Density functional theory of adsorption in pillared slit-like pores

We propose a density functional theory to describe adsorption of Lennard-Jones fluid in pillared slit like pores. Specifically, the pillars are built of chains that are bonded by their ends to the opposite pore walls. The approach we propose combines theory of quenched-annealed systems and theory of nonuniform fluids involving chain molecules. We compare the results of theoretical predictions with grand canonical ensemble Monte Carlo simulations and compute theoretical capillary condensation phase diagrams for several model systems.     

Diffusioosmosis and electroosmosis in a capillary slit with surface charge layers

This study analytically examines the steady diffusioosmotic and electroosmotic flows of an electrolyte solution in a fine capillary slit with each of its inside walls covered by a layer of adsorbed polyelectrolytes. In this solvent-permeable and ion-penetrable surface charge layer, idealized polyelectrolyte segments are assumed to distribute at a uniform density. The electric double layer and the surface charge layer may have arbitrary thicknesses relative to the gap width between the slit walls. The electrostatic potential distribution on a cross section of the slit is obtained by solving the linearized Poisson–Boltzmann equation, which applies to the case of low potentials or low fixed-charge densities. Explicit formulas for the fluid velocity profile due to the imposed electrolyte concentration gradient or electric field through the slit are derived as the solution of a modified Navier–Stokes/Brinkman equation. The results demonstrate that the structure of the surface charge layer can lead to an augmented or a diminished electrokinetic flow (even a reversal in direction of the flow) relative to that in a capillary with bare walls, depending on the characteristics of the capillary, of the surface charge layer, and of the electrolyte solution. For the diffusioosmotic flow with an induced electric field, competition between electroosmosis and chemiosmosis can result in more than one reversal in direction of the flow over a range of the Donnan potential of the adsorbed polyelectrolyte in the capillary.     

Isotherms of Capillary Condensation Influenced by Formation of Adsorption Films

Isotherms of capillary condensation are often used to determine the vapor sorption capacity of porous adsorbents as well as the pore size distribution by radii. In this paper, for calculating the volume of capillary condensate and of adsorption films in a porous body, an approach based on the theory of surface forces is used. Adsorption isotherms and disjoining pressure isotherms of wetting films are presented here in an exponential form discussed earlier. The calculations were made for straight cylindrical capillaries of different radii and slit pores of different width. The mechanisms of capillary condensation differ in cylindrical and slit pores. In cylindrical pores capillary condensation occurs due to capillary instability of curved wetting films on a capillary surface, when film thickness grows. In the case of slit pores, coalescence of wetting films formed on opposite slit surfaces proceeds under the action of attractive dispersion forces. Partial volumes of liquid in the state of both capillary condensate and adsorbed films are calculated dependent on the relative vapor pressure in a surrounding media. Copyright 2000 Academic Press.     

Phase Equilibria of Hydrogen Bonding Fluid in a Slit Pore with Broken Symmetry

Phase equilibria of hydrogen bonding (HB) fluid confined in a slit pore with broken symmetry were investigated by the density functional theory incorporated with modified fundamental measure theory, where the symmetry breaking originated from the distinct interactions between fluid molecules and two walls of the slit pore. In terms of adsorption-desorption isotherms and the corresponding grand potentials, phase diagrams of HB fluid under various conditions are presented. Furthermore, through phase coexistences of laying transition and capillary condensation, the effects of HB interaction, pore width, fluid-pore interaction and the broken symmetry on the phase equilibrium properties are addressed. It is shown that these factors can give rise to apparent influences on the phase equilibria of confined HB fluid because of the competition between intermolecular interaction and fluid-pore interaction. Interestingly, a significant influence of broken symmetry of the slit pore is found, and thus the symmetry breaking can provide a new way to regulate the phase behavior of various confined fluids.     

Diffusioosmosis of electrolyte solutions in a capillary slit with adsorbed polyelectrolyte layers

A theoretical study is presented for the steady diffusioosmotic flow of an electrolyte solution in a fine capillary slit with each of its inside walls coated with a layer of polyelectrolytes generated by an imposed tangential concentration gradient. In this solvent-permeable and ion-penetrable surface charge layer, idealized polyelectrolyte segments are assumed to be distributed at a uniform density. The electric double layer and the surface charge layer may have arbitrary thicknesses relative to the gap width between the slit walls. The Poisson-Boltzmann equation and a modified Navier-Stokes/Brinkman equation are solved numerically to obtain the electrostatic potential, dynamic pressure, tangentially induced electric field, and fluid velocity as functions of the lateral position in the slit in a self-consistent way, with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions. The existence of the surface charge layers can lead to a diffusioosmotic flow quite different from that in a capillary with bare walls. The effect of the lateral distribution of the induced tangential electric field and the relaxation effect due to ionic convection in the slit on the diffusioosmotic flow are found to be very significant in practical situations.     

