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

Computing Mixture Adsorption in Porous Materials through Flat Histogram Monte Carlo Methods

Mixture adsorption properties of porous materials are critical to determine their potential as adsorbents in separation applications. Toward the discovery of optimal adsorbents, in silico screening studies typically employ the grand canonical Monte Carlo (GCMC) technique to compute adsorption properties of gas mixtures in materials of interest at a given condition (i.e., composition, total pressure, and temperature) or to compute their adsorption properties for each component, followed by utilizing methods to predict mixture adsorption isotherms. However, the former approach results in the need for repeated calculations when different conditions such as compositions are considered. For the latter, the predictions may involve uncertainties, sometimes originating from the fitting quality to the pure component isotherms, and repeated simulations may also be needed for different temperatures. To this end, this study demonstrates the potential of flat histogram Monte Carlo methods in addressing the abovementioned shortfalls. Specifically, the so-called NVT + W method, first reported by Smit and co-workers, is extended herein to determine the macrostate probability distribution (MPD) of binary mixtures in porous materials. The obtained MPD can be reweighted to any conditions, yielding accurate adsorption isotherms of any desired compositions and temperatures. This approach, denoted as 2D NVT + W, is also compared with the widely adopted ideal adsorbed solution theory (IAST) method, and the former is found to offer more reliable predictions. Overall, the 2D NVT + W approach represents an efficient and effective alternative to compute mixture adsorption isotherms for porous materials, and the obtained MPD can be conveniently reused by peer researchers. A user-friendly Python code is also provided along with this article to employ this method.

Adsorption of simple gases into the porous glass MCM-41

The porous glass MCM-41 is an important adsorbent to study the process of adsorption of gases onto a cylindrical surface. In this work, we study the adsorption of oxygen, nitrogen, deuterium, and deuteriated methane gases into MCM-41 using a combination of neutron diffraction analysis and atomistic computer modeling to interpret the measured data. Adsorption is achieved by immersing a sample of MCM-41 in a bath of the relevant gas, keeping the gas pressure constant (0.1 MPa), and lowering the temperature in steps toward the corresponding bulk liquid boiling point. All four gases have closely analogous behaviors, with an initial layering of liquid on the inside surface of the pores, followed by a relatively sharp capillary condensation (CC) when the pore becomes filled with dense fluid, signaled by a sharp decrease in the intensity of (100) Bragg diffraction reflection. At the temperature of CC, there is a marked distortion of the hexagonal lattice of pores, as others have seen, which relaxes close to the original structure after CC, and this appears to be accompanied by notable excess heterogeneity along the pore compared to when CC is complete. In none of the four gases studied does the final density of fluid in the pore fully attain the value of the bulk liquid at its boiling point at this pressure, although it does approach that limit closely near the center of the pore, and in all cases, the pronounced layering near the silica interface seen in previous studies is observed here as well.

Surface structure of linear nanopores in amorphous silica: Comparison of properties for different pore generation algorithms

We compare the surface structure of linear nanopores in amorphous silica (a-SiO₂) for different versions of "pore drilling" algorithms (where the pores are generated by the removal of atoms from the preformed bulk a-SiO₂) and for "cylindrical resist" algorithms (where a-SiO₂ is formed around a cylindrical exclusion region). After adding H to non-bridging O, the former often results in a moderate to high density of surface silanol groups, whereas the latter produces a low density. The silanol surface density for pore drilling can be lowered by a final dehydroxylation step, and that for the cylindrical resist approach can be increased by a final hydroxylation step. In this respect, the two classes of algorithms are complementary. We focus on the characterization of the chemical structure of the pore surface, decomposing the total silanol density into components corresponding to isolated and vicinal mono silanols and geminal silanols. The final dehyroxylation and hydroxylation steps can also be tuned to better align some of these populations with the target experimental values.

