An exact formalism to study the thermodynamic properties of hard-sphere systems under spherical confinement

Abstract

This paper presents a modified grand canonical ensemble which provides a new simple and efficientscheme to study few-body fluid-like inhomogeneous systems under confinement. The new formalismis implemented to investigate the exact thermodynamic properties of a hard sphere (HS) fluid-likesystem with up to three particles confined in a spherical cavity. In addition, the partition function ofthis system was used to analyze the surface thermodynamic properties of the many-HS system andto derive the exact curvature dependence of both the surface tension and adsorption in powers of thedensity. The expressions for the surface tension and the adsorption were also obtained for the many-HS system outside of a fixed hard spherical object.We used these results to derive the dependence ofthe fluid-substrate Tolman length up to first order in density.