Phase-shift symmetries of the correlation and bridge functions in additive hard sphere mixtures

Abstract

We show that the Percus—Yevick (PY) theory of a hard sphere mixture with additive diameters can be expressed in one dimension by a set of first-order differential equations for the Ornstein—Zernicke total correlation functions h _αβ(r). This set reduces to a single equation and the correlation functions for the different α-β interactions become identical when expressed in terms of the shifted distance r—σ_αβ where σ_αβ is the α-β diameter. The three-dimensional case yields integro-differential equations for h _αβ(r) and the strong phase-shift symmetry is lost. However, the zeros of the bridge functions B _αβ(r) still occur approximately at the same values of the shifted distance. This property holds both in the PY approximation and in the bridge functions necesssary to reproduce the recent Monte Carlo results of Malijevský, A., Barosova, M., and Smith, W. R., 1997, Molec. Phys., 91, 65. The regularity makes it possible to simplify the Malijevský—Labík parametrization of B _αβ(r) and establishes a starting point for studying ternary hard sphere mixtures.