Zeolite diffusion, simulations molecular dynamics

Molecular-dynamic simulations are characterized by a solution of Newton s laws of motion for the molecules travelling through the zeolite pore system under control of the force field given by the properties of the host lattice, by interactions between the host and the molecules, and by interactions between the molecules. To date this has been possible only for the diffusion of simple molecules (e.g. methane or benzene) inside a zeolite lattice of limited dimensions [29, 37, 54], To take into account the effects of a chemical reaction as well would require quantum-mechanical considerations however, such simulations are in their infancy. 

Abstract The chemical activation of light alkanes by acidic zeolites was studied by a combined Classical Mechanics/Quantum Mechanics approach. The diffusion and adsorption steps were investigated by Molecular Mechanics, Molecular Dynamics and Monte Carlo simulations. The chemical reactions step was studied at the DPT (B3LYP) level with 6-31IG basis sets and 3T and 5T clusters to represent the acid site ofthe zeolite. 

In principle, the diffusion steps (a) and (e) could be studied through molecular dynamics simulations as long as rehable forces fields are available to describe the zeolite structure and its interaction with the substrates. Also, if the adsorption takes place without charge transfer between the reagents/products and the zeolite, steps (b) and (d) could also be investigated either by molecular dynamics or Monte Carlo simulations. Step (c) however can only be followed by quantum mechanical techniques because the available force fields cannot yet describe the breaking and formation of chemical bonds. 

The diffusion step was investigated by molecular dynamics (MD) simulations. For the adsorption step, molecular mechanics (MM), molecular dynamics (MD) and Monte Carlo (MC) techniques were used, under the same simulation conditions, in order to compare their performance. The influence of the force-field, the loading of alkane molecules and the relaxation of the zeolite framework on the adsorption energies were also investigated. For the chemical reaction... 

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]. 

P. Santikary and S. Yashonath, Molecular Dynamics Investigation of Sorption of Argon in NaCaA Zeolite, J. Chem. Soc. Faraday Trans. 88 (1992) 1063-1066 C. Fritzsche, R. Haberlandt, J. Kaerger, H. Pfeifer and K. Heinsinger, A MD Simulation on the Applicability of the Diffusion Equation for Molecules Adsorbed in a Zeolite, Chem. Phys. Lett. 198 (1992) 283-287. 

Paschek D and Krishna R. Diffusion of binary mixtures in zeolites Kinetic Monte Carlo versus molecular dynamics simulations. 

R. C. Runnebaum and E. J. Maginn, /. Phys. Chem. B, 101, 6394 (1997). Molecular Dynamics Simulations of Alkanes in the Zeolite Silicalite Evidence for Resonant Diffusion Effects. 

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. 

Molecular models can considerably impact the chemical process industry. Obviously, numerous problems fall beyond the realm of conventional molecular simulation (see the example above on zeolitic membranes). Examples include dynamics of protein folding, diffusion through microporous membranes and human cells, formation of quantum dots in heteroepitaxial growth of semiconductors, and pattern formation on catalyst surfaces. 

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

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. 

The derivation of Dt from coherent QENS is similar to a computation of Dt from the fluctuations in an equilibrium density distribution. This was accomplished by Tepper and co-workers for Ar in AIPO4-5 [6]. Using the Green-Kubo formahsm, they were able to extract this non-equilibrium quantity from just one equihbrium simulation. Moreover, the calculations being performed in reciprocal space, the variation of the diffusivity upon the wave vector was used to check when the system was in the linear regime [6]. The first application of non-equihbrium molecular dynamics (NEMD) to zeolites was performed by Maginn et al. on methane in sihcalite [7]. Standard equi-libriiun MD techniques were later used by Sholl and co-workers to determine the concentration dependence of diffusivities [8]. 

In recent molecular dynamics (MD) studies of propane in Na-Y zeolite, the HWHM obtained from the simulations have been compared with jump diffusion models and with the experiment [19]. Figure 4 shows fits of different models to the MD data, at three temperatures. The error bars on the MD points is too large to select the best model. However, the oscillatory behavior expected for the CE model does not seem to be present either in the MD data or in the experimental QENS broadenings (Fig. 5). 

Molecular dynamics calculations have also been carried out on a zeolite A system using the above force field. Simulations were carried out over a range of temperatures using a 12 ion model, and a full cell which contains 96 ions. It was shown that even at room temperature there is not much motion of the ions they tend to oscillate about their original positions. When the temperature was raised to 600K a marked difference was noted, and it was found that over a time scale of ca. 2ps there is a bulk movement of ions which occupy the sites in the 8-rings, in a concerted transportation process, This is found to repeat every Bps and shows evidence that bulk diffusion of ions through the structure may take place. 

Krishna R., Diffusion of Binary Mixtures in Zeolites Molecular Dynamics Simulations versus Maxwell-Stefan Theory. Chem. Phys. Lt. 326 (2000) pp ATI-AM... 

L. Leherte, J.-M. Andre, D. P. Vercauteren, and E. G. Derouane, /. Mol, Catal., 54, 426 (1989). Effects of Long-Range Interactions in Zeolite-like Systems Interaction Energies and Self-Diffusion Coefficient of Water in Ferrierite from Molecular Dynamics Simulation. 

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. 

Molecular dynamics can then be used to simulate the molecular trajectories for molecules in zeolites, the diffusivities for sorbates in zeolites, temporal changes in the pore structure due to changes in system variables (T, P) or sorption of moleculesl . As was described earlier, the integration time steps (10 sec) limit the timescales that can actually be simulated to nanosecond behavior and thus preclude the simulation of longer time processes. 

Jobic H, Theodorou DN (2007) Quasi-elastic neutron scattering and molecular dynamics simulation as complementary techniques for studying diffusion in zeolites. Microporous Mesoporous Mater 102(l-3) 21-50... 

Leroy, F., and Rousseau, B. 2004. Self-diffusion of n-alkanes in MFl type zeolite using molecular dynamics simulations with an anisotropic united atom (AUA) forcefield Mol. Simul. Vol. 30 pp 617-620. 

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

Molecular Dynamics simulation of the diffusion of /rparaffins In the Silicalite (a zeolite). A zig-zag pores B straight pores. From Runnebaum and Maginn [1997]. 

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