Gibbs Calculations of the Equilibrium Surface Tension in a Vapor–Liquid System

A correct way of calculating the equilibrium surface tension of planar and curved vapor–liquid interfaces is formulated for the first time according to Gibbs (i.e., as the excess free energy in the region of immiscible phase transitions). Calculations are performed using a modified lattice gas model that reflects a discrete–continuous distribution in the space of mixture components. The discrete size scale is associated with regions of around the size of a molecule that form the cells of the lattice structure. The continuous scale corresponds to the intermolecular motion of components inside the cells. The intermolecular interactions of comparable components are considered in a quasi-chemical approximation that describes direct correlations. It is shown that considering only the discreteness of the molecular distribution on a rigid lattice does not provide simultaneous satisfaction of two special conditions of chemical and mechanical equilibria for any degrees of interface curvature, and that the conditions of phase partitioning are insufficient for unambiguous calculations of the surface tension. The condition for the complete equilibrium of two phases must be supplemented with the conditions of the local mechanical and chemical equilibria at each point of the boundary transition region, and the local pressure value must be adjusted to the local value of the chemical potential.