Molecular Simulation of Naphthalene, Phenanthrene, and Pyrene Adsorption on MCM-41

The adsorption of three typical polycyclic aromatic hydrocarbons (PAHs), naphthalene, phenanthrene, and pyrene with different ring numbers, on a common mesoporous material (MCM-41) was simulated based on a well-validated model. The adsorption equilibriums (isotherms), states (angle distributions and density profiles), and interactions (radial distribution functions) of three PAHs within the mesopores were studied in detail. The results show that the simulated isotherms agreed with previous experimental results. Each of the PAHs with flat molecules showed an adsorption configuration that was parallel to the surface of the pore, in the following order according to the degree of arrangement: pyrene (Pyr) > phenanthrene (Phe) > naphthalene (Nap). In terms of the interaction forces, there were no hydrogen bonds or other strong polar forces between the PAHs and MCM-41, and the O⁻H bond on the adsorbent surface had a unique angle in relation to the PAH molecular plane. The polarities of different H atoms on the PAHs were roughly the same, while those of the C atoms on the PAHs decreased from the molecular centers to the edges. The increasing area of the π-electron plane on the PAHs with the increasing ring number could lead to stronger adsorption interactions, and thus a shorter distance between the adsorbate and the adsorbent.

2D-NLDFT adsorption models for porous oxides with corrugated cylindrical pores

In this work, we develop two-dimensional models based on the non-local density functional theory (2D-NLDFT) for the analysis of pore size distribution (PSD) of oxide materials with cylindrical pores with rough and heterogeneous walls. The existing standard NLDFT models for porous oxides assume the smooth energetically uniform surface of the pore walls. Due to this assumption, the calculated theoretical isotherms show typical layering transitions, which are not consistent with the experimental adsorption isotherms measured on real oxide materials. As a result, the fits of standard NLDFT models to N₂ or Ar adsorption isotherms show deviations from the experimental points in association with artifacts observed on the calculated PSD plots. The 2D-NLDFT framework allows us to improve the standard model by introducing the corrugation and energetic heterogeneity to the surface of cylindrical pores. The surface roughness and energetic heterogeneity are known characteristics of the oxide surfaces. With these assumptions we develop a comprehensive approach in which both branches of the adsorption isotherm may be used for the PSD analysis of mesoporous oxide materials. We validate this approach by using Ar data measured at 87 K on the reference set of MCM-41 silica samples (Kruk and Jaroniec, 2000). The generated kernels are smooth, do not show layering transitions and fit accurately the reference data.

Adsorption Thicknesses of Confined Pure and Mixing Fluids in Nanopores

In this paper, adsorption thicknesses of confined pure and mixing fluids in nanopores are quantitatively determined and their influential factors are specifically evaluated. First, a new analytical formulation is developed thermodynamically to calculate the adsorption thicknesses. Second, a new generalized equation of state (EOS), which considers the confinement effect-induced phenomena, is developed analytically for calculating the thermodynamic confined fluid phase behavior. Third, the modified model based on the generalized EOS and coupled with the parachor model is applied to calculate the vapor-liquid equilibrium (VLE) and fluid adsorptions for the pure CO₂, alkanes of C₁-C₁₀, and two mixtures of CO₂-C₁₀H₂₂ and CH₄-C₁₀H₂₂ in nanopores. Finally, the following five important factors are studied to evaluate their effects on the adsorption thickness: temperature, pressure, pore radius, wall-effect distance, and feed gas-to-liquid ratio (FGLR). The proposed modified EOS is found to be accurate for the VLE and adsorption isotherm calculations. The adsorption thicknesses of confined pure or mixing alkanes are increased with the increasing carbon number but decreased with the temperature increase. For the alkanes of C₁-C₁₀, the degree of temperature effect is strengthened with the carbon number increase. Moreover, the adsorption thicknesses are significantly decreased with the pore radius increase until r_p = 50 nm, after which they have slight changes or are even constant at any pore radii. On the other hand, the wall-effect distance (δ_p) increase causes the adsorption thickness to be linearly increased at δ_p/ r_p ≥ 0.02. In addition, the effects of the FGLR and pressure on the adsorption thicknesses at the nanoscale are found to be negligible.

Liquid Adsorption of Organic Compounds on Hematite α-Fe2O3 Using ReaxFF

ReaxFF-based molecular dynamics simulations are used in this work to study the effect of the polarity of adsorbed molecules in the liquid phase on the structure and polarization of hematite (α-Fe₂O₃). We compared the adsorption of organic molecules with different polarities on a rigid hematite surface and on a flexible and polarizable surface. We show that the displacements of surface atoms and surface polarization in a flexible hematite model are proportional to the adsorbed molecule's polarity. The increase in electrostatic interactions resulting from charge transfer in the outermost solid atoms in a flexible hematite model results in better-defined adsorbed layers that are less ordered than those obtained assuming a rigid solid. These results suggest that care must be taken when parametrizing empirical transferable force fields because the calculated charges on a solid slab in vacuum may not be representative of a real system, especially when the solid is in contact with a polar liquid.

