Dual Control Volume Grand Canonical Molecular Dynamics Research Articles

Molecular Simulations of Binary Gas Mixture Transport and Separation in Slit Nanopores

We propose a new method to simulate the gas mixture transport and separation in slit nanopores. The method is based on the random removal of molecules from the permeate side in the dual control volume–grand canonical molecular dynamics (DCV-GCMD) method. Each step in the random removal is independent of the previous steps. The conventional method, DCV-GCMD, simulates the gas mixture in control volumes based on the chemical potential of each component, in which the gas compositions have to be known in advance and kept constant. However, the transport process affects the composition of the produced gas mixture due to selective adsorption in the nanopores. This process has been modeled iteratively in the literature. We propose an alternative method to calculate the composition in the permeate side directly; in our approach, the computational efficiency is improved by an order of magnitude compared to the iterative method. Transport of gas mixtures of CH4/He and CO2/CH4 is investigated in graphene, graphite, and tetrahedral–octahedral–tetrahedral (TOT) structure slit pores. Pore width is the dominant factor in the species separation. The solid substrates and surface roughness have a pronounced effect on gas separation. The average pressure may have a pronounced effect when the pore width is less than 1.00 nm.

Flow of Gases in Organic Nanoscale Channels: A Boundary-Driven Molecular Simulation Study

In modeling fluid transport in organic nanopores of shale, particular attention should be paid to the gas–wall interactions, specifically the adsorption phenomena, and the fact that the size of pores are comparable with the mean-free-path of the gas molecules. The objective for this work is to investigate the significance of the adsorbed gas molecules in the total mass flux of organic nanoscale channels. Molecular dynamics (MD) has proven to be a credible technique to examine dynamics of atomic-level phenomena. In this study, transport of four different gases, methane and argon (high adsorption affinity) and helium and neon (low adsorption affinity), is studied, and their velocity and mass flux profiles are analyzed using dual control volume grand canonical molecular dynamics (DCV-GCMD) simulations. DCV-GCMD simulations are performed for different pressures, pressure gradients, and channel sizes. Computed normalized velocities are close to 1 for all the gases and channel heights, which shows that the velo...

Phase behavior and flow in shale nanopores from molecular simulations

Phase behavior and flow in shale nanopores, due to fluid heterogeneity, cannot be described by bulk and continuum-based formulations. The interactions between fluid and rock molecules are important in both phase behavior and flow. As a result, frameworks from bulk equations of state in phase behavior, and continuum mechanisms and Klinkenberg slippage in flow may become inapplicable. Recently, we have studied both phase behavior and flow in nanopores using density functional theory and various molecular simulations. This work addresses a number of issues related to the adsorption of mixtures of hydrocarbons, carbon dioxide and water as well as methane flow at different pressure conditions in nanopores. For flow, we use the dual control volume-grand canonical molecular dynamics (DCV-GCMD) simulation as in our previous work. We use a smaller pressure difference between high and low pressure reservoirs connected to the nanopores. We find that similar to our past work, the flux of methane in the slit pores can be two orders of magnitude higher than the results from the Hagen-Poiseuille equation.

Computational Study of Pressure-Driven Gas Transport in Nanostructured Carbons: An Alternative Approach.

We demonstrated a computationally efficient method in nonequilibrium molecular dynamics (NEMD) simulations to study pressure-driven gas transport in porous media. The reflecting particle method (RPM)14 was used to establish a steady-state gas flow along the transport channel, and the gas density in the feed chamber was properly adjusted to allow a constant pressure drop under various conditions by using a perturbation-relaxation loop developed here. This method was validated for methane flow through carbon nanotubes over a wide range of temperatures, giving results comparable to those of the commonly used dual control volume grand canonical molecular dynamics (DCV-GCMD) method but at least 20 times more efficient, even though the transport condition tested is favorable for the latter. This made it possible to perform systematic studies on the effects of temperature, pressure, and channel size on the transport behaviors. Our study shows that adsorption density varies significantly with temperature, which dramatically influences the transport mechanisms, especially in small channels at low temperatures and under high pressures. This newly developed NEMD method can be readily extended to study gas transport through channels with more complex surface morphology.

Molecular Simulations of Supercritical Fluid Permeation through Disordered Microporous Carbons

Fluid transport through microporous carbon-based materials is inherent in numerous applications, ranging from gas separation by carbon molecular sieves to natural gas production from coal seams and gas shales. The present study investigates the steady-state permeation of supercritical methane in response to a constant cross-membrane pressure drop. We performed dual control volume grand canonical molecular dynamics (DCV-GCMD) simulations to mimic the conditions of actual permeation experiments. To overcome arbitrary assumptions regarding the investigated porous structures, the membranes were modeled after the CS1000a and CS1000 molecular models, which are representative of real microporous carbon materials. When adsorption-induced molecular trapping (AIMT) mechanisms are negligible, we show that the permeability of the microporous material, although not significantly sensitive to the pressure gradient, monotonically decreases with temperature and reservoir pressures, consistent with diffusion theory. However, when AIMT occurs, the permeability increases with temperature in agreement with experimental data found in the literature.

Ion fluxes through nanopores and transmembrane channels

We introduce an implicit solvent Molecular Dynamics approach for calculating ionic fluxes through narrow nanopores and transmembrane channels. The method relies on a dual-control-volume grand-canonical molecular dynamics (DCV-GCMD) simulation and the analytical solution for the electrostatic potential inside a cylindrical nanopore recently obtained by Levin [Europhys. Lett. 76, 163 (2006)]. The theory is used to calculate the ionic fluxes through an artificial transmembrane channel which mimics the antibacterial gramicidin A channel. Both current-voltage and current-concentration relations are calculated under various experimental conditions. We show that our results are comparable to the characteristics associated to the gramicidin A pore, especially the existence of two binding sites inside the pore and the observed saturation in the current-concentration profiles.

