elastic theory with anisotropic fluid theory discussed earlier. Leslie had already written down in 1966 the important dissipative part of the stress tensor :

, (1)

where the quantity is the rate of strain tensor and is the director (this is contemporary notation, not Leslie’s) . Indeed apart from the additional term mentioned earlier, this had also appeared in Ericksen’s work. An important advance over Anzelius was the realisation that that the rate of change of the director must enter the theory in covariant form: , where is the fluid vorticity. Although Leslie had adopted the entropy flux proposed by Müller, in which the entropy flux required a constitutive relation, when n has fixed magnitude this flux takes the classical from of heat flux divided by temperature. The six quantities i , which have the dimensions of viscosity, and which depend in principle on density and temperature, have come to be called the Leslie coefficients, and in the absence of any anisotropy 4 is the usual fluid viscosity appearing in the Navier-Stokes equations. The local viscous body torque , where

, (2)Biographical Memoirs of the Royal Society 49¸ 315-33 (2003) 9


and the relaxation coefficients i, which also have the dimensions of viscosity, are related to the actual viscosities through the relations:

(3)

A subsequent addition to this is the so-called Parodi relation (1970) , reducing the number of independent viscosities to five. As a consequence of this last addition, the hydrodynamic theory of liquid crystals is sometimes known as the ELP theory.

It was characteristic of Leslie’s approach that he should not be satisfied with constructing an intellectual edifice, but also attempt to make some connection with experiment. Leslie made some detailed calculations on shear flow. He derived what came to be called shear alignment, in which the director orients itself at some defined angle to the flow direction, and found that there was a boundary layer effect and a relaxation length over which the shear alignment was adopted. He also referred to Mięsowicz’s work; in fact it would later turn out that the Leslie coefficients were linearly related to the viscosities measured by Mięsowicz. He made some order of magnitude calculations of the observable effects. And he also referred to more recent viscometric measurements on liquid crystals, making suggestions as to how a connection might be made between these measurements and his theory.

Despite its natural appeal, the true test of the Ericksen-Leslie theory was experiment. Viscometric confirmation was not long in coming. The long history of observations of liquid crystalline viscosity – going all the way back to 1898 – had demonstrated clearly that liquid crystals were non-Newtonian fluids. Fluid viscosity can be measured empirically using the classical Navier-Stokes formula for the Poiseuille fluid flux Q of a standard Newtonian fluid, yielding a

formula for the fluid viscosity: , in terms of the measurable quantities Q, the pressure

gradient P and the capillary radius R. Further work (Atkin 1970) showed that whereas the effective

viscosity eff was a function of in a classical isotropic (non-Newtonian) viscoelastic fluid, it was

a function of according to the Ericksen-Leslie theory. So here was an unambiguous test.

This result, though published only in 1970, was ready in 1968 before the second international liquid crystal conference at Kent State University. Frederickson and Fisher presented results at this conference on just the viscometric experiment envisaged by Ericksen, in which they changed the size of the capillary, and also the nature of the orienting condition at the boundaries. The effective

viscosity was emphatically not a function of , for each capillary and boundary condition yielded

a different curve for . However, hearing of the new scaling, Fisher and Frederickson

rapidly replotted their data. They found that indeed when eff is plotted as a function of , the

curves from different capillaries collapse onto one plot. This was the first of many confirmations of the Ericksen-Leslie theory.

DEVELOPING THE LIQUID CRYSTAL THEORY

The following few years were anni mirabiles for Leslie. In a series of papers in 1968 [8] he extended his dynamical theory of nematic liquid crystals to the chiral cholesterics, thereby incorporating not only the extra chiral terms in the nematic free energy proposed by F.C. Frank, but also introducing extra chiral terms in the dissipative stress tensor. A joint paper with Atkin [9] in



1970 completed the viscometric analysis by examining Couette flow. He also turned his attention to finding two-dimensional exact static solutions under electric and magnetic fields [10]

