## A Simulation Study of Diffusion in Microporous Materials

- Author(s): Abouelnasr, Mahmoud Kamal Forrest
- Advisor(s): Smit, Berend
- et al.

## Abstract

The goal of this work is to develop molecular simulation techniques to characterize the diffusion properties of crystalline microporous materials for separation applications. The conventional simulation type used to study the diffusion behavior of adsorbates in a microporous material is Molecular Dynamics. However, for slowly diffusing systems, these simulations become intractably long. In such situations, the diffusion process can be considered as a series of rare cage-to-cage hops, with the majority of the time (and computational effort) spent on unimportant movements within a cage. Recent work in the field has focused on the application of transition state theory (TST) to this process, allowing an estimation of the diffusion properties with a Monte Carlo simulation. In some cases, for example the diffusion of methane in zeolite LTA at low loading, TST gives a good approximation of the true (MD) diffusion. For the general case, the TST result requires a correction factor, which is calculated with a Bennett-Chandler simulation. The correction factor is the conditional probability the system will undergo a transition given that it is at the transition state; this correction factor is influenced by the number of particles in each cage. For the system of methane in zeolite LTA, there are between zero and fifteen particles in either cage at any time, meaning that 120 different correction factors must be calculated. We developed a mixing rule that relates the correction factor between two cages of unequal loading (a and b) to the correction factors between two cages of equal loading (a and a; b and b). This reduced by an order of magnitude the number of Bennett-Chandler simulations required, from 120 to 16.

Next, we investigated a fundamental change in the packing of methane adsorbed in zeolite LTA that occurs at high loadings, where a sub-lattice develops within each supercage leading to increased blocking a divergence between the self- and collective-diffusion coefficients. This qualitative change was replicated in a model kMC system that accounted for this topological shift.

As particles move within a cage, their speed fluctuates until at one moment, they happen to be travelling quickly enough to hop out of their potential energy well and through the window. As they fall into the potential energy well of the next cage, they speed up for some time until they re-equilibrate. During this time, they are more likely to hop again. Hopping is no longer a Markovian process, without memory of past events. This has a tremendous impact the diffusion behavior. This behavior was observed for methane adsorbed in zeolites ASV, LTA, and CGS, where various different departures from an expected random walk of Poisson-distributed hops were investigated. Because of the immense number of frameworks available for study, we developed a high-throughput computational screening method, applying TST to a vast database of >80,000 hypothetical zeolite structures in order to asses their suitability for carbon capture. From this large set of structures, several materials were identified with higher predicted performance for carbon capture by a factor of four or more. These high-performing structures were observed to exhibit certain structural similarities. The materials in this large database did not exhibit a Robseon upper bound.