Contact values of the radial distribution functions of additive hard-sphere mixtures in d dimensions: A new proposal

The contact values gij(σij) of the radial distribution functions of a d-dimensional mixture of (additive) hard spheres are considered. A “universality” assumption is put forward, according to which gij(σij)=G(η,zij), where G is a common function for all the mixtures of the same dimensionality, regardless of the number of components, η is the packing fraction of the mixture, and zij=(σiσj/σij)〈σd−1〉/〈σd〉 is a dimensionless parameter, 〈σn〉 being the nth moment of the diameter distribution. For d=3, this universality assumption holds for the contact values of the Percus–Yevick approximation, the scaled particle theory, and, consequently, the Boublik–Grundke–Henderson–Lee–Levesque approximation. Known exact consistency conditions are used to express G(η,0), G(η,1), and G(η,2) in terms of the radial distribution at contact of the one-component system. Two specific proposals consistent with the above-mentioned conditions (a quadratic form and a rational form) are made for the z dependence of G(η,z). For one-dim...

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