Molecular diffusion in zeolites

In order to describe the adsorption and diffusion in the zeolites in the framework of a modified lattice-gas, which takes into account the crystalline structure of the zeolite, the interaction among adsorbed molecules and the possibility of a transition of adsorbed molecules among different adsorption sites in the same unit cell and different unit cells that follows the model description of molecular diffusion in zeolites were previously proposed [88,104],... 

Skoulidas AI, Sholl DS (2001) Direct tests of the darken approximation for molecular diffusion in zeolites using equilibrium molecular dynamics. J. Phys. Chem. B. 105 3151-3154... 

It has been demonstrated that the combined application of various NMR techniques for observing molecular rotations and migrations on different time scales can contribute to a deeper understanding of the elementary steps of molecular diffusion in zeolite catalysts. The NMR results (self-diffusion coefficients, anisotropic diffiisivities, jump lengths, and residence times) can be correlated with corresponding neutron scattering data and sorption kinetics as well as molecular dynamics calculations, thus giving a comprehensive picture of molecular motions in porous solids. 

Studying molecular diffusion in zeolite crystallites is complicated by the small size of the objects of investigation. Inevitable deviations of the real structure of a sample from the ideal one lead to an additional complication of the situation. It is not unexpected, therefore, that in spite of considerable progress in the experimental techniques, there is still some controversy in the imder-standing of intracrystalline zeohtic diffusion (cf. the preceding chapters of this volume). 

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. 

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... 

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)... 

It has already been mentioned that zeolites are shape selective with respect to molecular adsorption. This property relates to their micropores stmcture. The zeolite framework shows a limited flexibility, which is essential. For instance, Yashonath et al. have shown in their classical dynamic simulations study of molecular diffusion within zeolite micropore that the zeolite framework flexibility affects significantly diffusion when the molecules have a size comparable with the micropore size. To get an idea of the order of magnitude of this flexibility, one can consider the hybrid semi-empirical DFT periodic study of chabazite zeolite of Ugliengo et al. V They introduced in the unit cell of chabazite Br0nsted acidic sites which are known to induce an increase of the volume of around 10 This increase of the volume relates with the difference of volume between a Si04 tetraheron and a... 

To understand the principles of shape-selective adsorption and catalysis, a detailed knowledge of the microdynamics of the molecules inside the zeolitic pore system is required. Garcia and Weisz 4) pointed out the relevance of NMR methods to yield a unifying picture for the phenomena, mechanisms, and magnitudes of diffusivities. In the past few years, a deeper insight into molecular motions in zeolites has been achieved, especially by combining investigations of molecular translation with studies of reorientation processes on different time scales 5-14). 

VI. Structure-Related Molecular Self-Diffusion in Zeolites by Pulsed-Field Gradient NMR Influence of Pore Diameter, Si/AI Ratio, and Concentrations of Internal OH Groups and Cations ... 

In zeolites Na X and ZSM-5, the self-diffusion coefficients were found to decrease with increasing concentration while for zeolite NaCa A they are essentially constant The highest diffusivities were observed in zeolite Na X. This is in agreement with the fact that due to the internal pore structure the steric restrictions of molecular propagation in zeolite Na X are smaller Aan those in Na Ca A and ZSM-5 (94). Mass transfer and chemical reaction in zeolite channels in which the individual molecules cannot pass each other (single-file... 

Of all the porous solids, diffusion in zeolites has certainly been studied most extensively, in part because there seemed to be an enormous difference between macroscopic and microscopic diffusion constants (from MD and from NMR). It is not practical to discuss all this work here, but references to other such molecular dynamics simulations are given in the papers of [69]. 

Although Knudsen diffusion, shape selectivity, and molecular sieving play an important role in the separation of mixtures, the mechanisms which control the majority of the multicomponent separations in zeolite membranes are surface diffusion, and sometimes, capillary condensation. In addition, molecular simulations and modeling of M-S diffusion in zeolites [69,70] show that the slower moving molecules are also sped up in some mixtures [71,72] in the presence of fast-diffusing molecules and other times, slower molecules inhibit diffusion of faster molecules because molecules have difficulty passing one another in zeolite pores [73]. 

Snurr RQ and Karger J. Molecular simulations and NMR measurements of binary diffusion in zeolites. J Phys Chem B 1997 101 6469-6473. 

Quantum chemistry approaches to zeolites are complemented by an active research community that uses classical force-field methods to study molecular adsorption and diffusion in zeolites and similar materials. This topic was comprehensively reviewed by Keil, Krishna, and Coppens in 2000.262 For more recent examples of activity in this area, see References 263-270. Examples of impressive agreement between adsorption isotherms and molecular dilfusivities predicted with calculations of this type and experimental data are available.271,272 There appear to be many future opportunities for linking the detailed understanding of multi-component adsorption and diffusion that is now emerging from this area with detailed quantum chemistry approaches to reactivity at active sites inside zeolites. 

Diffusion in Zeolites by Molecular Dynamics Simulations , Mol. SimuL, 2000, 25, 27... 

On the other hand, our knowledge of configurational diffusion in zeolites is far from being adequate. While Fick s law on diffusion has been commonly used to obtain diffusion coefficients in zeolites, there is experimental data such as the window or cage effect observed in erionite which cannot be interpreted by such equations. Data on diffusion of high molecular weight molecules in zeolites are almost nonexistent. Discrepancies also remain unresolved between diffusion coefficients determined by NMR and uptake data (22-23). Needless to say, much remains to be investigated, Uoth in theory (24-25) and in experimental measurement (26). 

In Chapter 1, Fyfe, Mueller, and Kokotailo describe the applications of solid-state NMR to the study of zeolite molecular sieve catalysts and related systems. Zeolites provide an apt arena in which to demonstrate the capabilities of modern techniques such as sample spinning, cross-polarization, and multidimensional correlation spectroscopy. In Chapter 2, Karger, and Pfeifer consider the question of molecular diffusion in catalyst systems. Applications of NMR techniques such as imaging, lineshape analysis, relaxation, pulsed field gradient echo spectroscopy, and NMR tracer exchange are described and compared with other, more traditional techniques such as radioactive tracing. In Chapter 3, Haw discusses the use of NMR to probe catalytic processes, showing how the combination of temperature control with novel NMR probes makes it possible to elucidate reaction mechanisms in situ. 

Molecular modeling of multicomponent diffusion in zeolites and zeolite membranes... 

Molecular dynamics (MD) simulations have been used to simulate non-equilibrium binary diffusion in zeolites. Highly anisotropic diffusion in boggsite provides evidence in support of molecular traffic control. For mixtures in faujasite, Fickian, or transport, diffusivities have been obtained from equilibrium MD through appropriate correlation functions and used in macroscopic models to predict fluxes through zeolite membranes under co- and counterdiffusion conditions. For some systems, MD cannot access the relevant time scales for diffusion, and more appropriate simulation techniques are being developed. 

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