Validity of Tolman's equation: How large should a droplet be?

Surface tension and the length δ (distance between the Gibbs surface of tension R_s and the equimolar surface R_e) of simple liquid droplet (Lennard-Jones and Yukawa) are computed over a wide range of droplet sizes up to about 4×10⁶ molecules. The study is based on the Gibbs theory of capillarity combined with the density-functional approach to gas-liquid nucleation. Since this method provides behavior of the surface tension fully consistent with the tension of the planner surface, the constant in Tolman's equation δ_∞ can be determined unequivocally from the asymptotic behavior of σ_s. Comparison of the tension given by Tolman's equation against the result of exact thermodynamic relations reveals that Tolman's equation is valid only when the droplet holds more than 10⁶ molecules for the simple fluid systems near their triple points, in contrast to the conventional wisdom that Tolman's equation may be applicable down to droplets holding a few hundreds of molecules.