Solution of the Percus-Yevick equation for pair-correlation functions of molecular fluids

Abstract

The Percus-Yevick (PY) integral equation has been solved for two model fluids: (i) a fluid of hard ellipsoids of a revolution represented by a Gaussian overlap model, and (ii) a fluid the molecules of which interact via a Gay-Berne [J. Chem. Phys. 74, 3316 (1981)] model potential. The method used involves an expansion of angle dependent functions appearing in the integral equation in terms of spherical harmonics. The dependence of the accuracy of the results on the number of terms taken in the basis set is explored for both fluids at different densities, temperatures, and lengths to width ratios of the molecules. We have compared our results with those of computer simulations wherever they are available. We find that the PY theory gives reasonable values of the harmonic coefficients for both fluids at all fluid densities when all terms involving the index l up to six in the expansion are considered. For the Gay-Berne fluid we have developed a perturbation expansion for a calculation of the structure and thermodynamic properties of the isotropic phase.