Efficient and Accurate Methods for Characterizing Effects of Framework Flexibility on Molecular Diffusion in Zeolites: CH₄ Diffusion in Eight Member Ring Zeolites

Abstract

Molecular dynamics (MD) and transition state theory (TST) methods are becoming efficient tools for predicting diffusion of molecules in nanoporous materials. The accuracy of predictions, however, often depends upon a major assumption that the framework of the material is rigid. This saves a considerable amount of computational time and is often the only method applicable to materials for which accurate force fields to model framework flexibility are not available. In this study, we systematically characterize the effect of framework flexibility on diffusion in four model zeolites (LTA, CHA, ERI, and BIK) that exhibit different patterns of window flexibility. We show that for molecules with kinetic diameters comparable to (or larger than) the size of the window the rigid framework approximation can produce order(s) of magnitude difference in diffusivities as compared to the simulations performed with a fully flexible framework. We also show that simple recipes to include the effect of framework flexibility are not generally accurate. To account for framework flexibility effects efficiently and reliably, we introduce two new methods in which the flexible structure is approximated as a set of discrete rigid snapshots obtained from simulations of dynamics of an empty framework, using either classical or, in principle, ab initio methods. In the first method, we perform MD simulations of diffusion in a usual manner but replace the rigid structure with a new random snapshot at a certain characteristic frequency corresponding to the breathing motion of the window, while keeping positions of adsorbate molecules constant. In the second method, we directly compute cage to cage hopping rates in each rigid snapshot using TST and average over a distribution of snapshots. Excellent agreement is obtained between diffusivities predicted with these two new methods and direct MD simulations using fully flexible structures. Both methods are orders of magnitude more efficient than the simulations with the fully flexible structure. The new methods are broadly applicable for fast and accurate predictions of both infinite dilution and finite loading diffusivities of simple molecules in zeolites and other nanoporous materials, generally without the need for an accurate flexible force field.

Complex Reaction Environments and Competing Reaction Mechanisms in Zeolite Catalysis: Insights from Advanced Molecular Dynamics

“…[67][68][69] These findings illustrate the complexity of accurately taking into account framework flexibility, [70] as anisotropic effects might be at play. …”

Shape-Selective Diffusion of Olefins in 8-Ring Solid Acid Microporous Zeolites

“…This explicit derivation of diffusivities has been extensively studied in literature, e.g. by Awati et al 33 , Krishna et al 34 , Smit and Maessen et al 26 , Garcia and Dubbeldam et al 35 , O'Malley et al 32 , Kiel et al [36][37][38][39] in various materials, for various hydrocarbons. For processes where diffusion barriers are too high, MD runs may be too slow to efficiently generate particle trajectories over the time-scale of the diffusion process.…”

“…Awati et al 33 investigated the ring diameter distribution in great detail, more specifically ring anharmonicity and ring shape (circular versus elliptical, framed 'dimensionality' in Ref. 33 ), and identified when diffusion through a flexible framework may be equally well modeled by diffusion through a rigid time-averaged framework. In an effort to maintain the efficiency of the rigid framework approximation while still including some degree of flexibility, they proposed to perform MD on a set of rigid snapshots, which were extracted from simulations of an empty framework.…”

“…They also studied the diffusion of methane in several 8-ring zeolites, and good agreement with a fully flexible structure was obtained. 33 For molecules that are smaller than the zeolite windows, framework deformation may cause flattening of the windows from a circular to a more elliptical shape ( Fig. 1), thus resulting in decreased diffusion.…”

Langevin and Fokker-Planck Analyses of Inhibited Molecular Passing Processes Controlling Transport and Reactivity in Nanoporous Materials

“…For hard-core interactions and a rigid pore, we find that P ∼ ðR − R c Þ σ , as R → R c , but with σ is below the TST value. This sharp transition would be smeared for flexible pores [23] and soft molecular interactions. For a deeper understanding of this behavior, we also analyze the equivalent high-dimensional Fokker-Planck (diffusion) equation (FPE) [22].…”