Entropic effects in diffusion-adsorption processes in micropores

We analyze the kinetics of diffusion-adsorption processes of one component systems in micropores. In realistic situations, the pores exhibit irregular forms which give rise to inhomogeneous adsorption with preferred sites for the adsorbing particles. By modeling the tortuosity of the pores by means of entropic barriers, we obtain a kinetic equation for the averaged concentration of particles along the pore and on its surface. The analysis performed yields expressions for the adsorption rate, the effective diffusion coeffcient, the adsorption isotherms and the concentration of the adsorbed particles. It is shown that this last quantity strongly depends on the form of the pore. This feature opens the possibility to design micropores with an optimal adsorption rate at selected sites. Our results show that to consider the geometry of the pore in the reaction-diffusion scheme is crucial to reproduce experimental observations of the concentration of adsorbed particles in micropores.     

Further observations on the polarized absorption spectrum of benzene crystals at 2000 Å

The structure of a hard sphere fluid confined by model slit and cylindrical pores is investigated. Results from grand canonical Monte Carlo (GCMC) simulations and from the hypernetted chain/mean spherical approximation (HNC/MSA) equation are reported. GCMC results are compared with those from the HNC/MSA equation, and agreement is good. The effect of confinement on liquids at the same chemical potentials is that the absorption of the hard sphere fluid into the pores decreases with increasing confinement, i.e., when going from planar to cylindrical geometry or by narrowing the pores. The adsorption on the pore walls has, in general, the opposite behaviour. For high bulk concentrations and certain values of cylindrical pore diameter the concentration profile is higher at the centre of the pore than next to the pore wall. A very strong, but continuous, transition occurs in the concentration profile, as a function of the cylinder's diameter. These results could be of some interest in catalysis studies.     

The adsorption of a hard sphere fluid in a slit-like pore filled with a disordered matrix of hard spheres: attractive wall-hard sphere interaction

The adsorption of a hard sphere fluid in a slit-like pore filled with a disordered hard sphere matrix is studied using the inhomogeneous Ornstein-Zernike equation with hypernetted chain closure. In contrast to previous studies, an attractive wall-hard sphere interaction is considered. The adsorption is affected by the attractive interaction both directly by the fluid-wall interaction and indirectly by the change in the structure of the matrix. Density profiles and pair distribution functions are reported. For comparison, grand canonical Monte Carlo simulation data are obtained. The agreement of the theoretical and simulation results is satisfactory but somewhat less pleasing than for the purely repulsive case.     

Demixing transitions in a binary Gaussian-core fluid confined in narrow slit-like pores

Using a mean-field density functional approach we investigate phase separation transition in a binary mixture of Gaussian-core molecules confined in narrow slit-like pores. We consider pores with repulsive and attractive walls. In the case of fluid confinement in pores with repulsive and non-selective attracting walls, no phase separation in the confined fluid, prior to the bulk separation transition, was observed. However, in the case of pores with the walls selectively attracting fluid particles, we reveal that the separation transition may take place as a two-step process. During the first step the composition change occurs within a few layers adjacent to the pore walls, whereas in the second step, it takes place in the pore interior.     

Phase behaviour of a Lennard-Jones fluid in a pore with permeable walls of a finite thickness: a density functional approach

A confinement of a Lennard-Jones fluid in a system of slitlike pores separated by semipermeable walls of a finite width is studied. The walls are modelled by square-well repulsive potential wells. The structure of the confined fluid is investigated by means of a density functional method. For high potential barriers separating the pores, the phase behaviour of the system is similar to that for a single slitlike pore with impenetrable walls. For intermediate and low potential barriers the system shows different phase behaviour. Within some temperature range the isotherms exhibit two hysteresis loops, which characterize the condensation of the fluid in different parts of the system, namely in the pore and inside the semipermeable walls. The systems characterized by low and intermediate potential barriers exhibit the triple point, such that at temperatures below that triple point the condensation instantaneously takes place in both the pore and inside the permeable wall.     

