Fluid In Slit-like Pores Research Articles

Adsorption behaviors of supercritical Lennard-Jones fluid in slit-like pores

Understanding the adsorption behaviors of supercritical fluid in confined space is pivotal for coupling the supercritical technology and the membrane separation technology. Based on grand canonical Monte Carlo simulations, the adsorption behaviors of a Lennard-Jones (LJ) fluid in slit-like pores at reduced temperatures over the critical temperature, Tc* = 1.312, are investigated; and impacts of the wall-fluid interactions, the pore width, and the temperature are taken into account. It is found that even if under supercritical conditions, the LJ fluid can undergo a “vapor-liquid phase transition” in confined space, i.e., the adsorption density undergoes a sudden increase with the bulk density. A greater wall-fluid attractive potential, a smaller pore width, and a lower temperature will bring about a stronger confinement effect. Besides, the adsorption pressure reaches a local minimum when the bulk density equals to a certain value, independent of the wall-fluid potential or pore width. The insights in this work have both practical and theoretical significances.

Restricted primitive model for electrolyte solutions in slit-like pores with grafted chains: Microscopic structure, thermodynamics of adsorption, and electric properties from a density functional approach

We apply a density functional theory to describe properties of a restricted primitive model of an ionic fluid in slit-like pores. The pore walls are modified by grafted chains. The chains are built of uncharged or charged segments. We study the influence of modification of the pore walls on the structure, adsorption, ion selectivity, and the electric double layer capacitance of ionic fluid under confinement. The brush built of uncharged segments acts as a collection of obstacles in the walls vicinity. Consequently, separation of charges requires higher voltages, in comparison to the models without brushes. At high grafting densities the formation of crowding-type structure is inhibited. The double layer structure becomes more complex in various aspects, if the brushes are built of charged segments. In particular, the evolution of the brush height with the bulk fluid density and with the charge on the walls depends on the length of the blocks of charged spheres as well as on the distribution of charged species along chains. We also investigated how the dependence of the double layer capacitance on the electrostatic potential (or on the charge on the walls) changes with grafting density, the chain length, distribution of charges along the chain, the bulk fluid density, and, finally, with the pore width. The shape of the electric double layer capacitance vs. voltage changes from a camel-like to bell-like shape, if the bulk fluid density changes from low to moderate and high. If the bulk density is appropriately chosen, it is possible to alter the shape of this curve from the double hump to single hump by changing the grafting density. Moreover, in narrow pores one can observe the capacitance curve with even three humps for a certain set of parameters describing brush. This behavior illustrates how strong the influence of brushes on the electric double layer properties can be, particularly for ionic fluids in narrow pores.

Electric double layer capacitance of restricted primitive model for an ionic fluid in slit-like nanopores: A density functional approach

We apply recently developed version of a density functional theory [Z. Wang, L. Liu, and I. Neretnieks, J. Phys.: Condens. Matter 23, 175002 (2011)] to study adsorption of a restricted primitive model for an ionic fluid in slit-like pores in the absence of interactions induced by electrostatic images. At present this approach is one of the most accurate theories for such model electric double layers. The dependencies of the differential double layer capacitance on the pore width, on the electrostatic potential at the wall, bulk fluid density, and temperature are obtained. We show that the differential capacitance can oscillate as a function of the pore width dependent on the values of the above parameters. The number of oscillations and their magnitude decrease for high values of the electrostatic potential. For very narrow pores, close to the ion diameter, the differential capacitance tends to a minimum. The dependence of differential capacitance on temperature exhibits maximum at different values of bulk fluid density and applied electrostatic potential.

Entropic solvation force between surfaces modified by grafted chains: a density functional approach

The behavior of a hard sphere fluid in slit-like pores with walls modified by grafted chain molecules composed of hard sphere segments is studied using density functional theory. The chains are grafted to opposite walls via terminating segments forming pillars. The effects of confinement and of “chemical” modification of pore walls on the entropic solvation force are investigated in detail. We observe that in the absence of adsorbed fluid the solvation force is strongly repulsive for narrow pores and attractive for wide pores. In the presence of adsorbed fluid both parts of the curve of the solvation force may develop oscillatory behavior dependent on the density of pillars, the number of segments and adsorption conditions. Also, the size ratio between adsorbed fluid species and chain segments is of importance for the development of oscillations. The choice of these parameters is crucial for efficient manipulation of the solvation force as desired for pores of different width.

