Calculation of the Surface Tension of the Vapor–Liquid Interface According to the Gibbs Thermodynamic Definition

Abstract

A procedure to calculate the surface tension is developed based on a modified lattice gas model (MLGM) for the vapor–liquid system in a strict correspondence to the thermodynamic Gibbs definition for any curvature of the boundary. It is shown that MLGM enables a calculation of molecular distributions in a layered model of the transition region of the interface with regard to the softness of a lattice structure. The state of coexisting phases must satisfy the Yang–Lee theory of condensation, and additional conditions for chemical, thermal, and mechanical equilibria are imposed on the properties of the transition region of an equilibrium droplet with any curvature in each layer. The new calculation procedure for the surface tension is compared with the existing calculation procedures for equilibrium and metastable droplets. A difference in size dependences of the surface tension σ(R) for equilibrium and metastable droplets with a radius R in vicinity of the line σ/σbulk = 1, where σbulk is the bulk surface tension, allows us to formulate the accuracy and reliability criterion for different modeling methods: if the mentioned line exceeds the calculation accuracy σ(R), then it indicates that the method does not correspond to the Gibbs definition.