On the Application of Widom's Test Particle Method to Homogeneous and Inhomogeneous Fluids

Abstract

Chemical potentials of a homogeneous and an inhomogeneous Lennard-Jones fluid have been determined by molecular dynamics simulations on the vector computer CYBER 205 by applying essentially the fictitious test particle method of Widom. For the homogeneous fluid we find, contrary to the previous result of Guillot and Guissani, that the simulated chemical potential is independent of the particle number. The crucial point, however, is a sufficiently large cut-off radius in the evaluation of the Boltzmann factor. Comparing with our WCA-type perturbation theory, we get agreement in the chemical potentials within 0.1 kT up to the density n[sgrave]³ = 0.80 and a difference of 0.2 kT at n[sgrave]³ = 0.85. For the inhomogeneous case we consider a fluid in a cylindrical pore and integrate Widom's equation over a certain probe volume as suggested earlier by us. Chemical potentials are then calculated independently in five different probe volumes, which are cylindrical shells. The results agree well from the second to the fourth shell. Inaccuracies in the innermost cylinder can be easily explained by bad statistics. In the shell close to the wall the extremely high local density is responsible for the inaccuracies. Extending the probe volume over all cylindrical shells besides the one closest to the wall is thought to yield rather reliable results for the chemical potential. As a by-product of the simulations we also obtained diffusion coefficients, which are given in an appendix.     

Computer Simulation of Isothermal Mass Transport in Graphite Slit Pores

Abstract

Results are presented from a simulation study of the mass transport of oxygen and nitrogen through graphite slit pores. The work is motivated by an attempt to understand the molecular origins of the kinetic selectivity displayed when air is separated into its major components using pressure swing adsorption. A combination of non-equilibrium molecular dynamics (NEMD), equilibrium molecular dynamics (EMD) and grand canonical Monte Carlo methods has been employed in our study to extract the maximum information. Transport diffusivities, self-diffusivities, permeabilities and Darken thermodynamic factors have been calculated as a function of pore width and temperature for pure component oxygen and nitrogen. In addition, new EMD simulation data for an 80:20 mixture of nitrogen and oxygen is reported, including a direct calculation of the Stefan-Maxwell coefficients. The results are discussed in terms of the oxygen selectivity and the possible mechanisms, which increase or decrease this quantity.

We find that the pore width behaviour of the diffusion coefficients consists of three distinct regimes: a regime at larger pore widths in which single component diffusion coefficients are largely independent of pore width, an optimum pore width at which both diffusivities increase substantially but the slit pore is selective towards nitrogen, and a regime at very low pore widths at which the diffusivities decrease sharply, but the slits are selective towards oxygen. The mechanism behind each of these regimes is discussed in terms of “entropic” effects and potential barrier heights.

We have also found that permeability selectivity is substantially reduced in a mixture of the two gases with a composition similar to that of air. Cross diffusion coefficients in the mixture have been calculated and shown to be non-negligible.     

Simulation of a Hard-Sphere Fluid in Bicontinuous Random Media

Abstract

The influence of solid-phase connectivity on size-exclusion partitioning and on diffusion of a dilute hard-sphere fluid in overlapping and nonoverlapping spheres models of porous media is investigated using molecular dynamics and Monte Carlo simulation techniques. Four models are examined, two of which are subject to constrained bicontinuity of the pore and solid phases and two in which the solid spheres in the assemblies are randomly distributed in space. It is shown that at moderate to high porosities, connected (bicontinuous) structures lead to a significant increase in the partition and diffusion coefficients when the particles of the pore fluid are of finite size. The consequences of solid phase connectivity are also clearly illustrated in the long-time decay of the velocity autocorrelation function (VACF) of the diffusing particles, particularly in the vicinity of the percolation threshold. Under these conditions the power law exponents on the long-time tail of the VACF are generally found to be higher in connected models than in random systems and the importance of this result is demonstrated using one of the scaling rules of percolation theory. The simulation results are also compared with the predictions of current theories of partitioning and diffusion in random sphere assemblies and, with reference to experimental data available from the literature, it is shown that bicontinuous models are better representations of real porous media.     

