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Modelling sorption in zeoite NaA with molecular density functional theory
H.G. Karge and J. Weitkamp (Eds.) Zeolite Science 1994: Recent Progress and Discussions
227
Studies in Surface Science and Catalysis, Vol. 98 9 1995 Elsevier Science B.V. All fights reserved.
MODELLING SORPTION IN ZEOITE NaA WITH M O L E C U L A R DENSITY FUNCTIONAL THEORY Martha C. Mitchell. Paul R. Van Tassel, Alon V. McCormick, and H. Ted Davis Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455
SUMMARY We have used molecular theory and simulation techniques to help elucidate the fundamental physics of adsorption of xenon in zeolite NaA. We have used the simulations to guide development of an approximate density functional theory of this system. INTRODUCTION Fluids confined to pores of molecular dimensions cannot be treated by standard bulk fluid theories. With the introduction of powerful computers, simulations (both Monte Carlo and molecular dynamics) have provided insights into molecular-level events that are occuring in zeolitic systems. However, an area that has received less attention for adsorption in zeolites is that of basic theory. A natural theoretical tool for zeolitic systems, which are strongly inhomogeneous, is density functional theory. In the past molecular density functional theory has focused primarily on systems where there is a one-dimensional symmetry (spheres, cylinders, or planar slit pores). In this paper we apply density functional theory to model a pure fluid confined to zeolitic micropore. First, we discuss grand canonical Monte Carlo simulations of adsorption in zeolite NaA and then we show the results of applying three-dimensional molecular density functional theory to predict adsorption of xenon in NaA. EXPERIMENTAL SECTION Density functional theory is one method for predicting adsorption in threedimensional, confined fluid systems [Percus, 1988]. This approach can be less timeconsuming than experiments. The basic idea is to construct an expression for the free energy of the system. Different forms of density functional theory are distinguished by their treatment of repulsive interactions. Here we apply the Tarazona model of density functional theory [Tarazona and Evans, 1984] to predict adsorption of xenon in the alpha cage of NaA. The Tarazona model has been shown to work well for a pure fluid in a planar slit pore [Vanderlick et al., 1989]. Because of the importance of zeolite-sorbate interactions and the imprtance of the geometry of the zeolite structure in determining these interactions in the xenon/NaA system, we modeled the alpha cage of NaA as a fully three-dimensional system, instead of approximating the alpha cage as a sphere (which would have a one-dimensional symmetry).
228 RESULTS AND DISCUSSION We have used the discoveries of a Monte Carlo simulation study of adsorption of xenon in zeolite NaA to guide our development of a molecular density functional theory model, namely, the recognition of the twelve-site structure of adsorption in the alpha cage at low loadings. We have used this, along with a zeolite-sorbent interaction that is the same as that used for the Monte Carlo simulations, in the construction of a free energy expression for this system. We then minimized this free energy to determine the density distribution for xenon atoms. We have compared our results from the density functional theory model to the results from the simulations. REFERENCES Percus, J.K. (1988) Journal of Statistical Physics, 52, 1157-1178. Tarazona, P.; Evans, R. (1984) Molecular Physics, 52, 847-857. Vanderlick, T.K.; Scriven, L.E.; Davis, H.T. (1989) Journal of Chemical Physics, 90, 24222436.
227
Studies in Surface Science and Catalysis, Vol. 98 9 1995 Elsevier Science B.V. All fights reserved.
MODELLING SORPTION IN ZEOITE NaA WITH M O L E C U L A R DENSITY FUNCTIONAL THEORY Martha C. Mitchell. Paul R. Van Tassel, Alon V. McCormick, and H. Ted Davis Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455
SUMMARY We have used molecular theory and simulation techniques to help elucidate the fundamental physics of adsorption of xenon in zeolite NaA. We have used the simulations to guide development of an approximate density functional theory of this system. INTRODUCTION Fluids confined to pores of molecular dimensions cannot be treated by standard bulk fluid theories. With the introduction of powerful computers, simulations (both Monte Carlo and molecular dynamics) have provided insights into molecular-level events that are occuring in zeolitic systems. However, an area that has received less attention for adsorption in zeolites is that of basic theory. A natural theoretical tool for zeolitic systems, which are strongly inhomogeneous, is density functional theory. In the past molecular density functional theory has focused primarily on systems where there is a one-dimensional symmetry (spheres, cylinders, or planar slit pores). In this paper we apply density functional theory to model a pure fluid confined to zeolitic micropore. First, we discuss grand canonical Monte Carlo simulations of adsorption in zeolite NaA and then we show the results of applying three-dimensional molecular density functional theory to predict adsorption of xenon in NaA. EXPERIMENTAL SECTION Density functional theory is one method for predicting adsorption in threedimensional, confined fluid systems [Percus, 1988]. This approach can be less timeconsuming than experiments. The basic idea is to construct an expression for the free energy of the system. Different forms of density functional theory are distinguished by their treatment of repulsive interactions. Here we apply the Tarazona model of density functional theory [Tarazona and Evans, 1984] to predict adsorption of xenon in the alpha cage of NaA. The Tarazona model has been shown to work well for a pure fluid in a planar slit pore [Vanderlick et al., 1989]. Because of the importance of zeolite-sorbate interactions and the imprtance of the geometry of the zeolite structure in determining these interactions in the xenon/NaA system, we modeled the alpha cage of NaA as a fully three-dimensional system, instead of approximating the alpha cage as a sphere (which would have a one-dimensional symmetry).
228 RESULTS AND DISCUSSION We have used the discoveries of a Monte Carlo simulation study of adsorption of xenon in zeolite NaA to guide our development of a molecular density functional theory model, namely, the recognition of the twelve-site structure of adsorption in the alpha cage at low loadings. We have used this, along with a zeolite-sorbent interaction that is the same as that used for the Monte Carlo simulations, in the construction of a free energy expression for this system. We then minimized this free energy to determine the density distribution for xenon atoms. We have compared our results from the density functional theory model to the results from the simulations. REFERENCES Percus, J.K. (1988) Journal of Statistical Physics, 52, 1157-1178. Tarazona, P.; Evans, R. (1984) Molecular Physics, 52, 847-857. Vanderlick, T.K.; Scriven, L.E.; Davis, H.T. (1989) Journal of Chemical Physics, 90, 24222436.