By the middle of this century we had a good understanding of how the physical properties of gases and solids could be related to the forces between their constituent molecules, but we lacked a theory of the liquid state. John Barker worked on all three phases of matter and on the intermolecular forces themselves, but he will be remembered particularly for the crucial role he played in creating a quantitative theory of liquids.
John Barker was born on 24 March 1925 at Corrigin, a small town in the wheat belt of Western Australia. His father, Thomas Louis Barker (1900-1978), was a general practitioner who had been born in Fiji and his mother, Dorothy Erica, neé Janes (1906-1949), was from Melbourne, The family moved several times in John's early years, first to Melbourne, then to a small town in the Mallee in Victoria, before settling at Red Cliffs in the Mildura irrigation district in north-west Victoria. Here he completed his primary education at Red Cliffs State School and then went, in 1936, to Mildura High School, where he was followed by his younger brother, Peter. Neither did well there and in 1938 they were sent as boarders to Ivanhoe Grammar School, to which John won a scholarship. It was here he first showed his true abilities. A master, Clement Jepson, introduced him to the delights of mathematics through Silvanus Thompson's Calculus Made Easy, and he acquired also a deep appreciation of English language and poetry. He was top of his form each year, Captain of School in his final year, and left in 1942 with a Commonwealth Scholarship to the University of Melbourne. Money was tight – his father was a better doctor than he was manager – but he sent John to Trinity College, the Anglican residential college of the University of Melbourne. Peter followed and ultimately graduated in medicine. John had originally intended to study chemistry, a subject that had fascinated him since he had read about the chemistry of photography in the studio of his maternal grandfather, but Jepson's teaching at school and his own abilities led him first to physics, in which he qualified for a BSc in 1944, and then to a second-class honours degree in mathematics in 1945. In this course he was greatly influenced by the lectures of H.C. Corben who was later to write a much-used textbook on classical mechanics.
He stayed at Melbourne for two years after graduation, as a demonstrator in physics, and then moved in 1948 to the Division of Aeronautics of the Council of Scientific and Industrial Research (CSIR), later the Commonwealth Scientific and Industrial Research Organization (CSIRO), Here he learnt much about wind tunnels and their instrumentation and more about the kinetic theory of gases from a long study of the monumental Mathematical Theory of Nonuniform Gases by Sydney Chapman and T.G. Cowling, a study that was to come in useful later in his career.
In 1949 his mother committed suicide and his father, profoundly depressed, was admitted to hospital. This tragedy hit John hard; he resigned his post at CSIR and went to England with no fixed plans. There he spent a rather unhappy year teaching mathematics at Acton Technical College, before returning to Australia early in 1950 on the Orion. It was a six-week voyage, during which he met and courted Sally or, more formally, Avril Hope Johnston, the daughter of William and Eileen Johnston from England. They were married in Sydney a few weeks after they landed; it was to prove a happy marriage that ended only with John's death over 45 years later. They had three children, Jonathan, who was born in 1952, David, in 1956, and Katie, in 1961. All graduated from the University of California; Jonathan is now a walnut farmer in that state, David is a computer analyst and Katie a court stenographer.
John rejoined CSIRO as soon as he and Sally were married, but this time in the Division of Industrial Chemistry, where Ian Brown was making precise measurements of the vapour pressure of liquid mixtures, and the Chief of the Division, Ian Wark, who supported John's work for many years, wanted someone to give theoretical support to the liquids work. John soon contributed directly to this programme by showing how to calculate the change of free energy on mixing two liquids from a knowledge of the total vapour pressure of the mixture and not, as was usually done, from the experimentally less accessible partial pressures of each component. He was not the first to tackle this problem but his iterative solution, in which full account was taken of the imperfection of the vapour mixture, was a great improvement on earlier methods and is used to this day.
