A thermodynamic theory of the equation of state for interfacial tensions has been developed in this thesis. By demonstrating that the classical phase rule for bulk phase systems is not applicable to capillary systems, a general phase rule for capillary systems containing both curved interfaces and three-phase lines has been derived. A distinction has been made between the phase rule for the moderately-curved capillary systems and the phase rule for highly-curved capillary systems. By applying the phase rule for moderately-curved capillary systems, it has been shown that there are two degrees of freedom for a two-component solid-liquid-vapour system, and three degrees of freedom for a two-component liquid-liquid lens-fluid system. This leads directly to the conclusion that there indeed exists an equation of state for interfacial tensions γ^sl = f(γ^lv, γ^sv) for two-component solid-liquid-vapour systems, and that this type of relation will not exist for liquid-liquid lens-fluid systems in general. Thus, the phase rule approach has proved the existence of the equation of state and clarified its range of applicability.

Although the phase rule is derived originally for "simple" systems, it has been shown in this thesis that the phase rule remains valid when the earth’s gravitational field is considered. It has also been shown that the number of degrees of freedom, and hence the existence of the equation of state, for the two-component solid-liquid-vapour surface systems, is independent of the particular configurations of the systems;​ the tilting plate system, as a good example, has been illustrated.

An explicit form of such an equation of state has been formulated by a thermodynamic approach in conjunction with a modified geometric mean combining rule proposed in this thesis. Coupling this equation of state with the Young equation provides an equation to determine the solid-vapour surface tension γ^sv from the experimental data for liquid surface tension γ^lv and contact angle θ. The solid-liquid interfacial tension γ^sl can then be calculated from either the equation of state or the Young equation. This new equation of state avoids the mathematical discontinuity in the previous equation of state formulation.

To determine the constant in the equation of state, surface tensions and contact angles of a series of liquids on three types of solid surfaces have been measured by using the automated Axisymmetric Drop Shape Analysis-Profile (ADSA-P) technique. Prior to the measurements, the thermodynamic status of contact angles has been studied, especially, with respect to contact angle hysteresis and the drop-size dependence of contact angles. The three surfaces used in this study are FC721, Teflon FEP and Polyethylene Terephthalate surfaces. TJsing ADSA-P, the accuracy of the measurements in this thesis is better than O.1 mJ/m² for liquid surface tensions, and better than 0.2° for contact angles in general.