Fabien Jousse

Activated diffusion of benzene in NaY zeolite: Rate constants from transition state theory with dynamical corrections

We calculated transition state theory and exact rate coefficients for benzene jumps in Na-Y zeolite between 150 and 500 K. This is the first exact flux correlation function rate calculation for a non-spherical molecule inside a zeolite. We calculated rates for jumps between SII and W sites, located near Na ions in 6-rings and in 12-rings windows, respectively. Partition function ratios were calculated using Voter’s displacement vector method. A general Arrhenius behavior is observed over the whole temperature range for all processes. The activation energies are close to the difference between the minimum energies in the sites, and between the sites and the transition states. The calculated prefactors present reasonable values around 1012–1013 s−1, in good agreement with nuclear magnetic resonance relaxation experiments. We were not able to decompose the prefactors into simple vibrational and entropic components, and therefore a complete calculation of the rate constant seems necessary to obtain reliable v...

Modeling the concentration dependence of diffusion in zeolites. III. Testing mean field theory for benzene in Na–Y with simulation

We have performed kinetic Monte Carlo (KMC) simulations of benzene tracer diffusion in Na–Y for various loadings and temperatures to test the analytical diffusion theory presented in Paper I of this series. Our theory and simulations assume that benzene molecules jump among SII and W sites, located near Na+ ions in 6-rings and in 12-ring windows, respectively. Our diffusion theory is based on a mean field approximation (MFA) which yields Dθ=16kθaθ2, where aθ≅11 A is the mean intercage jump length and 1/kθ is the mean supercage residence time. KMC simulations of D(θ), kθ, and aθ at 300 and 400 K show that our MFA is essentially exact for loadings that allow SII site vacancies, and that the concentration dependence is controlled by kθ. For higher loadings, the MFA error is independent of temperature, and increases roughly linearly with loading to a maximum value of ca. 25%, resulting from correlated motion. We present an analytical theory for such correlated motion at infinite vacancy dilution, which predic...

Correlation effects in molecular diffusion in zeolites at infinite dilution

Molecular diffusion in zeolites is often resumed to a random walk between specific adsorption sites within the channels and cavities of the materials. Several types of correlations between the steps of the walk come to precise this assumption: kinetic correlations due to the incomplete relaxation of the molecule in its final site, vacancy correlations arising at high loading because molecules are blocking each other, and geometrical correlations because zeolite channels and cages can boast nonsymmetric sites. The first and last correlation effects can be observed at infinite dilution. In this article we present a way of calculating an exact diffusion coefficient at infinite dilution as a function of the microscopic rate constants, taking into account both geometric and kinetic correlation effects. This is achieved by cutting the molecular motion into uncorrelated sequences of jumps, where all jumps inside one sequence are correlated to each other. This method is applied to study geometrical correlations o...

Dynamics of sorbed molecules in zeolites

Publisher Summary This chapter discusses the assumptions underlying modern atomistic and lattice approaches, and details the techniques and applications of modeling both rapid dynamics and activated diffusion. Practical applications of zeolites are typically run under steady-state conditions, making the relevant transport coefficient the Fickian diffusivity or other related permeability coefficient. However, modeling such steady-state transport through zeolites with atomistic models is challenging, prompting many researchers to simulate self-diffusion, which is the stochastic motion of tagged particles at equilibrium. The wide range of diffusional timescales encountered by molecules in zeolites presents unique challenges to the modeler, requiring that various simulation tools, each with its own range of applicability, be brought to bear on modeling dynamics in zeolites. The goals of simulating molecular dynamics in zeolites with atomistic detail are two-fold: to predict the transport coefficients of adsorbed molecules and to elucidate the mechanisms of intracrystalline diffusion. The chapter summarizes the major findings discovered over the last several years and enumerates future needs for the frontier of modeling dynamics in zeolites. With a rich variety of interesting properties and industrial applications, and with over 100 zeolite framework topologies synthetically available, each with its own range of compositions, zeolites offer size, shape, and electrostatically selective adsorption, diffusion, and reaction up to remarkably high temperatures.

Molecular Mechanical Investigation of the Energetics of Butene Sorbed in H-Ferrierite

Abstract The energetics and diffusion of the four butene isomers in a model of protonated ferrierite with Si/Al ratio of 8 is investigated using molecular mechanics, molecular dynamics, and a simple activated jump diffusion model, in order to determine the influence of the diffusion of the sorbent molecules onto the selectivity of ferrierite toward isobutene. Two main classes of adsorption sites are found, in the main 10-T channels and in cavities along 8-T channels. The magnitude of the self-diffusion coefficient mainly depends on the motions of the molecules in the 10-T channels, and it is found that isobutene diffuses more slowly than the linear isomers: at 623 K, D (isobutene) < 0.03 × 10−4 cm2/s, while D (trans-2-butene)  0.42 × 10−4 cm2/s. However, the sites in the 8-T cavities act as molecular traps for linear butenes and slow down their diffusion, while they do not influence the self-diffusion of isobutene. Therefore, the diffusion of isobutene is enhanced relative to the other isomers in ferrier...

Energetics and diffusion of butene isomers in channel zeolites from molecular dynamics simulations

We have investigated the minimum energy positions and the short time self-diffusion of butene isomers in 6 zeolite structures: TON, MTT, MEL, MFI, FER, and HEU. The minimum energy positions, and the corresponding interaction energies, reflect essentially the steric interaction between the guest molecule and the host zeolite walls. It is shown that in all structures except zeolite TON, trans-2-butene diffuses faster than the other isomers, while in all cases except for TON and MTT, the diffusion of isobutene could not be followed during a 200 ps molecular dynamics run. In zeolite TON the ratio of isobutene versus linear butene self-diffusion is larger than in the other zeolites, which indicates that in this particular structure, diffusion is probably not the rate-limiting process to butene isomerization.

Theoretical estimation of the vibrational perturbation of the molecular properties of hydrogen adsorbed within a zeolite A framework

Abstract An iterative numerical procedure is proposed to evaluate the variation of the dependence versus the internuclear distance of several molecular properties (polarizabilities, multipole moments) of hydrogen adsorbed within zeolite A. Dealing with a method which includes only the vibrational perturbation, it is shown that the dependence on internuclear distance of the properties of H2 does not change upon adsorption in NaA as compared to the gas.