Adsorption equilibrium of nitrogen dioxide in porous materials.

The effect of confinement on the equilibrium reactive system containing nitrogen dioxide and dinitrogen tetroxide is studied by molecular simulation and the reactive Monte Carlo (RxMC) approach. The bulk-phase reaction was successfully reproduced and five all-silica zeolites (i.e. FAU, FER, MFI, MOR, and TON) with different topologies were selected to study their adoption behavior. Dinitrogen tetroxide showed a stronger affinity than nitrogen dioxide in all the zeolites due to size effects, but exclusive adsorption sites in MOR allowed the adsorption of nitrogen dioxide with no competition at these sites. From the study of the adsorption isotherms and isobars of the reacting mixture, confinement enhanced the formation of dimers over the full range of pressure and temperature, finding the largest deviations from bulk fractions at low temperature and high pressure. The channel size and shape of the zeolite have a noticeable influence on the dinitrogen tetroxide formation, being more important in MFI, closely followed by TON and MOR, and finally FER and FAU. Preferential adsorption sites in MOR lead to an unusually strong selective adsorption towards nitrogen dioxide, demonstrating that the topological structure has a crucial influence on the composition of the mixture and must be carefully considered in systems containing nitrogen dioxide.

Computing the Heat of Adsorption using Molecular Simulations: The Effect of Strong Coulombic Interactions.

Molecular simulations are an important tool for the study of adsorption of hydrocarbons in nanoporous materials such as zeolites. The heat of adsorption is an important thermodynamic quantity that can be measured both in experiments and molecular simulations, and therefore it is often used to investigate the quality of a force field for a certain guest-host (g - h) system. In molecular simulations, the heat of adsorption in zeolites is often computed using either of the following methods: (1) using the Clausius-Clapeyron equation, which requires the partial derivative of the pressure with respect to temperature at constant loading, (2) using the energy difference between the host with and without a single guest molecule present, and (3) from energy/particle fluctuations in the grand-canonical ensemble. To calculate the heat of adsorption from experiments (besides direct calorimetry), only the first method is usually applicable. Although the computation of the heat of adsorption is straightforward for all-silica zeolites, severe difficulties arise when applying the conventional methods to systems with nonframework cations present. The reason for this is that these nonframework cations have very strong Coulombic interactions with the zeolite. We will present an alternative method based on biased interactions of guest molecules that suffers less from these difficulties. This method requires only a single simulation of the host structure. In addition, we will review some of the other important issues concerning the handling of these strong Coulombic interactions in simulating the adsorption of guest molecules. It turns out that the recently proposed Wolf method ( J. Chem. Phys. 1999, 110 , 8254 ) performs poorly for zeolites as a large cutoff radius is needed for convergence.

Influence of cation Na/Ca ratio on adsorption in LTA 5A: a systematic molecular simulation study of alkane chain length.

Recent adsorption isotherms of n-alkanes on Ca,Na-LTA-type zeolite afford development of a force field describing the interactions between calcium and n-alkanes in configurational-bias Monte Carlo simulations. The force field of Calero et al. (J. Am. Chem. Soc. 2004, 126, 11377-11386) is able to accurately describe the adsorption properties of linear alkanes in the sodium form of FAU-type zeolites. Here, we extend upon this type of force field by including calcium-type ions. The force field was fitted to reproduce the calcium and sodium cations positions on LTA 5A and the experimental adsorption properties of n-alkanes over all range of temperatures and pressures. This opens up a vast amount of experimental data on LTA 5A, both on adsorption and diffusion. Furthermore, evaluation of half a century of reported n-alkane adsorption data on LTA-type zeolites indicates that there are many inconsistencies between the various data sets, possibly as a result of (i) undisclosed calcium and sodium contents, (ii) less than perfect drying of the hygroscopic zeolite, and (iii) coadsorption of contaminants such as vacuum grease. Having obtained our force field, and confirmed its reliability on predictions outside the calibration set, we apply the force field on two "open" problems: (a) the heats of adsorption and Henry coefficient as a function of chain length and (b) the effect of cations in LTA-type zeolites. The molecular simulations shed new light on previous experimental findings, and we provide rationalizations on the molecular level that can be generalized to the class of cage/window-type nanoporous materials.

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.

A coarse-graining approach for the proton complex in protonated aluminosilicates.

We have developed a computational framework for the adsorption of linear alkanes in protonated aluminosilicates. These zeolites contain trace amounts of water that form hydrated proton complexes. The presence of hydrated protons makes the simulations at the fully atomistic level difficult. Instead of constructing an elaborate and complex model, we show that an approach based on a coarse-graining of the proton-complex accurately describes the available experimental isotherms, Henry coefficients, heats of adsorption, and oxygen-proton distances. Our approach is supported by MP2 quantum mechanical simulations. The model gives remarkably good agreement with experimental data beyond the initial calibration set.

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.

Incommensurate diffusion in confined systems.

Molecular simulations corroborate the existence of the disputed window effect, i.e., an increase in diffusion rate by orders of magnitude when the alkane chain length increases so that the shape of the alkane is no longer commensurate with that of a zeolite cage. This window effect is shown to be characteristic for molecular sieves with pore openings that approach the diameter of the adsorbate. Furthermore, the physical compatibility between the adsorbate and the adsorbent has a direct effect on the heat of adsorption, the Henry coefficients, the activation energy, and the frequency factors.

Coupling of thermal and mass diffusion in regular binary thermal lattice gases.

We have constructed a regular binary thermal lattice gas model in which the thermal diffusion and mass diffusion are coupled and form two nonpropagating diffusive modes. The power spectrum is shown to be similar in structure as for the one in real fluids, in which the central peak becomes a combination of coupled entropy and concentration contributions. Our theoretical findings for the power spectra are confirmed by computer simulations performed on this model.

Boltzmann approximation of transport properties in thermal lattice gases.

The transport properties of the Grosfils, Boon, and Lallemand model, a two-dimensional isotropic thermal lattice-gas, are evaluated in the Boltzmann approximation. This includes the (self)-diffusion, for which we have introduced an additional and passive color label to the otherwise identical particles in the system. Independently, those results are confirmed by the use of the decay of the velocity autocorrelation function. The theoretical predictions of the dynamical structure factors and results obtained by simulations show an excellent agreement up to fairly large wave vectors. In the hydrodynamic limit of small wave vectors, the Landau-Placzek formulas form an alternative and satisfactory description.