Phase transitions in a confined lattice gas: Prewetting and capillary condensation

The phase equilibria of a lattice gas confined two parallel walls are investigated in mean-field approximation. Only a finite number of the first-order layering transitions, characteristic of the adsorption isotherms π(μ) for a strongly attractive substrate, survive when the wall- separation H is finite. The sequence is truncated at chemical potential μ<μsat by the onset of capillary condensation where θ jumps to a large value corresponding to a densely occupied ‘liquid’ state. Confinement shifts the bulk first-order transition to smaller μ. For weaker wall potentials first-order prewetting transitions, between thick and thin adsorbed films, are observed but these are in competition with capillary condensation. The resulting phase diagram, plotted using the variables 1/H, μ and T, exhibits a prewetting surface bounded by a line of triple points where thick films, thin films and ‘liquid’ all coexist, and by a line of prewetting critical points. The factors that influence the extent of this surface are discussed. Results for the lines of coexistence between ‘liquid’ and ‘gas’ states and for the location of capillary critical points, where such lines terminate, are presented. These are similar to results obtained from earlier density functional calculations for continuum fluids.