Does water condense in carbon pores?

Using grand canonical Monte Carlo (GCMC) simulations of molecular models, we investigate the nature of water adsorption and desorption in slit pores with graphitelike surfaces. Special emphasis is placed on the question of whether water exhibits capillary condensation (i.e., condensation when the external pressure is below the bulk vapor pressure). Three models of water have been considered. These are the SPC and SPC/E models and a model where the hydrogen bonding is described by tetrahedrally coordinated square-well association sites. The water-carbon interaction was described by the Steele 10-4-3 potential. In addition to determining adsorption/desorption isotherms, we also locate the states where vapor-liquid equilibrium occurs for both the bulk and confined states of the models. We find that for wider pores (widths >1 nm), condensation does not occur in the GCMC simulations until the pressure is higher than the bulk vapor pressure, P0. This is consistent with a physical picture where a lack of hydrogen bonding with the graphite surface destabilizes dense water phases relative to the bulk. For narrow pores where the slit width is comparable to the molecular diameter, strong dispersion interactions with both carbon surfaces can stabilize dense water phases relative to the bulk so that pore condensation can occur for P < P0 in some cases. For the narrowest pores studied--a pore width of 0.6 nm--pore condensation is again shifted to P > P0. The phase-equilibrium calculations indicate vapor-liquid coexistence in the slit pores for P < P0 for all but the narrowest pores. We discuss the implications of our results for interpreting water adsorption/desorption isotherms in porous carbons.     

Effects of the juxtaposition of carbonaceous slit pores on the overall transport behavior of adsorbed fluids

It is a common approximation in the modeling of adsorption in microporous carbons to treat the pores as slit pores, whose walls are considered to consist of an infinite number of graphitic layers. In practice, such an approximation is appropriate as long as the number of graphitic layers in the wall is greater than three. However, it is understood that pore walls in microporous carbons commonly consist of three or fewer layers. As well as affecting the solid--fluid interaction within a pore, such narrow walls permit the interaction of fluid molecules through the wall, with consequences for the adsorption characteristics. We consider the effect that a distributed pore-wall thickness model can have on transport properties. At low density we find that the only significant deviation in the transport properties from the infinite pore-wall thickness model occurs in pores with single-layer walls. For a model of activated carbons with a distribution of pore widths and pore-wall thicknesses, the transport properties are generally insensitive to the effects of finite walls, in terms of both the solid-fluid interaction within a pore and fluid-fluid interaction through the pore walls.     

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.     

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.     

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.     

Adsorption of Fluids in Pores Formed between Two Hard Cylinders

We study adsorption in pores with curved hard walls that are made of two uniaxial cylinders by using a density functional approach. Two cases are considered: adsorption of hard spheres and adsorption of a Lennard-Jones fluid. In the case of hard spheres, we perform a comparison with the results of grand canonical ensemble Monte Carlo data. This comparison indicates that the applied approach is capable of reproducing the fluid structure quite satisfactorily. For hard spheres, we also make a comparison of the total adsorption effect (expressed as the average density of a confined fluid) inside pores with curved walls with that evaluated for a slitlike pore. We have found that the differences between adsorption in pores with curved walls and in slits with the same wall-to-wall distance are quite low. The calculations for the Lennard-Jones fluid have been concerned with the investigation of the capillary evaporation and with the evaluation of phase diagrams for different pores, including slitlike pores. We have found that the curvature of the pore walls shifts the transition toward lower values of the chemical potential and increases slightly the value of the critical temperature in comparison with the values obtained for a slitlike pore. Copyright 2000 Academic Press.     

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.     

Complex phase behavior of a fluid in slits with semipermeable walls modified with tethered chains

We study the phase behavior of a two-component fluid in a pore with the walls modified by tethered chains. The walls are completely permeable for one component of the fluid and completely impenetrable for the second component. The fluid is perfectly mixed in a bulk phase. We have found that depending on the details of the model the fluid undergoes capillary condensation inside the pore and wetting and layering transitions at the outer walls. Moreover, we have found transitions connected with the change of symmetry of the distribution of chains and fluid inside the pore.     

