2ND-ORDER PERCUS-YEVICK THEORY FOR A CONFINED HARD-SPHERE FLUID

A fluid of hard spheres confined between two hard walls and in equilib rium with a bulk hard-sphere fluid is studied using a second-order Per cus-Yevick approximation. We refer to this approximation as second-ord er because the correlations that are calculated depend upon the positi on of two hard spheres in the confined fluid. However, because the cor relation functions depend upon the positions of four particles (two ha rd spheres and two walls treated as giant hard spheres), this is the m ost demanding application of the second-order theory that has been att empted. When the two walls are far apart, this calculation reduces to our earlier second-order approximation calculations of the properties of hard spheres near a single hard wall. Our earlier calculations show ed this approach to be accurate for the single-wall case. In this work we calculate the density profiles and the pressure of the hard-sphere fluid on the walls. We find, by comparison with grand canonical Monte Carlo results, that the second-order approximation is very accurate, even when the two walls have a small separation. We compare with a sin glet approximation (in the sense that correlation functions that depen d on the position of only one hard sphere are considered). The singlet approach is fairly satisfactory when the two walls are far apart but becomes unsatisfactory when the two walls have a small separation. We also examine a simple theory of the pressure of the confined hard sphe res, based on the usual Percus-Yevick theory of hard-sphere mixtures. Given the simplicity of the latter approach the results of this simple (and explicit) theory are surprisingly good.