Adsorption and wetting transitions at a model of the interface between a solid and a binary fluid mixture

We have developed a statistical-mechanical model for the adsorption of binary fluid mixtures (liquids or gases) at solid substrates. This model, which is a generalization to mixtures of that due to Sullivan, allows us to relate the relative adsorption of the two species and the solid-fluid interfacial tensions to parameters which characterize the solid-fluid and fluid-fluid potential functions. By making simplifying assumptions for the form of the potential functions and imposing certain mixing rules the problem of calculating the interfacial structure of the binary mixture can be reduced to an effective one density problem. The wetting characteristics of the solid-binary fluid system are then determined by Sullivan's procedure. For a binary mixture which exhibits liquid-liquid phase separation and an upper critical end point the wetting ‘phase diagram’., which determines the boundaries between different classes of wetting behaviour, differs from that for a one component fluid for temperatures below the critical end point. This has important repercussions for the behaviour of the relative adsorption, the total coverage and the interfacial tensions as a function of temperature. We illustrate these by presenting the results of numerical calculations of the density profiles, relative adsorption and interfacial tension for the various solid-liquid interfaces which occur in a particular model binary liquid mixture near a solid. Depending on the strength of the attractive part of the solid-fluid potentials, the fluid exhibits a variety of transitions between different wetting classes as the temperature is increased. The relative adsorption can diverge or be identically zero at such a transition; this depends on whether or not the interface in question is completely wet by another (liquid) phase at the transition. One important result which emerges from our calculations is that the sign and magnitude of the relative adsorption depend strongly on the wetting class; the species with the more attractive solid-fluid potential is not always preferentially adsorbed at the substrate. If the potentials and temperature are such that there is partial wetting by vapour, or by the liquid phase which is relatively rich in the other species, the latter may be preferentially adsorbed. For temperatures in the vicinity of the critical end point our results for the interfacial properties are in agreement with the mean field predictions of Widom. We comment briefly on applications of the model to solid-gas interfaces and speculate on the possibility that two distinct wetting films, corresponding to complete wetting of such an interface by both phase separated liquids, might occur.