Semiempirical van der Waals/Cahn–Hilliard theory: Size dependence of the Tolman length

The interfacial density profiles, pressure tensor, and Tolman-length δT are determined for the critical droplets of nonane in the framework of the semiempirical van der Waals/Cahn–Hilliard theory. It is shown that the Tolman’s length is strongly size dependent, and tends to a negative value for large drops; indicating that Tolman’s approximation for the curvature dependence of the interfacial free-energy γ≈γ∞/(1+2δT,eq/R) based on the equilibrium values δT,eq, and γ∞, is inaccurate for typical liquid nuclei.