(776e) Predicting Mixture Diffusion in Zeolites: Accounting for Strong Correlations With a Simplified Theory and Examining the Role of Mixture Adsorption Thermodynamics

The Maxwell−Stefan (MS) equations have been extensively used to describe mixture diffusion in zeolites. Correlation effects can arise due to molecules unsuccessfully attempting to pass each other in the very narrow pores of the zeolite, e.g., at high loadings of adsorbed molecules. In an extreme situation, diffusion may even become anomalous, giving rise to a single-file phenomenon. These correlation effects are captured in the so called “exchange terms” within the framework of the MS equations. The exchange terms are often calculated from pure component data using empirical approaches with different fits for different combinations of zeolite hosts and molecules. These computations, in turn, can be fairly tedious, especially for large multicomponent systems. It is therefore advantageous to be able to use a simplified theory to capture the effect of strong correlations. To this end, the MS equations are simplified to predict mixture diffusion behavior in the case of strong correlation effects. Intermolecular exchange coefficients are not required. No empirical relations are employed. This simplified model is used to predict the diffusion behavior in the separation of a CH₄-C₃H₈ mixture through a silicalite membrane.¹

The calculation of mixture thermodynamic correction factors in the MS equations can also pose a computational hurdle especially for large systems, and if theories such as the Ideal Adsorbed Solution Theory (IAST) have to be employed. It is expected that, if a vacant adsorption site is available, the adsorption of a species inside the zeolite pore should be dictated by the pure component adsorption isotherm alone, and that mixture adsorption thermodynamics should not play a role, or else correlation effects should be present in adsorption as well, in which case theories such as the IAST cannot be used.  To this end, the MS equations are simplified to employ only the pure component thermodynamic correction factors. This simplified model was used to predict mixture diffusion for two cases of practical interest: ¹ (i) the separation of a N₂-CH₄ mixture through a SAPO-34 membrane, and (ii) the alkylation of C₆H₆ with C­₂H₄ over H-ZSM-5.

In all cases, predictions from the simplified models are favorably compared to results from the more complex MS equations or experiments, indicating that the simplified models can serve as good starting approximations, and can also speed up mixture diffusion calculations in zeolites.

References:

1. Rao, S. M.; Coppens, M.-O. J. Phys. Chem. C 2012,  116 (51), 26816-26821