Surface Tension of the Planar Interface of a Vapor-Liquid System on a Two-Dimensional Square Lattice

In an earlier work, the authors described a theoretical approach to deriving equations for equilibrium particle distributions by means of heterogeneous cluster variation (CV) that converges to the exact solution as the basis cluster grows. In this work, they present calculations of the surface tension (ST) of the planar interface of a vapor-liquid system on a two-dimensional square lattice by means of heterogeneous CV. The transitional region of the interface is a sequence of monomolecular layers with a variable fluid density fluida. Calculations are made for six types of clusters with different sizes inside the phases (2 x n, n = 1-4, 3 x 3, and the k(1s) cluster with the nearest neighbors of any central site), and for eight clusters inside the transitional region (2 x 1, 2 x 2, 2 x 3, 3 x 2, 2 x 4, 4 x 2, 3 x 3, k(1s)) that differ by each cluster's orientation relative to the normal to the surface. As the clusters grow, so does the accuracy of describing indirect correlations of laterally interacting particles. The temperature dependence of the ST is calculated. A monotonically growing ST is obtained as the temperature falls, starting from zero at the critical temperature. The calculation results converge to the exact Onsager solution as the clusters grow. Differences between thermodynamic requirements and ST calculations performed with the Ising model are discussed.