Volume Grand Canonical Molecular Dynamics Research Articles

Predictive Assessment of Surface Resistances in Zeolite Membranes Using Atomically Detailed Models

The diffusive transport of molecules through nanoporous membranes is determined by both intracrystalline diffusion and mass transport resistances associated with entering and leaving the membrane material. We compare two methods for assessing the relative importance of these resistances based on atomically detailed descriptions of the membrane material. For extremely thin membranes, net transport can be assessed using dual control volume grand canonical molecular dynamics (DCV-GCMD). We show that previous implementations of this technique may have been influenced by nonisothermal effects in interfacial regions and suggest a simple remedy to this situation. We also introduce an approximate method that uses information only from equilibrium MD simulations, which avoids the significant computational expense associated with DCV-GCMD. This approximate method can be used to rapidly assess the importance of interface-related resistances to mass transport over broad ranges of membrane operating conditions. This method will be useful in allowing a rapid determination of whether these interface resistances are significant in practical experimental situations. These two methods are compared by considering the transport of CH(4) and CF(4) through defect-free silicalite membranes.

Diffusivity of CH4 In Model Silica Nanopores: Molecular Dynamics and Quasichemical Mean Field Theory

Equilibrium molecular dynamics and dual control volume grand canonical molecular dynamics experiments were carried out aiming at the investigation of the dependence of transport diffusivity upon the adsorbent pore size and sorbate concentration of CH4 in cylindrical silica nanopores at 298 K, calibrated with respect to experimental data of zeolite VPI 5; the results of simulation were elaborated on the basis of the quasichemical mean field approximation via a theoretical model for surface diffusion. Our mapping procedure between simulation and quasichemical theory reveals that sorbate–sorbate energetics emerge as the physical reason for the variation of corrected (Darken) and hence transport diffusivity with respect to pore size and sorbed phase fractional occupancy.

Effect of Surface Resistances on the Diffusion of Binary Mixtures in the Silicalite Single Crystal Membrane

Diffusion of methane and argon mixtures through the silicalite single-crystal membrane is studied using the dual-control volume-grand canonical molecular dynamics method to understand how surface resistances alter selectivity and permeance. Comparison of results from intracrystalline transport and entrance simulations for binary mixtures of CH4 and Ar shows that the selectivity of silicalite membranes toward Ar is enhanced in the presence of the surface resistances. In both cases, however, diffusion of faster Ar molecules was inhibited by slower diffusing CH4 molecules, whereas diffusion of the latter remained unaffected. This behavior was explained by the difference between the magnitudes of surface resistances for two molecules, which is much smaller for Ar because of its smaller permeant-crystal interaction size. We find that selectivity of the membrane at the surface depends strongly on total feed pressure and temperature, whereas this dependence is weak for intracrystalline diffusion. Furthermore, we show that the selectivity at the surface diminishes with crystal thickness until a certain thickness is reached, whereas the intracrystalline selectivity remains constant with increasing thickness. Finally, a study of diffusion of C2H6 and CF4 mixtures shows that the diatomic ethane molecules diffuse faster inside the zeolite channels, but their desorption is hindered to a larger extent than that of a spherical molecule with larger diameter and lower heat of adsorption. This observation indicates that the difference in molecular geometry is also a significant factor to explain the exit effect.

Dual control cell reaction ensemble molecular dynamics: A method for simulations of reactions and adsorption in porous materials

We present a simulation tool to study fluid mixtures that are simultaneously chemically reacting and adsorbing in a porous material. The method is a combination of the reaction ensemble Monte Carlo method and the dual control volume grand canonical molecular dynamics technique. The method, termed the dual control cell reaction ensemble molecular dynamics method, allows for the calculation of both equilibrium and nonequilibrium transport properties in porous materials such as diffusion coefficients, permeability, and mass flux. Control cells, which are in direct physical contact with the porous solid, are used to maintain the desired reaction and flow conditions for the system. The simulation setup closely mimics an actual experimental system in which the thermodynamic and flow parameters are precisely controlled. We present an application of the method to the dry reforming of methane reaction within a nanoscale reactor model in the presence of a semipermeable membrane that was modeled as a porous material similar to silicalite. We studied the effects of the membrane structure and porosity on the reaction species permeability by considering three different membrane models. We also studied the effects of an imposed pressure gradient across the membrane on the mass flux of the reaction species. Conversion of syngas (H2/CO) increased significantly in all the nanoscale membrane reactor models considered. A brief discussion of further potential applications is also presented.

