Diffusion of binary mixtures of CF4 and n-alkanes in faujasite

Engineered nanoparticles as Selinexor drug delivery systems across the cell membrane and related signaling pathways in cancer cells

In the present work, molecular dynamics simulation is applied to evaluate the drug carrier efficiency of graphene oxide nanoflake (GONF) for loading of Selinexor (SXR) drug as well as the drug delivery by 2D material through the membrane in aqueous solution. In addition, to investigate the adsorption and penetration of drug-nanocarrier complex into the cell membrane, well-tempered metadynamics simulations and steered molecular dynamics (SMD) simulations were performed. Based on the obtained results, it is evident that intermolecular hydrogen bonds (HBs) and π-π interactions play a significant role in expediting the interaction between drug molecules and the graphene oxide (GO) nanosheet, ultimately resulting in the formation of a stable SXR-GO complex. The Lennard-Jones (L-J) energy value for the interaction of SXR with GONF is calculated to be approximately -98.85 kJ/mol. In the SXR-GONF complex system, the dominant interaction between SXR and GONF is attributed to the L-J term, resulting from the formation of a strong π-π interaction between the drug molecules and the substrate surface. Moreover, our simulations show by decreasing the distance of GONF with respect to cell membrane, the interaction energy of GONF-membrane significantly decrease to -1500 kJ/mol resulting in fast diffusion of SXR-GONF complex toward the bilayer surface that is favored opening the way to natural drug nanocapsule.

Selective Adsorption and Selective Transport Diffusion of CO2-CH4 Binary Mixture in Coal Ultramicropores

The adsorption and diffusion of the CO2-CH4 mixture in coal and the underlying mechanisms significantly affect the design and operation of any CO2-enhanced coal-bed methane recovery (CO2-ECBM) project. In this study, bituminous coal was fabricated based on the Wiser molecular model and its ultramicroporous parameters were evaluated; molecular simulations were established through Grand Canonical Monte Carlo (GCMC) and Molecular Dynamic (MD) methods to study the effects of temperature, pressure, and species bulk mole fraction on the adsorption isotherms, adsorption selectivity, three distinct diffusion coefficients, and diffusivity selectivity of the binary mixture in the coal ultramicropores. It turns out that the absolute adsorption amount of each species in the mixture decreases as temperature increases, but increases as its own bulk mole fraction increases. The self-, corrected, and transport diffusion coefficients of pure CO2 and pure CH4 all increase as temperature or/and their own bulk mole fractions increase. Compared to CH4, the adsorption and diffusion of CO2 are preferential in the coal ultramicropores. Adsorption selectivity and diffusivity selectivity were simultaneously employed to reveal that the optimal injection depth for CO2-ECBM is 800-1000 m at 308-323 K temperature and 8.0-10.0 MPa.

Methanol diffusion in zeolite HY: a combined quasielastic neutron scattering and molecular dynamics simulation study

The diffusion of methanol in zeolite HY is studied using tandem quasielastic neutron scattering (QENS) experiments and molecular dynamics (MD) simulations at 300–400 K.

Atomistic simulations of CO2 and N2 within cage-type silica zeolites

The behavior of CO(2) and N(2), both as single components and as binary mixtures, in two cage-type silica zeolites was studied using atomistic simulations. The zeolites considered, ITQ-3 and paradigm cage-type zeolite ZK4 (the all-silica analog of LTA), were chosen so that the principles illustrated can be generalized to other adsorbent/adsorbate systems with similar topology and types of interactions. N(2) was chosen both because of the potential uses of N(2)/CO(2) separations and because it differs from CO(2) most significantly in the magnitude of its Coulombic interactions with zeolites. Despite similarities between N(2) and CO(2) diffusion in other materials, we show here that the diffusion of CO(2) within cage-type zeolites is dominated by an energy barrier to diffusion located at the entrance to the narrow channels connecting larger cages. This barrier originates in Coulombic interactions between zeolites and CO(2)'s quadrupole and results in well-defined orientations for the diffusing molecules. Furthermore, CO(2)'s favorable electrostatic interactions with the zeolite framework result in preferential binding in the windows between cages. N(2)'s behavior, in contrast, is more consistent with that of molecules previously studied. Our analysis suggests that CO(2)'s behavior might be common for adsorbates with quadrupoles that interact strongly with a material that has narrow windows between cages.

