Zeolite diffusion, simulations

MD calculations may be used not only to gain important insight into the microscopic behavior of the system but also to provide quantitative information at the macroscopic level. Different statistical ensembles may be generated by fixing different combinations of state variables, and, from these, a variety of structural, energetic, and dynamic properties may be calculated. For simulations of diffusion in zeolites by MD methods, it is usual to obtain estimates of the diffusion coefficients, D, from the mean square displacement (MSD) of the sorbate, (rfy)), using the Einstein relationship (/) ... 

The outlook for theoretical simulations of diffusion in zeolites is certainly encouraging. Order of magnitude agreement between experimental and theoretical results constituted success at the inception of these calculations, but now methods have progressed and parameters refined to the point whereby theoretical methods can rival experimental methods in accuracy and cost-effectiveness. 

P. Demontis and G. B. Suffritti, in Zeolites and Related Microporous Materials State of the Art 1994, J. Weitkamp, H. G. Karge, H. Pfeifer, and W. Holderich, Eds., Elsevier Science Publishers, Amsterdam, 1994, pp. 2107-2113. Molecular Dynamics Simulations of Diffusion in a Cubic Symmetry Zeolite. 

Fig. 1 Comparison of experimental and simulated self-diffusivities of benzene in NaX zeolite (supercage depicted in inset) vs. inverse temperature for three loadings, 0, indicated. (View this art in color at www.dekker.com.)...

The simulation of diffusion through zeolite structures uses techniques like molecular dynamics and Monte-Carlo simulation. 

Mann, R. and Thomson, G., "Deactivation of a supported zeolite catalyst simulation of diffusion, reaction and coke deposition in a parallel bundle", Chem. Eng. Sci., 42, 3 (1987). 

Diserepaneies exist between diflusivity values obtained using different methods for measuring diflusion in zeohtes. These diserepaneies prompted the simulation of diffusion in zeolites by Monte Carlo teehniques [25]. Patwardhan [26] attempted to put the moleeular model involved on a more exact footing by formulating the sorption and diffusion proeess as a Markov proeess. AH transitions arising out of a particle jump have been taken to proceed at equal rates. 

For the detailed study of reaction-transport interactions in the porous catalytic layer, the spatially 3D model computer-reconstructed washcoat section can be employed (Koci et al., 2006, 2007a). The structure of porous catalyst support is controlled in the course of washcoat preparation on two levels (i) the level of macropores, influenced by mixing of wet supporting material particles with different sizes followed by specific thermal treatment and (ii) the level of meso-/ micropores, determined by the internal nanostructure of the used materials (e.g. alumina, zeolites) and sizes of noble metal crystallites. Information about the porous structure (pore size distribution, typical sizes of particles, etc.) on the micro- and nanoscale levels can be obtained from scanning electron microscopy (SEM), transmission electron microscopy ( ), or other high-resolution imaging techniques in combination with mercury porosimetry and BET adsorption isotherm data. This information can be used in computer reconstruction of porous catalytic medium. In the reconstructed catalyst, transport (diffusion, permeation, heat conduction) and combined reaction-transport processes can be simulated on detailed level (Kosek et al., 2005). 

Xenon has been considered as the diffusing species in simulations of microporous frameworks other than faujasite (10-12, 21). Pickett et al. (10) considered the silicalite framework, the all-silica polymorph of ZSM-5. Once again, the framework was assumed to be rigid and a 6-12 Lennard-Jones potential was used to describe the interactions between Xe and zeolite oxygen atoms and interactions between Xe atoms. The potential parameters were slightly different from those used by Yashonath for migration of Xe in NaY zeolite (13). In total, 32 Xe atoms were distributed randomly over 8 unit cells of silicalite at the beginning of the simulations and calculations were made for a run time of 300 ps at temperatures from 77 to 450 K. At 298 K, the diffusion coefficient was calculated to be 1.86 X 10 9 m2/s. This... 

June et al. (12) used TST as an alternative method to investigate Xe diffusion in silicalite. Interactions between the zeolite oxygen atoms and the Xe atoms were modeled with a 6-12 Lennard-Jones function, with potential parameters similar to those used in previous MD simulations (11). Simulations were performed with both a rigid and a flexible zeolite lattice, and those that included flexibility of the zeolite framework employed a harmonic term to describe the motion of the zeolite atoms, with a force constant and bond length data taken from previous simulations (26). 

The assumption that Xe atoms at low loadings diffuse as monomers rather than dimers has been tested. Santikary et al. (75) found, on the basis of MD simulations of Xe in NaY zeolite, that approximately 15% of Xe atoms diffuse as dimers at a concentration of 1 Xe atom per supercage. From a plot of the RDF of the Xe atoms, June et al. (12) found that approximately 10% were dimerized. This is an important point, as Xe atoms diffusing as dimers rather than monomers present a very different potential energy hypersurface. (This surface was used to locate the position of the minima in the TST method.)... 

In principle it is possible to verify these findings experimentally. Diffusion measurements characterizing single-crystal samples, free from defects and grain boundaries, should be able to demonstrate that smaller guests do not always diffuse faster. However, there are a number of problems in trying to find suitable experimental results with which to corroborate the claim of the theoretical simulations. One of these problems is the rather ideal distribution of cations that is assumed in the simulations of zeolites A and... 

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