Free Energy of a Nonuniform System. I. Interfacial Free Energy

It is shown that the free energy of a volume V of an isotropic system of nonuniform composition or density is given by : N_V∫_V [f₀(c)+κ(▿c)²]dV, where N_V is the number of molecules per unit volume, ▿c the composition or density gradient, f₀ the free energy per molecule of a homogeneous system, and κ a parameter which, in general, may be dependent on c and temperature, but for a regular solution is a constant which can be evaluated. This expression is used to determine the properties of a flat interface between two coexisting phases. In particular, we find that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature T_c, and that at a temperature T just below T_c the interfacial free energy σ is proportional to ${\mathrm{(T}}_c{\mathrm{-T)}}_{\frac{3}{2}}$ . The predicted interfacial free energy and its temperature dependence are found to be in agreement with existing experimental data. The possibility of using optical measurements of the interface thickness to provide an additional check of our treatment is briefly discussed.