Relationship between surface tension and Gibbs energy, and application of Constrained Gibbs Energy Minimization

In the context of a boundary phase model, surface tension (σ) of a solution can be regarded as a system property of an equilibrium between a bulk phase and a surface phase. In the present article, a geometric relationship is shown among molar Gibbs energy of the bulk phase (g), that of the surface phase (gs), and corresponding surface tension of the system. The geometric relationship is based on a phase equilibrium between the bulk phase and the surface phase, under a constraint: constant surface area (A). The relationship is consistent with the proposal of Butler, Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci., 135 (1932) 348 [1], and is mathematically equivalent to the Constrained Gibbs Energy Minimization (CGEM) for the surface tension calculation by Pajarre et al., Calphad 30 (2006) 196 [7]. The geometric relationship can be simply utilized by available CALPHAD type code, in order to calculate surface tension of a solution composed of any number of components. Role of various properties (surface tension (σi°) and molar surface area (Ai°) of pure components, excess Gibbs energy of the bulk phase and that of the surface phase) in the surface tension and surface concentration is examined using the CGEM.