Molecular simulation of nitrogen adsorption in nanoporous silica

Scattering of N2 Molecules from Silica Surfaces: Effect of Polymorph and Surface Temperature

The inelastic scattering of N₂ molecules from silica surfaces, taken at 100 K, has been investigated by adopting a semiclassical collision model in conjunction with the appropriate treatment of the long-range interaction forces. Such forces promote the formation of the precursor state that controls all basic elementary processes occurring at the gas–surface interphase. The probabilities for the different elementary surface processes triggered by quartz are determined and compared with those recently obtained for another silica polymorph (cristobalite). In addition, the final roto-vibrational distributions of N₂ molecules undergoing inelastic scattering have been characterized. N₂ molecules, impinging on both considered surfaces in low-medium vibrational states, preserve the initial vibrational state, while those inelastically scattered are rotationally excited and translationally colder. The surface temperature effect, investigated by raising the temperature itself from 100 K up to 1000 K, emerges more sharply for the cristobalite polymorph, mainly for the molecules impinging in the ground roto-vibrational state and with low collision energies.

How Gas-Solid Interaction Matters in Graphene-Doped Silica Aerogels

It was interesting to experimentally find that the thermal insulation of silica aerogels was improved by doping graphene sheets with high heat conductivity. The underlying mechanism is investigated in the present work from the perspective of gas-solid interaction using a comprehensive analysis of molecular dynamics (MD) simulations, theoretical modeling, and experimental data. The MD-modeled small pores are demonstrated to effectively represent big pores in silica aerogels because of similar heat conduction physics, because it is found that adsorption does not contribute to gas heat conduction. Meanwhile, based on the experimentally measured density, the porous structures are schematically re-engineered using molecular modeling for the first time. The evaluated pore size distributions numerically present a consistency with available experimental data. Inspired by the visualization of the 3D pore structure, we proposed a graphene/silica/nitrogen model to evaluate the role of graphene in heat conduction: it can not only reduce effective gas collision (impede heat transport) but also enhance the gas-solid coupling effect. The former is dominant because of the high porosity, leading to an improvement in thermal insulation. The competition between them can be the reason for the "trade-off" phenomenon in the graphene doping effect in the available experiment.

Delta Chem: A New Geometric Approach of Porosity for Symmetric Porous Materials

Porous materials, such as zeolites and metal-organic frameworks (MOFs), and zeolitic-organic frameworks (ZIFs), are frequently considered for shape-selective separations, molecular storage, and catalysis applications, mainly due to their hollow structures. The amount and chemical nature of sorbate molecules that may (or may not) be fitted inside their cavities, and hence the bulk of their applications, depend on their internal structure, that is, on their surface areas, available volumes, and shapes of their porosities. However, experimentally, the access to such strucutral information is somewhat limited and computationally can be expensive to calculate for structures of more than 100 atoms. Moreover, the large number of known and hypothetical structures reported makes computational geometry-based techniques particularly attractive to identify the most suitable structures for a desired application. In this context, Delta Chem is both a method and a program designed to quickly analyze porous structures, relying solely on their Cartesian coordinates, and characterize the shapes of their cages using regular convex polyhedra. The program also provides a systematic approach to determine the positions of the centers of porosity and the atoms that contribute to form the internal surfaces of these materials, as well as other geometric features of the porosities such as volumes and surface areas. It also includes a routine to compute the irreducible volumes of the cages, i.e., minimal regions of the cavities that can be used to represent the hole porosity shape via symmetry operations. The capabilities of the program are tested on well-studied porous systems, namely, Buckminsterfullerene, MOF-5, HKUST-1, UiO-66, and ZIF-8. As highlighted through the fullerene, it can equally be used to characterize the cavities of hollow molecules. Our approach is compared against other widely used polyhedra-based approaches for porous materials. Our results show that Delta Chem is a novel and systematic way of characterizing routinely porous materials and hollow molecules. Besides potential applications to systematically simplify computational studies of shape-dependent properties, like shape-selective catalysis and adsorption, Delta Chem can be used in many studies to generate basic geometrical models.

