Multicomponent fluids of hard hyperspheres in odd dimensions

TL;DR

This paper introduces an analytical approximation method for studying mixtures of hard hyperspheres in odd-dimensional spaces, enabling the evaluation of their thermodynamic and structural properties with good accuracy.

Contribution

It extends the exact solution of the Ornstein-Zernike equation with Percus-Yevick closure to arbitrary odd dimensions for multicomponent hypersphere mixtures.

Findings

Good agreement with computer simulations for five-dimensional binary mixtures.

The method accurately evaluates equations of state and structural functions.

Provides a general framework for arbitrary odd-dimensional hypersphere mixtures.

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.\ \textbf{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.