Diffusion of Aromatic Molecules in Zeolite NaY. 1. Constrained Reaction Coordinate Dynamics

Diffusion in channeled structures. III. Quantum corrections induced by lattice vibrations

For large energy barrier systems the lattice vibrations can play an important role in the diffusion of a guest component inside channeled structures. Here, quantum corrections to the guest diffusion are studied within a semiclassical framework in which the guest behaves classically and the lattice quantum mechanically. The permeability is expressed in terms of correlation functions that are calculated using path integrals. Forward-backward path integrals for propagators are combined, and, using the Martin-Siggia-Rose formalism [Phys. Rev. A. 8, 423 (1973)], are transformed into a set of generalized Langevin equations that reduce to the classical equation of motion at high temperatures. The random initial conditions to these equations are specified by the density matrix from which an approximate expression for the quantum mechanical potential of mean force is derived. The quantum potential of mean force and activation energy obtained for the guest inside the lattice is slightly higher than the one for the fully classical system, and the diffusion of the guest in the quantum lattice is slower compared to its fully classical counterpart. The macroscopic intrinsic permeability of alpha -quartz towards neon is reported, P'qtm(300K)=9.91x10(8) s/(mkg) within the semiclassical approximation and is lower than P'class (300K)=1.26x10(9) s/(mkg) obtained in the classical case at 300K for the same potential model.

Molecular simulation of loading-dependent diffusion in nanoporous materials using extended dynamically corrected transition state theory

A dynamically corrected transition state theory method is presented that is capable of computing quantitatively the self-diffusivity of adsorbed molecules in confined systems at nonzero loading. This extension to traditional transition state theory is free of additional assumptions and yields a diffusivity identical to that obtained by conventional molecular-dynamics simulations. While molecular-dynamics calculations are limited to relatively fast diffusing molecules, our approach extends the range of accessible time scales significantly beyond currently available methods. We show results for methane, ethane, and propane in LTL- and LTA-type zeolites over a wide range of temperatures and loadings, and demonstrate the extensibility of the method to mixtures.

Diffusion in Channeled Structures. II. Systems with Large Energy Barriers

The methods developed in a previous paper (Phys. Rev. E.: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2003, 68, 046127) are used to calculate the permeability of argon in alpha-quartz, a system containing large energy barriers. The permeability is reported at three different temperatures and follows Arrhenius behavior. The permeabilities obtained from a hopping model combined with transition state theory closely follow our predicted values but are systematically lower. Lattice flexibility cannot be neglected in this system, and the energy-transfer between alpha-quartz and the argon atom through lattice vibrations occurs on a fast enough time scale such that it plays a role in the guest diffusive motion.

Diffusion in channeled structures: xenon in a crystalline sodalite

The theory of Ronis and Vertenstein [J. Chem. Phys. 85, 1628 (1986)] is used to calculate the permeability of xenon in Theta-1, a crystalline sodalite containing one-dimensional channels. The required time-correlation functions are obtained from numerical simulations performed using a small number of target crystal atoms. The dynamics of the target atoms reproduce those of the full crystal by the means of a generalized Langevin equation of motion. An approximate expression for the potential of mean force inside the crystal is derived. The plane average space-dependent diffusion coefficient D(z) obeys the Smoluchowski prediction at infinite dilution. The permeability is reported and compared in detail with that obtained from transition state theory.