Towards mimicking natural protein channels with aligned carbon nanotube membranes for active drug delivery

AimsCarbon nanotube (CNT) membranes offer an exciting opportunity to mimic natural protein channels due to 1) a mechanism of dramatically enhanced fluid flow 2) ability to place ‘gatekeeper’ chemistry at the entrance to pores 3) the ability for biochemical reactions to occur on gatekeeper molecules and 4) an ability to chemically functionalize each side of the membrane independently.Main methodsAligned CNT membranes were fabricated and CNT pore entrances modified with gatekeeper chemistry. Pressure driven fluid flow and diffusion experiments were performed to study the mechanisms of transport through CNTs.Key findingsThe transport mechanism through CNT membranes is primarily 1) ionic diffusion near bulk expectation 2) gas flow enhanced 1–2 orders of magnitude primarily due to specular reflection 3) fluid flow 4–5 orders of magnitude faster than conventional materials due to a nearly ideal slip-boundary interface. The transport can be modulated by ‘gatekeeper’ chemistry at the pore entrance using steric hindrance, electrostatic attraction/repulsion, or biochemical state. The conformation of charged tethered molecules can be modulated by applied bias setting the stage for programmable drug release devices.SignificanceThe membrane structure is mechanically far more robust than lipid bilayer films, allowing for large-scale chemical separations, delivery or sensing based on the principles of protein channels. The performance of protein channels is several orders of magnitude faster than conventional membrane materials. The fundamental requirements of mimicking protein channels are present in the CNT membrane system.     

Interfacial interactions of glutamate, water and ions with carbon nanopore evaluated by molecular dynamics simulations

Molecular dynamics simulations were used to assess the transport of glutamate, water and ions (Na⁺ and Cl⁻) in a single wall carbon nanopore. The spatial profiles of Na⁺ and Cl⁻ ions are largely determined by the pore wall charges. Co-ions are repelled whereas the counter-ions are attracted by the pore charges, but this ‘rule’ breaks down when the water concentration is set to a level significantly below that in the physiological bulk solution. In such cases water is less able to counteract the ion-wall interactions (electrostatic or non-electrostatic), co-ions are layered near the counter-ions attracted by the wall charges and are thus layered as counter-ions. Glutamate is concentrated near the pore wall even at physiological water concentration, and irrespective of whether the pore wall is neutral or charged (positively or negatively), and its peak levels are up to 40 times above mean values. The glutamate is thus always layered as a counter-ion. Layering of water near the wall is independent of charges on the pore wall, but its peak levels near the wall are ‘only’ 6-8 times above the pore mean values. However, if the mean concentration of water is significantly below the level in the physiological bulk solution, its layering is enhanced, whereas its concentration in the pore center diminishes to very low levels. Reasons for such a ‘paradoxical’ behavior of molecules (glutamate and water) are that the non-electrostatic interactions are (except at very short distances) attractive, and electrostatic interactions (between the charged atoms of the glutamate or water and the pore wall) are also attractive overall. Repulsive interactions (between equally charged atoms) exist, and they order the molecules near the wall, whereas in the pore center the glutamate (and water) angles are largely randomly distributed, except in the presence of an external electric field. Diffusion of molecules and ions is complex. The translational diffusion is in general both inhomogeneous and anisotropic. Non-electrostatic interactions (ion-wall, glutamate-wall or water-wall) powerfully influence diffusion. In the neutral nanopore the effective axial diffusion constants of glutamate, water and Na⁺ and Cl⁻ ions are all < 10% of their values in the bulk, and the electrostatic interactions can reduce them further. Diffusion of molecules and ions is further reduced if the water concentration in the pore is low. Glutamate⁻ is slowed more than water, and ions are reduced the most especially co-ions. In conclusion the interfacial interactions influence the spatial distribution of glutamate, water and ions, and regulate powerfully, in a complex manner and over a very wide range their transport through nanosize pores.     

