Microscopic origin and relevance of surface parameters for confined ternary mixtures

On the basis of a microscopic Hamiltonian on a semi-infinite cubic lattice, we derive the excess surface free energy for a confined ternary mixture of oil, water and amphiphile. Using the standard mean-field approximation for a spin-1 model we calculate the surface parameters in terms of the microscopic coupling constants which provides a physical interpretation of their origin. We further discuss in detail the corresponding surface free-energy density in the continuous Ginzburg–Landau theory and demonstrate that it takes the form of an expansion in powers of the surface order parameter and its local gradient. In comparison with the commonly accepted expression, new terms are found and their significance for the description of surface phenomena is described.