Coarse-Graining of Adsorption in Microporous Materials: Relation between Occupancy Distributions and Local Partition Functions

We derive a recurrence equation that relates the effective interactions among the particles adsorbed in two adjacent cages of a microporous material to the local probability distributions of cage occupancies. We show that such a relation can be used to estimate the approximate values of local partition functions, which can in turn be used as input for coarse-grained models of adsorption. After validating this theory by reproducing with good approximation the local partition functions of a lattice gas, we apply this method to the problem of adsorption of methane in all-silica zeolites DAY and ITQ-29 at various temperatures. The adsorption isotherms we obtain from the coarse-grained models built on the basis of the estimated values of the local partition functions are in very good agreement with the adsorption isotherms calculated from atomistic simulations.