Ignacio Urrutia, Gabriela Castelletti
This paper presents a modified grand canonical ensemble which provides a new simple and efficient scheme to study few-body fluid-like inhomogeneous systems under confinement. The new formalism is implemented to investigate the exact thermodynamic properties of a hard sphere (HS) fluid-like system confined in a spherical cavity with up to three particles. In addition, the partition function of this system was used to analyze the surface thermodynamic properties of the many-HS system and to derive both, the exact curvature dependence of the surface tension and adsorption, in powers of the density. We use these results to derive for this system the dependence of the fluid-substrate Tolman length up to first order in density.
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http://arxiv.org/abs/1203.2145
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