Transport and adsorption under liquid flow: the role of pore geometry

We study here the interplay between transport and adsorption in porous systems with complex geometries under fluid flow. Using a lattice Boltzmann scheme extended to take into account the adsorption at solid/fluid interfaces, we investigate the influence of pore geometry and internal surface roughness on the efficiency of fluid flow and the adsorption of molecular species inside the pore space. We show how the occurrence of roughness on pore walls acts effectively as a modification of the solid/fluid boundary conditions, introducing slippage at the interface. We then compare three common pore geometries, namely honeycomb pores, inverse opal, and materials produced by spinodal decomposition. Finally, we quantify the influence of those three geometries on fluid transport and tracer adsorption. This opens perspectives for the optimization of materials' geometries for applications in dynamic adsorption under fluid flow.

Metal-Organic Frameworks in Adsorption-Driven Heat Pumps: The Potential of Alcohols as Working Fluids

A large fraction of global energy is consumed for heating and cooling. Adsorption-driven heat pumps and chillers could be employed to reduce this consumption. MOFs are often considered to be ideal adsorbents for heat pumps and chillers. While most published works to date on this topic have focused on the use of water as a working fluid, the instability of many MOFs to water and the fact that water cannot be used at subzero temperatures pose certain drawbacks. The potential of using alcohol-MOF pairs in adsorption-driven heat pumps and chillers is investigated. To this end, 18 different selected MOF structures in combination with either methanol or ethanol as a working fluid are considered, and their potential is assessed on the basis of adsorption measurements and thermodynamic efficiencies. If alcohols are used instead of water, then (1) adsorption occurs at lower relative pressures for methanol and even lower pressure for ethanol, (2) larger pores can be utilized efficiently, as hysteresis is absent for pores smaller than 3.4 nm (2 nm for water), (3) larger pore sizes need to be employed to ensure the desired stepwise adsorption, (4) the effect of (polar/apolar) functional groups in the MOF is far less pronounced, (5) the energy released or taken up per cycle is lower, but heat and mass transfer may be enhanced, (6) stability of MOFs seems to be less of an issue, and (7) cryogenic applications (e.g., ice making) become feasible. From a thermodynamic perspective, UiO-67, CAU-3, and ZIF-8 seem to be the most promising MOFs for both methanol and ethanol as working fluids. Although UiO-67 might not be completely stable, both CAU-3 and ZIF-8 have the potential to be applied, especially in subzero-temperature adsorption chillers (AC).

Well-defined hollow nanochanneled-silica nanospheres prepared with the aid of sacrificial copolymer nanospheres and surfactant nanocylinders

A new approach for synthesizing well-defined hollow nanochanneled-silica nanosphere particles is demonstrated, and the structural details of these particles are described for the first time. Positively charged styrene copolymer nanospheres with a clean, smooth surface and a very narrow size distribution are synthesized by surfactant-free emulsion copolymerization and used as a thermal sacrificial core template for the production of core-shell nanoparticles. A surfactant/silica composite shell with a uniform thickness is successfully produced and deposited onto the polymeric core template by charge density matching between the polymer nanosphere template surface and the negatively charged silica precursors and then followed by selective thermal decomposition of the polymeric core and the surfactant cylinder domains in the shell, producing the hollow nanochanneled-silica nanospheres. Comprehensive, quantitative structural analyses collectively confirm that the obtained nanoparticles are structurally well defined with a hollow core and a shell composed of cylindrical nanochannels that provide facile accessibility to the hollow interior space. Overall, the hollow nanochanneled-silica nanoparticles have great potential for applications in various fields.

Validity of the t-plot method to assess microporosity in hierarchical micro/mesoporous materials

The t-plot method is a well-known technique which allows determining the micro- and/or mesoporous volumes and the specific surface area of a sample by comparison with a reference adsorption isotherm of a nonporous material having the same surface chemistry. In this paper, the validity of the t-plot method is discussed in the case of hierarchical porous materials exhibiting both micro- and mesoporosities. Different hierarchical zeolites with MCM-41 type ordered mesoporosity are prepared using pseudomorphic transformation. For comparison, we also consider simple mechanical mixtures of microporous and mesoporous materials. We first show an intrinsic failure of the t-plot method; this method does not describe the fact that, for a given surface chemistry and pressure, the thickness of the film adsorbed in micropores or small mesopores (< 10σ, σ being the diameter of the adsorbate) increases with decreasing the pore size (curvature effect). We further show that such an effect, which arises from the fact that the surface area and, hence, the free energy of the curved gas/liquid interface decreases with increasing the film thickness, is captured using the simple thermodynamical model by Derjaguin. The effect of such a drawback on the ability of the t-plot method to estimate the micro- and mesoporous volumes of hierarchical samples is then discussed, and an abacus is given to correct the underestimated microporous volume by the t-plot method.