Shock-induced collapse of surface nanobubbles

The collapse of cavitation bubbles often releases high-speed liquid jets capable of surface damage, with applications in drug delivery, cancer treatment, and surface cleaning. Spherical cap-shaped surface nanobubbles have previously been found to exist on immersed substrates. Despite being known nucleation sites for cavitation, their collapsing dynamics are currently unexplored. Here, we use molecular dynamics simulations to model the shock-induced collapse of different surface nanobubble sizes and contact angles. Comparisons are made with additional collapsing spherical nanobubble simulations near a substrate, to investigate the differences in their jet formation and resulting substrate pitting damage. Our main finding is that the pitting damage in the surface nanobubble simulations is greatly reduced, when compared to the spherical nanobubbles, which is primarily caused by the weaker jets formed during their collapse. Furthermore, the pit depths for surface nanobubble collapse do not depend on bubble size, unlike in the spherical nanobubble cases, but instead depend only on their contact angle. We also find a linear scaling relationship for all bubble cases between the final substrate damage and the peak pressure impulse at the impact centre, which can now be exploited to assess the relative damage in other computational studies of collapsing bubbles. We anticipate the more controlled surface-damage features produced by surface nanobubble cavitation jets will open up new applications in advanced manufacturing, medicine, and precision cleaning.

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.

Advancing Computational Analysis of Porous Materials-Modeling Three-Dimensional Gas Adsorption in Organic Gels

Assessing the efficacy of specific porous materials for use in various applications has been a central focus for many experimental studies over the years, with a view to altering the material properties according to the desired characteristics. The application potential for one such class of nanoporous materials-organic resorcinol-formaldehyde (RF) gels-is of particular interest, due to their attractive and adjustable properties. In this work, we simulate adsorption analysis using lattice-based mean field theory, both in individual pores and within three-dimensional porous materials generated from a kinetic Monte Carlo cluster aggregation model. We investigate the impacts of varying pore size and geometry on the adsorptive behavior, with results agreeing with those previously postulated in the literature. The adsorption analysis is carried out for porous materials simulated with varying catalyst concentrations and solids contents, allowing their structural properties to be assessed from resulting isotherms and the adsorption and desorption processes visualized using density color maps. Isotherm analysis indicated that both low catalyst concentrations and low solids contents resulted in structures with open transport pores that were larger in width, while high catalyst concentrations and solids contents resulted in structures with bottleneck pores that were narrower. We present results from both the simulated isotherms and pore size analysis distributions, in addition to results from RF gels synthesized in the lab and analyzed experimentally, with significant similarities observed between the two. Not only do the results of this comparison validate the kinetic Monte Carlo model's ability to successfully capture the formation of RF gels under varying synthesis parameters, but they also show significant promise for the tailoring of material properties in an efficient and computationally inexpensive manner-something which would be pivotal in realizing their full application potential, and could be applied to other porous materials whose formation mechanism operates under similar principles.

Forced oscillation dynamics of surface nanobubbles

Surface nanobubbles have potential applications in the manipulation of nanoscale and biological materials, waste-water treatment, and surface cleaning. These spherically capped bubbles of gas can exist in stable diffusive equilibrium on chemically patterned or rough hydrophobic surfaces, under supersaturated conditions. Previous studies have investigated their long-term response to pressure variations, which is governed by the surrounding liquid's local supersaturation; however, not much is known about their short-term response to rapid pressure changes, i.e., their cavitation dynamics. Here, we present molecular dynamics simulations of a surface nanobubble subjected to an external oscillating pressure field. The surface nanobubble is found to oscillate with a pinned contact line, while still retaining a mostly spherical cap shape. The amplitude-frequency response is typical of an underdamped system, with a peak amplitude near the estimated natural frequency, despite the strong viscous effects at the nanoscale. This peak is enhanced by the surface nanobubble's high internal gas pressure, a result of the Laplace pressure. We find that accurately capturing the gas pressure, bubble volume, and pinned growth mode is important for estimating the natural frequency, and we propose a simple model for the surface nanobubble frequency response, with comparisons made to other common models for a spherical bubble, a constant contact angle surface bubble, and a bubble entrapped within a cylindrical micropore. This work reveals the initial stages of growth of cavitation nanobubbles on surfaces, common in heterogeneous nucleation, where classical models based on spherical bubble growth break down.

Water Bridges in Clay Nanopores: Mechanisms of Formation and Impact on Hydrocarbon Transport