Electrokinetic flow in a capillary with a charge-regulating surface polymer layer

An analytical study of the steady electrokinetic flow in a long uniform capillary tube or slit is presented. The inside wall of the capillary is covered by a layer of adsorbed or covalently bound charge-regulating polymer in equilibrium with the ambient electrolyte solution. In this solvent-permeable and ion-penetrable surface polyelectrolyte layer, ionogenic functional groups and frictional segments are assumed to distribute at uniform densities. The electrical potential and space charge density distributions in the cross section of the capillary are obtained by solving the linearized Poisson-Boltzmann equation. The fluid velocity profile due to the application of an electric field and a pressure gradient through the capillary is obtained from the analytical solution of a modified Navier-Stokes/Brinkman equation. Explicit formulas for the electroosmotic velocity, the average fluid velocity and electric current density on the cross section, and the streaming potential in the capillary are also derived. The results demonstrate that the direction of the electroosmotic flow and the magnitudes of the fluid velocity and electric current density are dominated by the fixed charge density inside the surface polymer layer, which is determined by the regulation characteristics such as the dissociation equilibrium constants of the ionogenic functional groups in the surface layer and the concentration of the potential-determining ions in the bulk solution.     

Fluids in nanospaces: molecular simulation studies to find out key mechanisms for engineering

We have analyzed various phenomena that occur in nanopores, focusing on elucidating their key mechanisms, to advance the effective engineering use of nanoporous materials. As ideal experimental systems, molecular simulations can effectively provide information at the molecular level that leads to mechanistic insight. In this short review, several of our recent results are presented. The first topic is the critical point depression of Lennard-Jones fluid in silica slit pores due to finite size effects, studied by our original Monte Carlo (MC) technique. We demonstrate that the first layers of adsorbed molecules in contact with the pore walls act as a “fluid wall” and impose extra finite size effects on the fluid confined in the central portion of the pore. We next present a new kernel for pore size distribution (PSD) analysis, based entirely on molecular simulation, which consists of local isotherms for nitrogen adsorption in carbon slit pores at 77 K. The kernel is obtained by combining grand canonical Monte Carlo (GCMC) method and open pore cell MC method that was developed in the previous study. We show that overall trends of the PSDs of activated carbons calculated with our new kernel and with conventional kernel from non-local density functional theory are nearly the same; however, apparent difference can be seen between them. As the third topic, we apply a free energy analysis method with the aid of GCMC simulations to investigate the gating behavior observed in a porous coordination polymer, and propose a mechanism for the adsorption-induced structural transition based on both the theory of equilibrium and kinetics. Finally, we construct an atomistic silica pore model that mimics MCM-41, which has atomic-level surface roughness, and perform molecular simulations to understand the mechanism of capillary condensation with hysteresis. We calculate the work required for the gas–liquid transition from the simulation data, and show that the adsorption branch with hysteresis for MCM-41 arise from spontaneous capillary condensation from a metastable state.     

Polymolecular adsorption and capillary condensation in narrow slit pores

Capillary condensation and polymolecular adsorption in narrow slits has been calculated, where the fields of surface forces overlap one another. The calculations were carried out on the basis of macroscopic theory of dispersion forces and the isotherms of lone adsorption layers at the free surface. It has been shown that under the effect of mutual attraction through a gap, polymolecular adsorption films lose their stability long before their thickness has approached the half-width of a flat slit. This results in hysteresis of the capillary condensation in an ensemble of plane-parallel slits.

In the case of systems having strong adsorbate-adsorbate interaction, there has been detected the existence of the lower limit of sizes of slit pores, wherein the capillary meniscus can coexist with adsorption films. With a slit width smaller than the critical one, the meniscus is likely to form a finite contact angle with “dry” surfaces of a slit. Thus an explanation has been given of the lower limit of the capillary condensation in an ensemble of flat-surface, slit pores. In the case of strong adsorbate-adsorbent interaction, the coexistence of meniscus with adsorption films within the scope of the approach used is possible in slits of any width.

