Statistical mechanics of nonspherical molecules. VIII. Hard-core models

Abstract

Calculations of some properties of systems composed of nonspherical hard-core molecules are presented. The intermolecular interactions are modeled by representing each molecule as an assemby of overlapping hard spheres. The specific cases treated include: triangles; planar squares; and linear arrays composed of three, four, and five spheres. The basic statistical property computed is exp(−potential energy/kT) for various values of separation distance and molecular orientation; the results are presented by calculating the distance dependence of the coefficients in the expansion of this quantity in a set of orthogonal functions of the Eulerian orientation angles for each molecule. A number of average properties are calculated with the aid of this function, including: second virial coefficients; the angular correlation contribution to the depolarized light scattering of dilute gases; and the deviation from the Clausius–Mosotti equation (for the dielectric constant of nonpolar fluids) that is linear in density. The properties of these fluids at high density are also calculated by invoking the blip-function theory, as adapted to nonspherical molecules, to calculate molecular pair corrleation functions and the equation of state. Comparisons are made with the scaled-particle equation of state for nonspherical hard-core molecules, and the pair correlation functions are used to calculate angular correlations, depolarized light scattering, and one of the terms contributing to the deviation from the Clausius–Mosotti equation for dense fluids.