Molecular insight into the micro-behaviors of CH4 and CO2 in montmorillonite slit-nanopores

Abstract

The Grand Canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulation methods were used to investigate the adsorption and diffusion properties of CH₄ and CO₂ in montmorillonite slit-nanopores. It is found that, both CH₄ and CO₂ could adsorb closely onto the pore surface, while different adsorption states occur for CH₄ and CO₂, respectively, in montmorillonite slit-nanopores. Competitive adsorption of CO₂ over CH₄ exists in montmorillonite slit-nanopores, especially at the lower pressures, which is attributed to the different interaction intensity between the CH₄–CO₂ molecules and the pore surface. The diffusion coefficients of CH₄ and CO₂ both decrease with the enhanced pressures, while the CO₂ has a relative weak diffusion coefficient comparing with CH₄. A well displacement of the residual CH₄ by CO₂ in montmorillonite slit-nanopores was investigated, which is found that the displacement efficiency increases with the enhanced bulk pressures. It was determined that, the CO₂ can be captured and reserved in the montmorillonite slit-nanopores during the displacement, and the sequestration amount of CO₂ gets enhanced with the bulk pressure increasing. This study provides micro-behaviours of CH₄ and CO₂ in montmorillonite slit-nanopores, for the purpose to give out useful guidance for enhancing shale gas extraction by injecting CO₂.     

Pore network modelling of affinity chromatography: determination of the dynamic profiles of the pore diffusivity of beta-galactosidase and its effect on column performance as the loading of beta-galactosidase onto anti-beta-galactosidase varies with time.

A three-dimensional pore network model for diffusion in porous adsorbent particles was employed in a dynamic adsorption model that simulates the adsorption of a solute in porous particles packed in a chromatographic column. The solution of the combined model yielded the dynamic profiles of the pore diffusion coefficient of beta-galactosidase along the radius of porous adsorbent particles and along the length of the column as the loading of beta-galactosidase onto anti-beta-galactosidase immobilized on the surface of the pores of the particles occurred, and, the dynamic adsorptive capacity of the chromatographic column as a function of the design and operational parameters of the chromatographic system. It was found that for a given column length the dynamic profiles of the pore diffusion coefficient were influenced by (a) the superficial fluid velocity in the column, (b) the diameter of the adsorbent particles, and (c) the pore connectivity of the porous structure of the adsorbent particles. The effect of the magnitude of the pore connectivity on the dynamic profiles of the pore diffusion coefficient of beta-galactosidase increased as the diameter of the adsorbent particles and the superficial fluid velocity in the column increased. The dynamic adsorptive capacity of the column increased as (i) the particle diameter and the superficial fluid velocity in the column decreased, and (ii) the column length and the pore connectivity increased. In preparative affinity chromatography, it is desirable to obtain high throughputs within acceptable pressure gradients, and this may require the employment of larger diameter adsorbent particles. In such a case, longer column lengths satisfying acceptable pressure gradients with adsorbent particles having higher pore connectivity values could provide high dynamic adsorptive capacities. An alternative chromatographic system could be comprised of a long column packed with large particles which have fractal pores (fractal particles) that have high pore connectivities and which allow high intraparticle diffusional and convective flow mass transfer rates providing high throughputs and high dynamic adsorptive capacities. If large scale monoliths could be made to be reproducible and operationally stable, they could also offer an alternative mode of operation that could provide high throughputs and high dynamic adsorptive capacities.     