In what turned out to be a particularly important paper for the development of liquid crystal devices, also in 1970 [11], he analysed the distorting effect of a magnetic field on twisted orientation patterns. This was the written version of the talk given by Leslie at the third international liquid crystal conference in Berlin in July 1970. The physical problem was what we now call a “hybrid” liquid crystal cell, in which the directors at the (parallel) cell boundaries are oriented in the planes of the boundary, but perpendicular to each other. Inside the cell the director twists around uniformly from one orientation to the other. A magnetic field across the cell, however, interacts with the director, and in Leslie’s hypothetical case, favoured director orientation along the magnetic field. The director will thus swing out of the plane of the boundary, but for reasons of symmetry will only do so at a threshold field. Mathematically this required a three-dimensional solution for the director

The general effect had been observed by Frederiks (1927) – giving rise to the eponymous Frederiks effect – and explained by Zocher (1933), but only in the case of a “normal” cell in which in the field-free case the director was uniform. Untwisting of twisted liquid crystal textures was observed and understood in principle, though not in any theoretical detail, by Charles Mauguin (1878-1958) in 1911. He showed, using an argument due to Poincaré, that a twisted structure could, in a suitable limit now known as the Mauguin régime, act as a wave guide, twisting the light polarisation axis with it. Leslie found a specific formula which generalised Zocher’s result.

The importance of the result, however, is not its mathematical sophistication (although it was by no means trivial). Rather it was the presence in the audience at Leslie’s Berlin talk of Martin Schadt and Wolfgang Helfrich, who were in the process of patenting the twisted nematic liquid crystal device. This has turned out to be the major (flat screen) liquid crystal display technology. Schadt and Helfrich (1971) realised that the mathematics would remain more or less unchanged if an electric field were to be substituted for a magnetic field. Leslie’s result thus formed the foundation for the emerging flat screen display industry, although he did not benefit directly financially.

The tale is told that while performing this calculation Leslie was supervising a televised undergraduate lecture. At that time Strathclyde classes were very large and some were given over a television link, with a lecturer sitting in at the back. Inevitably, he was concentrating hard on his work. The time for the end of the lecture came and went. Leslie continued with his algebra. The students remained in their places, waiting for a signal to leave, but none came. Finally, a bold student gingerly approached the lecturer…. could the students leave now, please?

A further set of papers [12] responded in detail to experiments by Pieranski and Guyon (1974) designed explicitly to test the Ericksen-Leslie theory. With the growth of the British LCD effort at R.S.R.E in Malvern, Leslie began an intensive collaboration with the engineers in the Malvern group. A paper with Clark [13] analyses the orientational relaxation when a field is removed, this being an obvious problem occurring in real devices. The original contribution here concerns so-called “backflow”. This is the flow induced when the director rotates, and occurs because coherent rotation, necessarily involving flow, is less dissipative than local rotation of the director. The consequence of this is that a relaxing director may appear to overshoot its equilibrium configuration before returning to equilibrium. In display device applications, for which the update time was all-important, this was an important lesson; in relaxation calculations flow-director rotation cannot be ignored.

Leslie continued to investigate flow problems in nematic liquid crystals until his death. His 1979 review article in Advances in Liquid Crystals was particularly influential in codifying the current state of his theory [14]. He also addressed a number of other issues. With his Strathclyde colleague Barratt [15], he considered reflection and refraction of light at liquid crystal boundaries, thereby treating an experimental problem addressed by Martinoty and Candau (1971). With his Malvern colleague Waters [16], he addressed light scattering from a nematic liquid crystal in the presence of an alternating electric field, including the complications of both conduction and



flexoelectricity. A collaboration with his colleague Steve Cowin (at that time at Tulane University) addressed the problem of the correct definition of kinetic energy and momentum in so-called Cosserat continua [17]. In these systems, dating from 1909 and which served as models for the director systems which were the precursors of the Ericksen-Leslie theory, bodies carry along internal frames of reference. The underlying problem, which still remains unsolved, is the lack of a local director angular momentum term in the nematic liquid crystal free energy. More recently he had been investigating flow-induced switching in bistable nematic devices [18].

SMECTIC LIQUID CRYSTALS

Leslie’s research underwent a change in direction following the discovery of the possibility by Clark and Lagerwall (1980) of liquid crystal display devices based on ferroelectricity in the smectic C phase. This is a layered structure in which the director n makes an angle with respect to the layer normal. A major stimulus to the development of a non-linear continuum theory for these materials came with the formation of the SERC-funded Smectic Continuum Theory Consortium. This loose group of British researchers was coordinated by M.G. Clark at the G.E.C. Hirst Research Centre in Wembley, and also included D.R. Tilley in Essex and J.R. Sambles (F.R.S. 2002) in Exeter, as well as Leslie himself. During this period Leslie’s group expanded; I.W. Stewart joined as a postdoctoral worker, along with research students J.S. Laverty, S.P.A. Gill and G.I. Blake. T. Carlsson and M. Nagakawa visited for extended periods.

