By means of a large-scale molecular dynamics simulation, we show that the Tolman length, although positive, is much smaller in magnitude than previously reported. We found that the range of interparticle interaction can significantly affect the magnitude of the Tolman length. When the range of interaction is longer than five molecular diameters, the Tolman length is on the order of a few hundredths of the molecular diameter, rather than a few tenths known previously.

A hybrid thermodynamic and density-functional theory for heterogeneous nucleation on mesoscopic wettable particles is developed. The nonlocal density-functional theory ͑DFT͒ is on basis of the weighted-density approximation ͑WDA͒ of Tarazona. The model system consists of a Lennard-Jones ͑LJ͒ fluid and a 9-3 LJ wall for the solid particle. Effects of the droplet curvature and compressibility are accounted for in the theory. A by-product of this work is the calculation of the Tolman length using the WDA-DFT ͑Appendix A͒. Important characteristics of the heterogeneous nucleation, including the chemical potential of the liquid condensate, the free energy of droplet formation, and the barrier height to nucleation, are obtained.

In the framework of density functional theory ͑DFT͒, a patching model for the density profile of the liquid-vapor interface is developed. The patching is based on analytical expressions of the asymptote of the density profiles. Derived from the model the surface tension of planar liquid-vapor interface as well as the Tolman length can be computed from analytic expressions. Two prototype systems are considered; the Yukawa and the Lennard-Jones. As a result, the temperature dependence of the surface tension as well as the Tolman length are obtained. The results are compared with numerical DFT calculations.