Exact solution of the Percus-Yevick integral equation for fluid mixtures of hard hyperspheres

Details Exact solution of the Percus-Yevick integral equation for fluid mixtures of hard hyperspheres Exact solution of the Percus-Yevick integral equation for fluid mixtures of hard hyperspheres

2011-08-10

arxiv.org/abs/1108.2212v2

Phys. Rev. E 84, 041203 (2011)

Physics

Condensed Matter

Statistical Mechanics

6 pages

Scientific paper

10.1103/PhysRevE.84.041203

Structural and thermodynamic properties of multicomponent hard-sphere fluids at odd dimensions have recently been derived in the framework of the rational function approximation (RFA) [Rohrmann and Santos, Phys. Rev. E \textbf{83}, 011201 (2011)]. It is demonstrated here that the RFA technique yields the exact solution of the Percus-Yevick (PY) closure to the Ornstein-Zernike (OZ) equation for binary mixtures at arbitrary odd dimensions. The proof relies mainly on the Fourier transforms $\hat{c}_{ij}(k)$ of the direct correlation functions defined by the OZ relation. From the analysis of the poles of $\hat{c}_{ij}(k)$ we show that the direct correlation functions evaluated by the RFA method vanish outside the hard core, as required by the PY theory.

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