Hydrogen bonding effects in adsorption of water-alcohol mixtures in zeolites and the consequences for the characteristics of the Maxwell-Stefan diffusivities

This work highlights a variety of peculiar characteristics of adsorption and diffusion of polar molecules such as water, methanol and ethanol in zeolites. These peculiarities are investigated with the aid of configurational-bias Monte Carlo (CBMC) simulations of adsorption isotherms, and molecular dynamics (MD) simulations of diffusivities in FAU, MFI, DDR, and LTA zeolites. Because of strong hydrogen bonding, significant clustering of the guest molecules occurs in all investigated structures. Because of molecular clustering, the inverse thermodynamic factor 1/Gamma(i) identical with (d[ln c(i)])/(d[ln f(i)]) exceeds unity for a range molar concentrations c(i) within the micropores. The degree of clustering is lowered as the temperature is increased. For the concentration ranges for which 1/Gamma(i) > 1, the Fick diffusivity, D(i), for unary diffusion is often lower than both the Maxwell-Stefan, D(i), and the self-diffusivity, D(i,self). For water-alcohol mixtures, the hydrogen bonding between water and alcohol molecules is much more predominant than for water-water, and alcohol-alcohol molecule pairs. Consequently, the adsorption of water-alcohol mixtures shows significant deviations from the predictions of the ideal adsorbed solution theory (IAST). The water-alcohol bonding also leaves its imprint on the mixture diffusion characteristics. The Maxwell-Stefan diffusivity, D(i), of either component in water-alcohol mixtures is lower than the corresponding values of the pure components; this behavior is distinctly different from that for mixtures of nonpolar guest molecules. The binary exchange coefficient D(12) for water-alcohol mixtures is also significantly lower than either self-exchange coefficients D(11) and D(22) of the constituent species. This implies that correlation effects are significantly stronger in water-alcohol mixtures than for the constituent species. Correlation effects are found to be significant for water-alcohol mixture diffusion in DDR and LTA zeolites, even though such effects are negligible for the pure constituents. The major conclusion to emerge from this investigation is that, unlike mixtures of nonpolar molecules, it is not possible to estimate water-alcohol mixture adsorption and diffusion characteristics on the basis of pure component data.

Testing the accuracy of correlations for multicomponent mass transport of adsorbed gases in metal-organic frameworks: diffusion of H2/CH4 mixtures in CuBTC

Mass transport of chemical mixtures in nanoporous materials is important in applications such as membrane separations, but measuring diffusion of mixtures experimentally is challenging. Methods that can predict multicomponent diffusion coefficients from single-component data can be extremely useful if these methods are known to be accurate. We present the first test of a method of this kind for molecules adsorbed in a metal-organic framework (MOF). Specifically, we examine the method proposed by Skoulidas, Sholl, and Krishna (SSK) ( Langmuir, 2003, 19, 7977) by comparing predictions made with this method to molecular simulations of mixture transport of H 2/CH 4 mixtures in CuBTC. These calculations provide the first direct information on mixture transport of any species in a MOF. The predictions of the SSK approach are in good agreement with our direct simulations of binary diffusion, suggesting that this approach may be a powerful one for examining multicomponent diffusion in MOFs. We also use our molecular simulation data to test the ideal adsorbed solution theory method for predicting binary adsorption isotherms and a method for predicting mixture self-diffusion coefficients.