Probing the self-assembled nanostructures of functional polymers with synchrotron grazing incidence X-ray scattering

For advanced functional polymers such as biopolymers, biomimic polymers, brush polymers, star polymers, dendritic polymers, and block copolymers, information about their surface structures, morphologies, and atomic structures is essential for understanding their properties and investigating their potential applications. Grazing incidence X-ray scattering (GIXS) is established for the last 15 years as the most powerful, versatile, and nondestructive tool for determining these structural details when performed with the aid of an advanced third-generation synchrotron radiation source with high flux, high energy resolution, energy tunability, and small beam size. One particular merit of this technique is that GIXS data can be obtained facilely for material specimens of any size, type, or shape. However, GIXS data analysis requires an understanding of GIXS theory and of refraction and reflection effects, and for any given material specimen, the best methods for extracting the form factor and the structure factor from the data need to be established. GIXS theory is reviewed here from the perspective of practical GIXS measurements and quantitative data analysis. In addition, schemes are discussed for the detailed analysis of GIXS data for the various self-assembled nanostructures of functional homopolymers, brush, star, and dendritic polymers, and block copolymers. Moreover, enhancements to the GIXS technique are discussed that can significantly improve its structure analysis by using the new synchrotron radiation sources such as third-generation X-ray sources with picosecond pulses and partial coherence and fourth-generation X-ray laser sources with femtosecond pulses and full coherence.

Effect of immobilized amines on the sorption properties of solid materials: impregnation versus grafting

The underlying mechanism of the adsorption process in functionalized materials is not yet fully understood. This incomplete understanding limits the possibility of designing optimal adsorbent materials for different applications. Hence, the availability of complementary methods to advance this field is of great interest. We present here results concerning the adsorption of CO(2) in amine-functionalized silica materials by Monte Carlo simulations, providing new insights into the capture process. Two different mechanisms of functionalization are compared: impregnation (a physical mixture of the amine and the support) and grafting (a chemical bond is formed between the amine and the support). We evaluate in this work a model of MCM-41 for N(2) and CO(2) adsorption with varying degrees of density of the functionalized chains. The results indicate that the mobility of the impregnated chains allows the creation of a network of microcavities, which enhance the low-pressure adsorption capabilities of these materials. Molecular simulations allow us to study in detail the conformational changes in the functionalized chains during the adsorption process. Materials functionalized densely by grafting undergo a change in the preferential orientation of the chains, which allows the adsorption of additional molecules close to the surface of the support. The adsorption of gas molecules close to the pore surface is usually the most energetically favorable configuration; however, for densely grafted materials the adsorption close to the surface occurs only at pressures large enough to provide energy to displace the functionalized chains.

Thermodynamics of water confined in porous calcium-silicate-hydrates

Water within pores of cementitious materials plays a crucial role in the damage processes of cement pastes, particularly in the binding material comprising calcium-silicate-hydrates (C-S-H). Here, we employed Grand Canonical Monte Carlo simulations to investigate the properties of water confined at ambient temperature within and between C-S-H nanoparticles or "grains" as a function of the relative humidity (%RH). We address the effect of water on the cohesion of cement pastes by computing fluid internal pressures within and between grains as a function of %RH and intergranular separation distance, from 1 to 10 Å. We found that, within a C-S-H grain and between C-S-H grains, pores are completely filled with water for %RH larger than 20%. While the cohesion of the cement paste is mainly driven by the calcium ions in the C-S-H, water facilitates a disjoining behavior inside a C-S-H grain. Between C-S-H grains, confined water diminishes or enhances the cohesion of the material depending on the intergranular distance. At very low %RH, the loss of water increases the cohesion within a C-S-H grain and reduces the cohesion between C-S-H grains. These findings provide insights into the behavior of C-S-H in dry or high-temperature environments, with a loss of cohesion between C-S-H grains due to the loss of water content. Such quantification provides the necessary baseline to understand cement paste damaging upon extreme thermal, mechanical, and salt-rich environments.

