2002/03/31 by Andrés Santos, A. Santos, S. B. Yuste +2 · 2 citations
Chemistry · Engineering · Materials Science · Physics and Astronomy · #Adsorption, diffusion, and thermodynamic properties of materials #Material Dynamics and Properties #Phase Equilibria and Thermodynamics #cond-mat.soft #cond-mat.stat-mech #physics.chem-ph
paper · pdf · doi:10.1063/1.1502247
published as J. Chem. Phys. 117, 5785-5793 (2002) · 10 pages, 11 figures; Figure 1 changed; Figure 5 is new; New references added; accepted for publication in J. Chem. Phys
arxiv created 2002/07/01 · openalex publication_date 2002/09/05 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 Boublík–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-dimensional systems, the proposals for the contact values reduce to the exact result. Good agreement between the predictions of the proposals and available numerical results is found for d=2, 3, 4, and 5.