Surface Resistance to Permeation through the Silicalite Single Crystal Membrane: Variation with Permeant

The variation of surface resistances to diffusion of molecules through the silicalite single-crystal membranes as a function of permeants has been investigated using the Dual Control Volume-Grand Canonical Molecular Dynamics method. For this purpose three spherical molecules, CH4, Ar, and CF4, have been selected. This selection enabled the study of a range of molecular diameters and interaction energies. Simulation results showed that the magnitude of surface resistance in zeolite membranes depends on the permeant-crystal interaction size and energy. Furthermore, the range of the surface resistance, defined as the distance from the surface beyond which the surface resistance becomes constant, is primarily a function of molecular size: For smaller molecules the range of surface resistances is shorter while its magnitude is lower. Variations in mass-transfer resistances and diffusivities were studied in further detail with a parametric sensitivity analysis by varying permeant-crystal interaction size and well depth, as well as molecular weight in the manner of a factorial design. This procedure allowed checking for the significance of these factors and their cross-interactions during adsorption from the gas phase into the silicalite. The parametric study showed that the Lennard-Jones gas-crystal size interaction dominates the surface resistance of molecules that penetrate silicalite crystals, but interaction energy is also significant. Although, different sets of parameters yield similar equilibrium concentration values in adsorption studies, the surface resistance varies drastically with variations in these parameters.

Molecular transport in nanopores

Simulation of the transport of methane in cylindrical silica mesopores have been performed using equilibrium and nonequilibrium molecular dynamics (NEMD) as well as dual control volume grand canonical molecular dynamics methods. It is demonstrated that all three techniques yield the same transport coefficient even in the presence of viscous flow. A modified locally averaged density model for viscous flow, combined with consideration of wall slip through a frictional condition, gives a convincing interpretation of the variation of the transport coefficient over a wide range of densities, and for various pore sizes and temperatures. Wall friction coefficients extracted from NEMD simulations are found to be consistent with momentum transfer arguments, and the approach is shown to be more meaningful than the classical slip length concept.

Hydrodynamic origin of diffusion in nanopores.

We study the transport of a subcritical Lennard-Jones fluid in a cylindrical nanopore, using a combination of equilibrium and nonequilibrium as well as dual control volume grand canonical molecular dynamics methods. We show that all three techniques yield the same value of the transport coefficient for diffusely reflecting pore walls, even in the presence of viscous transport. We also demonstrate that the classical Knudsen mechanism is not manifested, and that a combination of viscous flow and momentum exchange at the pore wall governs the transport over a wide range of densities.

The Diffusion Process of Methane through a Silicalite Single Crystal Membrane

The diffusion process of methane in a silicalite single-crystal membrane has been investigated using the Dual Control Volume-Grand Canonical Molecular Dynamics method. Simulations of full-membrane transport and the three individual contributions that comprise the overall process (entrance to the pores, intra-crystalline diffusion, and exit from the pores) show that the contribution of surface resistance to the overall transport resistance in zeolite membranes is larger and longer range than one might expect. A model is proposed on the basis of the additivity of these contributions. From the individual simulations of exit and entrance zones, it is shown that the adsorption and desorption resistances approach an asymptote with increasing crystal thickness. However, the asymptotic trend has not been observed in full membrane simulations within the thickness limit of this work, possibly because of the coupling between the entrance and exit effects. Since the surface resistance is limited to less than 1 μm and the single-crystal membrane comprises 100 μm, the surface resistance still represents a relatively small contribution to the overall resistance. Therefore, the diffusion process through the single-crystal membrane is dominated by the internal transport of the sorbate molecules along the principal (z-) axis of the crystal.

