In a recent series of theoretical studies, we have explored how fundamental intracage and intercage jumps control benzene mobility in Na-X (Si:Al=1.0) and Na-Y (Si:Al=2.0).Our calculations indicate that activation energies from long length scale diffusion measurements, e.g. pulsed field gradient NMR, should be interpreted as site-to-window activation energies. Moreover, we suggest that results from NMR relaxation experiments for benzene in a series of faujasites, while reported as diffusion coefficients, should be interpreted as time scales for intracage orientational randomization, and hence should not agree with pulsed field gradient NMR results. In an effort to model NMR relaxation data as closely as possible, which may complement diffusion data, we use kinetic Monte Carlo to calculate the orientational correlation function accounting for randomization of benzene's six-fold axis. The results presented below clearly indicate that NMR correlation imes for benzene in Na-Y with full Na(II) occupancy are indeed controlled by intracage hopping processes.
An important parameter characterizing the electrostatic environment of a zeolite is the Si:Al composition ratio, which ranges between one and infinity in different systems, and which varies inversely with the density of exchangeable cations in the solid. Molecular mobilities in zeolites tend to increase with increasing Si:Al ratio, especially for nucleophilic adsorbates which become trapped with long residence times at cationic sites. To deepen our understanding of this trend, we use kinetic Monte Carlo to calculate orientational correlation functions and mean square displacements for benzene in Na-Y (Si:Al>=2.0), to determine how decreasing Na(II) cation occupancy affects orientational randomization rates and diffusion coefficients. The results presented below indicate that calculated diffusion coefficients vary weakly with decreasing Na(II) occupancy until ca. one Na(II) per supercage, and that mean square displacements reveal no information about intracage motion or spatial patterns of Na(II) cations. Alternatively, we predict that cation vacancies cause non-exponential decay of the orientational correlation function, providing important information regarding intracage motion, diffusion and cation disorder.
The remainder of this paper is organized as follows: in Sec.II we discuss the relevant orientational correlation function and relate it to various NMR measurements of reorientation dynamics. In Sec.III we describe the structural and physical assumptions in our model, in addition to the kinetic Monte Carlo algorithm used to simulate benzene mobility in Na-Y. In Sec.IV we present the calculated orientational correlation functions and mean square displacements, and compare the information they provide regarding benzene mobility and zeolite structure. Finally, in Sec.V we give concluding remarks emphasizing the experimental implications of our theoretical findings.