Calculation of the surface tension and the surface energy of Lennard–Jones fluids from the radial distribution function in the liquid phase

Abstract

Calculation of the surface tension and surface energy of Lennard–Jones fluids from the radial distribution function and the density profile has been studied in detail, using Lekner and Henderson's approach. Three explicit analytical expressions for the function in the liquid phase are considered, together with very accurate expressions for the liquid and vapour densities. The well-known exponential and hyperbolic tangent models for the density profile in the interface zone are considered. The use of the direct correlation function using the Percus–Yevick and the hypernetted-chain approximations is also considered to calculate the surface tension. Finally, the results obtained are compared with values from experiment, from computer simulation, and from relevant theoretical developments. It is shown that the use of the newer models for the radial distribution function represents a significant improvement in applying Lekner and Henderson's approach. Nevertheless, in order to achieve good numerical agreement it would be desirable to perform calculations with expressions for the radial distribution function in the interface zone rather than in the liquid phase. This will be the subject of future work.