Phase behaviour of fluids confined between chemically decorated substrates

The phase behaviour of a lattice gas confined between two identical plane-parallel substrates decorated with weakly and strongly adsorbing stripes that alternate periodically in one transverse direction is explored within mean-field theory It is shown that in the limit of zero temperature (T = 0) the mean-field approximation becomes exact. A modular approach is used to enumerate the possible structural types of phases (morphologies) that can exist at T = 0. Analytic expressions for the grand potentials associated with the morphologies can be obtained and used to determine the exact phase diagram at T = 0, In addition to the known 'gas', 'liquid', and 'bridge' phases, new 'vesicle', 'droplet', and 'layered' morphologies arise, which were overlooked in previous studies of this model. These T = 0 morphologies are taken as trial starting solutions in an iterative numerical procedure for solving the mean-field equations for T > 0. The complete phase diagram is thus obtained and its structure is studied as a function of the relative strength of 'strong' and 'weak' stripes. A key finding is that the number of possible morphologies increases rapidly with the geometrical complexity of the decoration of the substrate. The implications for the determination of phase diagrams for very complex confined systems (e.g. fluids in random porous media) are discussed.