Lattice model of adsorption in disordered porous materials: mean-field density functional theory and Monte Carlo simulations

We present mean-field density functional theory calculations and Monte Carlo simulations for a lattice model of a fluid confined in a disordered porous material. The model is obtained by a coarse graining of an off-lattice model of adsorption of simple molecules in silica xerogels. In some of our calculations a model of a porous glass is also considered. The lattice models exhibit behavior that is qualitatively similar to that of their off-lattice counterparts but the computations required are much more tractable and this makes it feasible to investigate the effects of porous material microstructure at longer length scales. We focus on exploring in detail the behavior in the adsorption/desorption hysteresis region for these models. In agreement with recent results for a model that uses a random distribution of solid sites on the lattice [Kierlik et al., Phys. Rev. Lett. 87, 055701 (2001)] we show that the disorder of the solid matrix induces multiple metastable states within the hysteresis region, which are evident in both the mean-field theory calculations and the Monte Carlo simulations. These multiple metastable states can be connected by scanning curves that are very similar to those seen in experimental studies of adsorption hysteresis. The results from mean-field theory predict that while there is hysteresis in the adsorption/desorption isotherms it is not possible to locate a condition of phase equilibrium that satisfies thermodynamic consistency. A wider significance of these results is discussed.