Molecular simulation of adsorption and intrusion in nanopores

This paper reports Monte Carlo simulations of the adsorption or intrusion in cylindrical silica nanopores. All the pores are opened at both ends towards an external bulk reservoir, so that they mimic real materials for which the confined fluid is always in contact with the external phase. This realistic model allows us to discuss the nature of the filling and emptying mechanisms. The adsorption corresponds to the metastable nucleation of the liquid phase, starting from a partially filled pore (a molecular thick film adsorbed at the pore surface). On the other hand, the desorption occurs through the displacement at equilibrium of a gas/liquid hemispherical interface (concave meniscus) along the pore axis. The intrusion of the non-wetting fluid proceeds through the invasion in the pore of the liquid/gas interface (convex meniscus), while the extrusion consists of the nucleation of the gas phase within the pore. In the case of adsorption, our simulation data are used to discuss the validity of the modified Kelvin equation (which is corrected for both the film adsorbed at the pore surface and the curvature effect on the gas/liquid surface tension).     

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.     

Equilibrium adsorption in cylindrical mesopores: a modified Broekhoff and de Boer theory versus density functional theory

This paper presents a thermodynamic analysis of capillary condensation phenomena in cylindrical pores. Here, we modified the Broekhoff and de Boer (BdB) model for cylindrical pores accounting for the effect of the pore radius on the potential exerted by the pore walls. The new approach incorporates the recently published standard nitrogen and argon adsorption isotherm on nonporous silica LiChrospher Si-1000. The developed model is tested against the nonlocal density functional theory (NLDFT), and the criterion for this comparison is the condensation/evaporation pressure versus the pore diameter. The quantitative agreement between the NLDFT and the refined version of the BdB theory is ascertained for pores larger than 2 nm. The modified BdB theory was applied to the experimental adsorption branch of adsorption isotherms of a number of MCM-41 samples to determine their pore size distributions (PSDs). It was found that the PSDs determined with the new BdB approach coincide with those determined with the NLDFT (also using the experimental adsorption branch). As opposed to the NLDFT, the modified BdB theory is very simple in its utilization and therefore can be used as a convenient tool to obtain PSDs of all mesoporous solids from the analysis of the adsorption branch of adsorption isotherms of any subcritical fluids.     

Molecular dynamics simulations on the adsorption and surface phenomena of simple fluid in porous media

Equilibrium molecular dynamics simulations have been used to investigate the fluid adsorption phenomena and calculate the surface tension in porous media at different temperatures, densities and pore widths. The facts that most of the fluid particles are adsorbed adherent to the pore walls and the surface forms near the walls have been found, and that the surface is not stable which means there exists an oscillation phenomenon in pores have been also found. The surface tension in pores is much bigger than that in macrovolume systems like normal liquid–liquid and liquid–vapor interfaces, and it will increase with the increase of density and pore width, but will decrease with the increase of temperature.     

Water in extremely narrow planar pores with crystalline walls. 2. Thermodynamics

The free energy, entropy, and work of water vapor adsorption in planar pores with widths of 0.62 and 1.25 nm located in a silver iodide crystal parallel to its basal face have been computed at the molecular level. In contrast to adsorption on a free surface, the adsorption in the pores proceeds in three stages, i.e., the formation of molecular films on the walls, coalescence of the films, and densification of the fluid in the pore volume. At the second stage, the equilibrium between the fluid in the pore and the vapor over the pore at temperatures corresponding to normal conditions is thermodynamically unstable and accompanied by the development of a free energy barrier and the existence of metastable states. As temperature is elevated, the instability is gradually evened out; however, its signs remain preserved even at the boiling temperature of water. Extremely narrow pores with widths smaller than 1 nm are always filled with water under conditions of even a rather dry natural atmosphere. The filling of pores several nanometers wide in strongly unsaturated water vapors overcomes the free-energy barrier; however, the fluid that has filled the pore remains stable with respect to evaporation in vapors with densities lower than the density of saturated vapor by several orders of magnitude. The existence of the free-energy barrier and metastable states in nanosized breaks in crystals creates conditions for hysteresis of adsorption-desorption cycles.     

Monte Carlo simulation of polymer adsorption

We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation.     