Solvation force between surfaces modified by tethered chains: A density functional approach

The behavior of Lennard-Jones fluid in slitlike pores with walls modified by tethered chain molecules is studied using density functional theory. The effects of confinement and chemical modification of pore walls on the solvation force are investigated. Two models of the pore walls are considered. According to the first model, the chain molecules are chemically bonded by their end segments to opposite walls of the pore, forming flexible pillars. In the second model the chains build up a brush at each wall due to bonding of the first segment at one wall. The nonbonded terminating segment of a molecule is strongly attracted via a short-range potential to any wall of the pore. Then a pillarlike or looplike structure of chains can be formed. In the first model the solvation force at the wall-to-wall is repulsive for narrow pores and strongly attractive for wider pores of the order of the nominal chain length. Oscillations of the solvation force are induced by adsorbed fluid structure and by ordered structure of segments on the fragment of entirely attractive force curve. In the second model, however, the solvation force decays to zero as the pore width increases. Attractive force can be induced at intermediate separation between walls due to modification of the pore walls.

Phase transitions and ordering of confined dipolar fluids

We apply a modified mean-field density functional theory to determine the phase behavior of Stockmayer fluids in slit-like pores formed by two walls with identical substrate potentials. Based on the Carnahan-Starling equation of state, a fundamental-measure theory is employed to incorporate the effects of short-ranged hard-sphere-like correlations while the long-ranged contributions to the fluid interaction potential are treated perturbatively. The liquid-vapor, ferromagnetic-liquid-vapor, and ferromagnetic-liquid-isotropic-liquid first-order phase separations are investigated. The local orientational structure of the anisotropic and inhomogeneous ferromagnetic liquid phase is also studied. We discuss how the phase diagrams are shifted and distorted upon varying the pore width.

Phase behavior of a fluid confined in slitlike pores with walls modified by preadsorbed chain molecules

We have studied the microscopic structure, thermodynamics of adsorption, and phase behavior of Lennard-Jones fluid in slitlike pores with walls modified due to preadsorption of chain molecules. The chain species are grafted at the walls by terminating segments. Our theoretical considerations are based on a density functional approach in the semigrand canonical ensemble. The applied constraint refers to the constant number of grafted chain molecules in the pore without restriction of the number of chains at each of the walls. We have observed capillary condensation of Lennard-Jones fluid combined with the change of the distribution of chains from nonsymmetric to symmetric with respect to the pore walls. The phase diagrams of the model are analyzed in detail, dependent on the pore width, length of chains, and grafted density.

Density functional description of adsorption in slitlike pores modified with chain molecules: A simple model for pillaredlike materials

We propose a density functional theory to describe adsorption of Lennard-Jones fluid in slitlike pores modified by chain molecules. Specifically, the chains are bonded by their ends to the opposite pore walls, so they can form pillaredlike structure. Two models are studied. In the first model, the nonterminating segments of chains can change their configuration inside the pore upon adsorption of spherical species. In the second model, the chains configuration remains fixed, so that the system is similar to a nonuniform quenched-annealed mixture. We study capillary condensation of fluid species inside such modified pores and compare the results obtained for two models.

Phase Behavior of Lennard-Jones Fluids in Slit-like Pores with Walls Modified by Preadsorbed Molecules: A Density Functional Approach

We have studied the liquid−vapor coexistence of Lennard-Jones fluids in slit-like pores with the walls modified by preadsorbed molecules in the framework of the density functional approach. During the preadsorption step, the grafting of monomers, trimers, or chains consisting of spherical segments is performed. The model of tangentially bonded spheres is used for chain molecules. It is shown that the presence of grafted species may induce condensation and layering phase transitions. The crossover between evaporation and condensation is also influenced by grafted species. Phase transitions in the adsorbed fluid affect the microscopic structure of grafted chains and can result in the peculiarities of their thermodynamic behavior. The entire calculations are performed by using the semi-grand canonical ensemble.