It was clear, however, that his mathematical and physical skills would be better employed in trying to understand how the properties of the liquid mixtures arose from the underlying intermolecular forces. A seminal paper by H.C. Longuet-Higgins in 1951 had shown how to make this connection for some simple classes of mixtures of similar molecules by means of a perturbation expansion of the free energy – the differences between the intermolecular potentials causing small perturbations from the, presumed known, properties of one of the components. Barker found at once an ingenious way of extending this result to molecules with permanent electric dipoles. This, his first paper, occupied only half a page of the Journal of Chemical Physics and its conciseness, its difficult notation and the absence of any applications led to its being overlooked. Others (Cook & Rowlinson 1953; Pople 1954) found the same result a few years later without knowing of Barker's work. It did, however, mark his first use of perturbation theory, which was a technique he was to exploit with spectacular success fifteen years later.
His next theoretical papers were on solutions of highly polar molecules – the alcohols – and introduced a second theme that was to be a feature of his work for some years to come. This was the assumption that a liquid, which is usually almost as dense as the solid it forms on freezing, could be similarly represented by an array of molecules on or near the fixed sites of a regular three-dimensional lattice. Such a model is much more tractable than one in which the molecules are free to move at random over all space, and Barker exploited to the full his skill in manipulating the lattice sums required to calculate the free energy. The most striking early fruit of this work was the paper he presented (in absentia) with his colleague W. Fock to the Jubilee meeting of the Faraday Society in London in 1953, in which they showed how the strong dependence on orientation of the forces between alcohol molecules could lead to liquid mixtures that exhibited both upper and lower consolute temperatures; that is, to mixtures that formed two liquid phases over a restricted range of temperature, but which were completely miscible at sufficiently high or low temperatures. It was the first attempt at a quantitative solution of this notoriously difficult problem in the theory of solutions and although better results are now available they are close in spirit to the ideas of this 1953 paper.
E.A. Guggenheim of Reading University was then the leading British advocate of the use of lattice theories of liquids. He met Barker on a visit to Melbourne and encouraged him in his use of these methods. After his return to Britain he submitted many of Barker's papers to the Proceedings of the Royal Society where they formed a series of increasing sophistication. This work culminated in 1960-62 in what Barker called the 'tunnel model'. The inherent fault of lattice models of liquids is that they impose on the theoretical description a spatial ordering of the molecules that is not present in nature. Barker thought that he could solve this problem by replacing a fixed three-dimensional lattice with a fixed array of one-dimensional tunnels. The molecules within each tunnel could move freely and only the tunnel – tunnel interaction would have to be treated by 'lattice' methods. He was able to exploit the fact that one-dimensional problems in statistical mechanics can often be solved exactly and so he was left only with the tunnel – tunnel problem to be treated by approximate methods. It was an improvement on what had gone before but it was still not a satisfactory theory of liquids; that is, there was not a correct correspondence between the assumed intermolecular forces and the calculated thermodynamic properties of the fluid. In retrospect one can see a 'clutching at straws' in some of his later papers on lattice models. He knew, none better, of their quantitative imperfections, but on several occasions from 1955 onwards he was to insist they could 'in principle' be made exact, however difficult this was proving in practice. He was not alone in this view; it was shared by J.O. Hirschfelder in Wisconsin, by J. de Hoer in Amsterdam, by I. Prigogine in Brussels and by many lesser lights.
There had always been other methods of attack in which no lattice is imposed, but in which, for example, one generates coupled sets of integral equations the solution of which would yield the structure of the isotropic continuum fluid that a liquid was known to be. So far these equations, which certainly could not be solved exactly, had yielded approximate solutions that told one something of the properties of gases of low and moderate density but nothing useful about the liquid state. It was this impasse that had led many to the apparently simpler lattice models. Progress was made, however, with the continuum models in the late 1950s and the advocates of lattice models began to realize that their route was, perhaps, not the best way forward. Barker himself came to this view, paradoxically shortly before he published his only book, Lattice Theories of the Liquid State.