Enhanced CO2 solubility in hybrid MCM-41: molecular simulations and experiments

Grand canonical Monte Carlo simulations are performed in a hybrid adsorbent model in order to interpret the CO(2) solubility behavior. The hybrid adsorbent is prepared by confining a physical solvent (OMCTS) into the pores of a mimetic MCM-41 solid support. As a result, simulated adsorption isotherms of CO(2) nicely match the experimental data for three distinctive systems: bulk solvent, raw MCM-41, and hybrid MCM-41. The microscopic mechanisms underlying the apparition of enhanced solubility are then clearly identified. In fact, the presence of solvent molecules favors the layering of CO(2) molecules within the pores; therefore, the CO(2) solubility in the hybrid adsorbent markedly increases in comparison to that found in the raw adsorbent as well as in the bulk solvent. In addition, a good understanding of confined solvents' properties and solid surface structures is essential to fully evaluate the efficiency of hybrid adsorbents in capturing CO(2). The sorbent-solid interactions along with the solvent molecular size's impact on CO(2) solubility are therefore investigated in this study. We found that an ideal hybrid system should possess a weak solvent-solid interaction but a strong solvent-CO(2) interaction. Besides, an optimal solvent size is obtained for the enhanced CO(2) solubility in the hybrid system. According to the simulation results, the solvent layer builds pseudomicropores inside the mesoporous MCM-41, enabling more CO(2) molecules to be absorbed under the greater influence of spatial confinement and surface interaction. In addition, the molecular sieving effect is clearly observed in the case of larger solvent molecular sizes.

Molecular simulation of water confined in nanoporous silica

This paper reports on a molecular simulation study of the thermodynamics, structure and dynamics of water confined at ambient temperature in hydroxylated silica nanopores of a width H = 10 and 20 Å. The adsorption isotherms for water in these nanopores resemble those observed for experimental samples; the adsorbed amount increases continuously in the multilayer adsorption regime until a jump occurs due to capillary condensation of the fluid within the pore. Strong layering of water in the vicinity of the silica surfaces is observed as marked density oscillations are observed up to 8 Å from the surface in the density profiles for confined water. Our results indicate that water molecules within the first adsorbed layer tend to adopt a H-down orientation with respect to the silica substrate. For all pore sizes and adsorbed amounts, the self-diffusivity of confined water is lower than the bulk, due to the hydrophilic interaction between the water molecules and the hydroxylated silica surface. Our results also suggest that the self-diffusivity of confined water is sensitive to the adsorbed amount.

Molecular simulation of nitrogen adsorption in nanoporous silica

This article reports on a molecular simulation study of nitrogen adsorption and condensation at 77 K in atomistic silica cylindrical nanopores (MCM-41). Two models are considered for the nitrogen molecule and its interaction with the silica substrate. In the "pea" model, the nitrogen molecule is described as a single Lennard-Jones sphere and only Lennard-Jones interactions between the nitrogen molecule and the oxygens atoms of the silica substrate are taken into account. In the "bean" model (TraPPE force field), the nitrogen molecule is composed of two Lennard-Jones sites and a linear array of three charges on the atomic positions and at the center of the nitrogen-nitrogen bond. In the bean model, the interactions between the sites on the nitrogen molecule and the Si, O, and H atoms of the substrate are the sum of the Coulombic and dispersion interactions with a repulsive short-range contribution. The data obtained with the pea and bean models in silica nanopores conform to the typical behavior observed in the experiments for adsorption/condensation in cylindrical MCM-41 nanopores; the adsorbed amount increases continuously in the multilayer adsorption regime until an irreversible jump occurs because of capillary condensation and evaporation of the fluid within the pore. Our results suggest that the pea model can be used for characterization purposes where one is interested in capturing the global experimental behavior upon adsorption and desorption in silica nanopores. However, the bean model is more suitable to investigating the details of the interaction with the surface because this model, which accounts for the partial charges located on the nitrogen atoms of the molecule (quadrupole), allows a description of the specific interactions between this adsorbate and silica surfaces (silanol groups and siloxane bridges) or grafted silica surfaces. In particular, the bean model provides a more realistic picture of nitrogen adsorption in the vicinity of silica surfaces or confined in silica nanopores, where the isosteric heat of adsorption curves show that the nitrogen molecule in this model is sensitive to the surface heterogeneity.

