Loading Dependence of the Diffusion Coefficient of Methane in Nanoporous Materials

Abstract

In this work, we use molecular simulations to study the loading dependence of the self-and collective diffusion coefficients of methane in various zeolite structures. To arrive at a microscopic interpretation of the loading dependence, we interpret the diffusion behavior in terms of hopping rates over a free-energy barrier. These free-energy barriers are computed directly from a molecular simulation. We show that these free-energy profiles are a convenient starting point to explain a particular loading dependence of the diffusion coefficient. On the basis of these observations, we present a classification of zeolite structures for the diffusion of methane as a function of loading: three-dimensional cagelike structures, one-dimensional channels, and intersecting channels. Structures in each of these classes have their loading dependence of the free-energy profiles in common. An important conclusion of this work is that diffusion in nanoporous materials can never be described by one single effect so that we need to distinguish different loading regimes to describe the diffusion over the entire loading range.

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

“…An important observation made by Beerdsen et al 52 is that the appearance of the two local minima on top of the free-energy barrier at around 11 molecules per unit cell for methane causes an inflection at the corresponding loading in the diffusion curves. This inflection is similarly found in the adsorption isotherms, and both are related to a change in packing.…”

“…As such the dcTST method is able to explain different diffusion regimes over loading, and provides insight into the mechanisms behind an increase or decrease in diffusivity with loading. 52 …”

Molecular Simulations of Zeolites: Adsorption, Diffusion, and Shape Selectivity

“…That subsequently experimental data have been analyzed assuming this assumption to hold may have contributed to the large scatter in the experimental diffusion coefficients. 3,321 Clearly, these experiments may need to be reanalyzed. In this respect, it is important to mention that a permeation experiment on zeolitemembranesresultedinloadingdependent(Maxwell-Stefan) diffusion coefficients that are in excellent agreement with molecular dynamics simulations.…”

“…Chmelik et al 350 performed infrared microscopy experiments for diffusion of isobutane in MFI zeolite to show that the inflection in the Maxwell-Stefan diffusivity can be captured very well using KMC simulations and is in agreement with simulations that were published earlier. 306 Beerdsen et al 3 show that changes in the adsorption at the molecular level can have a large effect on the loading dependence of the diffusion coefficient. Some of these changes in the adsorption behavior can also induce inflections in the adsorption isotherm, which gives a molecular explanation of the correlation found by Krishna and coworkers between inflections in the adsorption isotherms and changes in the loading dependence of the collective or Maxwell-Sefan diffusion coefficient.…”

Diffusion in tight confinement: A lattice-gas cellular automaton approach. II. Transport properties

“…In order to provide the aforementioned balance which gives a D s trend of type III, one has to refine on the model in such a way to allow the introduction of an explicit dependence of the energy parameters on some local observables ͑e.g., the occupancy n͒, and then model this dependence to obtain the requested balance. On the other hand, this choice is reasonable since in real systems it is not uncommon for the energy of adsorption sites to be dependent on whether the neighboring sites are occupied, 20 and in principle this situation can be reproduced introducing occupancy-dependent adsorption energies, treated as adjustable parameters or obtained by means of a coarse graining of the interactions in a cell with a detailed arrangement of the adsorption sites.…”