Two interacting particles in a spherical pore

URRUTIA I.; CASTELLETTI G.

The Journal of Chemical Physics

American Institute of Physics

Lugar: Melville, New York 11747 ; Año: 2011 vol. 134 p. 1 - 12

1089-7690

In this work we analytically evaluate, for the first time, the exact canonical partition function for two interacting spherical particles into a spherical pore. The interaction with the spherical substrateand between particles is described by an attractive square-well and a square-shoulder potential. In addition, we obtain exact expressions for both the one particle and an averaged two particle densitydistribution. We develop a thermodynamic approach to few-body systems by introducing a method based on thermodynamic measures [I. Urrutia, J. Chem. Phys. 134, 104503 (2010)] for nonhardinteraction potentials. This analysis enables us to obtain expressions for the pressure, the surface tension, and the equivalent magnitudes for the total and Gaussian curvatures. As a by-product, we solve systems composed of two particles outside a fixed spherical obstacle.We study the low density limit for a many-body system confined to a spherical cavity and a many-body system surrounding aspherical obstacle. From this analysis we derive the exact first order dependence of the surface tension and Tolman length. Our findings show that the Tolman length goes to zero in the case of a purely hardwall spherical substrate, but contains a zero order term in density for square-well and square-shoulder wall-fluid potentials. This suggests that any nonhard wall-fluid potential should produce a non-nullzero order term in the Tolman length.