For some years his work seemed to lack a clear theme. He collaborated with others to produce sound but not exciting papers on a range of subjects: the virial expansion of the pressure of a gas, a scattering problem, the intermolecular forces themselves and the adsorption of gases on solids. The last was the product of an enjoyable year, 1958-59, that he spent with D.H. Everett and his colleagues in the Chemistry Department of Bristol University. Bristol was Sally's home town.
The breakthrough, when it came, was dramatic, For some years the proponents of continuum models had been simplifying their representations of the intermolecular forces, hoping to come forward with something that was tractable and reasonably realistic. In 1958 J.K. Percus and G.J. Yevick in New York had produced an acceptably accurate equation of state for a system composed of hard spherical molecules with no attractive forces between them (Percus & Yevick 1958). It was not a model for a liquid, for which the attractive forces are necessary, but it did yield the first reasonable description of the pressure and the structure of a non-trivial dense continuum system. Two big steps were needed to turn this, and similar work on this model, into an acceptable theory of liquids. First, the attractive forces must be incorporated and, secondly, a way must be found of softening the hard core of the molecule into a smoother repulsive force. It was generally assumed that this force could be derived from an intermolecular potential that varied with molecular separation, r, as r-n, where n was a number equal to about 12. During the 1960s it was realized that the calculated structure of the hard-sphere fluid was surprisingly close to that of real simple liquids, such as argon, as revealed by their x-ray and neutron diffraction patterns. This similarity made it likely that perturbation theory was the proper tool for making the two necessary modifications to the hard-sphere model to turn it into a true model of a liquid. In 1954, R.W. Zwanzig had shown how to add a particular simple form of attractive force – the negative square-well potential – to a hard-core molecule and to calculate the resulting change in physical properties by using perturbation theory (Zwanzig 1954). But at that time there was no adequate theory of the hard core fluid so the method had little application. In 1964 a way was found of softening the hard core to a potential proportional to r-n by expanding the free energy in powers of n-1 (Rowlinson 1964). This treatment aroused the interest of Douglas Henderson in the Physics Department at the University of Waterloo in Ontario, who quickly extended it to include the quantal corrections to the free energy that are important for light molecules such as hydrogen and helium (Henderson & Davison 1965; Chen et al. 1965). D.A. McQuarrie and J. Katz then combined Zwanzig's treatment of the attractive forces with the n-1 expansion for the repulsive (McQuarrie & Katz 1966). This combination was effective for dense gases at high temperatures, but it was still not a theory of liquids.
In 1966 John Barker and his Chief, Sefton Hamann, invited Henderson to spend a year on sabbatical leave at CSIRO. Barker and Henderson set out to examine carefully the successes and failures of all these partial solutions. They started with the hard-core square-well potential and extended Zwanzig's expansion to second order in the grand canonical ensemble which, as so often, proved more amenable than the more commonly used canonical ensemble. It worked well; that is, the theory reproduced the known properties of the liquid state even down to low temperatures; the thermodynamic properties and structure of this fluid were now known from computer simulations. So if they were to find a better theory for more realistic molecular models they had to do something better than the n-1 expansion. This they achieved by using a temperature-dependent effective diameter for their molecules, and their skill lay in choosing this so that the perturbation treatment of the attractive forces did not generate unreasonably large terms. Before this programme was completed Henderson had left Australia for Britain where, in April 1967, the Faraday Society was to hold a General Discussion in Exeter on The Structure and Properties of Liquids. The first work, on the square-well model, was submitted to the Journal of Chemical Physics but was initially rejected by the referee, Joseph Katz, because he thought this was all very well, but without an extension to more realistic potentials he could see little value in it. He was told by the authors that what he wanted was under way and he then recommended publication.
Barker completed the work with realistic potentials during the course of the Faraday Society meeting, and twice before the morning sessions Henderson read out a telegram from Melbourne announcing the new results. It was not entirely clear to those at the meeting how these results had been obtained but it was apparent that we had at last a quantitatively acceptable theory of the properties and structure of a realistic model of a liquid. Henderson used part of the closing session to summarize their findings and a short account of these appeared in the printed proceedings (Barker & Henderson 1967), although it does not appear in Barker's list of publications. Formal publication followed a few months later; the paper was accurately subtitled 'A successful theory of liquids'.
