Theory and simulation of cohesive diffusion in nanopores: Transport in subcritical and supercritical regimes

Simulating adsorptive expansion of zeolites: application to biomass-derived solutions in contact with silicalite

We have constructed and applied an algorithm to simulate the behavior of zeolite frameworks during liquid adsorption. We applied this approach to compute the adsorption isotherms of furfural-water and hydroxymethyl furfural (HMF)-water mixtures adsorbing in silicalite zeolite at 300 K for comparison with experimental data. We modeled these adsorption processes under two different statistical mechanical ensembles: the grand canonical (V-Nz-μg-T or GC) ensemble keeping volume fixed, and the P-Nz-μg-T (osmotic) ensemble allowing volume to fluctuate. To optimize accuracy and efficiency, we compared pure Monte Carlo (MC) sampling to hybrid MC-molecular dynamics (MD) simulations. For the external furfural-water and HMF-water phases, we assumed the ideal solution approximation and employed a combination of tabulated data and extended ensemble simulations for computing solvation free energies. We found that MC sampling in the V-Nz-μg-T ensemble (i.e., standard GCMC) does a poor job of reproducing both the Henry's law regime and the saturation loadings of these systems. Hybrid MC-MD sampling of the V-Nz-μg-T ensemble, which includes framework vibrations at fixed total volume, provides better results in the Henry's law region, but this approach still does not reproduce experimental saturation loadings. Pure MC sampling of the osmotic ensemble was found to approach experimental saturation loadings more closely, whereas hybrid MC-MD sampling of the osmotic ensemble quantitatively reproduces such loadings because the MC-MD approach naturally allows for locally anisotropic volume changes wherein some pores expand whereas others contract.

Speeding up simulation of diffusion in zeolites by a parallel synchronous kinetic Monte Carlo algorithm

Understanding the behaviors of molecules in tight confinement is a challenging task. Standard simulation tools like kinetic Monte Carlo have proven to be very effective in the study of adsorption and diffusion phenomena in microporous materials, but they turn out to be very inefficient when simulation time and length scales are extended. In this paper we have explored the possibility of application of a discrete version of the synchronous parallel kinetic Monte Carlo algorithm introduced by Martínez et al. [J. Comput. Phys. 227, 3804 (2008)] to the study of aromatic hydrocarbons diffusion in zeolites. The efficiency of this algorithm is investigated as a function of the number of processors and domain size. We show that with an accurate choice of domains size it is possible to achieve very good efficiencies thus permitting us to effectively extend space and time scales of the simulated system.

Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.

Modeling fluid diffusion using the lattice density functional theory approach: counterdiffusion in an external field

The dependence of the diffusivity on temperature, pressure, and composition is not understood well; consequently, data is preferred significantly over correlations in most practical situations. Even in dilute gases, the contributions of attractions and repulsions to the diffusivity are difficult to understand on a molecular level without performing simulations. We have developed a Lattice Density Functional Theory (LDFT) approach for modeling diffusion to supplement existing methods that are very rigorous but computationally demanding. The LDFT approach is analogous to the van der Waals equation in how it accounts for molecular interactions in that it has first-order corrections to ideal behavior; it is an extension of the Equilibrium LDFT for adsorption and phase behavior. In this work, the LDFT approach is presented and demonstrated by modeling the problem of color counterdiffusion in an externally-applied potential field. This potential field, in combination with the intermolecular potential function, creates a diffusion regime in which repulsions cause oscillations in the density profile. Using the LDFT approach, the oscillations were described and attributed to nearest-neighbor and next nearest-neighbor interactions. The LDFT approach gives qualitative and quantitative agreement with dual control-volume Grand Canonical Molecular Dynamics simulations.

The role of molecular interactions and interfaces in diffusion: Permeation through single-crystal and polycrystalline microporous membranes

In this second paper of a two part series, we investigate the implications of the interfacial phenomenon, caused by adsorbate-adsorbate interactions coupled with the difference in adsorbate density between the zeolite and the gas phase, upon benzene permeation through single-crystal and polycrystalline microporous NaX membranes. The high flux predicted for thin single-crystal membranes reveals that substantially enhanced flux should be expected in submicron films. Simulations also indicate that the standard local equilibrium assumption made for larger scale membranes is inapplicable at the submicron scale associated with nanometer size grains of thin and/or polycrystalline membranes. Apparent activation energies predicted for benzene permeation through NaX membranes via kinetic Monte Carlo (KMC) simulations are in good agreement with laboratory experiments. The simulations also uncover temperature-dependent flux pathways leading to non-Arrhenius behavior observed experimentally. The failure of the Darken approximation, especially in the presence of the interfacial phenomenon, leads to a substantial overprediction of the flux. Simulations of polycrystalline membranes suggest that this same interfacial phenomenon leads to resistance that can reduce flux by an order of a magnitude with only moderate polycrystallinity.