Atomically detailed simulations of surface resistances to transport of CH4, CF4, and C2H6 through silicalite membranes

Abstract We have used atomically detailed methods to examine the surface resistances associated with single-component permeation of CH 4 , CF 4 , and C 2 H 6 through single crystal silicalite membranes. Dual control volume grand canonical molecular dynamics (DCV-GCMD) simulations can be used for this purpose, but only for extremely thin membranes and for relatively rapidly diffusing species. We use calculations of this type to introduce a more computationally efficient but approximate method for describing surface resistances, the local equilibrium flux method (LEFM). Using LEFM calculations, it is possible to accurately and rapidly predict surface resistances for large ranges of membrane operating conditions. Using this approach, we identify the crystal thicknesses beyond which surface resistances are negligible for single-component permeation of CH 4 , CF 4 , and C 2 H 6 through silicalite membranes as functions of membrane feed and permeate pressure.

Gas Permeation Through Zeolite Single Crystal Membranes

Diffusion of methane and argon mixtures through single crystal membranes is studied using the Dual-Control Volume-Grand Canonical Molecular Dynamics method. This study focuses on understanding the impact of crystal structure on surface resistance and membrane performance by comparing diffusion through silicalite, mordenite, AlPO4-5 and ZSM-12. Results showed that the contribution of surface resistance on membrane selectivity varies with the structure of the zeolite framework. Surface resistance is larger and longer range in silicalite, with an overall trend of silicalite > ZSM-12 > mordenite > AlPO4-5. This difference is attributed primarily to the smaller diameter of the silicalite pores, but the one-dimensional pore systems also seem to focus the translational momentum such that the surface resistance is smaller and shorter range.

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.

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.

Molecular simulation of adsorption and transport diffusion of model fluids in carbon nanotubes

Grand canonical Monte Carlo (GCMC) and dual-control-volume grand canonical molecular dynamics (DCV-GCMD) simulations were carried out with Lennard-Jones model fluids in carbon nanotubes, with the objective of investigating the effect of varying molecular properties on adsorption and diffusion. The influence of the molecular weight, and the Lennard Jones parameters σ (a measure of the molecule size) and ε (a measure of the interaction strength) on adsorption isotherms, fluxes, and transport diffusivities was studied. For these simulations, the properties of component 1 in the mixture were held constant and one of the properties of component 2 was changed systematically. Furthermore, the validity of Graham's law, which relates the fluxes of two counter diffusing species to their molecular weight, was investigated on a molecular level. Graham's law is fulfilled for the whole range of molecular weights and Lennard-Jones parameters σ investigated. However, large deviations were observed for large values of ε2. Here, the interaction of the two components in the mixture becomes so strong that component 1 is dragged along by component 2.

Molecular simulation studies of self-assembled monolayers of alkanethiols on Au(111)

A review is presented of this group's recent molecular simulation studies of self-assembled monolayers (SAMs) of alkanethiols on Au(111) surfaces. SAMs are very useful for the systematic alteration of the chemical and structural properties of a surface by varying chain length, tail group and composition. The scientific and technological importance of SAMs cannot be overestimated. The present work has been centred on studies of atomic scale surface properties of SAMs. First, configurational-bias Monte Carlo simulations were performed in both semigrand canonical and canonical ensembles to investigate the preferential adsorption and phase behaviour of mixed SAMs on Au(111) surfaces. Second, a novel hybrid molecular simulation technique was developed to simulate atomic force microscopy (AFM) over experimental timescales. The method combines a dynamic element model for the tip-cantilever system in AFM and a molecular dynamics relaxation approach for the sample. The hybrid simulation technique was applied to investigate atomic scale friction and adhesion properties of SAMs as a function of chain length. Third, dual-control-volume grand canonical molecular dynamics (DCV-GCMD) simulations were performed of transport diffusion of liquid water and methanol through a slit pore with both inner walls consisting of Au(111) surfaces covered by SAMs under a chemical potential gradient. Surface hydrophobicity was adjusted by varying the terminal group of CH3 (hydrophobic) or OH (hydrophilic) of the SAMs. Finally, ab initio quantum chemical calculations were performed on both clusters and periodic systems of methylthiols on Au(111) surfaces. Based on the ab initio results, an accurate force field capable of predicting c(4×2) superlattice structures over a wide range of temepratures for alkanethiols on Au(111) was developed. The extension of current work is discussed briefly.

Composition dependent transport diffusion coefficients of CH 4/CF 4 mixtures in carbon nanotubes by non-equilibrium molecular dynamics simulations

Understanding transport diffusion on a molecular level helps to develop improved adsorbents with tailored rate and equilibrium properties. Dual-control-volume grand canonical molecular dynamics (DCV-GCMD) simulations allow the direct simulation of transport diffusion on a molecular level. DCV-GCMD simulations of CH 4/CF 4 mixtures in carbon nanotubes were carried out. An approach to get composition dependent transport diffusivities directly from DCV-GCMD simulations is introduced. Composition dependent transport diffusivities and fluxes are calculated for varying driving forces in order to investigate the influence of the very large driving force in simulations which is about four orders of magnitude larger than in real experimental systems. Whereas, the flux depends on the driving force the transport diffusivity is independent of it so that DCV-GCMD simulation can be used to simulate transport under experimental conditions. Furthermore, the results of composition dependent diffusivities at four different temperatures are presented. A linear function describes the composition dependence and reproduces the simulated concentration profiles very well. The analysis of the temperature dependence indicates that the transport in the investigated system is due to liquid-like molecular diffusion and not to activated diffusion.

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.

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 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 ...

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...