Numerical Analysis of the Thermodynamic Definition of the Surface Tension of a Vapor–Liquid System in the Lattice Gas Model

A numerical analysis is performed of Gibbs’ thermodynamic definition of the surface tension (ST) of a vapor–liquid system as excess free energy Δ F of a two-phase system with and without assuming the existence of an interface. Calculations are made using the simplest version of the lattice gas model (LGM) by assuming interaction between nearest neighbors in the quasi-chemical approximation (QCA). Different ways of calculating ST, which is expressed through different partial contributions from to excess energy Δ F (where i = A is molecule А and i = V denotes vacancies, 1 ≤ q ≤ κ, q is the number of monolayers inside a interface, and κ is its width), are compared. The ambiguity of ST values depending on the type of functions is obtained. These differences in ST values are demonstrated through the temperature dependence of ST for a planar boundary and the dependence of ST on the size of drops at a specific temperature. Results from calculating ST thermodynamically are compared to analogous calculations according to the version of the definition of ST that considers the specificity of vacancies in the LGM as a mechanical characteristic of the system.