Loading dependence of the diffusion coefficient of methane in nanoporous materials.

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.

Diffusion in confinement: agreement between experiments better than expected.

The diffusion of alkanes in nanoporous materials as measured by different experimental techniques is thought to be highly dependent on the measuring technique employed. However, when the data are corrected for the loading at which the measurement was performed, the different data series correspond with each other much better than expected.

Understanding diffusion in nanoporous materials.

Can we predict diffusion behavior of molecules in confinement by looking at the match between the molecule and the structure of the confinement? This question has proven difficult to answer for many decades. As a case study, we use methane and a simple model of ellipsoids to arrive at a molecular picture that allows us to make a classification of pore topologies and to explain their diffusion behavior as a function of loading. Our model is surprisingly simple: regarding a structure as consisting of interconnected ellipsoids is enough to understand the full loading dependence.

Dynamically corrected transition state theory calculations of self-diffusion in anisotropic nanoporous materials.

We apply the dynamically corrected transition state theory to confinements with complex structures. This method is able to compute self-diffusion coefficients for adsorbate-adsorbent systems far beyond the time scales accessible to molecular dynamics. Two example cage/window-type confinements are examined: ethane in ERI- and CHA-type zeolites. In ERI-type zeolites, each hop in the z direction is preceded by a hop in xy direction and diffusion is anisotropic. The lattice for CHA-type zeolite is a rhombohedral Bravais lattice, and diffusion can be considered isotropic in practice. The anisotropic behavior of ERI-type cages reverses with loading, i.e., at low loading the diffusion in the z direction is two times faster than in the xy direction, while for higher loadings this changes to a z diffusivity that is more than two times slower. At low loading the diffusion is impeded by the eight-ring windows, i.e., the exits out of the cage to the next, but at higher loadings the barrier is formed by the center of the cages.

Molecular understanding of diffusion in confinement.

We introduce a computational method to directly relate diffusivities to the microscopic behavior of the adsorbed molecules. We apply this method to gases in an MFI-type molecular sieve, the reference system in this field. Transitions in the number and nature of adsorption sites result in temporary local increases in the diffusion. This occurs at different loadings in each of the x, y, and z directions, giving rise to the complex loading behavior found experimentally. Our method can be applied to any adsorbent-adsorbate system, and provides a fundamental understanding of diffusion in confinement on a molecular level.

Molecular path control in zeolite membranes.

We report molecular simulations of diffusion in confinement showing a phenomenon that we denote as molecular path control (MPC); depending on loading, molecules follow a preferred pathway. MPC raises the important question to which extent the loading may affect the molecular trajectories in nanoporous materials. Through MPC one is able to manually adjust the ratio of the diffusivities through different types of pores, and as an application one can direct the flow of diffusing particles in membranes forward or sideward by simply adjusting the pressure, without the need for mechanical parts like valves. We show that the key ingredient of MPC is the anisotropic nature of the nanoporous material that results in a complex interplay between different diffusion paths as a function of loading. These paths may be controlled by changing the loading, either through a change in pressure or temperature.

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

A dynamically corrected transition state theory method is presented that is capable of computing quantitatively the self-diffusivity of adsorbed molecules in confined systems at nonzero loading. This extension to traditional transition state theory is free of additional assumptions and yields a diffusivity identical to that obtained by conventional molecular-dynamics simulations. While molecular-dynamics calculations are limited to relatively fast diffusing molecules, our approach extends the range of accessible time scales significantly beyond currently available methods. We show results for methane, ethane, and propane in LTL- and LTA-type zeolites over a wide range of temperatures and loadings, and demonstrate the extensibility of the method to mixtures.

Force field parametrization through fitting on inflection points in isotherms.

We present a method to determine potential parameters in molecular simulations of confined systems through fitting on experimental isotherms with inflection points. The procedure uniquely determines the adsorbent-adsorbate interaction parameters and is very sensitive to the size parameter. The inflection points in the isotherms are often related to a subtle interplay between different adsorption sites. If a force field can predict this interplay, it also reproduces the remaining part of the isotherm correctly, i.e., the Henry coefficients and saturation loadings.

Molecular simulation of loading dependent slow diffusion in confined systems.

An extension to transition state theory is presented that is capable of computing quantitatively the diffusivity of adsorbed molecules in confined systems at nonzero loading. This extension to traditional transition state theory yields a diffusivity in excellent agreement with that obtained by conventional molecular dynamics simulations. While molecular dynamics calculations are limited to relatively fast diffusing molecules or small rigid molecules, our approach extends the range of accessible time scales significantly beyond currently available methods. It is applicable in any system containing free energy barriers and for any type of guest molecule.