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

Abstract

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.

6 pages

References in corpus (1)

• Multicomponent fluids of hard hyperspheres in odd dimensions

Cited by in corpus (6)

• Structural and Thermodynamic Properties of Hard-Sphere Fluids
• Chemical-Potential Route: A Hidden Percus-Yevick Equation of State for Hard Spheres
• Rational-function approximation for fluids interacting via piece-wise constant potentials
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• Depletion force between disordered linear macromolecules
• Equation of state for five-dimensional hyperspheres from the chemical-potential route