SEMIPHENOMENOLOGICAL THEORY OF THE TOLMAN LENGTH

A semiphenomenological cluster theory of the curvature correction delt a(T) to the surface tension of a spherical liquid drop (known as a ''T olman length'') is presented. By using the Fisher droplet model of con densation [M. E. Fisher, Physics 3, 255 (1967)]. we obtain an equation relating delta(T) to the saturation vapor pressure at a given tempera ture T. For low temperatures an analytical solution is obtained. In a general case the equation is solved numerically for various nonpolar s ubstances. Not too close to T-c, delta(T) is found to be positive and of the order of 0.2 sigma, where sigma is a molecular diameter, in agr eement with molecular dynamics simulations. As T-->T-c(-) the Tolman l ength becomes negative and diverges, as predicted by the density-funct ional analysis.