Tricritical phenomena in quasi-binary mixtures. III. An extended classical treatment

Abstract

The phenomenological (classical) treatment of tricritical points is extended by adding higher‐order terms to the sixth‐order free‐energy polynomial of the Griffiths asymptotic theory. The free energy is expanded in powers of the experimental (laboratory) densities of a quasi‐binary mixture, e.g., the mole fraction x or the molar volume V_m. The higher‐order corrections introduce asymmetry into the temperature‐composition coexistence curve and yield an approximately parabolic relation between the two densities. This extended classical theory yields, for experimental susceptibilities (i.e., those defined in terms of one of the laboratory densities) of the three coexisting phases, a Griffiths first sum χ^1/2_α +χ^1/2_γ −χ^1/2_β whose limiting value (as the tricritical point is approached) is not zero, as the asymptotic theory predicts, but rather a nonzero constant. The square‐gradient one‐density approximation is applied to give an extended mean‐field treatment of interfacial tensions in the tricritical region.