A grand canonical Monte Carlo study of capillary condensation in mesoporous media: effect of the pore morphology and topology

We study by means of Grand Canonical Monte Carlo simulations the condensation and evaporation of argon at 77 K in nanoporous silica media of different morphology or topology. For each porous material, our results are compared with data obtained for regular cylindrical pores. We show that both the filling and emptying mechanisms are significantly affected by the presence of a constriction. The simulation data for a constricted pore closed at one end reproduces the asymmetrical shape of the hysteresis loop that is observed for many real disordered porous materials. The adsorption process is a quasicontinuous mechanism that corresponds to the filling of the different parts of the porous material, cavity, and constriction. In contrast, the desorption branch for this pore closed at one end is brutal because the evaporation of Ar atoms confined in the largest cavity is triggered by the evaporation of the fluid confined in the constriction (which isolates the cavity from the gas reservoir). This evaporation process conforms to the classical picture of "pore blocking effect" proposed by Everett many years ago. We also simulate Ar adsorption in a disordered porous medium, which mimics a Vycor mesoporous silica glass. The adsorption isotherm for this disordered porous material having both topological and morphological defects presents the same features as that for the constricted pore (quasicontinuous adsorption and steep desorption process). However, the larger degree of disorder of the Vycor surface enhances these main characteristics. Finally, we show that the effect of the disorder, topological and/or morphological, leads to a significant lowering of the capillary condensation pressure compared to that for regular cylindrical nanopores. Also, our results suggest that confined fluids isolated from the bulk reservoir evaporate at a pressure driven by the smallest size of the pore.     

Characteristic features of phase diagrams describing condensation of adsorbate in narrow pores

The phase diagrams describing condensation of adsorbate in micro- and mesoporous adsorbents having slit-shaped and cylindrical pores whose size varied from 1 to 20 monolayers were constructed. The study was performed using the lattice-gas model in the quasichemical approximation to take into account the intermolecular interactions. The phase diagrams for various values of the potential arising from different types of adsorbate--adsorbent interaction were analyzed for adsorption of helium, neon, methane, and carbon tetrachloride in graphite pores. Other adsorption systems are considered and the relationship between the pressure and temperature of adsorbate condensation is discussed. A nonmonotonic variation of the critical densities for pore widths from 3 to 10 molecular diameters was found. The pattern of this variation depends on the ratio of the energy of lateral interactions of the adsorbate molecules to the energy of interaction of the adsorbate molecules with pore walls. The critical temperature decreases monotonically with a decrease in the pore width. The stronger the adsorbate interaction with the pore walls, the greater the decrease in the critical temperature.     

Adsorption of a binary mixture of adhesive fluids in planar pores: a Monte Carlo study

Grand canonical Monte Carlo simulation is used to study the adsorption of a binary sticky hard-sphere fluid mixture in planar pores. The wall-component 1 and wall-component 2 contact densities are determined to calculate the pressure as a function of the composition of the mixture and the separation between the walls. From these data dependence of the solvation force between the plates on pore width is estimated. The simulation results are compared with the predictions of the Percus-Yevick approximation for planar pores. The density profiles of particular components show interesting shapes stemming from the interplay between the steric effects and the competitive adhesion among all possible species pairs. It is shown that narrowing of the pore causes selective partitioning of individual components of the mixture between the bulk phase and the interior of the pore. The agreement between the two methods is better at wider pores and for the component comprised of weakly adhesive particles.     

Capillary condensation in mesoporous silica with surface roughness

We construct an atomistic silica pore model mimicking templated mesoporous silica MCM-41, which has molecular-level surface roughness, with the aid of the electron density profile (EDP) of MCM-41 obtained from X-ray diffraction data. Then, we present the GCMC simulations of argon adsorption on our atomistic silica pore models for two different MCM-41 samples at 75, 80, and 87 K, and the results are compared with the experimental adsorption data. We demonstrate that accurate molecular modeling of the pore structure of MCM-41 by using the experimental EDP allows the prediction of experimental capillary evaporation pressures at all investigated temperatures. The experimental desorption branches of the two MCM-41 samples are in good agreement with equilibrium vapor–liquid transition pressures from the simulations, which suggests that the experimental desorption branch for the open-ended cylindrical pores is in thermodynamic equilibrium.     

Adsorption/desorption hysteresis in inkbottle pores: a density functional theory and Monte Carlo simulation study

The mechanisms of adsorption and desorption in inkbottle-shaped pores are considered for lattice models using grand canonical mean field density functional theory and Monte Carlo simulation. We find that they depend significantly on the particular pore geometry, the nature of the fluid-solid interaction, and the temperature. We find two mechanisms for desorption. One mechanism involves the emptying of the main cavity even as the density of fluid in the necks remains high, a mechanism observed recently in studies of an off-lattice model of an inkbottle. The other is a simultaneous desorption from the entire pore space, behavior that is more closely related to the traditional picture of pore blocking in the inkbottle system.