Effect of Twisted Fiber Anisotropy in Cardiac Tissue on Ablation with Pulsed Electric Fields

BackgroundAblation of cardiac tissue with pulsed electric fields is a promising alternative to current thermal ablation methods, and it critically depends on the electric field distribution in the heart.MethodsWe developed a model that incorporates the twisted anisotropy of cardiac tissue and computed the electric field distribution in the tissue. We also performed experiments in rabbit ventricles to validate our model. We find that the model agrees well with the experimentally determined ablation volume if we assume that all tissue that is exposed to a field greater than 3 kV/cm is ablated. In our numerical analysis, we considered how tissue thickness, degree of anisotropy, and electrode configuration affect the geometry of the ablated volume. We considered two electrode configurations: two parallel needles inserted into the myocardium (“penetrating needles” configuration) and one circular electrode each on epi- and endocardium, opposing each other (“epi-endo” configuration).ResultsFor thick tissues (10 mm) and moderate anisotropy ratio (a = 2), we find that the geometry of the ablated volume is almost unaffected by twisted anisotropy, i.e. it is approximately translationally symmetric from epi- to endocardium, for both electrode configurations. Higher anisotropy ratio (a = 10) leads to substantial variation in ablation width across the wall; these variations were more pronounced for the penetrating needle configuration than for the epi-endo configuration.For thinner tissues (4 mm, typical for human atria) and higher anisotropy ratio (a = 10), the epi-endo configuration yielded approximately translationally symmetric ablation volumes, while the penetrating electrodes configuration was much more sensitive to fiber twist.ConclusionsThese results suggest that the epi-endo configuration will be reliable for ablation of atrial fibrillation, independently of fiber orientation, while the penetrating electrode configuration may experience problems when the fiber orientation is not consistent across the atrial wall.     

GCEMC Simulations of “Swiss Cheese” Ion Exchange Membranes in Dilute Solutions of Primitive Model 1:1 Electrolytes with Different Sizes of Ions or 2:1 Electrolytes with Different Bjerrum Parameters

Abstract

Monte Carlo simulations using a Markov process corresponding to a (generalized) Grand Canonical Ensemble have been performed for a number of spherical micropores in equilibrium with dilute external bulk solutions of primitive model electrolytes. Dilute solutions of 1:1 electrolytes with a Bjerrum parameter B = 1.546 with cations three times larger than the anions have been simulated. Also, dilute solutions of 2:1 electrolytes with ions of equal size and reduced Bjerrum parameters B_r = 1.546 and 3 have been simulated. The pores are primitive pores with hard walls and the same dielectric permittivity in the wall and in the pore solution. They range from a pore radius = 5 times the mean ionic diameter to 35 times this diameter, and they carry a fixed charge equal to + 5,0 and ?5 elementary charges. The fixed charge is modelled as smoothly distributed on the pore-wall interface. In addition to the electric potential of the interfacial charge and the electric potential of the spherical double layer, a potential Δ between the pore solution and the bulk solution may be deliberately added. For single pores we may take Δ = 0, but then the pore is generally not electroneutral. In a “Swiss cheese” membrane with a lot of (equally sized) pores, the membrane phase has to approach electroneutrality for growing size of the phase. This is approximated by means of a membrane generated potential Δ in each pore (from the electrostatic interactions with the other pores). The potential A so chosen to obtain electroneutrality is the GCEMC Donnan potential. These non-ideal Donnan potentials are compared to the ideal values (with activity coefficients equal to zero). From the mean occupation numbers of cations and anions in the pores, the average pore values of the mean ionic and the single ionic activity coefficients of the ions are calculated. These are very dependent on pore sizes and on the potential in the pore. The excess energy and the electrostatic Helmholtz free energy of the ions in the pores are also simulated directly. The electrostatic entropy is found as the difference.     

