Hard-sphere radial distribution function from the residual chemical potential

Abstract

A method of determining the radial distribution function on the basis of expressions for the residual chemical potential of hard spheres and of the infinitely diluted mixture of a hard dumbbell (originated from overlapping of two spheres) in hard spheres is revised. The enlarged hard dumbbell (instead of the standard one used in our previous study [T. Boublík, Molec. Phys. 59, 775 (1986)]) is considered for determining its geometric functionals—a volume, surface area and mean radius; these quantities characterize hard-body geometry in the (self-consistent) expressions used for the residual chemical potentials. New formulas for the characteristic geometric quantities and improved expressions for the residual chemical potential result in an improvement of predictions of the radial distribution function for the larger reduced distances and enable an application of the method to inhomogeneous systems; the case of hard-sphere fluids near a hard wall is studied. The present version of the theory was successfully applied to pure hard-sphere fluids and binary mixtures with densities as high as ρ*= 0.925.