A life dedicated to the theory of simple fluids − in memory of Yiping Tang

Yiping Tang was born on 28 October 1966, into a peasant family in Hexian, China, not far from the west bank of the Yangtze River near its estuary. He grew up in the countryside and went to local elementary and middle schools until 1983 when he was admitted by Tsinghua University, one of the most competitive colleges in China. He graduated in July 1988 as a top-ranked student in his class with two bachelor's degrees, one in Chemical Engineering and the other in Applied Mathematics. That autumn he entered the graduate school in Tsinghua University without the National Graduate Entrance Examination. The exemption was a privilege reserved only for the best graduates at that time. While his thesis for the master’s degree was mainly concerned with experimental studies of salting effects on partially miscible liquid mixtures, it was clear that his passion as a researcher lied in liquid-state theories, in particular in analytical solutions to the Ornstein–Zernike (OZ) equation. Some original ideas for his later publications were probably conceived during a period of unemployment after he finished master's degree in July 1991 and before immigration to Canada in September 1992 for his PhD studies with Professor Benjamin C. Y. Lu at the University of Ottawa. After he obtained his PhD in 1997, he had been working as a senior research scientist first at Simulation Sciences Inc., Brea, CA, and then at Honeywell Process Solutions, London, Canada, until he died due to a brain tumour in 20 December 2014.

Tang made important contributions to liquid-state theories, in particular on the analytical solutions to the OZ equation for simple fluids and on the equations of state for simple as well as polymeric systems. Regrettably, the broader impact of his work was not widely recognised due to the perceived ending of liquid-state theories and the fading of analytical research in statistical mechanics after the advent of molecular simulation. For example, in a Specialist Periodical Report published in 1973 by the Royal Society of Chemistry, Ian R. McDonald, co-author of ‘Theory of Simple Liquids’ [1], concluded that, after a systematic and shrewd analysis of the literature, ‘it is not an exaggeration to say that the problem of the calculation of thermodynamic properties of simple mixtures is now largely solved’ [2]. This euphoric assessment was echoed by another comprehensive review published in the same volume that claimed significant further advances in liquid-state theories were unlikely.

McDonald's statement was justified, by and large, in light of successful developments in the 1960s and early 1970s on analytical and numerical methods for predicting the structural and thermodynamic properties of bulk fluids and, to a certain degree, by Moore's law for the exponential growth of computer capability and the widespread application of molecular simulation as a ‘universal and exact’ tool to solve statistical–mechanical problems. Indeed, by 1973, liquid-state theories were sufficiently accurate to predict the thermodynamic properties of simple fluids in good agreement with simulation data [3]. Nevertheless, theoretical predictions were far from satisfactory for the thermodynamic properties of fluid mixtures pertinent to industrial applications, in particular under conditions near the critical region of phase transitions. For practical applications, important equations for phase equilibrium calculations were mostly developed in the late 1970s to 1980s based on semi-empirical modifications of the van der Waals equation of state or various local composition models [4]. From a fundamental perspective, long-range fluctuations near the critical point of phase transitions were barely recognised and a quantitative description of fluid properties near solid surfaces or inside small pores remained a major challenge.

Progress in liquid-state theories, even for simple fluids, did not stop in 1973. In addition to the continued growth of analytical methods, most notably the developments of the mean spherical approximation (MSA) for electrolyte solutions by Lesser Blum and the fundamental measure theory for hard-sphere systems by Yaakov Rosenfeld, the past decades have witnessed tremendous advances in the applications of simple fluids as a useful reference to describe the physiochemical properties of industrial gases and liquid mixtures [5] and, on the fundamental side, to illustrate the rich phase behaviour of colloidal and macromolecular systems including protein solutions [6]. While a comprehensive review of these developments is beyond the scope of this short essay, we would like to highlight some significant contributions made by Yiping Tang, to whom this special issue is attributed.

Tang's foremost contribution to liquid-state theories was the first-order mean spherical approximation (FMSA) that facilitates analytical solutions to the OZ equation for a wide variety of model systems [7]. He demonstrated that analytical expressions could be derived to represent the structure and thermodynamic properties for various models of simple fluids by applying Zwanzig's high-temperature expansion to the total and direct correlation functions. Tang's work is complementary to Blum's theory because no analytical solution is available for non-electrolyte systems with the original MSA closure. Not only are these analytical equations convenient for practical applications, they are also more accurate than conventional liquid-state methods in comparison with the simulation results. While most liquid-state methods often entail complex numerical procedures, FMSA is conveniently applicable to one-component as well as fluid mixtures. In particular, a closed analytical form is highly desirable for developing more sophisticated equations of state for industrial systems (e.g. the statistical associating fluid theory [5]) including petroleum fluids and polymer solutions. Further, FMSA yields analytical expressions for direct correlation functions that are indispensable in the development of classical density functional theory beyond the mean-field approximation [8].

Another important contribution by Tang was to establish a seamless connection between the liquid-state methods and the renormalisation group (RG) theory for describing vapour–liquid equilibrium near and far from the critical point [9]. While there were previous efforts to amalgamate these two seemingly unrelated theoretical frameworks, Tang introduced a coherent and rigorous RG procedure to account for long-range fluctuations neglected in conventional liquid-state methods, and demonstrated its application to multicomponent systems.

Over the years Tang's industrially oriented tasks were concerned with phase stability analysis and phase equilibrium calculations for multicomponent systems with multiple phases. Although his daily work was not directly concerned with advances in liquid-state theories, he established insightful connections between the numerical algorithms for phase equilibrium calculations and the physical origin of non-equilibrium fluctuations underlying first-order phase transitions. Tang demonstrated the merits of his innovative methods and published his scientific work as a hobby [10]. Several of Tang's papers were published in Molecular Physics [11–15].