The value of corrections for the surface forces effect to be entered in the calculations of slit pores dimensions has been analyzed on the basis of the capillary condensation data obtained.

In wedge-shaped slits there also exists, besides lower limit the upper limit of capillary hysteresis.     

Mean field kinetic theory for a lattice gas model of fluids confined in porous materials

We consider the mean field kinetic equations describing the relaxation dynamics of a lattice model of a fluid confined in a porous material. The dynamical theory embodied in these equations can be viewed as a mean field approximation to a Kawasaki dynamics Monte Carlo simulation of the system, as a theory of diffusion, or as a dynamical density functional theory. The solutions of the kinetic equations for long times coincide with the solutions of the static mean field equations for the inhomogeneous lattice gas. The approach is applied to a lattice gas model of a fluid confined in a finite length slit pore open at both ends and is in contact with the bulk fluid at a temperature where capillary condensation and hysteresis occur. The states emerging dynamically during irreversible changes in the chemical potential are compared with those obtained from the static mean field equations for states associated with a quasistatic progression up and down the adsorption/desorption isotherm. In the capillary transition region, the dynamics involves the appearance of undulates (adsorption) and liquid bridges (adsorption and desorption) which are unstable in the static mean field theory in the grand ensemble for the open pore but which are stable in the static mean field theory in the canonical ensemble for an infinite pore.     

Layering, condensation, and evaporation of short chains in narrow slit pores

The phase behavior of short-chain fluids in slit pores is investigated by using a nonlocal-density-functional theory that takes into account the effects of segment size, chain connectivity, and van der Waals attractions explicitly. The layering and capillary condensation/evaporation transitions are examined at different chain length, temperature, pore width, and surface energy. It is found that longer chains are more likely to show hysteresis loops and multilayer adsorptions along with the capillary condensation and evaporation. Decreasing temperature favors the inclusion of layering transitions into the condensation/evaporation hysteresis loops. For large pores, the surface energy has relatively small effect on the pressures of the capillary condensation and evaporation but affects significantly on the layering pressures. It is also observed that all phase transitions within the pore take place at pressures lower than the corresponding bulk saturation pressure. The critical temperature of condensation/evaporation is always smaller than that of the bulk fluid. All coexistence curves for confined phase transitions are contained within the corresponding bulk vapor-liquid coexistence curve. As in the bulk phase, the longer the chain length, the higher are the critical temperatures of phase transitions in the pore.     

Electrokinetic flow and electric conduction of salt-free solutions in a capillary

The electrokinetic flow and accompanied electric conduction of a salt-free solution in the axial direction of a charged circular capillary are analyzed. No assumptions are made about the surface charge density (or surface potential) and electrokinetic radius of the capillary, which are interrelated. The Poisson–Boltzmann equation and modified Navier–Stokes equation are solved for the electrostatic potential distribution and fluid velocity profile, respectively. Closed-form formulas for the electroosmotic mobility and electric conductivity in the capillary are derived in terms of the surface charge density. The relative surface potential, electroosmotic mobility, and electric conductivity are monotonic increasing functions of the surface charge density and electrokinetic radius. However, the rises of the relative surface potential and electroosmotic mobility with an increase in the surface charge density are suppressed substantially when it is high due to the effect of counterion condensation. The analytical prediction that the electroosmotic mobility grows with increases in the surface charge density and electrokinetic radius agrees with the experimental results for salt-free solutions in circular microchannels in the literature.     

Electrostatic double-layer interaction between spherical particles inside a rough capillary

Predictions of electrostatic double-layer interaction forces between two similarly charged spherical colloidal particles inside an infinitely long "rough" capillary are presented. A simple model of a rough cylindrical surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The periodic roughness of the wall is characterized by the wavelength and amplitude of the undulations. The electrostatic double-layer interaction force between two spherical particles located axially inside this rough capillary is determined by solving the nonlinear Poisson-Boltzmann equation employing finite element analysis. The effect of surface roughness of the cylindrical enclosure on the interaction force between two particles is extensively studied on the basis of this model. The simulations are carried out for dimensionless amplitudes (amplitude/particle radii) ranging from 0.05 to 0.15 and scaled wavelengths (wavelength/particle radii) ranging from 0.4 to 4.0. The interaction force between the particles is significantly modified by the proximity of the rough capillary wall. Generally, the interaction force for rough capillaries oscillates around the corresponding interaction force in a smooth capillary depending on the magnitudes of the scaled amplitude and wavelength of the roughness. The influence of roughness on the electrostatic interactions becomes more pronounced when the surface potential of the cylinder wall is different from the sphere surface potentials. When the cylinder and the particle surfaces have large potential differences, the axial force experienced by a particle is dominated by the capillary roughness. There are dramatic oscillations of the force, which alternately becomes repulsive and attractive as the particle moves from the crest to the trough of the rough capillary wall. These results suggest that manipulation of colloidal particles in narrow microchannels may be subject to significant force variations owing to the roughness inherent in microfabricated channels etched on metal films.     

