Fluids confined to narrow pores: A low-dimensional approach.

Abstract

A fluid physisorbed in a narrow pore forms a nearly one- or two-dimensional monolayer, depending on the pore geometry, when the characteristic dimension of the pore is only slightly larger than the molecular size. In such cases, previous work shows that the average density of an adsorbed phase in equilibrium with a bulk phase can be predicted by treating the adsorbate as a low-dimensional (low-D) fluid, when the adsorbate density is low. For example, a fluid of hard spheres adsorbed inside a narrow planar pore resembles a fluid of hard disks. We improve the low-D model by regarding the adsorbate as a polydisperse fluid constrained to a lower dimension; thus, molecular size in the lower-dimensional space replaces the adsorbate position in the dimension normal to the adsorbate surface in the true geometry. The size distribution in the pseudo-low-D mixture is not chosen arbitrarily, but specified by the equilibrium condition between the low-D mixture and the bulk fluid. This equilibrium condition follows naturally from the formalism of the semigrand canonical ensemble, which provides a convenient thermodynamic description of polydisperse mixtures. The mapping of the adsorbed phase onto a polydisperse low-D fluid is examined for examples of hard-particle fluids. We report the average adsorbate density relative to the density of a bulk fluid in equilibrium with the adsorbed phase. The polydisperse low-D model provides a better representation of dense adsorbed layers than the simpler low-D model throughout the entire range of applicability of the models, as demonstrated by comparison to Monte Carlo simulations. The theory also fares better than a well-regarded smoothed density-functional theory in predicting density profiles for hard spheres in very-narrow-slit pores.