Statistical thermodynamics of particles adsorbed onto a spherical surface. I. Canonical ensemble

A system of equisized hard spheres adsorbed onto the surface of a substrate sphere of a different diameter is treated by application of the concepts of small-system thermodynamics. The various thermodynamic representations (or statistical mechanical ensembles) are not equivalent in such a case, and the Gibbs adsorption isotherm does not apply. For spaces of nonzero curvature, two different forms of the pressure equation are possible, depending on whether the interparticle separations are measured within the non-Euclidian space or in a Euclidian space of one higher dimensionality. The two forms of the third virial coefficient are reported, including finite size and finite volume corrections, for all particle sizes. The available data on closest packing of spheres around a central sphere is used together with the virial expansion to construct two-point approximants to the equation of state. The results are compared to canonical ensemble simulations of adsorbed hard spheres.