Capillary condensation in pores with rough walls: a density functional approach

The effect of surface roughness of slit-like pore walls on the capillary condensation of a spherical particles and short chains is studied. The gas molecules interact with the substrate by a Lennard-Jones (9,3) potential. The rough layer at each pore wall has a variable thickness and density and consists of a disordered quenched matrix of spherical particles. The system is described in the framework of a density functional approach and using computer simulations. The contribution due to attractive van der Waals interactions between adsorbate molecules is described by using first-order mean spherical approximation and mean-field approximation.     

Effect of surface roughness and softness on water capillary adhesion in apolar media

The roughness and softness of interacting surfaces are both important parameters affecting the capillary condensation of water in apolar media, yet are poorly understood at present. We studied the water capillary adhesion between a cellulose surface and a silica colloidal probe in hexane by AFM force measurements. Nanomechanical measurements show that the Young's modulus of the cellulose layer in water is significantly less (~7 MPa) than in hexane (~7 GPa). In addition, the cellulose surface in both water and hexane is rather rough (6-10 nm) and the silica probe has a comparable roughness. The adhesion force between cellulose and silica in water-saturated hexane shows a time-dependent increase up to a waiting time of 200 s and is much (2 orders of magnitude) lower than that expected for a capillary bridge spanning the whole silica probe surface. This suggests the formation of one or more smaller bridges between asperities on both surfaces, which is confirmed by a theoretical analysis. The overall growth rate of the condensate cannot be explained from diffusion mediated capillary condensation alone; thin film flow due to the presence of a wetting layer of water at both the surfaces seems to be the dominant contribution. The logarithmic time dependence of the force can also be explained from the model of the formation of multiple capillary bridges with a distribution of activation times. Finally, the force-distance curves upon retraction show oscillations. Capillary condensation between an atomically smooth mica surface and the silica particle show less significant oscillations and the adhesion force is independent of waiting time. The oscillations in the force-distance curves between cellulose and silica may stem from multiple bridge formation between the asperities present on both surfaces. The softness of the cellulose surface can bring in additional complexities during retraction of the silica particle, also resulting in oscillations in the force-distance curves.     

模拟吸附在狭缝微孔中的丙烷的微观结构

用巨正则系综MonteCarlo（GCEMC）方法模拟了活性碳孔吸附丙烷时的微观结构．在GCEMC模拟中,非极性丙烷分子采用单点LJ球状分子模型,狭缝活性碳孔墙采用10－4-3势能模型．在温度T＝134．3K下,模拟并观察到了丙烷分子在狭缝活性碳孔中的吸附、脱附以及毛细凝聚现象,得到了吸附等温线和孔中流体的局部密度轮廓图．从分子水平出发,详细分析了吸附、毛细冷凝时孔中流体的微观结构,为认识、理解吸附的微观机理提供了工具与借鉴．     

Molecular transport in narrow channels

The micro-hydrodynamic method is applid to the calculation of the molecular transport in narrow channels in case of capillary condensation, at the flow anisotropy resulted from the potential of the wall surface and/or of boundary vapor and fluid phases. The mechanisms of molecular transport in the one-phase and two-phase fluid flows as a dependence of fluid density and adsorption potential of channel walls are discussed.     

