Semiphenomenological theory of the Tolman length

A semiphenomenological cluster theory of the curvature correction dT to the surface tension of a spherical liquid drop (known as a ``Tolman length'') is presented. By using the Fisher droplet model of condensation [M. E. Fisher, Physics 3, 255 (1967)]. we obtain an equation relating dT to the saturation vapor pressure at a given temperature T. For low temperatures an analytical solution is obtained. In a general case the equation is solved numerically for various nonpolar substances. Not too close to Tc, dT is found to be positive and of the order of 0.2s, where s is a molecular diameter, in agreement with molecular dynamics simulations. As T¿Tc- the Tolman length becomes negative and diverges, as predicted by the density functional analysis.