Hard spheres in tubes: Density profile from a simple analytical method

Abstract

A simple analytic method to determine the radial distribution function on the basis of residual chemical potentials of a pair of hard models and of the corresponding combined body is applied to evaluate the density profile of a hard sphere in the spherical and cylindrical pores (tubes). The residual chemical potential of the considered hard bodies is obtained via expressions for geometric characteristics — a volume, surface area and mean radius of the considered body. An enlarged combined body is used instead of the fused hard sphere model. In the case of spherical pore only part of the large sphere (with radius R ⁎) characterizes the geometry of the spherical wall. In the case of tubes (cylindrical pores) the differences in the geometric quantities (e.g. Δ V of a hard sphere, cylindrical wall and combined body) are approximated by the arithmetic mean from those for planar wall and spherical pore. The simple analytic method is applied to determine the density profile of hard spheres in both the spherical and cylindrical pores of small radii, R ⁎ ≈ 2, and fair agreement with simulation data is found in the most important interval of distances nearby the wall.