Phase equilibria of fluid interfaces and confined fluids: Non-local versus local density functionals

Abstract

Phase transitions at fluid interfaces and in fluids confined in pores have been investigated by means of a density functional approach that treats attractive forces between fluid molecules in mean-field approximation and models repulsive forces by hard-spheres. Two types of approximation were employed for the hard-sphere free energy functional: (a) the well-known local density approximation (LDA) that omits short-ranged correlations and (b) a non-local smoothed density approximation (SDA) that includes such correlations and therefore accounts for the oscillations of the density profile near walls. Three different kinds of phase transition were considered: (i) wetting transition. The transition from partial to complete wetting at a single adsorbing wall is shifted to lower temperatures and tends to become first-order when the more-realistic SDA is employed. Comparison of the results suggests that the LDA overestimates the contact angle γ in a partial wetting situation. (ii) capillary evaporation of a fluid confined between two parallel hard walls. This transition, from dense ‘liquid’ to dilute ‘gas’, occurs in a supersaturated fluid (p > p sat). The lines of capillary coexistence calculated in the LDA and SDA are rather close, suggesting that non-local effects are not especially important in this case. (iii) capillary condensation of fluids confined between two adsorbing walls or in a single cylindrical pore. For a partial wetting situation the condensation pressures p(<p sat) obtained from the SDA are in remarkably good agreement with the macroscopic Laplace (or Kelvin) prediction for wall separations H or pore radii R c ≳ 5σ; σ is a molecular diameter. While, because of different packing, the density profiles of the fluid differ considerably between slits and cylinders this has little effect on the coexistence line until H or R c ∼ σ. In contrast to the LDA the SDA describes two-dimensional-like liquid-gas coexistence for very narrow pores (H < σ) and temperatures below the two-dimensional critical temperature and this has ramifications for the existence of capillary critical points.