Clays are prevalent in the earth's crust and usually deposited in the presence of water. An unusual finding in clays is that under certain conditions, water molecules can collectively form a bridge across a clay-hosted pore. However, there are relatively few studies focused on the formation mechanism of the water bridge in clay nanopores. In this work, we use molecular dynamics simulations to investigate the formation of the water bridge and its influence on fluid transport in slit-shaped illite nanopores. Two different basal illite surface chemistries are constructed: potassium-hydroxyl (P-H) and hydroxyl-hydroxyl (H-H) structures. Because pore size and water concentration are expected to control the formation of the water bridge, our simulations span a wide range of pore sizes and water concentrations. Generally, positive potassium layers and negative hydroxyl groups in P-H nanopore can induce partial charges which in return produce instant and local electric fields, favoring the formation of the water bridge. In P-H nanopores, the water bridge happens at a relatively low water concentration. However, in H-H nanopores, the water bridge only forms at high water concentrations. Additionally, smaller pore sizes favor the formation of water bridges. However, the presence of an electric field promotes the formation of a water bridge even in larger pore sizes in P-H pores. The results also indicate that in both P-H and H-H nanopores, water adsorption films initially create a smooth surface to promote the hydrocarbon flow. In P-H nanopores, further increases in the water concentration causes a sharp decline in the self-diffusion coefficients of the hydrocarbon and water due to the formation of the water bridge. The presence of electric fields in P-H pores can however weaken the confinement effect of illite and promote the hydrocarbon flow. In contrast, in H-H nanopores, the self-diffusion coefficients decline slowly with the increase of water concentration. This is because no water bridge is formed at low water concentrations in H-H nanopores.

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.

Mesoscale structure, mechanics, and transport properties of source rocks' organic pore networks

In source rocks, natural hydrocarbons are generated from organic matter dispersed in a fine-grained mineral matrix. The potential recovery of hydrocarbons is therefore influenced by the geometry of the organic hosted porous networks. Here, the three-dimensional structures of such networks are revealed using electron tomography with a subnanometer resolution. The reconstructions are first characterized in terms of morphology and topology and then used to build a multiscale simulation tool to study the mechanics and the transport properties of confined fluids. Our results offer evidence of the prevalent role of connected nanopores, which subsequently constitutes a material limit for long-term hydrocarbon production.

Organic matter is responsible for the generation of hydrocarbons during the thermal maturation of source rock formation. This geochemical process engenders a network of organic hosted pores that governs the flow of hydrocarbons from the organic matter to fractures created during the stimulation of production wells. Therefore, it can be reasonably assumed that predictions of potentially recoverable confined hydrocarbons depend on the geometry of this pore network. Here, we analyze mesoscale structures of three organic porous networks at different thermal maturities. We use electron tomography with subnanometric resolution to characterize their morphology and topology. Our 3D reconstructions confirm the formation of nanopores and reveal increasingly tortuous and connected pore networks in the process of thermal maturation. We then turn the binarized reconstructions into lattice models including information from atomistic simulations to derive mechanical and confined fluid transport properties. Specifically, we highlight the influence of adsorbed fluids on the elastic response. The resulting elastic energy concentrations are localized at the vicinity of macropores at low maturity whereas these concentrations present more homogeneous distributions at higher thermal maturities, due to pores’ topology. The lattice models finally allow us to capture the effect of sorption on diffusion mechanisms with a sole input of network geometry. Eventually, we corroborate the dominant impact of diffusion occurring within the connected nanopores, which constitute the limiting factor of confined hydrocarbon transport in source rocks.

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.

Adsorption on alumina nanopores with conical shape

Adsorption on porous solids depends on the morphology of the pores, the cylindrical one being the most studied in the literature. In this work, we present the first experimental investigation of adsorption and evaporation on conical nanopores produced by anodization of aluminium oxide. The pores are about 50 μm long, with the wide ends having a diameter of ∼79 nm and the narrow ones of ∼30 nm. Three different pores configurations are considered: open at both ends, open only at the narrow end and open only at the wide end. Despite the very small value of the conical angle α, estimated to be ∼0.06°, just barely above α = 0° corresponding to a cylindrical pore, the adsorption isotherms look strikingly different from those measured on cylindrical pores of similar size. First of all, the hysteresis loops of the conical pores with two open ends and with open wide ends practically coincide. Furthermore, they are narrower and the adsorption and evaporation branches are broader than those of the cylindrical pores with similar size. Finally, conical pores with open narrow ends exhibit a large hysteresis indicative of pore blocking. To unravel the mechanisms underlying adsorption and evaporation in such conical pores, we also report complementary results obtained using on-lattice grand canonical Monte Carlo simulations.

Mechanism of Kinetically Controlled Capillary Condensation in Nanopores: A Combined Experimental and Monte Carlo Approach

We find the rule of capillary condensation from the metastable state in nanoscale pores based on the transition state theory. The conventional thermodynamic theories cannot achieve it because the metastable capillary condensation inherently includes an activated process. We thus compute argon adsorption isotherms on cylindrical pore models and atomistic silica pore models mimicking the MCM-41 materials by the grand canonical Monte Carlo and the gauge cell Monte Carlo methods and evaluate the rate constant for the capillary condensation by the transition state theory. The results reveal that the rate drastically increases with a small increase in the chemical potential of the system, and the metastable capillary condensation occurs for any mesopores when the rate constant reaches a universal critical value. Furthermore, a careful comparison between experimental adsorption isotherms and the simulated ones on the atomistic silica pore models reveals that the rate constant of the real system also has a universal value. With this finding, we can successfully estimate the experimental capillary condensation pressure over a wide range of temperatures and pore sizes by simply applying the critical rate constant.

