The effective surface energy of heterogeneous solids measured by inverse gas chromatography at infinite dilution

Inverse gas chromatography (IGC) at infinite dilution has been widely used to access the nonspecific surface free energy of solid materials. Since most practical surfaces are heterogeneous, the effective surface energy given by IGC at infinite dilution is somehow averaged over the whole sample surface, but the rule of averaging has thus far not been established. To address this problem, infinite dilution IGC analysis was carried out on mixtures of known heterogeneity. These materials are obtained by mixing two types of solid particles with significantly different surface energies as characterized individually with IGC, and results are obtained for binary combinations in varying proportions. It is found that when all surface components have the same accessibility by probe molecules, the effective surface energy of such a heterogeneous surface is related to the surface energy distribution by a square root linear relationship, square root sigma(eff)(LW)= summation operator (i)phi(i) square root sigma(i)(LW), where sigma(i)(LW) refers to the nonspecific (Lifshitz-van der Waals) surface energy of patches i, and phi(i) to their area fraction.