Direct correlation functions and bridge functions in additive hard-sphere mixtures

Details Direct correlation functions and bridge functions in additive hard-sphere mixtures Direct correlation functions and bridge functions in additive hard-sphere mixtures

2000-03-24

arxiv.org/abs/cond-mat/0003401v1

Mol. Phys. 98, 439-446 (2000)

Physics

Condensed Matter

Statistical Mechanics

19 pages (including 7 figures)

Scientific paper

10.1080/002689700162432

A method to obtain (approximate) analytical expressions for the radial distribution functions in a multicomponent mixture of additive hard spheres that was recently introduced is used to obtain the direct correlation functions and bridge functions in these systems. This method, which yields results practically equivalent to the Generalized Mean Spherical Approximation and includes thermodynamic consistency, is an alternative to the usual integral equation approaches and requires as input only the contact values of the radial distribution functions and the isothermal compressibility. Calculations of the bridge functions for a binary mixture using the Boubl\'{\i}k-Mansoori-Carnahan-Starling-Leland equation of state are compared to parallel results obtained from the solution of the Percus-Yevick equation. We find that the conjecture recently proposed by Guzm\'{a}n and del R\'{\i}o (1998, {\em Molec. Phys.}, {\bf 95}, 645) stating that the zeros of the bridge functions occur approximately at the same value of the shifted distance for all pairs of interactions is at odds with our results. Moreover, in the case of disparate sizes, even the Percus-Yevick bridge functions do not have this property. It is also found that the bridge functions are not necessarily non-positive.

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