The choice of basic variables for the theory proved central. Leslie’s initial theory, developed in the summer of 1987 at Malvern, used the director n together with a vector a in the direction normal to the local layered structure. However, this theory turned out to be too complex, and eventually n was replaced by a vector c, the projection of the director onto the plane of the layers, a choice earlier adopted by Pierre-Gilles de Gennes (For.M.R.S. 1984). In the original (‘simpler’) theory the layers were assumed incompressible and the tilt angle constant, but in later versions of the theory both assumptions were relaxed [19,20]. Even the simpler theory [21], however, contains a quadratic elastic energy functional containing nine terms for non-chiral smectic C [22] , eleven for chiral materials [23], and a dissipative stress with as many as twenty viscosities.

A vital test for the static theory of the smectic C phase was whether it contained solutions describing the so-called focal conics. These structures are known to be the key optical signature of the smectic phase, and were used heuristically by Georges Friedel in the 1920s to identify the smectic phase structure. The theory passed this test, predicting Dupin cyclides (Nakagawa 1990) and parabolic cyclides [24], at least with a slightly simplified elastic energy function. There are also solutions corresponding to Frederiks transitions, which now enable the elastic constants to be determined (Atkin and Stewart 1997). Notwithstanding the apparent complexity of the dynamic theory, some progress has been possible in this field as well, particularly when dealing with shear flow in the case when the bounding plates and the layers are parallel. With Blake he treated simple flow instabilities [25]; Barratt and Duffy (1996), and again Leslie and Blake [26], treated the smectic equivalent of nematic backflow. The applications and implications of this theory are not as fully resolved as for the nematic theory, but an encouraging body of results is developing.

BIAXIAL NEMATIC LIQUID CRYSTALS

In 1980 Yu and Saupe discovered experimentally a biaxial nematic phase in a multicomponent lyotropic system. In biaxial phases all three principal components of the dielectric tensor are different, as compared to the usual uniaxial case, in which there are only different components parallel and perpendicular to the distinguished axis. By contrast with usual thermotropic liquid crystal systems consisting of small molecules, lyotropic phases are solutions of larger molecules in water, and the liquid crystallinity is controlled by the concentration of the rod-



like molecules. Subsequently the synthesis of analogous thermotropic materials has also been reported.

Leslie set to work to construct a continuum theory for these materials too. He felt that it must be possible to construct a natural generalisation of the Ericksen-Leslie theory by introducing two vectors to describe the biaxiality. This work, which also involved T. Carlsson and J.S. Laverty, progressed in parallel to the work on smectic theory.

The final theory [27] involves a quadratic elastic energy with twelve terms. By supposing that the dissipative stress is derivable from a dissipation function, Leslie found that the theory now involves twelve different viscosities. A very similar dissipative stress also arises in the theory for the smectic CM materials. It is interesting to note that from a conceptual point of view Leslie’s continuum smectic C theory is a theory for a biaxial material with non-standard invariance properties; the details of the layering structure are entirely lost in the continuum theory.

Elasticities must be measured to be useful. S. Chandrasekhar (1989) (F.R.S. 1983) had suggested that biaxial nematic systems could be aligned using crossed electric and magnetic fields, and that this might be used to measure the elasticities. Leslie’s static theory [28] shows that some caution would be required in interpreting such experiments, as the systems exhibit bistability in some equilibrium configurations. The dynamical theory was also used to make predictions about flow alignment and instability [29,30]

FINAL YEARS

In later life, Leslie played an extremely active role in the applied mathematics, rheology, and liquid crystal communities. For twenty years he was a mathematics tutor at the Open University. This attested to his commitment to mathematical education as well as to universal access to that education. His contribution was much appreciated by O.U. colleagues.