Much detail remained to be worked out: an extension to liquid mixtures, an application to the melting-line, and so on. Moreover, the key to their success, the precise choice of the temperature-dependent core and the way in which the total potential was divided between basis and perturbation, were clearly recipes that could be varied to see if even better results were possible. Such an advance, made three years later by J.D. Weeks, D. Chandler and H.C. Andersen (Weeks et al. 1971 a,b), proved to converge to an accurate answer even more rapidly than the original recipe of Barker and Henderson (except possibly for mixtures); most modern work follows this second route. Such developments are to be expected and do not detract from but rather add to the value and originality of the ideas of Barker and Henderson. The range of application of perturbation theories in general in the field of liquids and liquid mixtures is now enormous.
At CSIRO Barker had been promoted to a level where a move into management was the next natural step. This he resisted; he felt he had no abilities for that kind of work and that his talents would be wasted there. The collaboration with Henderson had proved extremely fruitful so when Henderson returned to Waterloo in 1967, Barker and his family decided to follow him. He obtained a professorship in applied mathematics and physics. Once there, however, both Barker and Henderson found that their teaching duties did not allow them the freedom to think and work all day on problems in statistical mechanics. They supervised several doctoral students of whom W.R. Smith, now Professor of Mathematics at Guelph, has contributed most to the theory of liquids.
Henderson wrote to Enrico Clementi at the IBM Research Laboratory (now the Almaden Research Center) in San Jose, California, since he knew that Clementi wanted to establish a strong team for a combined attack, by quantum and statistical mechanics, on the structure and properties of water. The idea of having two of the leading workers in statistical mechanics in his team proved irresistible and, after some lengthy negotiations that went as far as the Director of Research at Yorktown Heights, Barker and Henderson moved to San Jose in 1969. The Barkers had thought initially that they would stay for a year, after which they were proposing to return to Melbourne. In the event John stayed with IBM until his retirement twenty-five years later. It was to prove an ideal environment in which there were able colleagues with similar interests, freedom from distracting duties and some of the world's most powerful computers.
A complete theory of real liquids (as distinct from models simulated on a computer) has two necessary ingredients, a knowledge of the forces between the molecules and a statistical theory to link this knowledge to the physical properties of the liquid. Barker and Henderson had gone a long way towards solving the second problem but the testing of their theory depended heavily on the properties of computer-simulated models. It was natural therefore that Barker turned now to the other problem and the second half of his career was devoted, in the main, to the determination of accurate intermolecular potentials. Argon had become the test-bed of such work; it had a spherical monatomic molecule that was heavy enough for quantal corrections to be unimportant, and it was readily available so that most of its physical properties had been measured. The most relevant ones were the second virial coefficient and the viscosity of the gas, the density and vapour pressure of the liquid, and the lattice spacing and heat of sublimation of the solid. Early attempts to determine the intermolecular potential, which went back to 1924, were hampered by two assumptions that turned out to be false. The first was that the potential between a pair of argon atoms could be represented by an algebraically simple function of their separation, and the second was that the energy of a dense system of N atoms, such as a liquid or solid, could be found by adding the potential energies of interaction of each of the ½N(N-1) pairs of atoms. Even when these difficulties were overcome by using complicated algebraic forms for the pair potential with up to thirteen adjustable parameters, and introducing the so-called Axilrod-Teller correction for the departure of the energy of a triplet of atoms from the sum of the three pair interactions, no consensus was reached. In 1968 Barker and A. Pompe (of CSIRO) produced the best solution yet obtained by abandoning the evidence from the viscosity of the gas. This was a bold step since there were several consistent sets of measurements over a wide range of temperature and the theory connecting viscosity with the pair potential was clear and unambiguous. Nevertheless they were right; later work showed that the measurements of viscosity at high temperatures were at fault and the new measurements are in satisfactory agreement with the potential of Barker and Pompe, and in even better agreement with the later refinements of Barker, Fisher and Watts in 1971 and of Maitland and Smith (1971) who had used a different set of physical properties, including the spectrum of the Ar-Ar dimer, to generate a similar potential. Barker's work was soon extended to the other heavy inert gases, krypton and xenon, with equally good agreement. It remains one of the most satisfying syntheses of modern statistical mechanics.