Effects of wetting and anchoring on capillary phenomena in a confined liquid crystal

A fluid of hard spherocylinders of length-to-breadth ratio L/D=5 confined between two identical planar, parallel walls--forming a pore of slit geometry--has been studied using a version of the Onsager density-functional theory. The walls impose an exclusion boundary condition over the particle's centers of mass, while at the same time favoring a particular anchoring at the walls, either parallel or perpendicular to the substrate. We observe the occurrence of a capillary transition, i.e., a phase transition associated with the formation of a nematic film inside the pore at a chemical potential different from micro(b)-the chemical potential at the bulk isotropic-nematic transition. This transition terminates at an Ising-type surface critical point. In line with previous studies based on the macroscopic Kelvin equation and the mesoscopic Landau-de Gennes approach, our microscopic model indicates that the capillary transition is greatly affected by the wetting and anchoring properties of the semi-infinite system, i.e., when the fluid is in contact with a single wall or, equivalently, the walls are at a very large distance. Specifically, in a situation where the walls are preferentially wetted by the nematic phase in the semi-infinite system, one has the standard scenario with the capillary transition taking place at chemical potentials less than micro(b) (capillary nematization transition or capillary ordering transition). By contrast, if the walls tend to orientationally disorder the fluid, the capillary transition may occur at chemical potentials larger than micro(b), in what may be called a capillary isotropization transition or capillary disordering transition. Moreover, the anchoring transition that occurs in the semi-infinite system may affect very decisively the confinement properties of the liquid crystal and the capillary transitions may become considerably more complicated.     

Nanodrop on a nanorough solid surface: density functional theory considerations

The density distributions and contact angles of liquid nanodrops on nanorough solid surfaces are determined on the basis of a nonlocal density functional theory. Two kinds of roughness, chemical and physical, are examined. The former considers the substrate as a sequence of two kinds of semi-infinite vertical plates of equal thicknesses but of different natures with different strengths for the liquid-solid interactions. The physical roughness involves an ordered set of pillars on a flat homogeneous surface. Both hydrophobic and hydrophilic surfaces were considered. For the chemical roughness, the contact angle which the drop makes with the flat surface increases when the strength of the liquid-solid interaction for one kind of plates decreases with respect to the fixed value of the other kind of plates. Such a behavior is in agreement with the Cassie-Baxter expression derived from macroscopic considerations. For the physical roughness on a hydrophobic surface, the contact angle which a drop makes with the plane containing the tops of the pillars increases with increasing roughness. Such a behavior is consistent with the Wenzel formula developed for macroscopic drops. For hydrophilic surfaces, as the roughness increases the contact angle first increases, in contradiction with the Wenzel formula, which predicts for hydrophilic surfaces a decrease of the contact angle with increasing roughness. However, a further increase in roughness changes nonmonotonously the contact angle, and at some roughness, the drop disappears and only a liquid film is present on the surface. It was also found that the contact angle has a periodic dependence on the volume of the drop.     

Chemical reaction equilibrium in nanoporous materials: NO dimerization reaction in carbon slit nanopores

We present a molecular-level simulation study of the effects of confinement on chemical reaction equilibrium in nanoporous materials. We use the reaction ensemble Monte Carlo (RxMC) method to investigate the effects of temperature, nanopore size, bulk pressure, and capillary condensation on the nitric oxide dimerization reaction in a model carbon slit nanopore in equilibrium with a bulk reservoir. In addition to the RxMC simulations, we also utilize the molecular-dynamics method to determine self-diffusion coefficients for confined nonreactive mixtures of nitric oxide monomers and dimers at compositions obtained from the RxMC simulations. We analyze the effects of the temperature, nanopore width, bulk pressure, and capillary condensation on the reaction equilibrium with respect to the reaction conversion, fluid structure, and self-diffusion coefficients. We show that the influence of the temperature, nanopore size, and capillary condensation on the confined reaction equilibrium is quite dramatic while the effect of the bulk pressure on the reaction equilibrium in the carbon slit nanopore is only moderate. This work is an extension of previous work by Turner et al. [J. Chem. Phys. 114, 1851 (2001)] on the confined reactive nitric oxide system.     

Capillary condensation of short-chain molecules

A density-functional study of capillary condensation of fluids of short-chain molecules confined to slitlike pores is presented. The molecules are modeled as freely jointed tangent spherical segments with a hard core and with short-range attractive interaction between all the segments. We investigate how the critical parameters of capillary condensation of the fluid change when the pore width decreases and eventually becomes smaller than the nominal linear dimension of the single-chain molecule. We find that the dependence of critical parameters for a fluid of dimers and of tetramers on pore width is similar to that of the monomer fluid. On the other hand, for a fluid of chains consisting of a larger number of segments we observe an inversion effect. Namely, the critical temperature of capillary condensation decreases with increasing pore width for a certain interval of values of the pore width. This anomalous behavior is also influenced by the interaction between molecules and pore walls. We attribute this behavior to the effect of conformational changes of molecules upon confinement.