Confined fluids in a Janus pore: influence of surface asymmetry on structure and solvation forces

Density distribution, fluid structure and solvation forces for fluids confined in Janus slit-shaped pores are investigated using grand canonical Monte Carlo simulations. By varying the degree of asymmetry between the two smooth surfaces that make up the slit pores, a wide variety of adsorption situations are observed. The presence of one moderately attractive surface in the asymmetric pore is sufficient to disrupt the formation of frozen phases observed in the symmetric case. In the extreme case of asymmetry in which one wall is repulsive, the pore fluid can consist of a frozen contact layer at the attractive surface for smaller surface separations (H) or a frozen contact layer with liquid-like and gas-like regions as the pore width is increased. The superposition approximation, wherein the solvation pressure and number density in the asymmetric pores can be obtained from the results on symmetric pores, is found to be accurate for H > 4 sigma(ff), where sigma(ff) is the Lennard-Jones fluid diameter and within 10% accuracy for smaller surface separations. Our study has implications in controlling stick slip and overcoming static friction `stiction' in micro and nanofluidic devices.

Computer simulations of colloidal fluids in confinement

Computer-Simulationen von Kolloidalen Fluiden in Beschränkten Geometrien Kolloidale Suspensionen, die einen Phasenübergang aufweisen, zeigen eine Vielfalt an interessanten Effekten, sobald sie auf eine bestimmte Geometrie beschränkt werden, wie zum Beispiel auf zylindrische Poren, sphärische Hohlräume oder auf einen Spalt mit ebenen Wänden. Der Einfluss dieser verschiedenen Geometrietypen sowohl auf das Phasenverhalten als auch auf die Dynamik von Kolloid-Polymer-Mischungen wird mit Hilfe von Computer-Simulationen unter Verwendung des Asakura-Oosawa- Modells, für welches auf Grund der “Depletion”-Kräfte ein Phasenübergang existiert, untersucht. Im Fall von zylindrischen Poren sieht man ein interessantes Phasenverhalten, welches vom eindimensionalen Charakter des Systems hervorgerufen wird. In einer kurzen Pore findet man im Bereich des Phasendiagramms, in dem das System typischerweise entmischt, entweder eine polymerreiche oder eine kolloidreiche Phase vor. Sobald aber die Länge der zylindrischen Pore die typische Korrelationslänge entlang der Zylinderachse überschreitet, bilden sich mehrere quasi-eindimensionale Bereiche der polymerreichen und der kolloidreichen Phase, welche von nun an koexistieren. Diese Untersuchungen helfen das Verhalten von Adsorptionshysteresekurven in entsprechenden Experimenten zu erklären. Wenn das Kolloid-Polymer-Modellsystem auf einen sphärischen Hohlraum eingeschränkt wird, verschiebt sich der Punkt des Phasenübergangs von der polymerreichen zur kolloidreichen Phase. Es wird gezeigt, dass diese Verschiebung direkt von den Benetzungseigenschaften des Systems abhängt, was die Beobachtung von zwei verschiedenen Morphologien bei Phasenkoexistenz ermöglicht – Schalenstrukturen und Strukturen des Janustyps. Im Rahmen der Untersuchung von heterogener Keimbildung von Kristallen innerhalb einer Flüssigkeit wird eine neue Simulationsmethode zur Berechnung von Freien Energien der Grenzfläche zwischen Kristall- bzw. Flüssigkeitsphase undWand präsentiert. Die Resultate für ein System von harten Kugeln und ein System einer Kolloid- Polymer-Mischung werden anschließend zur Bestimmung von Kontaktwinkeln von Kristallkeimen an Wänden verwendet. Die Dynamik der Phasenseparation eines quasi-zweidimensionalen Systems, welche sich nach einem Quench des Systems aus dem homogenen Zustand in den entmischten Zustand ausbildet, wird mit Hilfe von einer mesoskaligen Simulationsmethode (“Multi Particle Collision Dynamics”) untersucht, die sich für eine detaillierte Untersuchung des Einflusses der hydrodynamischen Wechselwirkung eignet. Die Exponenten universeller Potenzgesetze, die das Wachstum der mittleren Domänengröße beschreiben, welche für rein zwei- bzw. dreidimensionale Systeme bekannt sind, können für bestimmte Parameterbereiche nachgewiesen werden. Die unterschiedliche Dynamik senkrecht bzw. parallel zu den Wänden sowie der Einfluss der Randbedingungen für das Lösungsmittel werden untersucht. Es wird gezeigt, dass die daraus resultierende Abschirmung der hydrodynamischen Wechselwirkungsreichweite starke Auswirkungen auf das Wachstum der mittleren Domänengröße hat.