Adsorption and structure of benzene on silica surfaces and in nanopores

Grand canonical Monte Carlo simulations are used to study the adsorption of benzene on atomistic silica surfaces and in cylindrical nanopores. The effect of temperature and surface chemistry is addressed by studying the adsorption of benzene at 293 and 323 K on both fully and partially hydroxylated silica surfaces or nanopores. We also consider the adsorption of benzene in a cylindrical nanopore of diameter D=3.6 nm and compare our results with those obtained for planar surfaces. The structure of benzene in the vicinity of the planar surface and confined in the cylindrical nanopore is determined by calculating orientational order parameters and examining positional pair correlation functions. The density profiles of adsorbed benzene reveal the strong layering of the adsorbate, which decays with the distance from the silica surface. At a given temperature and at low pressures, the film adsorbed at the fully hydroxylated silica surface is larger than that for the partially hydroxylated silica surface. This result is due to an increase in the density of silanol groups that induces an increase in the polarity of the silica surface, which becomes more attractive for the adsorbate. Our results also suggest that the benzene molecules prefer an orientation in which their ring is nearly perpendicular to the surface when fully hydroxylated surfaces are considered. When partially hydroxylated surfaces are considered, a second preferential orientation is observed where the benzene ring forms an angle of approximately 50 degrees with the silica surface. In this case, the average orientation of the benzene molecules appears disordered as in the bulk phase. These results suggest that determining the experimental orientation of benzene in the vicinity of a silica surface is a difficult task even when the surface chemistry is known. Capillary condensation in the nanopores involves a transition from a partially filled pore (a thin film adsorbed at the pore surface) to a completely filled pore configuration where the confined liquid coexists at equilibrium with the external gas phase. The disordered orientation of the adsorbed benzene molecules in the case of the partially hydroxylated surface favors the condensation of benzene molecules (the condensation pressure for this substrate is lower than that for the fully hydroxylated surface). Finally, these results are consistent with the structural analysis, showing that (1) benzene tends to relax its liquid structure a little in order to optimize its molecular arrangement near the pore wall and (2) the disordering of the liquid structure induced by the surface becomes stronger as the interaction with the pore wall increases.

Modeling of N2 adsorption in MCM-41 materials: hexagonal pores versus cylindrical pores

Low-temperature nitrogen adsorption in hexagonal pores and equivalent cylindrical pores is analyzed using nonlocal density functional theory extended to amorphous solids (NLDFT-AS). It is found that, despite significant difference of the density distribution over the cross-section of the pore, the capillary condensation/evaporation pressure is not considerably affected by the pore shape being slightly lower in the case of hexagonal geometry. However, the condensation/evaporation step in the hexagonal pore is slightly larger than that in the equivalent cylindrical pore because in the latter case the pore wall surface area and, hence, the amount adsorbed at pressures below the evaporation pressure are underestimated by 5%. We show that a dimensionless parameter defined as the ratio of the condensation/evaporation step and the upper value of the amount adsorbed at the condensation/evaporation pressure can be used as an additional criterion of the correct choice of the gas-solid molecular parameters along with the dependence of condensation/evaporation pressure on the pore diameter. Application of the criteria to experimental data on nitrogen adsorption on a series of MCM-41 silica at 77 K corroborates some evidence that the capillary condensation occurs at equilibrium conditions.

Modeling micelle-templated mesoporous material SBA-15: atomistic model and gas adsorption studies

We report the development of a realistic molecular model for mesoporous silica SBA-15, which includes both the large cylindrical mesopores and the smaller micropores in the pore walls. The methodology for modeling the SBA-15 structure involves molecular and mesoscale simulations combined with geometrical interpolation techniques. First, a mesoscale model is prepared by mimicking the synthesis process using lattice Monte Carlo simulations. The main physical features of this mesoscale pore model are then carved out of an atomistic silica block; both the mesopores and the micropores are incorporated from the mimetic simulations. The calculated pore size distribution, surface area, and simulated TEM images of the model structure are in good agreement with those obtained from experimental samples of SBA-15. We then investigate the adsorption of argon in this structure using Grand Canonical Monte Carlo (GCMC) simulations. The adsorption results for our SBA-15 model are compared with those for a similar model that does not include the micropores; we also compare with results obtained in a regular cylindrical pore. The simulated adsorption isotherm for the SBA-15 model shows semiquantitative agreement with the experimental isotherm for a SBA-15 sample having a similar pore size. We observe that the presence of the micropores leads to increased adsorption at low pressure compared to the case of a model without micropores in the pore walls. At higher pressures, for all models, the filling proceeds via the monolayer-multilayer adsorption on the mesopore surface followed by capillary condensation, which is mainly controlled by the mesopore diameter and is not influenced by the presence of the micropores.

