In this paper we calculate the sorption characteristics (isotherm and isosteric heat) of Ar and N2 in dehydrated zeolite 4A on the basis of classical statistical mechanics. It is demonstrated that the canonical partition functions for various numbers of sorbate molecules, which are involved in the calculations, can be evaluated by the Monte Carlo method proposed by Bennett and Voter. In contrast to most statistical mechanics calculations of sorptions previously done, which were intended for the low sorbate concentration case (i.e., the sorbate-sorbate interaction is not considered), this Monte Carlo method provides the way of evaluating the partition functions even if the sorbate concentration is considerably high (i.e., even if the gas in contact with the crystal is of high pressure). In this method, sorbate-sorbate interaction can be fully taken into account and one can predict how many sorbate molecules can be accommodated in the zeolite. The combination of the London approximation for dispersion energy and the point charge model for polarization energy (the assumption that the lattice atoms in the zeolite have a point charge) is applied to calculating the Ar-zeolite 4A interaction potential. The isotherm and isosteric heat calculated from this potential agree with the corresponding experimental ones. Close examinations, however, reveal that the coincidence is due to the overestimation of polarization energy. This originates from the inadequate point charge distribution and the fault inherent in the point charge model. The effect of the three-body interaction among two Ar atoms and zeolite 4A is examined, indicating that this effect is not significant for the Ar-zeolite 4A sorption system. The three-body interaction among Ar atoms is of no importance. It is shown for N2-zeolite 4A that the quadrupole of N2 interacting with the electric field in the zeolite fills the role of rendering energetic heterogeneity to the N2-zeolite 4A interaction potential. Furthermore, the models for partition functions presented by Ruthven et al. and based on the lattice gas model are compared, for various numbers of sorbates, with the Monte Carlo simulation values, showing that for the calculated Ar-zeolite 4A interaction potential the lattice gas model is preferable to the Ruthven model. An adjustable parameter in the lattice gas model, namely, the number of trap sites in a cavity, is determined as 6-7, which is in accord with the number of sites in the calculated interaction potential.
ASJC Scopus subject areas
- Physical and Theoretical Chemistry