Analytical approximations to virial coefficients for pure and mixed systems

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Abstract
Analytic approximations, in the form of finite polynomial expansions in T -1, are given to the pressure virial coefficients of pure Lennard-Jones systems with strictly pairwise-additive potentials. Results are given through fifth order in both two and three dimensions. These analytic forms are combined in Padé approximants for the compressibility factor in three dimensions, and the critical constants found from them are in agreement with those obtained elsewhere; equally good agreement is found in the two dimensional case. Also reported are calculations of two- and three-dimensional third virial coefficients of mixtures of the heavier rare gases and simple molecules. The interactions are represented by single centre models, Lennard-Jones potentials which are shown to give mixed second virial coefficients in reasonable agreement with experimental values. The calculated and experimental third virials do not agree, but the inclusion of three-body interactions, through the triple-dipole and related terms, improves the agreement for pure systems and probably for mixtures also. When suitable reduced units are used, the results for pure and mixed systems can be represented on a single curve for each specific contribution, two-body, triple-dipole, etc. The temperature dependence of the two-body contributions includes a sharply defined peak, and the reduction to a single curve is least accurate in the immediate vicinity of that peak. Both two- and three-body contributions are summarized as polynomial expansions in T -1, and these are believed accurate in the range 0·8 ⩽ (kT/ϵ) ⩽ 4, except for the two-body terms in the immediate neighbourhood of the peak. Monte Carlo results for the compressibility factor of hot dilute mixtures are found to be in good agreement with the virial data.