Surface and Interfacial Tension of Two-Component Two-Phase Separating Systems of Cubic Shape

A numerical analysis of the thermodynamic determination of the surface tension (ST) between a fluid and a solid of a binary mixture and the interfacial tension (IT) between two dense phases as an excess value of free energy is carried out ΔF two-phase system with and without taking into account the presence of a phase boundary. Stratification is considered for cubic condensates, which were previously discussed in thermodynamic approaches. A microscopic analysis is given of the generalization of the Gibbs thermodynamic approach, introducing surface tension on the mathematical interface, to the case of a complex boundary shape with the introduction of local surface tensions for faces, edges, and vertices of faces. Depending on the type of averaging of local inhomogeneous regions, two forms of layered dividing surfaces are constructed: with straight and smoothed angles. The calculation was carried out in the simplest version of the lattice gas model (LGM) taking into account the interaction of nearest neighbors in the quasi-chemical approximation on a rigid lattice. Each node of a two-component mixture in the LGM system can be occupied by the components of the mixture A + B and vacancy V. Two main methods of calculating ST and IT, which are expressed through different partial contributions of $$M_{f}^{i}$$ into excess free energy ΔF (here, i = A, B, V are vacancies and 1 ≤ f ≤ t, where t is the number of different types of nodes, depending on the position of the node inside the corner regions of the cube), are compared. An ambiguity of the values of ST and IT depending on the type of functions $$M_{f}^{i}$$ is obtained when calculating the dependence of ST and IT on the domain size at a fixed temperature. The role of vacancies as the main mechanical characteristic of a two-component mixture in the LGM under the condition of strict phase equilibrium according to three partial equilibria (mechanical, thermal, and chemical) is discussed. It is shown that, if calculations of the IT are carried out for two dense stratified phases without taking into account vacancies, this distorts the real value of the IT.