Effects of potential models on the adsorption of ethane and ethylene on graphitized thermal carbon black. Study of two-dimensional critical temperature and isosteric heat versus loading

Adsorption of ethylene and ethane on graphitized thermal carbon black and in slit pores whose walls are composed of graphene layers is studied in detail to investigate the packing efficiency, the two-dimensional critical temperature, and the variation of the isosteric heat of adsorption with loading and temperature. Here we used a Monte Carlo simulation method with a grand canonical Monte Carlo ensemble. A number of two-center Lennard-Jones (LJ) potential models are investigated to study the impact of the choice of potential models in the description of adsorption behavior. We chose two 2C-LJ potential models in our investigation of the (i) UA-TraPPE-LJ model of Martin and Siepmann (J. Phys. Chem. B 1998,102, 25692577) for ethane and Wick et al. (J. Phys. Chem. B 2000,104, 8008-8016) for ethylene and (ii) AUA4-LJ model of Ungerer et al. (J. Chem. Phys. 2000,112, 5499-5510) for ethane and Bourasseau et al. (J. Chem. Phys. 2003, 118, 3020-3034) for ethylene. These models are used to study the adsorption of ethane and ethylene on graphitized thermal carbon black. It is found that the solid-fluid binary interaction parameter is a function of adsorbate and temperature, and the adsorption isotherms and heat of adsorption are well described by both the UA-TraPPE and AUA models, although the UA-TraPPE model performs slightly better. However, the local distributions predicted by these two models are slightly different. These two models are used to explore the two-dimensional condensation for the graphitized thermal carbon black, and these values are 110 K for ethylene and 120 K for ethane.

Prediction of high-pressure adsorption equilibrium of supercritical gases using density functional theory

In this paper, we present the results of the prediction of the high-pressure adsorption equilibrium of supercritical. gases (Ar, N-2, CH4, and CO2) on various activated carbons (BPL, PCB, and Norit R1 extra) at various temperatures using a density-functional-theory-based finite wall thickness (FWT) model. Pore size distribution results of the carbons are taken from our recent previous work 1,2 using this approach for characterization. To validate the model, isotherms calculated from the density functional theory (DFT) approach are comprehensively verified against those determined by grand canonical Monte Carlo (GCMC) simulation, before the theoretical adsorption isotherms of these investigated carbons calculated by the model are compared with the experimental adsorption measurements of the carbons. We illustrate the accuracy and consistency of the FWT model for the prediction of adsorption isotherms of the all investigated gases. The pore network connectivity problem occurring in the examined carbons is also discussed, and on the basis of the success of the predictions assuming a similar pore size distribution for accessible and inaccessible regions, it is suggested that this is largely related to the disordered nature of the carbon.

Effects of surface heterogeneity on the adsorption of nitrogen on graphitized thermal carbon black