Adsorption of fluids in slitlike pores containing a small amount of mobile ions

We apply density functional theory to investigate changes in the phase behavior of a fluid caused by the presence of mobile ions inside the pore. The approach has been based on the fundamental measure density functional theory and on the theory of nonuniform electrolytes developed recently by O. Pizio, A. Patrykiejew, S. Sokołowski [J. Chem. Phys. 121 (2005) 11,957]. We have evaluated capillary condensation phase diagrams for pores of different widths and for different concentrations of confined ions. The calculations have demonstrated that the presence of ions leads to lowering the critical temperature and to an increase of the value of the chemical potential at the capillary condensation point.

Phase behavior of ionic fluids in slitlike pores: A density functional approach for the restricted primitive model

We present a density functional theory of nonuniform ionic fluids. This theory is based on the application of the electrostatic contribution to the free energy functional arising from mean spherical approximation for a bulk restricted primitive model and from the energy route bulk equation of state. In order to employ this functional we define a reference fluid and additional averaged densities, according to the approach introduced by Gillespie, Nonner and Eisenberg [J. Phys.: Condens. Matter 14, 12129 (2002)]. In the case of bulk systems the proposed theory reduces to the mean spherical approximation equation of state, arising from the energy route and thus it predicts the first-order phase transition. We use this theory to investigate the effects of confinement on the liquid-vapor equilibria. Two cases are considered, namely an electrolyte confined to the pore with uncharged walls and with charged walls. The dependence of the capillary evaporation diagrams on the pore width and on the electrostatic potential is determined.

Microscopic structure and properties of an interface between coexisting phases of an associating fluid adsorbed in slitlike pores

Using density functional theory, we calculate density profiles of an associating fluid in slitlike pores. These profiles characterize an interface between two coexisting, adsorbed phases, e.g., between gaseous and liquid phases formed during capillary condensation. Our study has been carried out for weakly, as well as for strongly, associated fluids confined in pores of different widths. We also investigate the role of the fluid–wall interaction.

On the structure of Lennard-Jones fluids confined in crystalline slitlike pores

The structure of Lennard-Jones fluid in slitlike pores with crystalline walls is studied by canonical ensemble Monte Carlo simulation method. It is assumed that each pore wall is a perfect (100) plane of the face centered cubic crystal. The effects of the wall–wall separation on the ordering and freezing of a confined fluid are investigated for a series of systems with the density corresponding to the two completely filled layers of commensurate c(2×2) phase. It is demonstrated that the structure of a solid phase very strongly depends on the pore diameter. Thus, the formation of partially filled film that spans the space between the both pore walls occurs only when the pore width is smaller than a certain value. For wider pores only two monolayers at each pore wall occur. Then, the formation of commensurate structures of square symmetry in each layer occurs only over certain ranges of the pore width, while for other pore widths, the incommensurate phases of hexagonal symmetry in each layer are formed. The melting of solid phases has been found to be either the first order or continuous transition. In particular, the first order melting transitions have been found to be accompanied by a change (decrease) in the number of adsorbate layers within a pore. We have been able to single out seven regions of the pore width, which exhibit different structure and properties of adsorbed phases.

Density functional theory and Monte Carlo simulations for hard sphere fluids in square and rectangular channels

The density distribution of hard spheres in square and rectangular channels is studied using density functional theory and grand canonical ensemble Monte Carlo simulations. The theory uses the weighted density approximation for the excess Helmholtz free energy functional with the Curtin–Ashcroft approximation for the weighting function. The theoretical predictions are in good quantitative agreement with the simulations except for very high densities. The theory predicts pronounced layering in the channel as the density is increased, with high values of density at the surfaces and even higher densities at the corners where any two surfaces meet. Interesting interference effects are observed in the density profiles when compared to the case of a hard sphere fluid in slitlike pores.