Diffusion and separation of CO2 and CH4 in silicalite, C168 schwarzite, and IRMOF-1: a comparative study from molecular dynamics simulation

Recently we have investigated the storage and adsorption selectivity of CO(2) and CH(4) in three different classes of nanoporous materialssilicalite, IRMOF-1, and C(168) schwarzite through Monte Carlo simulation (Babarao, R.; Hu, Z.; Jiang, J. Langmuir, 2007, 23, 659). In this work, the self-, corrected, and transport diffusivities of CO(2) and CH(4) in these materials are examined using molecular dynamics simulation. The activation energies at infinite dilution are evaluated from the Arrhenius fits to the diffusivities at various temperatures. As loading increases, the self-diffusivities in the three frameworks decrease as a result of the steric hindrance; the corrected diffusivities remain nearly constant or decrease approximately linearly depending on the adsorbate and framework; and the transport diffusivities generally increase except for CO(2) in IRMOF-1. The correlation effects are identified to reduce from MFI, C(168) to IRMOF-1, in accordance with the porosity increasing in the three frameworks. Predictions of self-, corrected, and transport diffusivities for pure CO(2) and CH(4) from the Maxwell-Stefan formulation match the simulation results well. In a CO(2)/CH(4) mixture, the self-diffusivities decreases with loading, and good agreement is found between simulated and predicted results. On the basis of the adsorption and self-diffusivity in the mixture, the permselectivity is found to be marginal in IRMOF-1, slightly enhanced in MFI, and greatest in C(168) schwarzite. Although IRMOF-1 has the largest storage capacity for CH(4) and CO(2), its selectivity is not satisfactory.

Molecular dynamics simulations for water and ions in protein crystals

The spatial and temporal properties of water and ions in bionanoporous materials-protein crystals-have been investigated using molecular dynamics simulations. Three protein crystals are considered systematically with different morphologies and chemical topologies: tetragonal lysozyme, orthorhombic lysozyme, and tetragonal thermolysin. It is found that the thermal fluctuations of C(alpha) atoms in the secondary structures of protein molecules are relatively weak due to hydrogen bonding. The solvent-accessible surface area per residue is nearly identical in the three protein crystals; the hydrophobic and hydrophilic residues in each crystal possess approximately the same solvent-accessible surface area. Water distributes heterogeneously and has different local structures within the biological nanopores of the three protein crystals. The mobility of water and ions in the crystals is enhanced as the porosity increases and also by the fluctuations of protein atoms particularly in the two lysozyme crystals. Anisotropic diffusion is found preferentially along the pore axis, as experimentally observed. The anisotropy of the three crystals increases in the order: tetragonal thermolysin < tetragonal lysozyme < orthorhombic lysozyme.

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.

Mass transport of O2 and N2 in nanoporous carbon (C168 schwarzite) using a quantum mechanical force field and molecular dynamics simulations

A hierarchical approach is used to calculate the single-component fluxes of N2 and O2 in nanoporous carbon molecular sieves (represented by C168 schwarzite) over a wide range of pressures and pressure drops. The self- and corrected diffusivities are calculated using equilibrium molecular dynamics simulations with force fields for the gas-carbon interactions obtained from quantum mechanical calculations. These results are combined with previously reported adsorption isotherms of N2 and O2 in C168 to obtain transport diffusivities and, by use of the Fick's equation of mass transport, to obtain single-component fluxes across the membrane. The diffusion coefficients and fluxes are also calculated using an empirical potential, which has been obtained by fitting low coverage adsorption data of N2 and O2 on a planar graphite sheet. By analyzing the diffusivities calculated with the ab initio potential in the limit of infinite dilution over the temperature range from 80 to 450 K, it is observed that the N2/O2 separation is energetically driven and a high selectivity of O2 over N2 can be obtained at low temperatures. However, with the empirical potential both the energetic and entropic contributions to selectivity were found to be close to unity. Similarly, by calculating single-component fluxes and ideal selectivities at 300 K and finite pressures it is found that the ab initio potential better explains the large O2/N2 selectivities of similarly sized molecules that have been observed experimentally. An interesting reversal in ideal selectivity is observed by adjusting the pressure at the two ends of the membrane. As a consequence, we predict that a highly selective kinetic separation in favor of either nitrogen or oxygen could be obtained with the same membrane depending on the operating conditions.