Leslie was a member of the editorial board of several journals, including Liquid Crystals, The Journal of Non-Newtonian Fluid Mechanics and Continuum Mechanics and Thermodynamics. He was fellow both of the Institute of Mathematics and its Applications and of the Institute of Physics, thus marking with pride two of the disciplines making up the complex which came to be known as Liquid Crystal Science. He was also elected chair of the British Liquid Crystal Society 1987-91, and was extremely active in that post. The Royal Society of Edinburgh elected him as a fellow in 1980, and notwithstanding his proud Scottish heritage, he was extremely proud of his membership of what he always referred to as the Royal Society of London.

The tremendous success of the theory that eventually bore his name also brought him honours. In 1980, Johns Hopkins University elected him as a member of their Society of Scholars, in 1982 he was awarded the annual award of the British Society of Rheology, and in 1996 St. Andrews University honoured one of the most successful native sons by awarding him the Sykes Gold Medal (following their award of a D.Sc. degree in 1995). In 1997 the British Liquid Crystal Society awarded him its premier award, the G.W. Gray medal. It is characteristic of Leslie’s modest attitude, that it was suggested to him that he might accept this award, he demurred strongly, taking the view that such prizes might better be directed to younger scientists who would be more encouraged by the award of a medal. It took intervention at a much higher level to convince Leslie that he should accept. His intensely humorous acceptance speech at the annual British Liquid Crystal Society meeting will long be remembered.

In his last few years he travelled widely, often accompanied by Ellen, and was a well-known figure in the liquid crystal community. He built up a mathematical liquid crystal group at Strathclyde, which has gone from strength to strength even after his death. He was due to retire at the end of the 1999-2000 academic year. To mark his retirement, the British Liquid Crystal Society held its annual meeting at Strathclyde University in March 2000. As preparation for his retirement he and Ellen sold the villa in Bearsden which had been their home for 25 years, and bought a bungalow in Argyll with fine views over the Clyde estuary. Biographical Memoirs of the Royal Society 49¸ 315-33 (2003) 13


His daughter Sheena was married in September 1998 (a granddaughter Emma was born in April 2000). Just before the wedding Leslie noticed a slight stiffness in his hip, and joked that he might have difficulty walking her down the aisle. The problem worsened over the following couple of years, and he began to take painkillers. By the time of the March 2000 British Liquid Crystal Society meeting, Leslie could be seen to be in considerable discomfort.

The hospital consultant prescribed a hip-replacement operation. Unfortunately there was a 9-month waiting list at the local NHS hospital, and to shorten the period of discomfort and provide some sense of certainty, Leslie decided to have the operation at a local private hospital. He entered hospital on Wednesday June 7 for what was supposed to be a routine operation. The operation was carried out the following day, and was initially thought to be successful. The hospital began a course in physiotherapy, but after a few days Leslie began to exhibit symptoms of breathlessness, and so the physiotherapy course was suspended. The hospital, fearing (as it turned out, correctly) a pulmonary embolism, gave him aspirin. On Thursday June 15, they prepared to transfer him to a different hospital in order to sort out the problem, but as the nurses were preparing to transfer him to the trolley, Leslie collapsed and died very shortly afterward.

His premature death deprived his family of a loved and loving father and grandfather. He is also missed greatly by his friends and colleagues in the liquid crystal and applied mathematics communities both in the United Kingdom and further afield.



ACKNOWLEDGEMENTS

We are grateful to Mrs Ellen Leslie and Mrs Norma McGrory (née Leslie) for many recollections concerning the Leslie family over the years. Dr. Iain Stewart was a close colleague of Leslie’s, and provided many memories of academic and personal conversations. Dr. Stewart was kind enough to provide us an almost complete copy of the Leslie collected works. Leslie himself, in collaboration with Professor T. Carlsson (Chalmers University, Göteborg), wrote an important article on the development of the continuum theory of liquid crystals. This article illuminates, in characteristically modest fashion, his own contribution, and has provided important source material. We are grateful to Professor Carlsson for the opportunity of discussing it with him and for allowing us to borrow some of the technical discussion. Obituaries written by his colleagues Professors D.M. Sloan, M.A. Hayes and R.J. Knops and by Professor I. Müller have also helped to round the picture we have of Professor Leslie. We also thank Mr. A.H.M. Brown, Prof. M.G. Clark, Professor W.D. Collins, Professor S.C. Cowin, Professor J.L. Ericksen, Professor R. Ferrier, Professor G.W. Gray F.R.S., Professor C. Hilsum F.R.S., Professor R.J. Knops, Professor M. Macbeath, Professor B.R. Morton, Professor E.P. Raynes F.R.S., Professor N. Riley, Professor I.A. Shanks F.R.S., Professor D.M. Sloan, Professor E.P. Virga and Professor K. Walters F.R.S..

