Sorbate-Loading Dependence of Diffusion Mechanism in a Cubic Symmetry Zeolite of Type ZK4. A Molecular Dynamics Study

Nonuniformity of Transport Coefficients in Ultrathin Nanoscale Membranes and Nanomaterials

The quest to reduce transport resistance in separations using nanomaterials has led to considerable interest in nanoscale adsorbents and ultrathin membranes. It is now established that interfacial resistance limits the performance of such nanosized materials; however, the origin of this resistance is uncertain. While it is associated with surface pore blockages and distortions in some materials, its existence even in ideal materials is largely putative. Here, we report equilibrium molecular dynamics (EMD) simulations with ideal zeolite-based nanosheets, indicating the transport resistance to be entirely distributed within the solid, without contribution from an interfacial effect. We demonstrate the presence of an internal entry region over which fluid decorrelation occurs, and in which the local transport coefficient inside the crystal is nonuniform and position-dependent, increasing to the uniform value in the bulk material at larger distances. Our EMD-based diffusivity profiles within the nanomaterial enable us to unequivocally determine the entry length, and reveal an internal excess resistance, frequently assumed to be an interfacial resistance, due to significant reduction of the internal transport coefficient in the entrance and exit regions. A decrease in the entry length with loading in PON zeolite nanosheets is seen. We demonstrate a reduction in external resistance in the external bulk chambers used in simulations, triggered by the interplay of incomplete decorrelation in the nanosheet and periodic boundary conditions imposed on the system comprising the nanosheet and surrounding bulk reservoirs when the nanosheet thickness is less than the entry length. Our analysis of the transport dynamics within the nanosheet demonstrates that, at least for ideal systems, decomposition of the inhomogeneous diffusivity-based internal resistance into an interfacial and a uniform transport coefficient-based internal contribution is not appropriate for finite-sized systems. Our results will enable the improved design of nanoscale membranes and materials for applications in separation and other processes.

Scaling-Up Simulations of Diffusion in Microporous Materials

We introduce and demonstrate the coarse-graining of static and dynamical properties of host-guest systems constituted by methane in two different microporous materials. The reference systems are mapped to occupancy-based pore-scale lattice models. Each coarse-grained model is equipped with an appropriate coarse-grained potential and a local dynamical operator, which represents the probability of interpore molecular jumps between different cages. Coarse-grained thermodynamics and dynamics are both defined based on small-scale atomistic simulations of the reference systems. We considered two host materials: the widely studied ITQ-29 zeolite and the LTA-zeolite-templated carbon, which was recently theorized. Our method allows for representing with satisfactory accuracy and a considerably reduced computational effort the reference systems while providing new interesting physical insights in terms of static and diffusive properties.

Local free energies for the coarse-graining of adsorption phenomena: The interacting pair approximation

We investigate the coarse-graining of host-guest systems under the perspective of the local distribution of pore occupancies, along with the physical meaning and actual computability of the coarse-interaction terms. We show that the widely accepted approach, in which the contributions to the free energy given by the molecules located in two neighboring pores are estimated through Monte Carlo simulations where the two pores are kept separated from the rest of the system, leads to inaccurate results at high sorbate densities. In the coarse-graining strategy that we propose, which is based on the Bethe-Peierls approximation, density-independent interaction terms are instead computed according to local effective potentials that take into account the correlations between the pore pair and its surroundings by means of mean-field correction terms without the need for simulating the pore pair separately. Use of the interaction parameters obtained this way allows the coarse-grained system to reproduce more closely the equilibrium properties of the original one. Results are shown for lattice-gases where the local free energy can be computed exactly and for a system of Lennard-Jones particles under the effect of a static confining field.

A coarse-grained method based on the analysis of short molecular dynamics trajectories for the simulation of non-Markovian dynamics of molecules adsorbed in microporous materials

We developed a coarse-grained model suitable for the study of adsorbed molecules in microporous materials. A partition of the space available to the motion of adsorbed molecules was carried out, which allows to formulate the dynamics in terms of jumps between discrete regions. The probabilities of observing given pairs of successive jumps were calculated from Molecular Dynamics (MD) simulations, performed on small systems, and used to drive the motion of molecules in a lattice-gas model. Dynamics is thus reformulated in terms of event-space dynamics and this allows to treat the system despite its inherent non markovity. Despite the assumptions enforced in the algorithm, results show that it can be applied to various spherical molecules adsorbed in the all-silica zeolite ITQ-29, establishing a suitable direct bridge between MD simulation results and coarse-grained models.

