Competitive adsorption of xenon and krypton in zeolite NaA: 129Xe nuclear magnetic resonance studies and grand canonical Monte Carlo simulations

Investigation of competitive adsorption is carried out using the Xe–Kr mixture in zeolite $\mathrm{Na}A$ as a model system. The ${\mathrm{Xe}}_n{\mathrm{Kr}}_m$ clusters are trapped in the alpha cages of this zeolite for times sufficiently long that it is possible to observe individual peaks in the nuclear magnetic resonance (NMR) spectrum for the clusters. The ${}^{129}\mathrm{Xe}$ nuclear magnetic resonance spectra of several samples of varying Xe and Kr loadings have been observed and analyzed to obtain the ${}^{129}\mathrm{Xe}$ chemical shifts and the intensities of the peaks which are dependent on the average krypton and xenon occupancies. The detailed distributions, $\mathrm{f(}{\mathrm{Xe}}_n{\mathrm{Kr}}_m\mathrm{),}$ the fractions of cages containing $n$ Xe atoms and $m$ Kr atoms can be observed directly in this system from the relative intensities since individual peaks for ${\mathrm{Xe}}_n{\mathrm{Kr}}_m$ mixed clusters are observed in the NMR spectrum. Grand canonical Monte Carlo (GCMC) simulations of mixtures of Xe and Kr in a rigid zeolite $\mathrm{Na}A$ lattice provide the detailed distributions and the average cluster shifts. The agreement with experiment is excellent. The calculated absolute chemical shifts for the ${\mathrm{Xe}}_n$ peaks and ${\mathrm{Xe}}_n\mathrm{Kr}$ peaks at 300 K are in good agreement with experiment. A strictly statistical model of a binary mixture, derived from the hypergeometric distribution, in which the component atoms are distinguishable but equivalent in competition for eight lattice sites per cage under mutual exclusion provides a limiting case for the distributions, with which the GCMC simulations and the properties of the actual Xe–Kr system may be compared. The selectivity coefficients of the Xe–Kr mixture in zeolite $\mathrm{Na}A$ is well described by the ideal adsorbed solution model.