Determination of phase equilibria in confined systems by open pore cell Monte Carlo method

We present a modification of the molecular dynamics simulation method with a unit pore cell with imaginary gas phase [M. Miyahara, T. Yoshioka, and M. Okazaki, J. Chem. Phys. 106, 8124 (1997)] designed for determination of phase equilibria in nanopores. This new method is based on a Monte Carlo technique and it combines the pore cell, opened to the imaginary gas phase (open pore cell), with a gas cell to measure the equilibrium chemical potential of the confined system. The most striking feature of our new method is that the confined system is steadily led to a thermodynamically stable state by forming concave menisci in the open pore cell. This feature of the open pore cell makes it possible to obtain the equilibrium chemical potential with only a single simulation run, unlike existing simulation methods, which need a number of additional runs. We apply the method to evaluate the equilibrium chemical potentials of confined nitrogen in carbon slit pores and silica cylindrical pores at 77 K, and show that the results are in good agreement with those obtained by two conventional thermodynamic integration methods. Moreover, we also show that the proposed method can be particularly useful for determining vapor-liquid and vapor-solid coexistence curves and the triple point of the confined system.

Molecular simulation of adsorption and transport in hierarchical porous materials

Adsorption and transport in hierarchical porous solids with micro- (~1 nm) and mesoporosities (>2 nm) are investigated by molecular simulation. Two models of hierarchical solids are considered: microporous materials in which mesopores are carved out (model A) and mesoporous materials in which microporous nanoparticles are inserted (model B). Adsorption isotherms for model A can be described as a linear combination of the adsorption isotherms for pure mesoporous and microporous solids. In contrast, adsorption in model B departs from adsorption in pure microporous and mesoporous solids; the inserted microporous particles act as defects, which help nucleate the liquid phase within the mesopore and shift capillary condensation toward lower pressures. As far as transport under a pressure gradient is concerned, the flux in hierarchical materials consisting of microporous solids in which mesopores are carved out obeys the Navier-Stokes equation so that Darcy's law is verified within the mesopore. Moreover, the flow in such materials is larger than in a single mesopore, due to the transfer between micropores and mesopores. This nonzero velocity at the mesopore surface implies that transport in such hierarchical materials involves slippage at the mesopore surface, although the adsorbate has a strong affinity for the surface. In contrast to model A, flux in model B is smaller than in a single mesopore, as the nanoparticles act as constrictions that hinder transport. By a subtle effect arising from fast transport in the mesopores, the presence of mesopores increases the number of molecules in the microporosity in hierarchical materials and, hence, decreases the flow in the micropores (due to mass conservation). As a result, we do not observe faster diffusion in the micropores of hierarchical materials upon flow but slower diffusion, which increases the contact time between the adsorbate and the surface of the microporosity.

Atomistic model of micelle-templated mesoporous silicas: structural, morphological, and adsorption properties

The structural, morphological, and adsorption properties of MCM-41 porous silicas are investigated using a realistic numerical model obtained by means of ab initio calculations [Ugliengo, P.; et al. Adv. Mater.2008, 20, 1]. Simulated X-ray diffraction, small angle neutron scattering, and electronic microscopy for the atomistic model are in good agreement with experimental data. The morphological features are also assessed from chord length distributions and porous volume and specific geometrical surface calculations, etc. The N(2), CO(2), and H(2)O adsorption isotherms in the atomistic model of MCM-41 are also in reasonable agreement with their experimental counterpart. An important finding of the present work is that water forms a film adsorbed on specific hydrophilic regions of the surface while the rest of the surface is depleted in water molecules. This result suggests that the surface of MCM-41 materials is heterogeneous, as it is made up of both hydrophilic and hydrophobic patches. While adsorption and irreversible capillary condensation can be described using the thermodynamical approach by Derjaguin (also known as the Derjaguin-Broekhoff-De Boer model), the Freundlich equation fits nicely the data for reversible and continuous filling in small pores.

Capillary condensation of adsorbates in porous materials

Hysteresis in capillary condensation is important for the fundamental study and application of porous materials, and yet experiments on porous materials are sometimes difficult to interpret because of the many interactions and complex solid structures involved in the condensation and evaporation processes. Here we make an overview of the significant progress in understanding capillary condensation and hysteresis phenomena in mesopores that have followed from experiment and simulation applied to highly ordered mesoporous materials such as MCM-41 and SBA-15 over the last few decades.