Testing predictions of macroscopic binary diffusion coefficients using lattice models with site heterogeneity

Quantitatively predicting mass transport rates for chemical mixtures in porous materials is important in applications of materials such as adsorbents, membranes, and catalysts. Because directly assessing mixture transport experimentally is challenging, theoretical models that can predict mixture diffusion coefficients using only single-component information would have many uses. One such model was proposed by Skoulidas, Sholl, and Krishna (Langmuir, 2003, 19, 7977), and applications of this model to a variety of chemical mixtures in nanoporous materials have yielded promising results. In this paper, the accuracy of this model for predicting mixture diffusion coefficients in materials that exhibit a heterogeneous distribution of local binding energies is examined. To examine this issue, single-component and binary mixture diffusion coefficients are computed using kinetic Monte Carlo for a two-dimensional lattice model over a wide range of lattice occupancies and compositions. The approach suggested by Skoulidas, Sholl, and Krishna is found to be accurate in situations where the spatial distribution of binding site energies is relatively homogeneous, but is considerably less accurate for strongly heterogeneous energy distributions.

Air separation by single wall carbon nanotubes: Mass transport and kinetic selectivity

Mass transport of pure nitrogen, pure oxygen, and their mixture (air) has been studied at 100 K in a single wall carbon nanotube of 12.53 A diameter. Phenomenological coefficients, and self- and corrected diffusivities are calculated using molecular-dynamics simulations, and transport diffusivities are obtained by combining these results with thermodynamic factors obtained from previous grand canonical Monte Carlo simulations [G. Arora and S. I. Sandler, J. Chem. Phys. 123, 044705 (2005)]. For mixtures, cross-term diffusion coefficients are found to be of similar order of magnitude as main-term diffusion coefficients over the entire range of pressure studied. These results are then combined with a continuum description of mass transport to determine the ideal and kinetic separation factors for a nanotube membrane. High permeances are observed for both pure components and the mixture inside the nanotubes. The concentration profiles, diffusivity profiles, and membrane fluxes are calculated, and it is demonstrated that by carefully adjusting the upstream and downstream pressures, a good kinetic selectivity can be achieved for air separation using single wall carbon nanotubes.

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.

Large Distinct Diffusivity in Binary Mixtures Confined to Zeolite NaY

Mutual diffusion coefficients have been computed from molecular dynamics simulation of two different binary mixtures confined to zeolite NaY. In one of these mixtures, where one component is from the linear regime and the other from the anomalous regime of the levitation effect [S. Yashonath, P. Santikary, J. Phys. Chem., 1994, 98, 6368], the magnitude of distinct diffusivity, Dd, is unusually large and comparable to the mixture self-diffusivity Ds. Distinct van Hove correlations suggest that the large Dd seems to arise from the presence of distinct physisorption sites for the two components. The contribution from Dd might be important for achieving good separation of mixtures, for which zeolites are used extensively.

Molecular dynamics simulation of self- and mutual diffusion coefficients for confined mixtures

The self- and mutual diffusion coefficients for binary mixtures of Ar-Kr both in the bulk and in the nanopores were studied by molecular dynamics simulations. The composition dependences and the relationships between the self- and the mutual diffusion coefficients both in the bulk and in the nanopores were further discussed. It was found that the simulation results (D(c.m.)) are close to the calculated ones (D(s)) for the Ar-Kr system. Both self- and mutual diffusion coefficients in nanopores are much lower than that of the bulk, and they ever decrease as the pore width decreases. Nevertheless, the self- and mutual diffusion coefficients increase as the mole fraction of Ar increases, and as expected, increase as the temperature increases. The self-diffusion coefficients of mixtures both in the bulk and in the nanopores are predicted by the Carman model and by the molecular cluster model.

