Grand canonical Monte Carlo simulation of argon adsorption at the surface of silica nanopores: effect of pore size, pore morphology, and surface roughness

Argon adsorption (77 K) in atomistic silica nanopores of various sizes and shapes has been studied by means of grand canonical Monte Carlo simulations (GCMC). We discuss the effects of confinement (pore size), pore morphology (ellipsoidal, hexagonal, constricted pore), and surface texture (rough/smooth) on the thickness variation of the adsorbed film with pressure onto the disordered inner surface of porous materials (usually called t-plot or t-curve). We show that no confinement effect occurs when the diameter of the regular cylindrical pore is larger than 10 nm. For pores smaller than 6 nm, we find that the film thickness increases as the pore size decreases. We show that the adsorption isotherm in the rough pore can be described as the sum of an adsorbed amount similar to that found for a smooth pore (of the same radius) and a constant contribution due to atoms "trapped" in the infractuosities of the rough surface which act as a microporous texture. Simulation snapshots for Ar adsorption in hexagonal and ellipsoidal smooth pores indicate that at low pressures the gas/adsorbate interface retains memory of the pore shape and becomes cylindrical prior to the capillary condensation of the fluid in the pore. The film thickness in the hexagonal pore is close to that obtained for a cylindrical pore having a similar dimension. By contrast, we find that the film thickness for an ellipsoidal pore is always larger than that for an equivalent cylindrical pore (having the same length and volume but a circular section). We show that this effect strengthens as the pore size decreases and/or the pore asymmetry increases. Ar adsorption in a cylindrical constricted pore shows that the presence of the narrower part considerably modifies the adsorption mechanism. Finally, we report GCMC simulations of Ar adsorption (77 K) on a plane silica reference substrate for different intermolecular potentials. We discuss the effect of the interaction on the shape of the adsorption isotherm and compare our results with experiments.     

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).     

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.     

Thermodynamic pressure of simple fluids confined in cylindrical nanopores by isothermal-isobaric Monte Carlo: influence of fluid/substrate interactions

The thermodynamic pressure or grand potential density is calculated by isobaric-isothermal Monte Carlo algorithm for simple Lennard-Jones fluid confined in cylindrical pores presenting chemical heterogeneities along their axis. Heuristic arguments and simulation results show that the thermodynamic pressure of the confined fluid contains two contributions. The first term is the usual pressure of the bulk fluid for a density equal to the confined fluid density defined as the total number of confined particles divided by the accessible volume due to thermal agitation. A second term has to be added, which is empirically shown to be proportional to the fluid/wall interface area and almost constant along the adsorption and desorption branches. This interfacial contribution, calculated for various pore models, has small variations reminiscent of the fluid adsorption/desorption properties calculated in the various pores. In particular, it is shown that this interfacial quantity is maximum for a fluid/substrate interaction intensity of the same order as the fluid/fluid one, while the thermodynamic pressure at which rapid desorption occurs presents a minimum. Stronger or weaker fluid/wall affinity favors gas state nucleation on the desorption of confined fluids.     

Interaction thresholds for adsorption of quantum gases on surfaces and within pores of various shapes

Adsorption within pores and on surfaces occurs because of the attractive potential provided by the adsorbent. If the attraction is too weak, however, adsorption does not occur to any significant extent. This paper evaluates the criterion for such adsorption, at zero temperature, of the quantum gases 4He and H2. This criterion is expressed as a relationship between a threshold value of the well-depth (D) of the adsorption potential (on a semi-infinite planar surface) and the hard-core diameter (sigma) of the gas-surface pair potential. Six geometries are considered, of which two result in two-dimensional (2D) adsorbed phases, two result in one-dimensional (1D) phases, and two result in zero-dimensional phases. These are monolayer films on semi-infinite substrates or within a slit pore, linear or axial phases within cylindrical pores (within bulk solids) or cylindrical tubes, and single-particle adsorption within spherical pores or hollow spherical cavities, respectively. The criteria for film adsorption are consistent with analogous criteria for film wetting to occur, evaluated with a simple thermodynamic model.     

Capillary condensation in a geometrically and a chemically heterogeneous pore: a molecular simulation study

A computer simulation study has been carried out, using an extended Gibbs ensemble Monte Carlo technique, to examine the influence of so-called geometric and chemical disorder on the thermodynamic behavior of simple fluids confined in porous media. The technique allows the equilibrium coexistence of gas and liquid phases to be calculated in a single run. The phase diagram of Lennard-Jones fluid has been calculated in a perfectly cylindrical pore as a reference. Some disorder is then introduced in the porous material, first by spatially modifying the external potential of the initially cylindrical pore, to imitate the geometric disorder of a more realistic pore (undulation, constrictions, etc.) and second by modulating the amplitude of the same initially cylindrical potential to reproduce the energetic disorder of realistic pores due to chemical variations along it. It is shown that the chemical disorder has a much stronger effect on the phase diagram of the confined fluid. The complete adsorption/desorption isotherms are also calculated to help in understanding the large effects of chemical disorder.     