A critical comparison of equilibrium, non-equilibrium and boundary-driven molecular dynamics techniques for studying transport in microporous materials

Transport in an idealized model with variable pore diameter as well as an AlPO4-5 zeolite is examined using three different molecular dynamics techniques: (1) equilibrium molecular dynamics (EMD); (2) external field nonequilibrium molecular dynamics (EF–NEMD); and (3) dual control volume grand canonical molecular dynamics (DCV–GCMD). The EMD and EF–NEMD methods yield identical transport coefficients for all the systems studied. The transport coefficients calculated using the DCV–GCMD method, however, tend to be lower than those obtained from the EMD and EF–NEMD methods unless a large ratio of stochastic to dynamic moves is used for each control volume, and a streaming velocity is added to all inserted molecules. Through development and application of a combined reaction–diffusion–convection model, this discrepancy is shown to be due to spurious mass and momentum transfers caused by the control volume equilibration procedure. This shortcoming can be remedied with a proper choice of streaming velocity in conjunction with a well-maintained external field, but the associated overhead makes it much less efficient than either the EMD or EF–NEMD techniques.

Effect of pressure, membrane thickness, and placement of control volumes on the flux of methane through thin silicalite membranes: A dual control volume grand canonical molecular dynamics study

The flux of methane through the straight channels of thin silicalite membranes is studied via dual control volume grand canonical molecular dynamics. The adsorption layers on the surfaces of the thin membranes are found to provide a significant resistance to the flux of methane. This strong surface effect for thin membranes requires that the control volumes (where insertions and deletions are performed) must be placed far enough away from the membrane surface that they do not overlap with the surface adsorption layer. The permeance (flux/pressure drop) of methane through the surface layer is shown to be insensitive to both the average pressure and the pressure drop. In contrast, the permeance through the interior of the membrane increases with decreasing average pressure. These results are explained using a model which treats the transport through the surface barrier as driven by the pressure gradient and transport through the zeolite as driven by the chemical potential gradient. A new force field named DACNIS is presented which accurately describes the adsorption isotherms of methane and ethane in silicalite.

Effect of the Surface Energy Barrier on Sorbate Diffusion in AlPO4-5

The importance of pore exit effects on the diffusion of molecules in AlPO4-5 pores is evaluated using two molecular modeling techniques. In the first approach, a dual control volume grand canonical molecular dynamics technique is used to obtain molecular fluxes of methane out of the truncated crystal as a function of temperature and sorbate loading. The simulation results indicate the presence of a low-temperature surface barrier for diffusion, which retards the flux of methane relative to its apparent flux in the intracrystalline regions of the material. This pore exit barrier tends to diminish as temperature and loading increase. An explanation based on clustering phenomena is proposed to explain the latter. Next, a simple activated transport model is proposed to predict the relative importance of the surface barrier on the transport of sorbates in AlPO4-5. The potential of mean force for a single sorbate molecule along the pore axis of a truncated crystal provides the required activation energy barriers for the model. The model correctly predicts the reduction in the importance of exit effects with an increase in the temperature. It is also observed that exit effects become more important as the ratio of the size of the sorbate molecule to the pore size approaches unity. In particular, exit effects are significant in micrometer-thick AlPO4-5 crystals in the case of large molecules such as SnBr4 and CCl4 at room temperature.

Combined Diffusive and Viscous Transport of Methane in a Carbon Slit Pore

The transport of mass through porous materials can occur by essentially two different mechanisms: (1) diffusion and (2) viscous flow. The former occurs when there is a gradient in chemical potential of the pore fluid, while the latter occurs in the presence of a pressure gradient. In general, fluid transport occurs by both of these mechanisms and their respective contributions to the total intra-pore flux are approximately additive. Experimentally, there is no unambiguous way of determining the individual contributions to the total flux of these two modes of transport. Fortunately, molecular simulations does provide a solution. We present a novel simulation method in which the separate contributions to the total flux are determined. The method involves the use of two non-equilibrium molecular dynamics techniques: dual control volume grand canonical molecular dynamics (DCV GCMD) and an algorithm for simulating planar Poiseuille flow. We apply this technique to study the combined (viscous and diffusive) transport of methane through single slit-shaped graphite pores of width 2.5, 5.0 and 10.0 methane diameters. We find that the viscous contribution to the total intrapore flux through each of these pores is 10%, 15% and 34%, respectively.

