Expanded Formulation of Thermodynamic Scaling in the Critical Region

A description of the thermodynamic properties in the critical region of a physical system is obtained from a scaled expression for the free-energy F(ρ, T). In general, a nonsymmetric coexistence curve is predicted, with the symmetric case (e.g., magnets) included as a special example. For fluids, deviations from symmetry give rise to an expression for the average density below the critical point nonlinear in the temperature near T (in contrast to the usual "law of rectilinear diameter"); these asymmetries also contribute to the discontinuity in the specific heat along the critical isochore. To lowest order, the formulation reduces to Widom's homogeneous scaling; the classical equations of state of the van der Waals type are incorporated as a special case.