Capillary condensation and adsorption in cylindrical and slit-like pores
The nature of adsorption of simple fluids confined in model pores is investigated by means of a density functional approach. For temperatures T corresponding to a partial wetting situation a first-order phase transition (capillary condensation) from dilute ‘gas’ to dense ‘liquid’ occurs at relative pressures p/psat close to those predicted by the macroscopic Kelvin equation, even for radii Rc or wall separations H as small as 10 molecular diameters. In a complete wetting situation, where thick films develop, the Kelvin equation is, in general, not accurate. At fixed T the adsorption Γm(p) exhibits a loop; Γm jumps discontinuously at the first-order transition, but the accompanying metastable portions of the loop could produce hysteresis similar to that observed in adsorption measurements on mesoporous solids. Metastable thick films persist to larger p/psat in slits than in cylinders and this has repercussions for the shape of hysteresis loops. For a given pore size the loop in Γm shrinks with increasing T and disappears at a capillary critical temperature Tcapc(< Tc). If T > Tcapc condensation no longer occurs and hysteresis of Γm will not be observed. Such behaviour is found in experiments. A prewetting (thick–thin film) transition can occur for confined fluids. The transition is shifted to a smaller value of p/psat than that appropriate to prewetting at a single planar wall. Whereas the magnitude of the shift is very small for slits, it is substantial for cylinders and this leads to the possibility of finding a triple point, where ‘liquid’ and thick and thin films coexist, in cylindrical pores whose radii may not be too large for investigation by experiment or computer simulation. Adsorption of supercritical fluids (T > Tc, the bulk critical temperature) in cylinders is mentioned briefly.