Corresponding states vapour–liquid phase equilibria of confined square–well fluid

Corresponding states vapour–liquid phase equilibria of confined square-well fluid are studied by means of grand-canonical transition-matrix Monte Carlo simulation and histogram reweighting method. In this study, square-well fluid is considered under hard and attractive slit pore confinements ranging from 1.5 to 40 molecular diameters. Corresponding states vapour–liquid phase coexistence envelopes display insignificant effect of wall?fluid interaction for slit pore confinements ranging from 1.5 to 3 molecular diameters. On the other hand, significant effect of wall?fluid interaction on the corresponding state coexistence envelope is observed for slit pore confinements ranging from 4 to 40 molecular diameters. Moreover, at a given slit width, shrinking in corresponding state coexistence envelope is observed with increase in the wall?fluid interaction. However, in the larger slit pore width of 30 to 40 molecular diameters, shrinking in the corresponding state vapour–liquid coexistence envelopes become indifferent with the stronger wall?fluid interactions studied in this work. Structural behaviour of coexisting phases in slit pores are also investigated through local density profiles, to understand the overall behaviour of corresponding states coexistence envelopes. Fluctuating positive and negative deviations in the corresponding state spreading pressure with respect to corresponding bulk value is observed for studied wall?fluid interactions and slit pore confinements.     

Transport rates of proteins in porous materials with known microgeometry.

Many biological and biotechnological systems involve the diffusion of macromolecules through complicated macroporous (pore size on the order of 10-100 microns) environments. In this report, we present and evaluate an experimental system for measuring the rate of protein transport in an inert, macroporous membrane. For this particular membrane system, the microgeometry was characterized in terms of distribution of pore size, position, and orientation. Although the rate of protein desorption was much less than expected based on continuum diffusion models, we demonstrate that the measured transport rates are consistent with diffusion of protein in a complex, interconnected network of water-filled pores. The porous systems exhibit transitional behavior in quantitative agreement with the behavior of percolation lattices (mean square error 7%, n = 29). Predictive mathematical models of the diffusion process were developed: these models used percolation concepts to describe pore topology, continuum models of diffusion/dissolution to describe protein movement at each single pore, and measured pore size distributions. Effective diffusion coefficients for protein transport in aqueous, constricted macropores were predicted by this technique. Predicted diffusion coefficients, based on measured and derived microstructural parameters, agree with experimentally measured diffusion coefficients within a factor of 2. This approach may be useful in the design of porous polymer systems for biological applications and for evaluating other biological systems where conduction of mass, heat, momentum, or charge occurs in a heterogeneous environment.     

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

Abstract

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.     

Adsorption and diffusion of CO2 and CH4 in covalent organic frameworks: an MC/MD simulation study

Covalent organic frameworks (COFs) are a promising gas separation material which have been developed recently. In this work, we have used grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations to investigate the adsorption and diffusion properties of CO₂ and CH₄ in five recent synthesised COF materials. We have also considered the properties of amino-modified COFs by adding –NH₂ group to the five COFs. The adsorption isotherm, adsorption/diffusion selectivity, self/transport diffusion coefficients have been examined and discussed. All of the five COFs exhibit promising adsorption selectivity which is higher than common nanoporous materials. An S-shaped adsorption isotherm can be found for CO₂ instead of CH₄ adsorption. The introduction of –NH₂ group is effective at low pressure region (<200?kPa). The diffusion coefficients are similar for TS-COFs but increase with the pore size for PI-COFs, and the diffusion coefficients seem less dependent on the –NH₂ groups.     

Kinetics of Diffusion and Convection in 3.2-Å Pores: Exact Solution by Computer Simulation

The kinetics of transport in pores the size postulated for cell membranes has been investigated by direct computer simulation (molecular dynamics). The simulated pore is 11 Å long and 3.2 Å in radius, and the water molecules are modeled by hard, smooth spheres, 1 Å in radius. The balls are given an initial set of positions and velocities (with an average temperature of 313° K) and the computer then calculates their exact paths through the pore. Two different conditions were used at the ends of the pore. In one, the ends are closed and the balls are completely isolated. In the other, the ball density in each end region is fixed so that a pressure difference can be established and a net convective flow produced. The following values were directly measured in the simulated experiments: net and diffusive (oneway) flux; pressure, temperature, and diffusion coefficients in the pore; area available for diffusion; probability distribution of ball positions in the pore; and the interaction between diffusion and convection. The density, viscosity, and diffusion coefficients in the bulk fluid were determined from the theory of hard sphere dense gases. From these values, the “equivalent” pore radius (determined by the same procedure that is used for cell membranes) was computed and compared with the physical pore radius of the simulated pore.     

