Dispersion-force effects in interfacial premelting of ice

We calculate the van der Waals contribution to the surface free energy of ice-water-substrate systems as a model for interfacial melting. The result for each substrate is the excess surface free energy per unit area F(L) as a function of the thickness L of a hypothetical water layer between the ice and the substrate. A minimum in this funciton as L\ensuremath{\rightarrow}\ensuremath{\infty} is a necessary condition for complete interfacial melting, equivalent to complete wetting at the melting point. Retarded potential effects ensure that this condition is fulfilled for large L, a consequence of the relative refractive indices of ice, water, and the substrates in the visible. Whether or not complete melting occurs for a given substrate depends on the interactions at short range. When taken alone, the van der Waals interaction predicts incomplete melting, via a global minimum at finite L, for some substrates, and complete melting for others. We have carried out the calculation for cases in which the materials in contact with ice are conductors (gold, copper, silver, tungsten, silicon), dielectric crystals (MgO, sapphire, fused quartz), and polymers polyvinylchloride, Teflon, polystyrene, among others), and find examples of both behaviors. Where complete melting is indicated, the interfacial interactions will stabilize a finite thickness liquid film at temperatures below the melting point. We find that these thicknesses are small at temperatures below -0.1 \ifmmode^\circ\else\textdegree\fi{}C, and we compare our results to experimental observations. Using a simple model, we find that electrical interactions, if present, can be much stronger than the van der Waals interaction.