ANALYTICAL TREATMENT OF A SIMPLE FLUID ADSORBED IN A SLIT-PORE

A model for a simple fluid confined to a slit-pore (fluid sandwiched b etween two plane-parallel substrates with infinitesimally smooth surfa ces) is presented. The analysis is based on thermodynamic perturbation theory, in which the free energy is split into a zero-order (unpertur bed) contribution from a hard-sphere fluid reference system and a corr ection accounting for both fluid-fluid and fluid-substrate attractions . The correction is evaluated in the mean-field approximation and the (unperturbed) local density is assumed uniform in order to obtain a cl osed expression for the correction. The resulting equation of state ha s the same temperature and density dependence as the van der Waals equ ation of state for the bulk fluid, although it differs from the latter in that the a parameter (a(p)) is a function of the separation s(z) o f the substrate surfaces. The inequality a(p)(s(z))less than or equal to a(b) holds, from which it follows that the critical temperature of the pore fluid is lower than that of the bulk fluid. For mesoscopic po res, the lowering is in semi-quantitative agreement with experiment. T he excess coverage Gamma is calculated for bulk isochoric paths T-->T- 0b, where T-0b is the bulk liquid-gas coexistence temperature for a gi ven isochore. If the fluid-substrate attraction is great enough, Gamma vs T may exhibit a discontinuity reflecting pore condensation. The mo del predicts pore condensation over a density range comparable with th e experimental one. (C) 1998 American Institute of Physics. [S0021-960 6(98)51537-1]