AN ACCURATE ANALYTICAL REPRESENTATION OF THE BRIDGE FUNCTION OF HARD SPHERES AND A QUESTION OF EXISTENCE OF A GENERAL CLOSURE TO THE ORNSTEIN-ZERNIKE EQUATION

摘要

The bridge function of hard spheres is accurately calculated from computer simulation data on the pair distribution function via the inverted Ornstein-Zernike equation at reduced densities ρ* ≡ Nσ^sup 3^/V ranging from 0.2 to 1.02, i.e. from low densities through densities in a vicinity of the phase transition to crystal to densities of metastable fluid region. The data are used to propose an analytical representation of the bridge function as a function of the interparticle distance and density. They are further used to construct the so-called Duh-Haymet plot. It is demonstrated that a "general closure" to the Ornstein-Zernike equation in the form B(r) = f[γ(r)], where γ is the indirect (or series) correlation function, does not match the data. Nor does an extended closure B(r) = f[γ(r),ρ*] even in the simplest case of the one component hard sphere fluid. A relative success of literature closures to the Ornstein-Zernike equation is discussed. [PUBLICATION ABSTRACT]