In this paper, we study the surface heterogeneity and the surface mediation on the intermolecular potential energy for nitrogen adsorption on graphitized thermal carbon black (GTCB). The surface heterogeneity is modeled as the random distribution of effective carbonyl functional groups on the graphite surface. The molecular parameters and the discrete charges of this carbonyl group are taken from Jorgensen, et al. (J. Am. Chem. Soc., (1984) 106, 6638) while those for nitrogen (dispersive parameters and discrete charges) are taken from Murthy et al. (Mol. Phys., (1983) 50, 531) in our Grand Canonical Monte Carlo (GCMC) simulation. The solid surface mediation in the reduction of intermolecular potential energy between two fluid molecules was taken from a recent work by Do et al. (Langmuir, (2004) 20, 7623). Our simulation results accounting for the surface heterogeneity and surface mediation on intermolecular potential energy were compared with the experimental data of nitrogen at 77 and 90 K. The solid-fluid dispersive parameters are determined from the Lorentz-Berthelot (LB) rule. The fraction of the graphite surface covered with carbonyl functional groups was then derived from the consideration of the Henry constant, and for the data of Kruk et al. (Langmuir, (1999) 15, 1435) we have found that 1% of their GTCB surface is covered with effective carbonyl functional groups. The damping constant, due to surface mediation, was determined from the consideration of the portion of the adsorption isotherm where the first layer is being completed, and it was found to take a value of 0.0075. With these parameters, we have found that the GCMC simulation results describe the data over the complete range of pressure substantially better than any other MC models in the literature. The implication of this work is demonstrated with local adsorption isotherms of 10 and 20 A slit pores. One was obtained without allowance for surface mediation, while the other correctly accounts for these factors. The two local isotherms differ substantially, and the implication is that if we used incorrect local isotherms (i.e. without the surface mediation) the pore size distribution would be incorrectly derived.

Improvement of the Derjaguin-Broekhoff-de Boer theory for capillary condensation/evaporation of nitrogen in mesoporous systems and its implications for pore size analysis of MCM-41 silicas and related materials

In this work, we propose an improvement of the classical Derjaguin-Broekhoff-de Boer (DBdB) theory for capillary condensation/evaporation in mesoporous systems. The primary idea of this improvement is to employ the Gibbs-Tolman-Koenig-Buff equation to predict the surface tension changes in mesopores. In addition, the statistical film thickness (so-called t-curve) evaluated accurately on the basis of the adsorption isotherms measured for the MCM-41 materials is used instead of the originally proposed t-curve (to take into account the excess of the chemical potential due to the surface forces). It is shown that the aforementioned modifications of the original DBdB theory have significant implications for the pore size analysis of mesoporous solids. To verify our improvement of the DBdB pore size analysis method (IDBdB), a series of the calcined MCM-41 samples, which are well-defined materials with hexagonally ordered cylindrical mesopores, were used for the evaluation of the pore size distributions. The correlation of the IDBdB method with the empirically calibrated Kruk-Jaroniec-Sayari (KJS) relationship is very good in the range of small mesopores. So, a major advantage of the IDBdB method is its applicability for small mesopores as well as for the mesopore range beyond that established by the KJS calibration, i.e., for mesopore radii greater than similar to4.5 nm. The comparison of the IDBdB results with experimental data reported by Kruk and Jaroniec for capillary condensation/evaporation as well as with the results from nonlocal density functional theory developed by Neimark et al. clearly justifies our approach. Note that the proposed improvement of the classical DBdB method preserves its original simplicity and simultaneously ensures a significant improvement of the pore size analysis, which is confirmed by the independent estimation of the mean pore size by the powder X-ray diffraction method.

Pore size distribution analysis of activated carbons: Application of density functional theory using nongraphitized carbon black as a reference system

The application of nonlocal density functional theory (NLDFT) to determine pore size distribution (PSD) of activated carbons using a nongraphitized carbon black, instead of graphitized thermal carbon black, as a reference system is explored. We show that in this case nitrogen and argon adsorption isotherms in activated carbons are precisely correlated by the theory, and such an excellent correlation would never be possible if the pore wall surface was assumed to be identical to that of graphitized carbon black. It suggests that pore wall surfaces of activated carbon are closer to that of amorphous solids because of defects of crystalline lattice, finite pore length, and the presence of active centers.. etc. Application of the NLDFT adapted to amorphous solids resulted in quantitative description of N-2 and Ar adsorption isotherms on nongraphitized carbon black BP280 at their respective boiling points. In the present paper we determined solid-fluid potentials from experimental adsorption isotherms on nongraphitized carbon black and subsequently used those potentials to model adsorption in slit pores and generate a corresponding set of local isotherms, which we used to determine the PSD functions of different activated carbons. (c) 2005 Elsevier Ltd. All rights reserved.

