The density profile and surface tension of a drop

Abstract

We obtain, by two independent routes, a statistical mechanical expression for the surface tension σ of a spherical surface. We show, for the penetrable-sphere model, that the thermodynamic arguments of Tolman are consistent with these results in the sense that they lead to the same relation between σ and the position of the surface of tension, R_s. This consistency holds, however, only to order of R_e^–1∼R_s^–1, where R_e is the radius of the equimolar dividing surface, so neither argument can be used for drops of molecular size. Mechanical arguments that have been used to relate σ and and R_s are unreliable at a microscopic level, and lead to values of R_s that are essentially arbitrary.