ARE THE (SOLID-LIQUID) KELVIN EQUATION AND THE THEORY OF INTERFACIAL-TENSION COMPONENTS COMMENSURATE

The theory of interfacial tensions, ITC theory, developed over the las t half-century from contact angle and wetting studies, has proven to b e reliable in many fields of physical and biophysical chemistry. Howev er, interfacial tensions for curved solid surfaces in liquids, estimat ed in various ways from the Kelvin equation (itself, of course, a very successful theory), give very different results from those estimated by ITC theory. That is, a clear distinction must be made between the K elvin equation parameter (KEP) of classical freezing theory and the co ntact angle parameter (CAP) of ITC theory. The difference between KEPs and CAPs is to some degree caused by the incorrect application of add ition rules, Antonow's rule, for example, but a more profound discrepa ncy remains even when correct addition rules are used. One source of a discrepancy in. measures of solid-vapor surface tension has been know n since Gibbs, but has often not been acted upon, and does not appear to have been routinely quantified. Discrepancies in solid-liquid inter facial tensions have not, to my knowledge, been identified and discuss ed quantitatively in such detail before. In this paper, solid-liquid C APs, from ITC theory, and KEPs, from freezing theory, are given for wa ter and for naphthalene. Naphthalene is apolar and so is independent o f certain aspects of ITC theory. Both substances show a large discrepa ncy between their KEP and their CAP. The effects of the discrepancy on the freezing of water ice are described. Several possible reasons for the discrepancy are discussed. Of the reasons for the discrepancy tha t have been identified, order-of-magnitude quatification suggests that only strain in the solid lattice or gross systematic differences betw een macroscopic and molecular level contact angles are potentially lar ge enough to account for it. If there is a lattice strain component in KEPs and the capillarity approximation is to be retained in freezing studies, there may be an additional stochastic effect in freezing, whi ch will determine the magnitude of the interfacial tension of nucleati ng clusters and which will be very difficult to calculate from first p rinciples.