Advances in Chemical Physics (Volume 139) by Stuart A. Rice

By Stuart A. Rice

This sequence presents the chemical physics box with a discussion board for serious, authoritative reviews of advances in each quarter of the self-discipline.

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Percus–Yevick is a typical candidate for the thermodynamic inconsistency: indeed, the virial and the compressibility EOS provide the following analytic results in terms of the packing fraction Z     bP 1 þ 2Z þ 3Z2 bP 1 þ Z þ Z2 ¼ ¼ ð33Þ 2 r v r c ð1 À ZÞ ð1 À ZÞ3 where Z ¼ p6 rs3 . It appears that the PY virial and compressibility EOS, respectively, underestimate and overestimate the HS simulation results. These last are quite accurately parametrized in terms of a heuristic EOS developed by Carnahan and Starling (CS) [31], which reads   bP 1 þ Z þ Z2 À Z3 ¼ ð34Þ r CS ð1 À ZÞ3 This parametrization is usually considered as exact and is useful to test the quality of the results from IETs calculations for the HS fluid.

1. Percus–Yevick Approximation A very popular closure relation is the Percus–Yevick (PY) approximation [39]. For a generic potential uðrÞ, this approximation assumes that cðrÞ ¼ ½1 À ebuðrÞ Š  gðrÞ ð31Þ In other words, the bridge function corresponding to PY relation reads BðrÞ ¼ ln½1 þ gðrފ À gðrÞ ð32Þ The solution of the system formed by Eqs. (21) and (32) is usually obtained thanks to numerical iterative procedures. However, in the special case of 18 jean-marc bomont hard-sphere (HS) fluid, the solution is found to be analytical.

Both of them occupy the same space so that the resulting particle, referred to as a strong test particle, interacts with the other particles with the combined potentials of the two original particles. Note that the cavity function is related to the work, À ln yð0Þ, required to insert a strong test particle, of the same size as a single particle, with twice the potential energy (2E) according to the relation [70, 80] À ln yð0Þ ¼ bm2 ð0Þ À 2bm1 ð67Þ where m2 ð0Þ is the excess chemical potential of the strong test particle of bond length L ¼ 0 and m1 is that of a single particle.

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