Further Reflections on the Geometric Mean Combining Rule for Interfacial Tension

Wettability is a widely used method to estimate the surface (free) energies of solids. The measured contact angles are usually processed within the framework of Fowkes and Good that uses a geometric mean combining rule of interfacial interactions. Recently, this method of calculating the interfacial tension has been questioned as it appears to yield somewhat unphysical results of interfacial energetics in certain situations. We would like to demonstrate that these unphysical results are consequences of the neglect of the preferential enrichment or depletion of the most surface-active functionalities of a molecule composed of various chemical groups at the liquid-air, liquid-liquid, and liquid-solid interfaces that the quintessential Fowkes-Good analysis does not account for. When the base state of the surface energy is estimated using Lifshitz theory and the preferential segregation of the functional groups at the interface is taken into account, the difficulty associated with the Fowkes-Good approach seems to disappear. This, however, raises new challenges and opportunities related to the estimation of surface energetics based on wettability.