The photograph of Leslie in 1961 at his graduation ceremony, and that of Leslie with Ericksen in the mid-1970s, have been kindly provided by Mrs. Ellen Leslie.



REFERENCES TO OTHER AUTHORS

R.J. Atkin, Arch. ration. Mech. Analysis 38, 224 (1970)R.J. Atkin and I.W. Stewart, E.J.A.M. 8, 253 (1997)P.J. Barratt and B.R. Duffy, Liq. Cryst. 21, 865 (1996)S. Chandrasekhar, oral communication, 8th Liquid Crystal Conference of Socialist Countries, Krakow, Poland (1989)N.A. Clark and S. Lagerwall, App. Phys. Letts. 36, 899 (1980).B.D. Coleman and W. Noll, Arch. ration. Mech, Anal. 13, 167 (1963)J.L. Ericksen, Arch. ration. Mech. Anal. 9, 371 (1961)J. Fisher and A.G. Frederickson. Mol. Cryst. Liq. Cryst. 8, 267 (1969).F.C. Frank, Disc. Faraday Soc. 25, 19 (1958)V.K. Fréedericksz and V. Zolina, Trans. Am. Electrochem. Soc. 55, 85 (1929)G. Friedel, Annales de Physique 18, 273 (1922)A.E. Green and R.S. Rivlin, Z. Angew. Math. Phys. 15, 290 (1964a)A.E. Green and R.S. Rivlin, Arch. ration. Mech. Anal. 17, 113 (1964b)H. Kelker and P.M. Knoll, Liq. Cryst. 5, 19 (1989). P. Martinoty and S. Candau, Mol. Cryst. Liq. Cryst. 14, 243 (1971)M. Nakagawa, J. Phys. Soc. Japan 59, 81 (1990)J.G. Oldroyd, Proc. Roy. Soc. A200, 523 (1950), ibid A245, 278 (1958).C.W. Oseen, Trans. Faraday Soc. 29, 883 (1933)O. Parodi, J. Phys. (Paris) 31, 581 (1970)P. Pieranski and E. Guyon, Phys. Rev. Lett. 32, 924 (1974) M. Schadt and W. Helfrich, App. Phys. Lett. 18, 127 (1971)H. Zocher, Trans. Faraday Soc. 29, 945 (1933)L.J. Yu and A. Saupe, Phys. Rev. Lett. 45, 1000 (1980)



BIBLIOGRAPHY

The following publications are those referred to directly in the text. The second column gives the publication number in the full Leslie bibliography.

(1) (1) With B.W. Martin: ‘Laminar flow in the open thermosyphon, with special reference to small Prandtl numbers.’ J. Mech. Eng. Sci. 1, 184-193 (1959).

(2) (3) ‘The slow flow of a viscoelastic liquid past a sphere.’ Q. Jl. Mech. appl. Math. 14, 36-48 (1961).

(3) (4) ‘The motion of a. flat plate from rest in a. viscoelastic liquid.’ Proc. Edin. Math. Soc. 13, 223-233 (1963).

(4) (5) ‘Hamel flow of certain anisotropic fluids.’ J. Fluid Mech. 18, 595-601 (1964).

(5) (6) ‘The stability of Couette flow of certain anisotropic fluids.’ Proc. Camb. Phil. Soc. 60, 949-955, (1964).

(6) (7) ‘Some constitutive equations for anisotropic fluids.’ Q. Jl. Mech. Appl. Math. 19, 357-370 (1966).

(7) (8) ‘Some constitutive equations for liquid crystals.’ Arch. ration. Mech. Anal. 28, 265-283 (1968).

(8) (10) ‘Continuum theory of cholesteric liquid crystals.’ Mol. Cryst. Liq. Cryst 7, 407-420 (1969).