Influence of adsorbate interaction on transport in confined spaces

This article provides a review of the recent theory of transport in nanopores developed in the author's laboratory. In particular the influence of fluid-solid interactions on the transport coefficient is examined, showing that such interactions reduce the value of the coefficient by almost an order of magnitude in comparison to the Knudsen theory for non-interacting systems. The activation energy and potential energy barriers for diffusion in smooth pores with a one-dimensional potential energy profile are also discussed, indicating the inadequacy of the commonly used assumption of proportionality between the activation energy and heat of adsorption or the minimum pore potential energy. A further feature affected by fluid-solid interactions is the nature of the reflection of fluid molecules colliding with a pore wall surface, varying from being nearly specular - such as in carbon nanotubes - to nearly diffuse for amorphous solids. Diffuse reflection leads to momentum loss and reduced transport coefficients. However, fluid-solid interactions do not affect the transport coefficient in the single-file diffusion regime when the surface reflection is diffuse, and the transport coefficient in this case is largely independent of the adsorbed density.

Mechanisms influencing levitation and the scaling laws in nanopores: Oscillator model theory

We provide here a detailed theoretical explanation of the floating molecule or levitation effect, for molecules diffusing through nanopores, using the oscillator model theory (Phys. Rev. Lett. 2003, 91, 126102) recently developed in this laboratory. It is shown that on reduction of pore size the effect occurs due to decrease in frequency of wall collision of diffusing particles at a critical pore size. This effect is, however, absent at high temperatures where the ratio of kinetic energy to the solid-fluid interaction strength is sufficiently large. It is shown that the transport diffusivities scale with this ratio. Scaling of transport diffusivities with respect to mass is also observed, even in the presence of interactions.

Simulation of binary mixture adsorption of methane and CO2 at supercritical conditions in carbons

Knowledge of the adsorption behavior of coal-bed gases, mainly under supercritical high-pressure conditions, is important for optimum design of production processes to recover coal-bed methane and to sequester CO2 in coal-beds. Here, we compare the two most rigorous adsorption methods based on the statistical mechanics approach, which are Density Functional Theory (DFT) and Grand Canonical Monte Carlo (GCMC) simulation, for single and binary mixtures of methane and carbon dioxide in slit-shaped pores ranging from around 0.75 to 7.5 nm in width, for pressure up to 300 bar, and temperature range of 308-348 K, as a preliminary study for the CO2 sequestration problem. For single component adsorption, the isotherms generated by DFT, especially for CO2, do not match well with GCMC calculation, and simulation is subsequently pursued here to investigate the binary mixture adsorption. For binary adsorption, upon increase of pressure, the selectivity of carbon dioxide relative to methane in a binary mixture initially increases to a maximum value, and subsequently drops before attaining a constant value at pressures higher than 300 bar. While the selectivity increases with temperature in the initial pressure-sensitive region, the constant high-pressure value is also temperature independent. Optimum selectivity at any temperature is attained at a pressure of 90-100 bar at low bulk mole fraction of CO2, decreasing to approximately 35 bar at high bulk mole fractions. (c) 2005 American Institute of Chemical Engineers.

Transport of simple fluids in nanopores: Theory and simulation

A theory is discussed of single-component transport in nanopores, recently developed by Bhatia and coworkers. The theory considers the oscillatory motion of molecules between diffuse wall collisions, arising from the fluid-wall interaction, along with superimposed viscous flow due to fluid-fluid interaction. The theory is tested against molecular dynamics simulations for hydrogen, methane, and carbon tetrafluoride flow in cylindrical nanopores in silica. Although exact at low densities, the theory performs well even at high densities, with the density dependency of the transport coefficient arising from viscous effects. Such viscous effects are reduced at high densities because of the large increase in viscosity, which explains the maximum in the transport coefficient with increase in density. Further, it is seen that in narrow pore sizes of less than two molecular diameters, where a complete monolayer cannot form on the surface, the mutual interference of molecules on opposite sides of the cross section can reduce the transport coefficient, and lead to a maximum in the transport coefficient with increasing density. The theory is also tested for the case of partially diffuse reflection and shows the viscous contribution to be negligible when the reflection is nearly specular. (c) 2005 American Institute of Chemical Engineers AIChE J, 52: 29-38, 2006.

