The theory of surface tension components and the equation of state approach

Abstract

There are at present two main approaches to the calculation of solid surface tensions from contact angles: the theory of surface tension components and the equation of state approach. These are compared on the basis of their abilities to predict both the outcome of a specially designed contact-angle experiment and the engulfing behavior of microscopic particles at advancing solidification fronts. Each of these experiments provides an independent test of the validity of the two approaches. The equation of state passes both tests. The theory of surface tension components is shown to be inadequate. A theoretical assessment of the Fowkes equation for surface tension components reveals that the “dispersion components” of solid or liquid surface tension are, in fact, meaningless functions of the corresponding total solid and liquid surface tensions. More generally, it is found that contact angles can never be used to measure surface tension components. This is a consequence of Young’s equation and the existence of an equation of state relating the solid-liquid surface tension to the total surface tension of the liquid and solid. Equation of state results are compared with direct measurements of solid surface tension made with an Israelachvili machine and recently reported in the literature.Key wordsSolid surface tensioncontact anglessurface tension componentsequation of state