Fluids in narrow pores: Adsorption, capillary condensation, and critical points

Abstract

By means of a density functional approach the phase equilibria of a simple fluid confined by two adsorbing walls have been investigated as a function of wall separation H and chemical potential μ for temperature T corresponding to both partial and complete wetting situations. For large values of H and small undersaturations Δμ ≡ μsat−μ, we recover the macroscopic formulas for the undersaturation at which a first- order phase transition (capillary condensation) from dilute ‘‘gas’’ to a dense ‘‘liquid’’ occurs in a single, infinitely long slit. For smaller H we compute the lines of coexistence between gas and liquid in the (Δμ, 1/H) plane at fixed values of T. The adsorption Γ(Δμ), at fixed T and H, is characterized by a loop. At the first order transition Γ jumps discontinuously by a finite amount; however metastable states exist and these could give rise to hysteresis of the adsorption isotherms obtained for the single slit. The loop disappears at a capillary critical point (Δμc, 1/Hc) at each T. For H<Hc, or Δμ>Δμc, condensation can no longer occur and no metastable states are present. The location of the critical points is described and for a complete wetting situation we find that these lie outside the bulk two phase region. Our theory provides a simple explanation of phase transitions observed in earlier computer simulations and mean-field lattice gas calculations for confined fluids and suggests that measurements of the forces between plates, either by simulation or in real fluids, should provide rather direct information about capillary condensation and, possibly, capillary critical points. The relevance of our results for adsorption experiments on mesoporous solids is discussed briefly.