N-octane diffusivity enhancement via carbon dioxide in silica slit-shaped nanopores – a molecular dynamics simulation

Equilibrium molecular dynamics simulations were conducted to study the competitive adsorption and diffusion of mixtures containing n-octane and carbon dioxide confined in slit-shaped silica pores of width 1.9 nm. Atomic density profiles substantiate strong interactions between CO₂ molecules and the protonated pore walls. Non-monotonic change in n-octane self-diffusion coefficients as a function of CO₂ loading was observed. CO₂ preferential adsorption to the pore surface is likely to attenuate the surface adsorption of n-octane, lower the activation energy for n-octane diffusivity, and consequently enhance n-octane mobility at low CO₂ loading. This observation was confirmed by conducting test simulations for pure n-octane confined in narrower pores. At high CO₂ loading, n-octane diffusivity is hindered by molecular crowding. Thus, n-octane diffusivity displays a maximum. In contrast, within the concentration range considered here, the self-diffusion coefficient predicted for CO₂ exhibits a monotonic increase with loading, which is attributed to a combination of effects including the saturation of the adsorption capacity of the silica surface. Test simulations suggest that the results are strongly dependent on the pore morphology, and in particular on the presence of edges that can preferentially adsorb CO₂ molecules and therefore affect the distribution of these molecules equally on the pore surface, which appears to be required to provide the effective enhancement of n-octane diffusivity.     

Effects of conjugated and unconjugated bile acids on the activity of the Vibrio cholerae porin OmpT

Abstract

During infection, the enteric pathogen Vibrio cholerae encounters a bile-containing environment. Previous studies have shown that bile and/or bile acids exert several effects on the virulence and physiology of the bacterial cells. These observations have led to the suggestion that bile acids may play a signaling role in infection. We have previously reported that the bile component deoxycholic acid blocks the general diffusion porin OmpT in a dose-dependent manner, presumably as it transits through the pore. V. cholerae colonizes the distal jejunum and ileum, where a mixture of various conjugated and unconjugated bile acids are found. In this work, we have used patch clamp electrophysiology to investigate the effects of six bile acids on OmpT. Two bile acids (deoxycholic and chenodeoxycholic acids) were found to block OmpT at physiological concentrations below 1 mM, while glycodeoxycholic acid was mildly effective and cholic, lithocholic and taurodeoxycholic acids were ineffective in this range. The block was also voltage-dependent. These observations suggest the presence of a specific binding site inside the OmpT pore. Since deconjugation is due to the activity of the endogenous flora, the preferential uptake of some unconjugated bile acids by OmpT may signal the presence of a hospitable environment. The results are also discussed in terms of the possible molecular interactions between the penetrating bile acid molecule and the channel wall.     

Molecular Dynamics Studies of Diffusion in Model Cylindrical Pores at Very Low Densities

Abstract

Molecular dynamics simulation has been used to study diffusion of methane at ambient temperature in cylindrical pores at very low densities. The cylinders were modelled as a continuum solid which interacts with the methane in the radial direction only. At the lowest densities, the VACF method does not yield reliable values of the self diffusion coefficient, D_s , but a suitable choice of time step and run length enables values of D_s to be found from MSD plots that are below the classical Knudsen diffusion coefficients. When density is increased, D_s passes through a maximum although the adsorption isotherm remains inside the Henry law region. Maxima are found for two cylinder radii and for two adsorbent field strengths. The existence of a maximum is attributed to transient intermolecular interactions. Analysis of a molecular trajectory demonstrates that long diffusion paths can be triggered by the rare event of an intermolecular encounter which forces a molecule into the repulsive part of the wall potential. At sufficiently high density, subsequent collisions quench the tendency towards long paths, and D_s decreases again. The issue of simulation artefact as a source of these observations is discussed.     