Adsorption of simple fluid on silica surface and nanopore: effect of surface chemistry and pore shape

This paper reports a molecular simulation study on the adsorption of simple fluids (argon at 77 K) on hydroxylated silica surfaces and nanopores. The effect of surface chemistry is addressed by considering substrates with either partially or fully hydroxylated surfaces. We also investigate the effect of pore shape on adsorption and capillary condensation by comparing the results for cylindrical and hexagonal nanopores having equivalent sections (i.e., equal section areas). Due to the increase in the polarity of the surface with the density of OH groups, the adsorbed amounts for fully hydroxylated surfaces are found to be larger than those for partially hydroxylated surfaces. Both the adsorption isotherms for the cylindrical and hexagonal pores conform to the typical behavior observed in the experiments for adsorption/condensation in cylindrical nanopores MCM-41. Capillary condensation occurs through an irreversible discontinuous transition between the partially filled and the completely filled configurations, while evaporation occurs through the displacement at equilibrium of a hemispherical meniscus along the pore axis. Our data are also used to discuss the effect of surface chemistry and pore shape on the BET method. The BET surface for fully hydroxylated surfaces is much larger (by 10-20%) than the true geometrical surface. In contrast, the BET surface significantly underestimates the true surface when partially hydroxylated surfaces are considered. These results suggest that the surface chemistry and the choice of the system adsorbate/adsorbent is crucial in determining the surface area of solids using the BET method.

Adsorption of fluids in a pore with chemical heterogeneities: the cooperative effect

In this work, we study the cooperative adsorption of fluids in a heterogeneous pore, in which the pore walls are composed of homogeneous substrates with chemical groups (CGs) decorating them. The adsorption caused by the homogeneous substrates alone and that by CGs do not add up to the overall adsorption, indicating the existence of a cooperative effect. The cooperative effect is the source of cooperative adsorption, and is characterized in this work by the ratio of the overall adsorption to the sum of adsorption by the substrate only and that by CGs. It is found that the cooperative adsorption does not depend monotonically on the substrate or the CGs. Two different origins of the cooperative adsorption play different roles depending on which one dominates the overall adsorption. Our simulations reveal that, when the homogeneous substrate dominates the overall adsorption, weakening of the attractive fluid-substrate interaction or alternatively strengthening of the fluid-CGs interaction leads to a stronger cooperative effect and enhances the cooperative adsorption. However, when CGs dominate the overall adsorption, weakening of the attractive fluid-CG interaction or strengthening the fluid-substrate interaction results in strong cooperative adsorption. In order to investigate the effects of the distribution of CGs on cooperative adsorption, a design-test method is generalized and used in this work. Simulation results show that the overall adsorption can be significantly affected by the CG distribution.

Microscopic mechanism of adsorption in cylindrical nanopores with heterogenous wall structure

We study the microscopic mechanism of adsorption in nanometric cylindrical pores with strongly heterogeneous walls using grand canonical Monte Carlo simulations. The pore surface structure is modeled by a new lattice-site approach. Each site is characterized by two amplitudes--structural and energetic--that locally modify the structural and energetic properties of the surface. The amplitudes are randomly distributed over the pore wall. We have shown that different structural and energetic distribution functions lead to different mechanism of adsorption. The energetic site distribution plays the most crucial role in the submonolayer region. The structural site distribution modifies the multilayer adsorption. A method to analyze the stability of the adsorbed system using static susceptibility is proposed. Potential applications in multiscale modeling are discussed.

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.

Phase equilibria and interfacial tension of fluids confined in narrow pores

Correlation between phase behaviors of a Lennard-Jones fluid in and outside a pore is examined over wide thermodynamic conditions by grand canonical Monte Carlo simulations. A pressure tensor component of the confined fluid, a variable controllable in simulation but usually uncontrollable in experiment, is related with the pressure of a bulk homogeneous system in equilibrium with the confined system. Effects of the pore dimensionality, size, and attractive potential on the correlations between thermodynamic properties of the confined and bulk systems are clarified. A fluid-wall interfacial tension defined as an excess grand potential is evaluated as a function of the pore size. It is found that the tension decreases linearly with the inverse of the pore diameter or width.