Although this work was aimed at real liquids it needed, for its intermediate tests, the work on computer simulation of model fluids. This was a field that Barker entered just before his arrival at IBM, and was a natural development of the range of his skills given the powerful resources available at San Jose. Work started at Waterloo led to one of the first successful simulations of water, a liquid very different from argon. This simulation involved the development of methods of accounting, within a computer simulation, for the long-ranged interactions between the strong dipoles of the water molecules. The method adopted, that of the so-called 'reaction field', aroused some initial criticism but is now widely accepted, to the extent that the original inventors are often forgotten.
By the early 1970s it was becoming clear that the fundamental physics of the bulk equilibrium properties of liquids and simple mixtures was understood. Even the incredibly difficult problem of the gas-liquid critical point (a field Barker always avoided) had yielded by 1971. There were many applications still to be made and the more complicated mixtures, such as aqueous or polymer solutions, were still there as a challenge to the chemical engineers and those who had to use the theories, but such problems were not his prime concern. A new challenge was the field of inhomogeneous systems such as the state of a fluid in the boundary layer between a gas and a liquid or between a liquid and a solid. Farid Abraham, then at the IBM Science Center at Palo Alto, was working on the problem of the nucleation of droplets of liquid in a vapour, a difficult example of an inhomogeneous and non-equilibrium system. He moved to San Jose and joined John in a simulation of small liquid clusters. A third partner in this enterprise was G.M. Pound, of Stanford University, and the two research students he encouraged to work with Ahraham and Barker, J.K. Lee and J. Miyazaki. The first paper gave some information on the structure of the clusters, but these were too small to tell us much about the liquid-gas interface. The next year they undertook the simulation of a planar liquid surface. To maintain the planarity of the surface they imposed an external field on the system that forcibly retained the molecules in the liquid state. This had the unfortunate consequence of inducing oscillations in the liquid density in the layers just below the surface. Others had found similar effects. These were, however, artefacts caused by the wall-like nature of the bounding external Field. They realised their error and more accurate results soon followed. Some years later, when Barker spent the spring in Oxford, he collaborated with J.R. Henderson and showed that the density profile of the liquid falls off as it enters the gas phase as the inverse third power of the distance from the surface, although, paradoxically, recent work suggests that there might, after all, be very weak oscillations in density on the liquid side of the meniscus, albeit ones that would be too weak to detect experimentally or by computer simulation (Evans et al. 1993).
Extracting good values of the surface tension from these simulated models proved to be unexpectedly difficult. It was not until nearly twenty years later, when much bigger computations were possible, that he was finally satisfied that there was good agreement between the computed tension and that calculated from the two- and three-body intermolecular potentials for argon, krypton and xenon. The light inert gas, neon, was, for many years, outside the scope of these calculations because of the importance for this liquid of the quantal departures from classical mechanical behaviour. In the late 1970s he worked on path-integral Monte Carlo methods that he wanted to apply to the even lighter liquid, helium, for which quantum mechanics is a necessary tool, not merely the source of minor 'corrections'. He never did get results for helium that satisfied him, but in 1989 the less demanding task of calculating the surface tension of neon was accomplished.