Hybrid MD-Nernst Planck model of α-hemolysin conductance properties

Motivated by experiments in which an applied electric field translocates polynucleotides through an α-hemolysin protein channel causing ionic current transient blockade, a hybrid simulation model is proposed to predict the conductance properties of the open channel. Time scales corresponding to ion permeation processes are reached using the Poisson–Nernst–Planck (PNP) electro-diffusion model in which both solvent and local ion concentrations are represented as a continuum. The diffusion coefficients of the ions (K⁺ and Cl^?) input in the PNP model are, however, calculated from all-atom molecular dynamics (MD). In the MD simulations, a reduced representation of the channel is used. The channel is solvated in a 1?M KCl solution, and an external electric field is applied. The pore specific diffusion coefficients for both ionic species are reduced 5–7 times in comparison to bulk values. Significant statistical variations (17–45%) of the pore-ions diffusivities are observed. Within the statistics, the ionic diffusivities remain invariable for a range of external applied voltages between 30 and 240?mV. In the 2D-PNP calculations, the pore stem is approximated by a smooth cylinder of radius ～9?Å with two constriction blocks where the radius is reduced to ～6?Å. The electrostatic potential includes the contribution from the atomistic charges. The MD-PNP model shows that the atomic charges are responsible for the rectifying behaviour and for the slight anion selectivity of the α-hemolysin pore. Independent of the hierarchy between the anion and cation diffusivities, the anionic contribution to the total ionic current will dominate. The predictions of the MD-PNP model are in good agreement with experimental data and give confidence in the present approach of bridging time scales by combining a microscopic and macroscopic model.     

Modeling of adsorption in nanopores

Adsorption in nonporous materials has been studied using Grand Canonical Monte Carlo simulations. We discuss three types of materials: (a) a model of cylindrical pores with smooth walls, representing MCM-41 like materials, (b) a model of cylindrical pores with regular structured walls (model of carbon nanotubes) and (c) a material with crystalline wall structure (zeolites). Typical problems related to the stability of adsorbed layers have been analyzed. We have shown that the mechanism of adsorption is strongly dependent on the structure of the pore walls. In the case of amorphous walls it may lead to metastable configurations. In nanotubes, the ordered corrugation structure of walls determines the low temperature structure of the adsorbed system. In 3D ordered porous system, such as zeolites, the mechanism of adsorption is mostly determined by characteristic sites of adsorption.Figure Adsorbed atoms and energy fluctuations at the pressure of the first layer formation of krypton atoms: (a) instantaneous numbers of adsorbed atoms (per nm² of the pore wall) as a function of the time of simulation (Monte Carlo steps) observed in a relatively long run, (b) the bimodal distribution of the energy fluctuations is a consequence of the behavior of the systems as shown in (a).     

Molecular-Dynamics Simulation of the Surface Diffusion of n-Alkanes on Pt(111)

Abstract

In the present study, the equilibrium adsorption and the dynamics of surface diffusion in a model of ethane and n-butane on a Pt(111) surface were simulated with molecular dynamics. At low temperatures, we found that both admolecules adsorb in a specific binding site. Through analysis of the trajectories, several features of the dynamics were resolved. At low temperature, we observed that diffusion occurs through a nearest-neighbor hopping mechanism involving both lateral rotation and axial translation. At high temperatures, the admolecule makes multiple-site hops and nonlocalized long flights. The temperature dependence of the diffusion coefficients was analyzed and was found to exhibit good Arrhenius behavior. The apparent diffusion coefficients follow trends seen in related experimental studies. In the case of ethane, a comparison between the diffusion barrier measured in the molecular-dynamics simulations and the theoretical barrier predicted by transition-state theory indicates that the simulated barrier is larger than the theoretical value. This finding is consistent with conclusions in recent studies of metal-atom diffusion on metal surfaces, where it was found that systems with low corrugation exhibit a non-unique relationship between the dynamical diffusion barrier and the potential-energy-surface topology.