Multicomponent fluids of hard-hyperspheres in odd dimensions

Abstract

Mixtures of hard hyperspheres in odd space dimensionalities are studied with an analytical approximation method. This technique is based on the so-called Rational Function Approximation and provides a procedure for evaluating equations of state, structure factors, radial distribution functions, and direct correlations functions of additive mixtures of hard hyperspheres with any number of components and in arbitrary odd-dimension space. The method gives the exact solution of the Ornstein-Zernike equation coupled with the Percus-Yevick closure, thus extending to arbitrary odd dimension the solution for hard-sphere mixtures [J. L. Lebowitz, Phys. Rev. 133, 895 (1964)]. Explicit evaluations for binary mixtures in five dimensions are performed. The results are compared with computer simulations and a good agreement is found.