Phase coexistence in binary mixtures in thin films with symmetric walls: model calculations for two- and three-dimensional Ising lattices

Binary mixtures (A, B) that undergo phase separation in the bulk are considered in thin film geometry, assuming that one of the components is preferentially attracted to one of the walls. We discuss the average profile of the order parameter {volume fraction phi(z) of one of the components} in the z-direction (perpendicular to the surfaces), paying attention to the lateral inhomogeneity of the thin film when the average volume fraction corresponds to a state inside the coexistence curve. We consider the situation where due to (short range) surface forces a second-order wetting transition would occur in semi-infinite geometry: in the thin film geometry, this transition is rounded off and its only remnant is a smooth increase of the adsorbed mass in the surface-enriched layer in the transition region. Monte Carlo calculations for nearest neighbor Ising square and simple cubic lattices are used to derive typical concentration profiles. In the two-dimensional case, also the kinetics of domain formation after the quench from a disordered state is considered, and it is shown that the typical concentration oscillations perpendicular to the wall (''surface directed spinodal decomposition'') do not occur, due to strong lateral fluctuations of the local position of the interface between the enrichment layer at the surface and the neighboring depleted region. Finally, also phase-separated states in thin films with competing walls (where one surface prefers A and the other prefers B) are briefly treated, and experimental applications are discussed.