Packing effects on argon and methanol adsorption inside graphitic cylindrical and slit pores: a GCMC simulation study

Using Grand Canonical Monte Carlo simulation, we have studied the effects of confinement on argon and methanol adsorption in graphitic cylindrical and slit pores. Linear chain, zigzag and incomplete helical packing are observed for argon adsorption in cylindrical pores. However, for methanol adsorption different features appear because the electrostatic interactions favour configurations that maximize the hydrogen bonding among methanol molecules. We have found zigzag chains with hydrogen-bonded structures for methanol adsorption in cylindrical and slit pores. To investigate how dense the adsorbed phase is and how many molecules could be packed per unit physical volume of the solid, we consider two different definitions of pore density; one based on the physical volume and the other on the accessible volume. That based on accessible volume gives a measure of the fluid density, while that based on the physical volume gives a measure of how much adsorbate can be stored per unit volume of the adsorbent. It is found that the adsorbate is denser in cylindrical pores, but that slit pores can pack more molecules per unit solid volume. We also discuss the effects on the isosteric heat of argon and methanol of pore size, pore geometry and loading.     

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.     

Adsorption-induced deformation of mesoporous solids: macroscopic approach and density functional theory

We present a theoretical study of the deformation of mesoporous solids during adsorption. The proposed thermodynamic model allows one to link the mechanical stress and strain to the solvation pressure exerted by the adsorbed molecules on the pore wall. Two approaches are employed for calculation of solvation pressure as a function of adsorbate pressure: the macroscopic Derjaguin-Broekhoff-de Boer theory of capillary condensation, and the microscopic density functional theory. We revealed that the macroscopic and microscopic theories are in quantitative agreement for the pores >8 nm diameter within the whole range of adsorbate pressures. For smaller pores, the macroscopic theory gradually deteriorates, and the density functional theory extends the thermodynamic model of adsorption-induced deformation to the nanometer scales.     

Adsorption hysteresis in ordered mesoporous silicas

We review some recent progress in experimental studies of the adsorption hysteresis of simple molecules in ordered mesoporous silicas. We show that the nature of the adsorption hysteresis due to capillary condensation can be examined with less ambiguity by measuring the hysteresis loop for the ordered mesoporous silicas with three types of pore geometries (cylindrical, interconnected cylindrical, and interconnected spherical) over a wide temperature range. The adsorption hysteresis arises from the metastability of a confined phase and the temperature at which the hysteresis disappears is lower than the critical temperature of vapor-liquid equilibrium in pores. The hysteresis occurs mainly on the desorption rather than adsorption branch, irrespective of the pore geometries.     

Physical adsorption of gases: the case for absolute adsorption as the basis for thermodynamic analysis

We discuss the thermodynamics of physical adsorption of gases in porous solids. The measurement of the amount of gas adsorbed in a solid requires specialized volumetric and gravimetric techniques based upon the concept of the surface excess. Excess adsorption isotherms provide thermodynamic information about the gas-solid system but are difficult to interpret at high pressure because of peculiarities such as intersecting isotherms. Quantities such as pore density and heats of adsorption are undefined for excess isotherms at high pressure. These difficulties vanish when excess isotherms are converted to absolute adsorption. Using the proper definitions, the special features of adsorption can be incorporated into a rigorous framework of solution thermodynamics. Practical applications including mixed-gas equilibria, equations for adsorption isotherms, and methods for calculating thermodynamic properties are covered. The primary limitations of the absolute adsorption formalism arise from the need to estimate pore volumes and in the application to systems with larger mesopores or macropores at high bulk pressures and temperatures where the thermodynamic properties may be dominated by contributions from the bulk fluid. Under these circumstances a rigorous treatment of the thermodynamics requires consideration of the adsorption cell and its contents (bulk gas, porous solid and confined fluid).     

Dibenzodioxin adsorption on inorganic materials

Dibenzodioxin adsorption/desorption on solid surfaces is an important issue associated with the formation, adsorption, and emission of dioxins. Dibenzodioxin adsorption/desorption behaviors on inorganic materials (amorphous/mesoporous silica, metal oxides, and zeolites) were investigated using in situ FT-IR spectroscopy and thermogravimetric (TG) analysis. Desorption temperatures of adsorbed dibenzodioxin are very different for different kinds of inorganic materials: approximately 200 degrees C for amorphous/mesoporous silica, approximately 230 degrees C for metal oxides, and approximately 450 degrees C for NaY and mordenite zeolites. The adsorption of dibenzodioxin can be grouped into three categories according to the red shifts of the IR band at 1496 cm(-1) of the aromatic ring for the adsorbed dibenzodioxin: a shift of 6 cm(-1) for amorphous/mesoporous silica, a shift of 10 cm(-1) for metal oxides, and a shift of 14 cm(-1) for NaY and mordenite, suggesting that the IR shifts are proposed to associated with the strength of the interaction between adsorbed dibenzodioxin and the inorganic materials. It is proposed that the dibenzodioxin adsorption is mainly via the following three interactions: hydrogen bonding with the surface hydroxyl groups on amorphous/mesoporous silica, complexation with Lewis acid sites on metal oxides, and confinement effect of pores of mordenite and NaY with pore size close to the molecular size of dibenzodioxin.     