Correct procedures for the calculation of heats of adsorption for heterogeneous adsorbents from molecular simulation

Several procedures for calculating the heat of adsorption from Monte Carlo simulations for a heterogeneous adsorbent are presented. Simulations have been performed to generate isotherms for nitrogen at 77 K and methane at 273.15 K in graphitic slit pores of various widths. The procedures were then applied to calculate the heat of adsorption of an activated carbon with an arbitrary pore size distribution. The consistency of the different procedures shows them to be correct in calculating interaction energy contributions to the heat of adsorption. The currently favored procedure for this type of calculation, from the literature, is shown to be incorrect and in serious error when calculating the heat of adsorption of activated carbon.

Structural Transitions of Nitrogen Confined in Slit Graphite Pores

The structure of ordered phases that are formed when nitrogen is confined in slit graphite pores of height h is investigated using Monte Carlo simulations. The pore wall consists of a single-structured graphite sheet. Canonical ensemble simulations are carried out for temperatures ranging from 15 to 70Kwith layer density distributions, in-plane, out-of-plane angular distributions and snapshots evaluated at different temperatures. At each pore height the pore densities are obtained from independent grand ensemble simulations. At the smallest pore height studied (h)7 Å), where a single layer of molecules is accommodated at the center of the pore, the orientations are predominantly wall parallel, forming a biaxially incommensurate herringbone structure.Whentwo or more fluid layers are formed in the slit pore, the orientation of molecules adsorbed next to the wall can exist in either the herringbone or hexagonal phases. In all the multilayered cases studied, with the exception of the h ) 10 Å pore, where both wall layers form a commensurate herringbone structure, the low-temperature wall structures are incommensurate, possessing 6-fold hexagonal symmetry. The presence of the pinwheel structures, which were observed at low temperatures in the h ) 12 Å and h ) 14 Å pores, is determined by the pore height or the proximity and/or density of the adjacent fluid layers when inner layers are present.

To what extent can mutual shifting of folded carbonaceous walls in slit-like pores affect their adsorption properties?

We have performed systematic Monte Carlo studies on the influence of shifting the walls in slit-like systems constructed from folded graphene sheets on their adsorption properties. Specifically, we have analysed the effect on the mechanism of argon adsorption (T = 87 K) and on adsorption and separation of three binary gas mixtures: CO2/N2, CO2/CH4 and CH4/N2 (T = 298 K). The effects of the changes in interlayer distance were also determined. We show that folding of the walls significantly improves the adsorption and separation properties in comparison to ideal slit-like systems. Moreover, we demonstrate that mutual shift of sheets (for small interlayer distances) causes the appearance of small pores between opposite bulges. This causes an increase in vapour adsorption at low pressures. Due to overlapping of interactions with opposite walls causing an increase in adsorption energy, the mutual shift of sheets is also connected with the rise in efficiency of mixtures separation. The effects connected with sheet orientation vanish as the interlayer distance increases.

Adsorption of quadrupolar, diatomic nitrogen onto graphitized thermal carbon black and in slit-shaped carbon pores. Effects of surface mediation

In this paper, we study the effect of solid surface mediation on the intermolecular potential energy of nitrogen, and its impact on the adsorption of nitrogen on a graphitized carbon black surface and in carbon slit-shaped pores. This effect arises from the lower effective interaction potential energy between two particles close to the surface compared to the potential energy of the same two particles when they are far away from the surface. A simple equation is proposed to calculate the reduction factor and this is used in the Grand Canonical Monte Carlo (GCMC) simulation of nitrogen adsorption on graphitized thermal carbon black. With this modification, the GCMC simulation results agree extremely well with the experimental data over a wide range of pressure; the simulation results with the original potential energy (i.e. no surface mediation) give rise to a shoulder in the neighbourhood of monolayer coverage and a significant over-prediction of the second and higher layer coverages. The influence of this surface mediation on the dependence of the pore-filling pressure on the pore width is also studied. It is shown that such surface mediation has a significant effect on the pore-filling pressure. This implies that the use of the local isotherms obtained from the potential model without surface mediation could give rise to a serious error in the determination of the pore-size distribution.