Barker had always paid more attention to the properties of solids than most of those working in classical statistical mechanics. The phonon dispersion curves of the solid inert gases, as measured by neutron scattering, played an important role in his determination of the Ar-Ar potential. In the last part of his career he put a lot of effort into a study of the forces between atoms and the surfaces of solids. This work ranged widely over both static and dynamic problems. Among the latter, he studied energy exchange (including translational to rotational), trapping and desorption of atoms, and the use of helium reflection and diffraction as a tool for the study of surface structure. He used simple models, such as hard spheres and hard ellipsoids, in order to understand complex physical processes, and also made detailed studies of accurate gas-solid potential energy functions. An important example of this last kind of work was his detailed study of the interaction of xenon atoms with the 111-surface of platinum. Here he was able to invert the experimental results to obtain the potential energy, a technique that had hitherto been used mainly for work on gases, although the theoretical possibility of using it for surface studies was known. It is probably too early to judge the influence of this work, but he himself hoped that the Xe-Pt work would prove a benchmark in this field, in the same way that his work on the inert gas atoms had served for intermolecular forces in the gas phase.
John's career at IBM prospered throughout the 1970s and 1980s. As at CSIRO, he resisted all moves into management but was glad to be rewarded, with Douglas Henderson, with prizes from the company that recognized the importance of their work together. Other honours had come his way; he had received a DSc from Melbourne in 1958 and, as the true Australian he always remained, he was particularly pleased to be elected to the Australian Academy of Science in 1967. His election to the Royal Society of London followed in 1981 and it was a happy coincidence that he was appointed Hinshelwood Lecturer in the Physical Chemistry Laboratory at Oxford that year so that he was already in England for his formal admission in June. In 1984 he was a visiting lecturer in statistical mechanics at Sydney, and in 1992 La Trobe University, in Melbourne, awarded him an honorary DSc.
His health caused him some problems in his last years. He had a heart attack in the 1980s but made a complete recovery. More serious was a fall from a ladder in 1994 in which he received a severe blow to the head. This caused a subdural haematoma that did not heal rapidly, but required surgery to relieve pressure on the brain. He had difficulty in reading, which was overcome only after a long and frustrating rehabilitation in which he was helped by his brother, Peter, who, for a time, left his practice in Australia to come to California. That year he retired from IBM, but plans to return to Melbourne to take up a research fellowship had to be abandoned. His last published paper was, fittingly, a short account of his collaboration with Douglas Henderson, which was published in a Festschrift that marked Henderson's sixtieth birthday. After a short illness, John died in the presence of his family on 27 October 1995.
Pure science was the guiding theme of his career; he had no particular commitment to teaching, he had no desire to build a big research group, he had no great interest in the practical applications of his work and, as we have seen, none in administration. But his devotion to pure research was not selfish. Much of his early work was, perforce, carried out without collaborators, but at IBM he often worked and published with others, both inside and outside the Research Center. Those who worked with him found him a generous colleague, who was always helpful and intellectually honest in all his dealings. He attended conferences sparingly and his contributions to any discussion were helpful rather than critical. If he saw a fault in one of the papers he would be more likely to have a quiet word with the author in the bar than to make a parade of a public rebuttal in the lecture theatre. Outside his science his scholarly approach led him to a deeper knowledge of the arts and of foreign languages than was apparent to those who only knew him professionally. Their idealism led him and Sally to be active supporters of the Labor Party during their time in Melbourne and his kindliness and generosity made him an ideal family man. Carlyle (1841) might have had him in mind when he wrote of 'The noble silent men, scattered here and there each in his own department; silently thinking, silently working; whom no Morning Newspaper makes mention of! They are the salt of the Earth. A country that has none or few of these is in a bad way.'
This memoir was originally published in Historical Records of Australian Science, vol.11, no.2, 1996. It was written by J.S. Rowlinson, Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, U.K.
I am indebted to Mrs Sally Barker, Dr Peter Barker and Mr Jonathan Barker, and to Professor D. Henderson, both by correspondence and in print (Henderson 1995) for their help in writing this memoir. The portrait photograph is reproduced by kind permission of Mrs Sally Barker.
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