Second-order Percus-Yevick theory for a confined hard-sphere fluid

A fluid of hard spheres confined between two hard walls and in equilibrium with a bulk hard-sphere fluid is studied using a second-order Percus-Yevick approximation. We refer to this approximation as second-order because the correlations that are calculated depend upon the position of two hard spheres in the confined fluid. However, because the correlation functions depend upon the positions of four particles (two hard spheres and two walls treated as giant hard spheres), this is the most demanding application of the second-order theory that has been attempted. When the two walls are far apart, this calculation reduces to our earlier second-order approximation calculations of the properties of hard spheres near a single hard wall. Our earlier calculations showed this approach to be accurate for the single-wall case. In this work we calculate the density profiles and the pressure of the hard-sphere fluid on the walls. We find, by comparison with grand canonical Monte Carlo results, that the second-order approximation is very accurate, even when the two walls have a small separation. We compare with a singlet approximation (in the sense that correlation functions that depend on the position of only one hard sphere are considered). The singlet approach is fairly satisfactory when the two walls are far apart but becomes unsatisfactory when the two walls have a small separation. We also examine a simple theory of the pressure of the confined hard spheres, based on the usual Percus-Yevick theory of hard-sphere mixtures. Given the simplicity of the latter approach the results of this simple (and explicit) theory are surprisingly good.     

Helium-4 Bose fluids formed in one-dimensional 18 A diameter pores

Bose fluids restricted in one dimension (1D) are realized by adsorbing 4He atoms on the 1D pore walls with a diameter of about 18 A. The Bose fluid appears above an adsorbed amount after the pore walls are coated with the inert 4He atoms. Heat capacity of the fluid was observed to have a temperature-linear term at low temperatures. This corresponds to the phonon heat capacity of the Bose fluid in the 1D pores. We estimate the phonon velocity and the interaction of the 1D Bose fluid.     

Adsorption and interfacial phenomena of a Lennard-Jones fluid adsorbed in slit pores: DFT and GCMC simulations

ABSTRACT

Confinement of fluids in porous media leads to the presence of solid–fluid (SF) interfaces that play a key role in many different fields. The experimental characterisation of SF interfacial properties, in particular the surface tension, is challenging or not accessible. In this work, we apply mean-field density functional theory (DFT) to determine the surface tension and also density profile of a Lennard-Jones fluid in slit-shaped pores for realistic amounts of adsorbed molecules. We consider the pore walls to interact with fluid molecules through the well-known 10-4-3 Steele potential. The results are compared with those obtained from Monte Carlo simulations in the Grand Canonical Ensemble (GCMC) using the test-area method. We analyse the effect on the adsorption and interfacial phenomena of volume and energy factors, in particular, the pore diameter and the ratio between SF and fluid–fluid dispersive energy parameters, respectively. Results from DFT and GCMC simulations were found to be comparable, which points to their reliability.     

Effects of polydispersity in quenched-annealed fluids: An integral equation approach

An extension of the replica Ornstein-Zernike (ROZ) equations for partly quenched polydisperse systems is presented. Explicit calculations have been performed for a monodisperse hard sphere fluid confined by a polydisperse hard sphere disordered matrix by using Percus-Yevick and hypernetted chain (HNC) approximations. The chemical potential of adsorbed fluid species has been evaluated. A numerical solution of the ROZ equations makes use of the orthonormal polynomials with the weight function corresponding to the distribution function of the diameters of matrix species. We have also compared the results of theoretical predictions with Monte Carlo simulation in a canonical ensemble. The result of this comparison suggests that the HNC approximation performs slightly better in predicting the structural properties of the system.     

