First-order curvature corrections to the surface tension of multicomponent systems

The dependence of surface tension on curvature is investigated for the case of an equilibrium phase coexistence in multicomponent systems. Employing Gibbs's method of description of heterogeneous systems, an equation is derived to determine the dependence of surface tension on curvature for widely arbitrary paths of variation of the independent thermodynamic parameters. It is supposed hereby merely that the temperature is kept constant and that the variations of the different molar fractions are such that the radius of the dividing surface varies monotonically in dependence on the change of the state parameters of the ambient phase along any of the chosen paths. In the analysis, an approach developed by Blokhuis and Bedeaux for one-component systems is utilized. It relies on the expansion of the surface free energy on curvature of the dividing surface. An equation is derived that connects the first-order correction term in the expansion with the interaction potential of the particles in the multicomponent solution and with the two-particle distribution functions in the planar interfacial layer between the two phases coexisting in equilibrium at planar interfaces. The connection of the first-order curvature correction to the surface tension and the first moment of the pressure tensor at a planar interface is analyzed as well.