Pair correlation of hard spheres near a hard wall

Abstract

An inhomogeneous fluid of hard spheres near a flat hard well is considered. The density profile of this fluid is obtained from the Percus-Yevick (PY) equation for a homogeneous hard-sphere fluid by considering the wall to be a giant hard sphere. This density profile is used as input for the PY equation for the pair correlation functions of the inhomogeneous fluid. Solutions of this equation are obtained at low to intermediate density but at high densities the computational problems seem to be intractable. Using the bulk correlation functions and the density profile as input and accepting the result of the first iteration from the inhomogeneous PY equation gives a result which is fair when both hard spheres are equidistant from the wall and which is particularly good when the spheres are both equidistant and in contact. This approximation fails when the line between the centers of the hard spheres is close to normal to the surface. However, this approximation can be combined with Percus' shielding approximation to produce results which are in good agreement with Monte Carlo results at high densities. © 1984 American Chemical Society.