(9) (12) With R.J. Atkin: ‘Couette flow of nematic liquid crystals.’ Q.J. Mech. Appl. Math. 23, S3-S24, (1970).

(10) (11) ‘Some magneto-hydrostatic effects in nematic liquid crystals.’ J. Phys. D 3, 889-897 (1970).

(11) (13) ‘Distortion of twisted orientation patterns in liquid crystals by magnetic fields’ Mol. Cryst. Liq. Cryst. 12, 57-72, (1970).

(12) (18) ‘Analysis of a flow instability in nematic liquid crystals.’ J. Phys. D 9, 925-937 (1976).

(13) (20) With M.G. Clark: ‘A calculation of orientational relaxation in nematic liquid crystals.’ Proc. Roy. Soc. A361, 463-485 (1978).

(14) (R1) ‘Theory of flow phenomena in liquid crystals’, Advances in Liquid Crystals, Ed. G.H. Brown, Academic Press, New York, Volume 4, pp. 1-81 (1979).

(15) (21) With P.J. Barratt: ‘Reflection and refraction of an obliquely incident shear wave at a solid- nematic interface,’ J. Phys. (Paris) 40, C3, 73-77 (1979).

(16) (30) With C.M. Waters: ‘Light scattering from a nematic liquid crystal in the presence of an electric field.’ Mol. Cryst. Liq. Cryst. 123, 101-117 (1985).

(17) (23) With S.C. Cowin; ‘On kinetic energy and momenta in Cosserat continua.’ Z. Angew. Math. Phys. 31, 247- 260 (1980).

(18) (63) With J.G. MacIntosh and P.J. Kedney: ‘Flow-induced switching in a bistable nematic device,’ Mol. Cryst. Liq. Cryst. 330, 525-533 (1999).

(19) (59) With G. McKay: ‘A continuum theory for smectic liquid crystals allowing layer dilation and compression.’ Eur. J. App. Maths. 8, 273-280 (1997).



(20) (64) With C. Anderson: ‘A study of smectics in a confined geometry’, Mol. Cryst. Liq. Cryst. 330, 609-616 (1999).

(21) (35) With M. Nakagawa and LW. Stewart: ‘A continuum theory for smectic C liquid crystals.’ Mol. Cryst. Liq, Cryst. 198, 443-454 (1991).

(22) (38) With I.W. Stewart, T. Carlsson and M. Nakagawa: ‘Equivalent smectic C liquid crystal energies) Continuum Mech. Thermodyn., 3, 237-250 (1991).

(23) (42) With T. Carlsson and I.W. Stewart: ‘An elastic energy for the ferroelectric cliiral smectic C* phase’. J. Phys. A 25, 2371-2374 (1992).

(24) (52) With I.W. Stewart and M. Nakagawa: ‘Smectic liquid crystals and the parabolic cyclides’. Q.J. Mech.

appl. Math. 47, 511-525 (1994).

(25) (56) With G.I. Blake: ‘Flow and field induced instabilities in a smectic C liquid crystal.’ Meccanica 31, 611-621, (1996).

(26) (54) With G.I. Blake: ‘Flow and backflow effects in a continuum theory for smectic C liquid crystals’. Mol. Cryst. Liq. Cryst. 262, 403-415 (1995).

(27) (44) With J.S. Laverty and T. Carlsson: ‘Continuum theory for biaxial nematic liquid crystals’. Q. Jl. Mech. Appl. Math. 45. 595-606 (1992).

(28) (41) With T. Carlsson and J.S. Laverty: ‘Biaxial nematic liquid crystals in flow properties and evidence of bistability in the presence of electric and. magnetic fields’. Mol. Cryst. Liq. Cryst. 212, 189-196 (1992).

(29) (39) With T. Carlsson and J.S. Laverty: ‘Flow properties of biaxial nematic liquid crystals.’ Mol. Cryst. Liq. Cryst. 210, 95-127 (1992).

(30) (51) ‘Flow alignment in biaxial nematic liquid crystals’. J. Non-Newton. Fl. Mech. 54, 241-250 (1994).


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Frank Matthews Leslie - ePrints Soton€¦ · Web viewFrank Matthews Leslie. 8 March 1935 – 15 June 2000. Elected F.R.S. 1995. R.J. ATKIN. School of Mathematics and Statistics,