Mean field lattice model for adsorption isotherms in zeolite NaA

Abstract

Using a lattice model for adsorption in microporous materials, pure component adsorption isotherms are obtained within a mean field approximation for methane at 300 K and xenon at 300 and 360 K in zeolite NaA. It is argued that the increased repulsive adsorbate–adsorbate interactions at high coverages must play an important role in determining the adsorption behavior. Therefore, this feature is incorporated through a “coverage-dependent interaction” model, which introduces a free, adjustable parameter. Another important feature, the site volume reduction, has been treated in two ways: a van der Waal model and a 1D hard-rod theory [van Tassel et al., AIChE J. 40, 925 (1994)]; we have also generalized the latter to include all possible adsorbate overlap scenarios. In particular, the 1D hard-rod model, with our coverage-dependent interaction model, is shown to be in best quantitative agreement with the previous grand canonical Monte Carlo isotherms. The expressions for the isosteric heats of adsorption indicate that attractive and repulsive adsorbate–adsorbate interactions increase and decrease the heats of adsorption, respectively. It is concluded that within the mean field approximation, our simple model for repulsive interactions and the 1D hard-rod model for site volume reduction are able to capture most of the important features of adsorption in confined regions.

Diffusion of interacting particles in discrete geometries: Equilibrium and dynamical properties

“…One of the first such analyses was performed by Ruthven [31]. Similar studies have been performed both analytically [32][33][34][35][36][37] and numerically [29,38,39]. We refer to Ref.…”

Statistical thermodynamics of lattice models in zeolites: Implications of local versus global mean field interactions

“…This is equivalent to our earlier adsorption model, 5 where the zeolite is modeled as a large collection of identical sites ͑M͒. Using this description, 5 the canonical ensemble partition function for an M site lattice with N adsorbates is…”

“…3 Lattice models have been recently used to describe adsorption in zeolites. [4][5][6] Monte Carlo simulations of methane and xenon in zeolite NaA show that adsorption occurs onto a 12-site cuboctohedral lattice. Using this lattice description, the grand partition function is evaluated by computing all possible energetic states for the lattice within a single cage.…”

“…Using this lattice description, the grand partition function is evaluated by computing all possible energetic states for the lattice within a single cage. 4 In an alternate treatment, 5 we have used the Brag-Williams or mean field approximation to treat the adsorbate-adsorbate interactions on the lattice. This results in simplified expressions that can be used to evaluate the adsorption isotherms and other thermodynamic properties of the adsorbed phase.…”

“…Using this approach the theory based on the GMFA reduces to a model consisting of a collection of single-site subsystems interacting via the average coverage of the ensemble, providing a basis for the model used in our earlier work. 5 In contrast, the LMFA retains the zeolite cage as the subsystem and the thermodynamic properties are more conveniently developed in the grand canonical ensemble.…”