Spherically inhomogeneous fluids. II. Hard-sphere solute in a hard-sphere solvent

Abstract

The inhomogeneous Ornstein–Zernike equation and the Triezenberg–Zwanzwig expression for the density profile are solved using the Percus–Yevick closure for the inhomogeneous pair correlations of a hard-sphere fluid in the vicinity of an isolated hard-sphere particle. Results are presented for the solvent density profiles (solute–solvent radial distribution function) around solutes of diameter 0.01–50 times the diameter of the solvent hard spheres. At larger solute diameters, values obtained for the contact density are comparable in accuracy to those given by the scaled-particle theory, and significantly more accurate than those given by the Percus–Yevick analytic results for a bulk asymmetric mixture. A superposition approximation is introduced and this gives the effective solvent-mediated solute-solute interaction. The approximation is expected to be accurate for an asymmetric mixture at low concentrations. Two lower order approximations, the Asakura–Oosawa depletion attraction, and the Derjaguin curvature correction, are tested and found to be qualitatively correct.