Direct molecular simulation of gradient-driven diffusion of large molecules using constant pressure

Dual control volume grand canonical molecular dynamics (DCV-GCMD) is a boundary-driven nonequilibrium molecular-dynamics technique for simulating gradient-driven diffusion in multicomponent systems. Two control volumes are established at opposite ends of the simulation box. Constant temperature and chemical potential of diffusing species are imposed in the control volumes (i.e., constant-μ1⋯μn−1μnVT). This results in stable chemical potential gradients and steady-state diffusion fluxes in the region between the control volumes. We present results and detailed analysis for a new constant-pressure variant of the DCV-GCMD method in which one of the diffusing species for which a steady-state diffusion flux exists does not have to be inserted or deleted. Constant temperature, pressure, and chemical potential of all diffusing species except one are imposed in the control volumes (i.e., constant-μ1⋯μn−1NnPT). The constant-pressure method can be applied to situations in which insertion and deletion of large molecules would be prohibitively difficult. As an example, we used the method to simulate diffusion in a binary mixture of spherical particles with a 2:1 size ratio. Steady-state diffusion fluxes of both diffusing species were established. The constant-pressure diffusion coefficients agreed closely with the results of the standard constant-volume calculations. In addition, we show how the concentration, chemical potential, and flux profiles can be used to calculate local binary and Maxwell–Stefan diffusion coefficients. In the case of the 2:1 size ratio mixture, we found that the binary diffusion coefficients were asymmetric and composition dependent, whereas the Maxwell–Stefan diffusion coefficients changed very little with composition and were symmetric. This last result verified that the Gibbs–Duhem relation was satisfied locally, thus validating the assumption of local equilibrium.

Transport Diffusion of Oxygen−Nitrogen Mixtures in Graphite Pores: A Nonequilibrium Molecular Dynamics (NEMD) Study

The technique of dual control volume grand canonical molecular dynamics (DCV GCMD) is used to study the diffusivity of a mixture of nitrogen and oxygen in a graphite slit pore as a function of pore width. We find evidence in support of combined viscous and diffusive transport through these narrow slit pores. The viscous contribution to the flow becomes weaker as the pore width decreases. The fluid velocity profiles show evidence of microscopic slip but still retain a classical Navier−Stokes parabolic signature. The concentration profiles for each component in the mixture show an approximately linear variation with distance along the pore length, suggesting that cross-coupling effects are weak. We find that the diffusion of oxygen−nitrogen mixtures through a graphite pore displays a complex dependence upon the pore width. Molecular packing appears to play a very significant role in determining the flow of the mixture. Thermodynamic effects are of more importance in these simulations than sieving effects; hence, we do not find a greater diffusivity for oxygen compared to nitrogen.

Massively parallel molecular dynamics simulation of gas permeation across porous silica membranes

In this work, we simulate the pressure-driven gas permeation of gases in porous silica models using a dual control volume grand canonical molecular dynamics (DCV-GCMD) technique. This technique allows spatial variation of chemical potential and hence an accurate simulation of this steady-state process. The molecular sieving nature of microporous zeolites and amorphous silica made by sol–gel methods are discussed and compared. One mesoporous and one microporous membrane model are tested with Lennard-Jones gases corresponding to He, H 2, Ar, and CH 4. The mesoporous membrane model clearly follows a Knudsen diffusion mechanism, while the microporous model, having a hard-sphere cut-off pore diameter of ∼3.4 Å, demonstrates molecular sieving of CH 4 ( σ=3.8 Å), but anomalous behavior for Ar ( σ=3.4 Å).

Direct molecular simulation of gradient-driven diffusion

Recent work in the active area of grand canonical molecular dynamics methods is first briefly reviewed followed by an overview of the dual control volume grand canonical molecular dynamics (DCV-GCMD) method, designed to enable the dynamic simulation of a system with a steady-state chemical potential gradient. A short review of the methods and systems used to prototype the DCV-GCMD method and its parallel implementation follows. Finally a new, novel implementation of the DCV-GCMD method that enables the establishment of a steady-state chemical potential gradient in a multicomponent system without having to insert or delete one of the components is presented and discussed.