Phasebehaviour of a fluid in slit-like pores with differentlyadsorbing walls: application of a density functional approach

We study the adsorption of a Lennard-Jones gas in a slit-likepore formed by two walls exhibiting different adsorbingproperties. The calculations are carried out by means of adensity functional approach. We show that changes in thepotential field exerted by one wall can lead to substantialmodifications in the phase behaviour of confined fluids.

The influence of random changes in the adsorbing potential on phase transitions in a Lennard-Jones fluid confined to energetically heterogeneous slit-like pores

A density functional approach is used to study the adsorption and phase behaviour of a Lennard-Jones (LJ) fluid in slit-like pores with energetically heterogeneous walls, investigating how the randomly varying part of the fluid-solid potential imposed on a periodic ‘back-ground’ potential modifies the phase behaviour of the confined fluid. Non-local density functional theory is employed to describe the system. To study the system with a random external field, the method used is based on investigations of several replicas of the system and on averaging the final thermodynamic results over the replicas.

Capillary Condensation in Pores with Energetically Heterogeneous Walls: Density Functional versus Monte Carlo Calculations

We investigate adsorption of a Lennard–Jones fluid in slit-like pores with energetically heterogeneous walls by using Grand Canonical Monte Carlo simulations and a density functional approach. The model of a fluid-wall potential is qualitatively similar to that invoked by Röcken et al. (J. Chem. Phys.108, 8089, (1999); i.e., it consists of a homogeneous part that varies in the direction perpendicular to the wall and a periodic part, varying also in one direction parallel to the wall, but in contrast to the above mentioned work, both parts of the fluid-wall potential are modeled by Lennard–Jones (9, 3) type functions. The structure of the adsorbed film is characterized by local densities. We evaluate the phase diagrams for several systems characterized by different corrugation of the adsorbing potential and discuss the discrepancies between theoretical predictions and computer simulations.

Critical Properties of Lennard-Jones Fluids in Narrow Slit-Shaped Pores

The critical properties of the Lennard-Jones fluid in slitlike pores of different widths have been studied by the Gibbs ensemble Monte Carlo method and the lattice gas model. Graphite pores up to 10 molecular diameters in width and similar pores with weaker solid−fluid interactions have been considered. Strong layering of the adsorbate in the graphite pores confirmed the applicability of the lattice gas model to such systems. The vapor−liquid phase diagrams for the confined fluids obtained with the two methods are in reasonable agreement with each other. Linear dependence of the critical temperature on the inverse pore width was found. It is demonstrated that the critical temperature may depend strongly on the strength of the sold−fluid interactions. The lattice gas model showed nonmonotonic dependence of the critical density on the pore width.

Adsorption and phase transitions in a two-siteassociating Lennard-Jones fluid confined to energeticallyheterogeneous slit-like pores; application of the density functionalmethod

A density functional approach is used to study adsorption and phasebehaviour of the two-bonding-site associating Lennard-Jones (LJ)fluid in slit-like pores with energetically heterogeneous walls.Phase behaviour of strongly and weakly associating, polymerizingfluid in the pores with a periodic surface potential, characterizedby different strengths and the spacings between adjacent minima, aswell as different pore widths is discussed. A comparison of theresults obtained for strongly and weakly associating fluidselucidates the role of bonding between fluid species in thepore-filling mechanism. An interplay between layering transitions,the formation of an intermediate `bridge' phase and the finalcapillary condensation in the pores with energetically corrugatedwalls is discussed in detail.

Density functional approach to adsorption of a polydisperse fluid in slit-like pores

An extension of the Kierlik-Rosinberg version of density functional theory to the case of a polydisperse fluid of hard spheres in contact with a single wall and also adsorbed in slit-like pores is presented. A comparison with Monte Carlo results show that the theory is capable of precisely reproducing density profiles of a polydisperse fluid near a hard wall. Several model calculations of adsorption in slit like pores are presented. The influence of the confinement on the polydispersity, as compared with bulk fluid, is discussed.