Diffusion in tight confinement: A lattice-gas cellular automaton approach. II. Transport properties

In this second paper the authors study the transport properties of the lattice-gas cellular automaton presented in Paper I [J. Chem. Phys. 126, 194709 (2007)] to model adsorption and dynamics of particles in a lattice of confining cells. Their work shows how a surprisingly simple parallel rule applied to a static network of cells joined by links set in space and time can generate a wide range of dynamical behaviors. In their model the cells are the elementary constituent objects of the network. They are a portion of space structured in sites which are energetically different. Each cell can accommodate a given maximum number of particles, and each pair of neighboring cells can exchange at most one particle at a time. The predictions of the model are in qualitative agreement with both experimental observations and molecular dynamics simulation results.

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.

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.

Adsorption and Dynamics of Long-Range Interacting Fullerenes in a Flexible, Two-Dimensional, Nanoporous Porphyrin Network

Herein, a detailed investigation of the adsorption and dynamics of C60 and C70 fullerenes hosted in a self-assembled, two-dimensional, nanoporous porphyrin network on a solid Ag surface is presented. Time-resolved scanning tunneling microscopy (STM) studies of these supramolecular systems at the molecular scale reveal distinct host-guest interactions giving rise to a pronounced dissimilar mobility of the two fullerenes within the porphyrin network. Furthermore, long-range coverage-dependent interactions between the all-carbon guests, which clearly affect their mobility and are likely mediated by a complex mechanism involving the Ag substrate and the flexible porphyrin host network, are observed. At increased fullerene coverage, this unprecedented interplay results in the formation of large fullerene chains and islands. By applying a lattice gas model with nearest-neighbor interactions and by evaluating the fullerene-pair distribution functions, the respective coverage-dependent guest-guest interaction energies are estimated.

Understanding Diffusion in Confined Systems: Methane in a ZK4 Molecular Sieve. A Molecular Dynamics Simulation Study

The equilibrium probability distribution of N methane molecules adsorbed in the interior of n alpha cages of the ZK4 zeolite, the all-silica analogue of zeolite A, is modeled by a modified hypergeometric distribution where the effects of mutual exclusion between particles are extracted from long molecular dynamics simulations. The trajectories are then analyzed in terms of time-correlation functions for the fluctuations in the occupation number of the alpha cages. The analysis digs out the correlations induced by the spatial distribution of the adsorbed molecules coupled with a migration mechanism where a molecule can pass from one alpha cage to another, one-by-one. These correlations lead to cooperative motion, which manifests itself as a nonexponential decay of the correlators. Our results suggest ways of developing improved lattice approaches that may be useful for studying diffusion in much larger systems and for a much longer observation time.

Selectivity of a model zeolite ring over hydrocarbons with different symmetry, travelling with different orientations and speeds

We explore the selectivity of a model zeolite ring over representative hydrocarbons of crude oil. The model ring consists of 7 silicon tetrahedral units and one chemically active aluminum site through which hydrocarbons with symmetries varying from almost spherically symmetric to linear chains (1D), planar (2D), and pyramidal (3D) structures diffuse. The selectivity is further investigated when the hydrocarbons travel with different orientations and speeds. The semiclassical Born-Oppenheimer molecular dynamics approximation is used to characterize the chemical dynamics, as well as to determine the energetics and reaction products. The simulations reveal noticeable differences in energy profiles and charge populations. Our results are important to understand aspects of mass transport and some of the factors that control the catalytic activity in zeolites.

Diffusion anomaly as a function of molecular length of linear molecules: levitation effect

Previous work on monatomic spherical sorbates has shown the existence of an anomalous peak in self-diffusivity (D) when plotted as a function of size of the diffusant. Molecular dynamics studies on linear molecules of different lengths l in zeolite NaY at 140 and 200 K are reported. It is seen that there is a peak in D as a function of l, suggesting that the levitation effect exists for linear molecules, the simplest member of polyatomics. This is confirmed by the lowering of the activation energy for the molecule whose length l exhibits highest D. Related quantities of interest such as the guest-host interaction energy and preexponential factor are discussed.