Diffusion of Alkane Mixtures in Zeolites: Validating the Maxwell−Stefan Formulation Using MD Simulations

Molecular dynamics (MD) simulations have been carried out for pure components, binary, ternary, and quaternary mixtures containing methane, ethane, propane, and n-butane in FAU zeolite at 300 K for a range of molecular loadings Theta, approaching saturation limits. The n-dimensional matrix of Maxwell-Stefan (M-S) diffusivities [Delta], defined by (N) = -rho[Delta][Gamma](nabla Theta), was determined along with the self-diffusivities, D(i)(,self). Additionally, configurational-bias Monte Carlo (CBMC) simulations were carried out to obtain the pure component sorption isotherms and the saturation capacities Theta(i)(,sat). From the information on Delta(ij), D(i)(,self), and Theta(i)(,sat), the various M-S diffusivities were determined: (1) component D(i), reflecting the interactions of the species i with the zeolite, self-exchange D(ii), and (2) binary exchange D(ij). The obtained data underline the major advantage of the M-S formulation that at a given occupancy, theta = Sigma(N)(n)(i=l)Theta(j)/Theta(j)(,sat) within the zeolite, the D(i) has nearly the same value for species i whether this species is present on its own or in a mixture with other species. The same advantage holds, too, for the self-exchange D(ii); the value at a given occupancy, theta, is the same whether determined from pure component, binary, or ternary mixture data. For all binary and ternary mixtures studied, it was verified that the binary exchange coefficient D(ij) can be interpolated from the corresponding values of the self-exchange parameters D(ii) and D(jj) using a generalization of the interpolation formula developed earlier (Skoulidas et al., Langmuir, 2003, 19, 7977). We also demonstrate that if the occupancy dependence of the pure component parameters D(i) and D(ii) are modeled properly, this information is sufficient to provide very good estimates of the matrix [Delta] for mixtures with 2, 3, or 4 components over the entire range of loadings. Simulations of mixture diffusion of alkanes in MFI and LTA confirm that the above-mentioned advantages of the M-S formulation also hold for these zeolite topologies.

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.

Computer simulations of adsorption and diffusion for binary mixtures of methane and hydrogen in titanosilicates

Equilibrium molecular dynamics (MD) simulations of equimolar mixtures of hydrogen and methane were performed in three different titanosilicates: naturally occurring zorite and two synthetic titanosilicates, ETS-4 and ETS-10. In addition, single-component MD simulations and adsorption isotherms generated using grand canonical Monte Carlo simulations were performed to support the mixture simulations. The goal of this study was to determine the best membrane material to carry out hydrogen/methane separations. ETS-10 has a three-dimensional pore network. ETS-4 and zorite have two-dimensional pore networks. The simulations carried out in this study show that the increased porosity of ETS-10 results in self-diffusion coefficients for both hydrogen and methane that are higher in ETS-10 than in either ETS-4 or zorite. Methane only showed appreciable displacement in ETS-10. The ability of the methane molecules to move in all three directions in ETS-10 was demonstrated by the high degree of isotropy shown in the values of the x, y, and z components of the self-diffusion coefficient for methane in ETS-10. From our simulations we conclude that ETS-10 would be better suited for fast industrial separations of hydrogen and methane. However, the separation would not result in a pure hydrogen stream. In contrast, ETS-4 and zorite would act as true molecular sieves for separations of hydrogen and methane, as the methane would not move through membranes made of these materials. This was indicated by the near-zero self-diffusion coefficient of methane in ETS-4 and zorite.

Rapid Diffusion of CH4/H2 Mixtures in Single-Walled Carbon Nanotubes

Equilibrium molecular dynamics (EMD) are used to examine the self-diffusion and macroscopic diffusion of CH4/H2 mixtures adsorbed inside a (10,10) single-walled carbon nanotube. EMD can be used to determine the macroscopic diffusion coefficients of adsorbed mixtures by evaluating the matrix of Onsager transport coefficients. Earlier studies have indicated the diffusion of light gases adsorbed as single components in carbon nanotubes is extremely rapid compared to that in other known nanoporous materials. The results presented here indicate that extremely rapid diffusion can also occur for mixtures of adsorbed molecules. The rapid diffusion of adsorbed molecules and the strong coupling between the fluxes of the adsorbed species in a mixture have interesting implications for uses of carbon nanotubes in membrane-based applications.