Free volume theory of self-diffusion in zeolites: Molecular simulation and experiment

Neutron scattering and molecular dynamics are used to unravel the microscopic mechanisms that govern methane diffusion in MFI zeolite (silicalite-1). First, using neutron scattering for silicalite-1 loaded with different methane amounts, we analyze the experimental dynamic structure factor $S(q,\omega )$ in terms of molecular rotations and translations. While the rotational diffusion is found to be nearly independent of the zeolite loading, the translational diffusivity drastically decreases with the adsorbed amount. To gain insights into the diffusion mechanisms, trajectories obtained using molecular dynamics simulations are analyzed by determining mean square displacements $〈\Delta r^2\left(t\right)〉$ and incoherent scattering functions $F(q,t)$. We also determine how anisotropy affects diffusion by considering independently the $x$, $y$ and $z$ directions. While the activation energy for diffusion is found to be weakly dependent on methane loading, the self-diffusivity decreases as the loading increases. Both the experimental and molecular simulation results suggest that steric repulsion between confined molecules – which increases as the loading increases – drastically affects diffusion. Using a free volume theory, we provide a simple formalism to predict consistently diffusion in the internal porous network of MFI zeolite. To demonstrate the applicability of this simple yet robust framework, we show that the free volume theory accurately captures diffusion in each direction of space but also when the size of the adsorbate molecule is arbitrarily increased.