The phase behaviour of a fluid in a slitlike pore with permeable walls

The confinement of a lattice fluid in a set of slitlike pores separated by semipermeable walls with a finite width has been studied. The walls are modelled by a square-well repulsive potential with a finite height. The thermodynamic properties and the phase behaviour of the system are evaluated by means of Monte Carlo simulations. For some states theoretical calculations have been made using a mean-field-type theory. These investigations confirm previous findings for confined Lennard-Jones fluids, obtained from a density functional approach. For intermediate and low potential barriers that separate the pores, the isotherms exhibit two hysteresis loops and the liquid-vapour coexistence curve divides into two branches describing condensation inside the pore and inside the permeable wall. These two branches are separated by a triple point. At temperatures lower than the triple point temperature, the condensation takes place instantaneously in both the pore and inside the permeable wall. It was found that when the temperature is scaled by the bulk critical temperature, the phase diagram emerging from this simple mean-field treatment is close to the phase diagram obtained from simulation.     

Demixing of a binary mixture in slit-like pores at high temperatures

We investigate the fluid—fluid demixing transitions in the case of adsorption of so-called symmetric binary mixtures in slit-like pores at temperatures higher than the bulk gas—liquid critical temperature. The aim of the study is to determine how the demixing of such mixtures in the pores depends on the bulk phase composition and on the parameters characterizing the pore. The calculations have been carried out by means of a density functional theory. In the case of an equimolar bulk mixture, the demixing transition inside the pore occurs only when the adsorption potentials of both species are identical. The occurrence of this transition is manifested by a cusp in the adsorption isotherm. For nonequimolar bulk phase compositions, the transition can also take place if the adsorption energies of both components are different. However, the difference in the adsorption energies should be small enough, otherwise a continuous demixing takes place. For non-equimolar compositions two branches of the grand canonical potential intersect, whereas for equimolar bulk composition they meet tangentially. We have determined phase behaviour for several model systems.     

Adsorption thermodynamics of a lattice–gas model with non-additive lateral interactions

In the present paper, we study the adsorption thermodynamics of a lattice–gas model with non-additive interactions between adsorbed particles. We have assumed that the energy which links a certain atom with any of its nearest neighbors strongly depends on the state of occupancy in the first coordination sphere of that adatom. By means of Monte Carlo simulations in the grand canonical ensemble the adsorption isotherms, isothermal susceptibility (or equivalently the mean square density fluctuations of adparticles), and isosteric heat of adsorption were calculated and their striking behavior was analyzed and discussed in terms of the low temperature phases formed in the system.     

Adsorption of water—methanol mixtures in carbon and aluminosilicate pores: a molecular simulation study

A theoretical study is reported of the adsorption behaviour of water—methanol mixtures in slit carbon and in uncharged alumino-silicate micropores. The adsorption isotherms are obtained for a pore of width of 2 nm and at a temperature of 298 K from grand canonical ensemble Monte Carlo simulations. The results show that the graphite and uncharged silicate surfaces are covered by a dense layer of flatly adsorbed water and methanol molecules having weaker hydrogen bonding. In the interior of the pore, the fluid exhibits bulk-like behaviour with a stronger hydrogen bonded structure. Solvation forces are also calculated as a function of pore size. The positive values found for the solvation force for all pore sizes reflect the hydrophobic interactions of the mixture with the carbon and uncharged alumino-silicate walls.     

Application of the density functional method to study phase transitions in an associating Lennard-Jones fluid adsorbed in energetically heterogeneous slit-Like pores

A density functional approach is used to study the adsorption of the four-bonding-site model associating Lennard-Jones fluid in slit-Like pores with energetically heterogeneous walls. The fluid-wall potential is qualitatively similar to that invoked by Röcken, P., Somoza, A., Tarazona, P., and Findenegg, G. H., 1999, J. chem. Phys., 108, 8089, 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. Both parts are modelled by Lennard-Jones 9,3-type functions. The structure of the adsorbed film is characterized by the local densities of all particles and the densities of the monomers. The phase diagrams are evaluated for several systems characterized by different corrugation of the adsorbing potential. The adsorbing field is strong enough to allow for the layering transition. As well as the formation of the so-called bridge phase that fills the pore space over the most energetic parts of the wall and of capillary condensation, the layering transition is observed within the first layer adjacent to the pore walls. If the adsorbing potential due to each pore wall is shifted in phase by π/2, the bridge phase is not formed.     

