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The Influence of Surface Barriers on Diffusion of Alkane-Zeolite Systems - a Molecular Dynamics Study

Nils E. R. Zimmermann and Frerich J Keil. Department of Chemical Engineering, Hamburg University of Technology, Eissendorfer Str. 38, Hamburg, 21073, Germany

Zeolites represent a very important class of nanoporous materials that are frequently involved in industrial processes such as catalysis, separation, and ion-exchange. Therefore, the understanding and proper description of adsorption, diffusion, and reaction inside zeolite pores is crucial to process designing purposes. From a scientific point of view, zeolites represent ideal host materials for studying adsorption and confined diffusion of gases due to their regular, well-defined structure and vast variety in topology/pore-system architecture.

Although much effort has been made in order to understand the processes mentioned above, a lot of questions remain open to date. For example, consider diffusion in zeolites; why do diffusivities obtained from macroscopic, e.g. uptake measurements, and microscopic measurements (PFG-NMR) sometimes deviate tremendously? Is it because of non-idealities in the pore structures (holes, stacking failures), additional transport resistances at the gas-zeolite interface (so-called surface barriers), or because of the influence of extra-framework species that can either block pores or change adsorption/diffusion properties? There is thus a large list of possibilities that may affect those differences [1].

The present work addresses the problem of clarification of the discrepancies between uptake and microscopic measurements. For this purpose we investigate the role of surface barriers at the gas-zeolite interface for small alkanes by means of equilibrium molecular dynamics (EMD) simulations where a zeolite membrane is in contact with a bulk gas phase. By applying dynamically corrected Transition State Theory (dcTST) [2] we determine hopping rates and diffusion coefficients and, thus, transport resistances for the interface region and the bulk zeolite, respectively. The critical membrane length is then being determined as the length where the surface resistance is small compared to the intra-crystalline diffusion resistance. We concentrate on average loadings that correspond to maximum 30% of the adsorption isotherm because there is evidence that surface barriers are not important at high pressures/loadings [3].

Recently, Beerdsen et al. [2] investigated systematically the concentration dependence of diffusivities in bulk zeolites by using dcTST. It was shown that dcTST describes diffusion in alkane-zeolite systems accurately. Additionally, insights into the diffusion process are obtained by the change of free-energy profiles with loading. Gulin-Gonzalez et al. [4] showed that, when dynamical correction is not accounted for, TST surface resistances can exceed the true ones by a factor of 1.6 to 3.3. Not only is the dynamical correction quantitatively important; on the basis of the reactive flux data also pictorial insights into the dynamical behavior can be gained [5]. By plotting the whole swarm of trajectories (starting from the dividing surface) as a function of reaction coordinate and an additional order parameter at different times, the adsorption/desorption mechanism can be elucidated.

Zeolites are usually modeled as rigid lattices because of the huge computational expenses needed when the motion of the lattice atoms is taken into account. Recently, we showed that the rigid-lattice assumption seems to be a better description for bulk-zeolite simulations because appropriate/transferable framework potentials are still missing [6]. For zeolite systems with a surrounding gas phase, the kinetic energy exchange around the interface region is, however, a critical modeling issue [3]. In order to circumvent the expensive flexible-lattice simulations, we model the energy transfer with the aid of a thermostat. The use of a so-called global thermostat (e.g. Nose-Hoover chain) is hereby not appropriate, because the energy transfer occurs locally at the interface region. Therefore, we use a stochastic thermostat that acts locally, i.e. only on molecules that are in the vicinity of the interface. The thermostat thus mimics a flexible zeolite interface. The termination plane of the zeolite poses another critical modeling issue. It affects the extent of surface barrier influence, and, therefore, this influence was investigated systematically.


[1] J. Karger, D. M. Ruthven "Diffusion in Zeolites - and other microporous solids"; Wiley, New York; 1992.

[2] E. Beerdsen, D. Dubbeldam, B. Smit; J. Phys. Chem. B, 110, 22754-22772; 2006.

[3] D. A. Newsome, D. S. Sholl; J. Phys. Chem. B, 109, 7237-7244; 2005.

[4] J. Gulin-Gonzalez, A. Schuring, S. Fritzsche, J. Karger, S. Vasenkov; Chem. Phys. Lett., 430, 60-66; 2005.

[5] B. G. Peters, G. T. Beckham, N. E. R. Zimmermann, B. L. Trout, J. W. Tester, submitted in J. Am. Chem. Soc.

[6] N. E. R. Zimmermann, S. Jakobtorweihen, E. Beerdsen, B. Smit, F. J. Keil; J. Phys. Chem. C, 111, 17370-17381; 2007.