Diffusion in zeolites

As noted in the previous section, in practical zeolite catalysis, diffusion controls the selectivity and activity for many reactions. When the zeolite micropore channel or cavity is significantly larger than the molecular dimensions, diffusion is of the Knudsen type. This implies that it scales with as illustrated in Fig. 4.40. 

Molecular dynamics simulation can be applied in such cases, since the activation energy for diffusion is low and hence simulations over a period of a few picoseconds are adequate. When the dimensions of the zeolite micropore decrease, the molecular residence near the surface increases and now diffusion becomes dominated by its motion along the zeolite wall. Micropore diffusion becomes fast compared with Knudsen-type diffusion when the dimensonal matches are such that the diffusing molecule will not leave the surface potential minimum regime except when desorbing from the micropore out of the zeolite. Typical surface-potential dominated diffusion (creeping motion) is illustrated in Fig. 4.41. 

In contrast to the behavior in a wide-pore zeolite such as faujasite, one observes in Fig. 4.41 that, in the one-dimensional mordenite micropores with a diameter of 6.5 A, the rate of diffusion is independent of the length of the hydrocarbon. 

Diffusional constants may depend strongly on micropore filling. This, in essence, is due to site blocking effects. It explains the often observed relationship between overall experimentally measured diffusional rate constant activation energies and heats of adsorption. 

In zeolites, diffusion constants will depend strongly on molecular shape. For example, in silicalite branched alkanes prefer to absorb in channel cross-sections, but linear alkanes prefer adsorption in the channels themselves. This has important consequences for differences in diffusion rates within mixtures. At high concentration, the rate of the diffusion of the branched alkane will control the rate of diffusion of the other alkanesl l 

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Karge and Rutbveu, Diffusion in Zeolites and Qthei Miciopoious Solids, Wiley, New York, 1992. 

Numerical values for solid diffusivities D,j in adsorbents are sparse and disperse. Moreover, they may be strongly dependent on the adsorbed phase concentration of solute. Hence, locally conducted experiments and interpretation must be used to a great extent. Summaries of available data for surface diffusivities in activated carbon and other adsorbent materials and for micropore diffusivities in zeolites are given in Ruthven, Yang, Suzuki, and Karger and Ruthven (gen. refs.). 

The effect of temperature on diffusivities in zeolite ciystals can be expressed in terms of the Eyring equation (see Ruthven, gen. refs.). 

J. Karger, D. M. Ruthven 1992, Diffusion in Zeolites, Wiley Sons, Chichester, 500 pp. Contains some NMR experiments, but mostly other techniques. 

D. M. Ruthven, M. F. M. Post 2001, (Diffusion in zeolite molecular sieves), in Introduction to Zeolite Science and Practice, eds. H. van Bekkum, E. M. Fla-nigen, J.C. Jansen, Elsevier, Amsterdam. 

Diffusion in zeolites), in Handbook of Zeolite Science and Technology, eds. S. M. Auerbach, K. A. Carrado, P. K. Dutta, Marcel Dekker, New York, Basel. 

Karger and Ruthven, Diffusion in Zeolites and Other Microporous Solids,... 

Force field, diffusion in zeolites, 42 6 Forcing transform, pulsed-field gradient NMR, 39 392-394 Formaldehyde... 

MO LCAO methods, 34 136 Molecular-beam surface scattering, 26 26, 27 Molecular Cage, 34 226 Molecular design in cyclodextrin, 32 427 Molecular dynamics diffusion in zeolites, 42 2, 4-6 argon, 42 20... 

Karger, J. and Ruthven, D.M. (1992) Diffusion in Zeolites and Other Micropo-rous Solids, )ohn Wiley Sons, New York. 

Karger, J. and Vasenkov, S. (2005) Quanbtabon of diffusion in zeolite catalysts. Micropor. Mesopor. Mater., 85, 195-206. 

Jobic, H. and Methivier, A. (2005) Intracrystalline diffusion in zeolites studied by neutron scattering techniques. Oil Gas Sci. Technol., 60 (5) 815-830. 

Figure 13.14 was published as Figure 11 from the article Intracrystalline Diffusion in Zeolites Studied by Neutron Scattering Techniques by H. Jobic and A. Methivier, Oil and Gas Science and Technology - Rev. IFP, Vol. 50 (2005),... 

Figure 13.15 was published in Studies in Surface Science and Catalysis, 137, Ruthven, D.M., Post, M.F.M., Diffusion in zeolite molecular sieves, p. 525-577, Copyright Elsevier (2001)... 

This expose complements recently published comprehensive reviews [4,5,11] which relate to diffusion in zeolites.In comparison with the state of the art about ten years ago [1], significant progress has been achieved which was stimulated especially by discovering, and then covering the gap between the... 

The sequence of IR spectra demonstrates that the molecules of the preloaded component A (pyridine, benzene) are displaced by the ingoing component B (benzene, ethylbenzene) when the preloaded sample is contacted with the vapour phase of the second compound. The process is slow because in both cases component A is more strongly held by the sorbent than component B (vide infra). But these experiments showed, that in principle, it should be possible to monitor counter-diffusion in zeolites via the IR method. 

Some additional complexity arises from the possibility of different adsorption sites and the presence of pores, which reflect in nonideal adsorption isotherms and mass-transfer problems. The mass transport can be relatively slow in pores and interparticle spaces [13], as it is the case of P25, for which, in suspension, there are particles ranging from 0.2 to 2 p,m, formed by 30-nrn-sizcd primary particles. In such spaces, the diffusion coefficient is comparable to liquid diffusion in zeolites. 

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 (/) ... 

Fig. 2. Energy profile as a function of position for the surface-mediated and centralized modes of Xe diffusion in zeolite Y. The upper curve refers to the centralized mode of diffusion, and the lower curve to the surface-mediated mode of diffusion. Reprinted with permission from Ref. 18. Copyright 1993 American Chemical Society.

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. 

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