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

Abstract

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* ≡ Nσ3/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.