Density functional models of the interfacial tensions near the critical endpoints and tricritical point of three-phase equilibria

We treat two different density-functional models of the structures and tensions of the interfaces between phases on approach to the tricritical point of three-phase equilibrium. The major objective is to account for some of the results of earlier experimental measurements of these tensions. The thermodynamic background is first reviewed, including representations of the properties near the critical endpoints and tricritical point and of the wetting transitions that may occur on approach to those critical points. The first of the models treated is analytically soluble. Its properties are illuminating but at the price of some artificiality paid for its analytical solubility. The second model, called model T, is in a class of those treated in the past and analyzed numerically. Some of its properties are obtained with sufficient precision to allow one to conclude with near certainty what the analytically exact results would be. This model, too, illuminates the experimental measurements. It is noted where its properties are in accord with those of the analytically soluble model and where the two differ.