Molecular dynamics of the sorption and diffusion behaviour of spherical sorbates in the confined region of zeolites Y and A

Abstract

The sorbate–zeolite RDFs and sorbate–zeolite energy distribution functions suggest that the sorbates are largely localized inside the cages at the lowest temperature (188 K) studied. At low temperature, the sorbate prefers to confine itself near the inner surface of the cage, but with an increase in temperature it starts occupying the region near the cage centre. The peak observed near –12 kJ/mol in the sorbate–zeolite energy distribution corresponds to unbound and mobile sorbates. In the absence of any sorbate–zeolite dispersion interaction, the presence of zeolite has a purely geometrical role. Increase in the strength of sorbate–zeolite interaction increases the monomer population and decreases the population of dimers and higher?sized clusters. The lifetime of monomers as well as dimers increases with the strength of the sorbate–zeolite dispersion interactions. The variation of MSD with time shows a crossover from free?particle (ballistic) to diffusive behaviour. In the short?time limit, the MSD shows a t² dependence on time and a linear dependence on temperature. In the long?time limit, the MSD shows a linear time dependence and an exponential temperature dependence corresponding to the well?known Arrhenius behaviour. The power spectra exhibit a peak near 16 cm?¹, which has been shown to correspond to the stretching frequency of Xe–Xe dimers. It is shown that the motions parallel to the inner surface of the cage are reflected in the low?frequency part of the power spectrum, while the motions perpendicular to the inner surface of the zeolite appear at relatively higher frequencies (28 cm?¹). At higher sorbate loadings, a shoulder at 16 cm?¹ is observed, which is assigned to the Xe–Xe dimers. The intercage diffusion of xenon seems to consist of two subprocesses. First, the sorbate has to free itself from the adsorption site, which is located well inside the cage. Second, the sorbate which has freed itself from the adsorption site has to overcome the barriers, if any, while diffusing across the 12?ring window. The barrier height encountered by the sorbate while passing through the 12?ring window is positive but small. Analysis of the diffusion pathways exhibits two alternative mechanisms of diffusion — the surface?mediated (s.m.) and centralized diffusion (c.d.) modes. The barrier height for the s.m. mode is positive, but for the c.d. mode it is negative. At low temperatures, the predominant mechanism for intercage diffusion is the s.m. mode, because the sorbates do not have sufficient kinetic energy to excite to the centre of the cage. At higher temperatures, the c.d. mode becomes the predominant mode since there already exists a significant number of activated sorbate species near the cage centre and because the barrier is negative for diffusion across the window. We would like to mention that the distribution of barrier heights obtained by us here has some similarity with that reported by Austin et al. [4]. It is to be noted that the present results are based on a rigid zeolite framework and therefore correspond to a situation of static disorder, as suggested by Zwanzig [5]. The work of Austin et al. [4] corresponds to what is commonly known as dynamic disorder, B = B(t) [5]. If the framework atoms were included in MD integration, then the zeolite coordinates would be time?dependent, and the results would correspond to dynamic disorder. The activation energy obtained from the Arrhenius plot of k?c? is 3.02 kJ/mol. The calculation of f?R?(t) shows that ?_COTT, which is associated with the time of recrossings, is comparable to the cage?residence time t?c?. This is not surprising because the activation energy for k?c? is of the order of kT. Detailed studies on the temperature dependence of k?c? show that it deviates from Arrhenius behaviour at higher temperatures (above 637 K). The sorbate atom exhibits higher activation energies at higher temperatures. In contrast to k?c?, both k?v? and D do not show deviation from Arrhenius behaviour, suggesting that non?Arrhenius behaviour is restricted to properties dependent on the short?time behaviour of the system. Molecular dynamics simulation results of argon in NaCaA zeolite show that the sorbate atoms undergo localized?to?delocalized transitions in the temperature range 260–340 K. Intercage diffusion of Ar proceeds via two alternative diffusion mechanisms — surface?mediated and centralized modes. This observation is similar to that of the Xe–NaY system. It has been observed that the local energy barrier for both s.m. and c.d. modes is negative. In the Xe–NaY system, the c.d. mode was barrierless but the s.m. mode had a positive barrier. In the Ar–NaCaA system, the activation energy obtained from the Arrhenius plot of k?c? is found to be negative below 500 K and positive above 500 K. This change in sign of activation energy around 500 K has been attributed to the change in the principal mode of intercage diffusion from the s.m. mode to the c.d. mode. An Arrhenius plot of the diffusion coefficient yields a value of 1.8 kJ/mol for the activation energy, which may be compared with 4.2 kJ/mol for Xe in NaY. It is shown that the expected Arrhenius behaviour is recovered when properties dependent on long?time behaviour, such as the diffusion coefficient and the rate of cage visits, are investigated. It is found that the intercage diffusion is either zero or negligible in the absence of sorbate–zeolite dispersion interactions. The sorbate–zeolite dispersion interactions enhance the rate of intercage diffusion by a few orders of magnitude. This enhancement is attributed to three factors:

A decrease in the dimensionality of sorbate motion from 3 (in the absence of sorbate–zeolite interactions) to some value between 2 and 3, which increases D and k?c?. The predominance of the surface?mediated mode in the presence of sorbate–zeolite dispersion interactions. The negative barrier height for diffusion across the 8?ring window, which increases both k?c? and k?v?.

These results, and those for xenon in zeolite Y, indicate that the cage residence times for argon in NaCaA are smaller than those for xenon in NaY. It should be possible to verify these results experimentally.