Massively parallel dual control volume grand canonical molecular dynamics with LADERA II. Gradient driven diffusion through polymers

This paper, the second part of a series, extends the capabilities of the LADERA FORTRAN code for massively parallel dual control volume grand canonical molecular dynamics (DCVGCMD). DCV-GCMD is a hybrid of two more common molecular simulation techniques (grand canonical Monte Carlo and molecular dynamics) which allows the direct molecularlevel modelling of diffusion under a chemical potential gradient. The present version of the code, LADERA-B has the capability of modelling systems with explicit intramolecular interactions such as bonds, angles, and dihedral rotations. The utility of the new code for studying gradient-driven diffusion of small molecules through polymers is demonstrated by applying it to two model systems. LADERA-B includes another new feature, which is the use of neighbour lists in force calculations. This feature increases the speed of the code but presents several challenges in the parallel hybrid algorithm. There is discussion on how these problems were addressed and how our implementation results in a significant increase in speed over the original LADERA. Scaling results are presented for LADERA-B on two massively parallel message-passing machines.

Massively parallel dual control volume grand canonical molecular dynamics with LADERA II. Gradient driven diffusion through polymers

This paper, the second part of a series, extends the capabilities of the LADERA FORTRAN code for massively parallel dual control volume grand canonical molecular dynamics (DCVGCMD). DCV-GCMD is a hybrid of two more common molecular simulation techniques (grand canonical Monte Carlo and molecular dynamics) which allows the direct molecularlevel modelling of diffusion under a chemical potential gradient. The present version of the code, LADERA-B has the capability of modelling systems with explicit intramolecular interactions such as bonds, angles, and dihedral rotations. The utility of the new code for studying gradient-driven diffusion of small molecules through polymers is demonstrated by applying it to two model systems. LADERA-B includes another new feature, which is the use of neighbour lists in force calculations. This feature increases the speed of the code but presents several challenges in the parallel hybrid algorithm. There is discussion on how these problems were addressed and how our implement...

Massively parallel dual control volume grand canonical molecular dynamics with LADERA I. Gradient driven diffusion in Lennard-Jones fluids

A new algorithm to enable the implementation of dual control volume grand canonical molecular dynamics (DCV-GCMD) on massively parallel (MP) architectures is presented. DCVGCMD can be thought of as hybridization of molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) and was developed recently to make possible the simulation of gradient-driven diffusion. The method has broad application to such problems as membrane separations, drug delivery systems, diffusion in polymers and zeolites, etc. The massively parallel algorithm for the DCV-GCMD method has been implemented in a code named LADERA which employs the short range Lennard-Jones potential for pure fluids and multicomponent mixtures including bulk and confined (single pore as well as amorphous solid materials) systems. Like DCV-GCMD, LADERA's MP algorithm can be thought of as a hybridization of two different algorithms, spatial MD and spatial GCMC. The DCV-GCMD method is described fully followed by the DCV-GCMD parallel algorithm employed in LADERA. The scaling characteristics of the new MP algorithm are presented together with the results of the application of LADERA to ternary and quaternary Lennard-Jones mixtures.

Massively parallel dual control volume grand canonical molecular dynamics with LADERA I. Gradient driven diffusion in Lennard-Jones fluids

A new algorithm to enable the implementation of dual control volume grand canonical molecular dynamics (DCV-GCMD) on massively parallel (MP) architectures is presented. DCVGCMD can be thought of as hybridization of molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) and was developed recently to make possible the simulation of gradient-driven diffusion. The method has broad application to such problems as membrane separations, drug delivery systems, diffusion in polymers and zeolites, etc. The massively parallel algorithm for the DCV-GCMD method has been implemented in a code named LADERA which employs the short range Lennard-Jones potential for pure fluids and multicomponent mixtures including bulk and confined (single pore as well as amorphous solid materials) systems. Like DCV-GCMD, LADERA's MP algorithm can be thought of as a hybridization of two different algorithms, spatial MD and spatial GCMC. The DCV-GCMD method is described fully followed by the DCV-GCMD parallel algorithm employed in ...