Phase behavior and fluid-solid surface tension of argon in slit pores and carbon nanotubes

Phase behaviors of argon in several types of cylindrical and slit pores are examined by grand-canonical Monte Carlo simulations. Condensation processes in single- and multi-walled carbon nanotubes along with those in hard-wall tubes are compared. Effects of the pore size on pressure-tensor components, the fluid-wall surface tension, and the adsorption are also compared for the different fluid-pore interactions. The chemical potential at which the fluid begins to condense in the single-walled nanotube is greater than that in the multi-walled nanotube by an amount nearly equal to the difference in the potential-well depth of the fluid-pore interaction, and the adsorption isotherms overlap each other almost completely for narrow pores and partially for wider pores. Similar analyses are performed for slit pores of two different hydrocarbon models.     

Capillary freezing or complete wetting of hard spheres in a planar hard slit?

Extensive simulations of a hard sphere fluid confined between two planar hard walls show the onset of crystalline layers at the walls at about 98.3% of bulk crystallization density rho(f) independent of the wall separations L(z), and is, hence, a single wall phenomenon. As the bulk density far from the wall rho(b) increases, the thickness of the crystalline film appears to increase logarithmically, with (rho(f)-rho(b)) indicating complete wetting by the hard sphere crystal of the wall-fluid interface. Increasing rho(b) further, we observe a jump in the adsorption which depends on L(z) and corresponds to capillary freezing. The formation of crystalline layers below bulk crystallization, the logarithmic growth of the crystalline film, its independence of L(z), and its clear distinction from capillary freezing lend strong evidence for complete wetting by the hard sphere crystal at the wall-fluid interface.     

Adsorption thermodynamics of a lattice-gas model with non-additive lateral interactions on triangular and honeycomb lattices

Adsorption thermodynamics of a lattice-gas model with non-additive interactions between adsorbed particles for triangular and honeycomb lattices is discussed in the present study. The model used here assumes that the energy which links a certain atom with any of its nearest-neighbors strongly depends on the state of occupancy in the first coordination sphere of that adatom. By means of Monte Carlo simulations in the grand canonical ensemble the adsorption isotherms and isothermal susceptibility (or equivalently the mean square density fluctuations of adparticles) were calculated and their striking behavior was analyzed and discussed in terms of the low temperature phases formed in the system.     

Constant pressure Gibbs ensemble Monte Carlo simulations of adsorption into narrow pores

An extension to the Gibbs ensemble method for the study of adsorption of fluids into pores is proposed. Since equality of pressure is not a necessary condition for full thermodynamic equilibrium between the bulk fluid and that confined in a narrow cavity, previous studies have been performed with the volume of both simulation cells fixed. More naturally, the pressure of the bulk fluid should be constrained and the volume (and hence density) allowed to attain its equilibrium value. Thus we propose a scheme in which volume fluctuations within the bulk box are permitted; the volume of the pore remains constant. The pressure is an input parameter and the amount of adsorption, as a function of applied pressure, is obtained directly. We demonstrate that the novel moves obey microscopic reversibility. Such a method is most useful when the equation of state for the model fluid is unknown. Thus, we illustrate the method by simulating an associating model of water adsorbed into a slit-shaped carbon pore with activated sites. Good qualitative correspondence with experiment is obtained; further refinement of our model is expected to yield quantitative agreement.     

Molecular simulation study of triangle-well fluids confined in slit pores

Grand canonical Monte Carlo simulations are used to study the behaviour of triangle-well (TW) fluids with variable well widths confined inside slit pores. The effect of individual factors influencing the properties of confined fluids such as fluid–fluid interactions, pore size and pore wall–fluid interactions are obtained using simulations as it is difficult to experimentally determine the same. An interesting observation of this study is that inside the narrow pore of slit height h* = 5 at the high-pressure condition of P* = 0.8, for the TW fluid with long-range attraction or for the fluid at a low temperature for even a short-range attraction, the density profiles show layering such that there is a sticking tendency of the particles at centre, while there is a depletion of particles near the wall (as the layers at the centre have higher density peak heights than near the walls).