Phase behavior and structure of a fluid confined between competing (solvophobic and solvophilic) walls

We consider a model fluid with long-range r(-6) (dispersion) interparticle potentials confined between competing parallel walls. One wall is solvophilic and would be completely wet at bulk liquid-gas coexistence μ(co)(-), whereas the other is solvophobic and would be completely dry at μ=μ(co)(+). When the wall separation L is large and the system is below the bulk critical temperature T(C) and close to bulk liquid-gas coexistence, a delocalized interface or soft-mode phase forms with a liquid-gas interface near the center of the slit; this interacts with the walls via the power-law tails of the interparticle potentials. We use a coarse-grained effective Hamiltonian approach to derive explicit scaling expressions for the Gibbs adsorption Γ, the surface tension γ, the solvation force f(s), and the total susceptibility χ. These quantities depend on the dimensionless scaling variable (L/σ)(3)βδμ, where β=(k(B)T)(-1), σ is the diameter of the fluid particles and δμ=μ-μ(co) is the chemical potential deviation from bulk coexistence. Using a nonlocal density functional theory, we calculate density profiles for the asymmetrically confined fluid at different chemical potentials and for sufficiently large L confirm the scaling predictions for the four thermodynamic quantities. Since the upper critical dimension for complete wetting with power-law potentials is less than 3, we argue that our (mean-field) scaling predictions should remain valid in treatments that incorporate the effects of interfacial fluctuations. As the wall separation L is decreased at μ(co), we predict a capillary evaporation transition from the delocalized interface phase to a dilute gas state with just a thin adsorbed film of liquidlike density next to the solvophilic wall. This transition is closely connected to the first-order prewetting transition that occurs at the solvophilic wall in the semi-infinite system. We compare the phase diagram for the competing walls system with the phase diagrams for the fluid confined between identical solvophilic and identical solvophobic walls. Comparisons are also made with earlier studies of asymmetric confinement for systems with short-range forces.