RESEARCH NOTE Radial distribution functions of hard sphere mixtures

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Abstract
A simple method is proposed to determine radial distribution functions of pure hard sphere fluids and mixtures of hard spheres of different diameters. The range of centre-centre distances of a pair of hard spheres is divided into two parts: that from the closest approach up to the distance x m of the first minimum, and that for distances x > x m. Radial distribution functions in the former interval are determined via a method proposed earlier to calculate the background correlation function; the approach is based on the evaluation of the residual chemical potential of a homo- or heteroatomic dumb-bell and chemical potentials of the individual hard spheres in the system studied. Values of the radial distribution functions (RDFs) in the latter interval are evaluated from an analytical continuation of the RDF by employing a formula for damped oscillations. A comparison with Monte Carlo data of radial distribution functions of pure fluids and equimolar binary mixtures (with diameter ratio 0·9) reveals fair accuracy for the proposed method. Because of its simplicity, the method is especially useful for determining radial distribution functions of individual pairs of multicomponent mixtures.