The Three-Body Direct Correlation Function of Hard Sphere and Hard Ellipsoid Fluids

Abstract

In previous work, the direct correlation functions of hard spheres and hard ellipsoidal fluids were calculated. In the present work, using Marko variational method and Pynn–Wulf approximation, the three-body direct correlation function of hard ellipsoid fluid is calculated. In these calculations, the triplet direct correlation function of hard spheres is required. The new expressions for the direct correlation function of hard spheres and hard ellipsoids and triplet correlation of hard spheres, introduced by Muller and coworker, are used. The Fourier transform of new triplet direct correlation of hard sphere fluid is compared with the simulation data. As mentioned in previous work, the expansion coefficients of two-body correlations of hard ellipsoids (components of three-body correlations) are fairly in agreement with the Monte Carlo simulation and the other theories. The Fourier transform of new triplet direct correlation of hard spheres and hard ellipsoid fluids is calculated. These Fourier transforms can be used for calculation of triplet structure factor of hard spheres and hard ellipsoid fluids. The Fourier transforms of triplet correlation of hard ellipsoids with elongations $$x = 1.50,\,\,1.20,\,\,1.10$$ as limited cases are compared with exact result of hard spheres of unit diameter. There is qualitative agreement between hard ellipsoids and hard spheres results of triplet correlations.