Nature of adsorption and desorption branches in cylindrical pores

To examine the nature of the adsorption and desorption branches in hysteretic adsorption isotherms of gases on mesoporous materials, we measured the temperature dependence of the adsorption and desorption isotherms of argon, oxygen, and carbon dioxide onto MCM-41 with a pore diameter of 4.4 nm. The results clearly show that in the open-ended cylindrical pores of MCM-41, capillary condensation rather than evaporation takes place near a thermodynamical equilibrium transition, as opposed to the general statement that capillary evaporation can occur via a meniscus formed at the pore mouth, and, thus, takes place at equilibrium.     

Adsorption hysteresis in self-ordered nanoporous alumina

We performed systematic adsorption studies using self-ordered nanoporous anodic aluminum oxide (AAO) in an extended range of mean pore diameters and with different pore topologies. These matrices were characterized by straight cylindrical pores having a narrow pore size distribution and no interconnections. Pronounced hysteresis loops between adsorption and desorption cycles were observed even in the case of pores closed at one end. These results are in contrast with macroscopic theoretical models and detailed numerical simulations of the adsorption in a single pore. Extensive measurements involving adsorption isotherms, reversal curves, and subloops carried out in closed-bottom pores suggest that the pores do not desorb independently from one another.     

Modeling of Adsorption in Finite Cylindrical Pores by Means of Density Functional Theory

Adsorption of argon at its boiling point in finite cylindrical pores is considered by means of the non-local density functional theory (NLDFT) with a reference to MCM-41 silica. The NLDFT was adjusted to amorphous solids, which allowed us to quantitatively describe argon adsorption isotherm on nonporous reference silica in the entire bulk pressure range. In contrast to the conventional NLDFT technique, application of the model to cylindrical pores does not show any layering before the phase transition in conformity with experimental data. The finite pore is modeled as a cylindrical cavity bounded from its mouth by an infinite flat surface perpendicular to the pore axis. The adsorption of argon in pores of 4 and 5 nm diameters is analyzed in canonical and grand canonical ensembles using a two-dimensional version of NLDFT, which accounts for the radial and longitudinal fluid density distributions. The simulation results did not show any unusual features associated with accounting for the outer surface and support the conclusions obtained from the classical analysis of capillary condensation and evaporation. That is, the spontaneous condensation occurs at the vapor-like spinodal point, which is the upper limit of mechanical stability of the liquid-like film wetting the pore wall, while the evaporation occurs via a mechanism of receding of the semispherical meniscus from the pore mouth and the complete evaporation of the core occurs at the equilibrium transition pressure. Visualization of the pore filling and empting in the form of contour lines is presented.     

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.     

NMR studies of cooperative effects in adsorption

The conversion of gas adsorption isotherms into pore size distributions generally relies upon the assumption of thermodynamically independent pores. Hence, pore-pore cooperative adsorption effects, which might result in a significantly skewed pore size distribution, are neglected. In this work, cooperative adsorption effects in water adsorption on a real, amorphous, mesoporous silica material have been studied using magnetic resonance imaging (MRI) and pulsed-gradient stimulated-echo (PGSE) NMR techniques. Evidence for advanced adsorption can be seen directly using relaxation time weighted MRI. The number and spatial distributions of pixels containing pores of different sizes filled with condensate have been analyzed. The spatial distribution of filled pores has been found to be highly nonrandom. Pixels containing the largest pores present in the material have been observed to fill in conjunction with pixels containing much smaller pores. PGSE NMR has confirmed the spatially extensive nature of the adsorbed ganglia. Thus, long-range (≥40 μm) cooperative adsorption effects, between larger pores associated with smaller pores, occur within mesoporous materials. The NMR findings have also suggested particular types of pore filling mechanisms occur within the porous solid studied.     

Capillary condensation hysteresis in overlapping spherical pores: a monte carlo simulation study

The mechanisms of hysteretic phase transformations in fluids confined to porous bodies depend on the size and shape of pores, as well as their connectivity. We present a Monte Carlo simulation study of capillary condensation and evaporation cycles in the course of Lennard-Jones fluid adsorption in the system of overlapping spherical pores. This model system mimics pore shape and connectivity in some mesoporous materials obtained by templating cubic surfactant mesophases or colloidal crystals. We show different mechanisms of capillary hysteresis depending on the size of the window between the pores. For the system with a small window, the hysteresis cycle is similar to that in a single spherical pore: capillary condensation takes place upon achieving the limit of stability of adsorption film and evaporation is triggered by cavitation. When the window is large enough, the capillary condensation shifts to a pressure higher than that of the isolated pore, and the possibility for the equilibrium mechanism of desorption is revealed. These finding may have important implications for practical problems of assessment of the pore size distributions in mesoporous materials with cagelike pore networks.     

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.