Equilibrium and nonequilibrium transport of oxygen in carbon nanotubes

The equilibrium and nonequilibrium transport of O(2) through open-ended, hydrogen-terminated, single-walled carbon nanotubes is examined using classical molecular dynamics simulations. It is found in both cases that the O(2) forms well-defined layers around the nanotube interior and/or exterior, and that molecular transport approaches normal mode-diffusion as the nanotube diameter increases. The interactions between the O(2) and the nantubes are stronger than that among the O(2), and this difference increases as the nanotube diameter decreases.

A Study of Pore Blockage in Silicalite Zeolite Using Free Energy Perturbation Calculations

Binary systems consisting of large coadsorbed molecules (n-hexane, cyclohexane, and benzene) with smaller penetrant molecules (methane) were simulated to investigate the mechanisms of pore blockage in the zeolite silicalite. Benzene and cyclohexane trap the methane molecules in the zeolite channels on the time scales of molecular dynamics simulations. Minimum energy paths for methane diffusion past the blocking molecules were determined, and free energy perturbation calculations were carried out along the paths to get the rate constants of methane hopping past coadsorbed benzene and cyclohexane molecules, which adsorb in the channel intersections. Three principal diffusion pathways were found in both the methane/benzene and methane/cyclohexane systems. Minima which were connected by low-energy pathways were grouped together into macrostates. Using the calculated hopping rates between macrostates, kinetic Monte Carlo was then used to obtain the diffusivity of methane with a coadsorbate benzene loading such that all channel intersections are filled by benzene - conditions where molecular dynamics simulations fail. Passage of methane across cyclohexane molecules involved pushing the cyclohexane molecules into the channels from their preferred channel intersection positions.

Translational and rotational diffusion of SF6 in zeolite NaY

Temperature dependence of equilibrium as well as dynamical properties of SF(6) in zeolite NaY have been investigated by molecular dynamics simulation. By about 200 K, SF(6) begins to have increased mobility. Strong orientational preference is exhibited by SF(6) during its passage through the 12-ring window, the bottleneck for diffusion. The preference is for orientation with C(3) followed by C(2) and then C(4) molecular symmetry axis perpendicular to the window plane. Translational motion is diffusive with an activation energy of 5.5 kJ/mol. Rotational-diffusion coefficient has an activation energy of 2.83 kJ/mol. Rotational motion is facile within the alpha-cage. Translational motion is hindered during passage through the 12-ring window when C(4) is perpendicular to the window plane. Orientational correlation functions P(1) and P(2) around C(2), C(3) and C(4) are reported. Only the long time decay of C(4) shows oscillations. This is attributed to the hindered rotation during intercage migration while passing through the 12-ring window.

Lattice density functional theory of molecular diffusion

A density functional theory of diffusion is developed for lattice fluids with molecular flux as a functional of the density distribution. The formalism coincides exactly with the generalized Ono-Kondo density functional theory when there is no gradient of chemical potential, i.e., at equilibrium. Away from equilibrium, it gives Fick's first law in the absence of a potential energy gradient, and it departs from Fickian behavior consistently with the Maxwell-Stefan formulation. The theory is applied to model a nanopore, predicting nonequilibrium phase transitions and the role of surface diffusion in the transport of capillary condensate.

Infinitely fast diffusion in single-file systems

We have used dynamic Monte Carlo(DMC) methods and analytical techniques to analyze single-file systems for which diffusion is infinitely fast. We have simplified the master equation removing the fast reactions, and we have introduced a DMC algorithm for infinitely fast diffusion. The DMC method for fast diffusion give similar results as the standard DMC with high diffusion rates. We have investigated the influence of characteristic parameters, such as pipe length, adsorption, desorption, and conversion rate constants on the steady-state properties of single-file systems with a reaction, looking at cases when all the sites are reactive and when only some of them are reactive. We find that the effect of fast diffusion on single-file properties of the system is absent even when diffusion is infinitely fast. Diffusion is not important in these systems. Smaller systems are less reactive and the occupancy profiles for infinitely long systems show an exponential behavior.

Steady-state properties of single-file systems with conversion

We have used Monte Carlo methods and analytical techniques to investigate the influence of the characteristic parameters, such as pipe length, diffusion, adsorption, desorption, and reaction rate constants on the steady-state properties of single-file systems with a reaction. We looked at cases when all the sites are reactive and when only some of them are reactive. Comparisons between mean-field predictions and Monte Carlo simulations for the occupancy profiles and reactivity are made. Substantial differences between mean-field and the simulations are found when rates of diffusion are high. Mean-field results only include single-file behavior by changing the diffusion rate constant, but it effectively allows passing of particles. Reactivity converges to a limit value if more reactive sites are added: sites in the middle of the system have little or no effect on the kinetics. Occupancy profiles show approximately exponential behavior from the ends to the middle of the system.