Adsorption-induced deformation of microporous carbons: pore size distribution effect

What Drives Deformation of Smart Nanoporous Materials During Adsorption and Electrosorption?

Nanoporous solids have high surface area, so processes at the surface affect the sample as a whole. When guest species adsorb in nanopores, be they molecules adsorbing from the gas phase, or ions adsorbing from solution, they cause material deformation. While often undesired, adsorption- or electrosorption-induced deformation provides a potential for nanoporous materials to be used as actuators. Progress in this direction requires understanding the mechanisms of adsorption- or electrosorption-induced deformation. These two processes are rarely discussed together, and this Perspective aims to fill this gap to some extent, focusing on driving forces for both processes. Typically the main driving force for both is the solvation (disjoining) pressure, acting normally to the pore walls. However, in some cases, solvation pressure is not sufficient to describe the effects even qualitatively. We highlight examples in which the surface stress acting along the solid surface is an additional driving force for deformation.

Temperature Evolution of Sorbonorit-4 Methane-Induced Deformation through the Eyes of Classical Density Functional Theory

Activated carbons are widely used industrial adsorbents due to their attractive sorption properties. Although extensive research on activated carbon has been carried out for several centuries, some aspects of the adsorption-induced deformation of activated carbon remain unclear. The puzzling temperature dependence of the methane-induced deformation of activated carbon is investigated in the present work. Several experimental studies have shown that an increase in temperature leads to a reversal of the sign of adsorption strain at low pressures, i.e., the contraction turns into an expansion. Here we suggest a possible explanation for this effect by applying classical density functional theory to the adsorption isotherms of nitrogen, carbon dioxide, and methane as well as to methane-induced deformation isotherms. Our calculations show that the adsorption stress generated in the smallest pores predominates at higher temperatures and leads to material swelling. Lowering the temperature, on the other hand, leads to a predominance of larger pores and compression of the activated carbon material. We also investigated the possibility of determining the pore size distribution from methane-induced deformation and adsorption data and the predictive capabilities of our theoretical approach.

Molecular Simulation of Argon Adsorption and Diffusion in a Microporous Carbon with Poroelastic Couplings

Neglected for a long time in molecular simulations of fluid adsorption and transport in microporous carbons, adsorption-induced deformations of the matrix have recently been shown to have important effects on both sorption isotherms and diffusion coefficients. Here we investigate in detail the behavior of a recently proposed 3D-connected mature kerogen model, as a generic model of aromatic microporous carbon with atomic H/C ∼ 0.5, in both chemical and mechanical equilibrium with argon at 243 K over an extended pressure range. We show that under these conditions the material exhibits some viscoelasticity, and simulations of hundreds of nanoseconds are required to accurately determine the equilibrium volumes and sorption loadings. We also show that neglecting matrix internal deformations and swelling can lead to underestimations of the loading by up to 19% (swelling only) and 28% (swelling and internal deformations). The volume of the matrix is shown to increase up to about 8% at the largest pressure considered (210 MPa), which induces an increase of about 33% of both pore volume and specific surface area via the creation of additional pores, yet does not significantly change the normalized pore size distribution. Volume swelling is also rationalized by using a well-known linearized microporomechanical model. Finally, we show that self-diffusivity decreases with applied pressure, following an almost perfectly linear evolution with the free volume. Quantitatively, neglecting swelling and internal deformations tends to reduce the computed self-diffusivities.

Insights into the CO2 Capture Characteristics within the Hierarchical Pores of Carbon Nanospheres Using Small-Angle Neutron Scattering

Understanding adsorption processes at the molecular level has transformed the discovery of engineered materials for maximizing gas storage capacity and kinetics in adsorption-based carbon capture applications. In this work, we studied the molecular mechanism of gas (CO₂, H₂, methane, and ethane) adsorption inside an interconnected porous network of carbon. This was achieved by synthesizing novel macro-meso-microporous carbon (M³C) nanospheres with interconnected pore structures. The M³Cs showed a CO₂ capture capacity of 5.3 mmol/g at atmospheric CO₂ pressure, with excellent kinetics. This was due to fast CO₂ adsorption within the interconnected hierarchical macro-meso-microporous M³C. In situ small-angle neutron scattering (SANS) under various CO₂ pressures indicated that the macro- and mesopores of M³C enable fast diffusion of CO₂ molecules inside the micropores, where adsorbed CO₂ molecules densify into a liquid-like state. This strong densification of CO₂ molecules causes fast CO₂ diffusion in the macro- and mesopores of M³C, restarting the adsorption cycle for fresh CO₂ molecules until all pores are completely filled. Notably, M³C also showed good capture capacities for hydrogen and various hydrocarbons, with excellent selectivity toward ethane over methane.

A New Adsorption Equation for Nano-Porous Shale Rocks and Its Application in Pore Size Distribution Analysis

Adsorption equations are important to analyze the pore size distribution (PSD) of shale and the adsorption behavior on it. However, the accurate description of nitrogen adsorption on shale by current adsorption equations is difficult to achieve due to the heterogeneous pore structure of shale. In our study, new adsorption isotherms that can properly depict the adsorbed amount of nitrogen were built for shale rocks considering both the processes of nitrogen adsorption and the cylindrical pore shape property of shale. When performing a regression analysis on five sets of experimental adsorption data using the developed adsorption equations, the R-square ranged from 0.739 to 0.987. Based on the pore shape determined by adsorption–desorption curves, the distinct R-square indicated that our equation is not valid for shale samples with ink-bottle pores and pores formed by schistose materials, but that it is suitable for shale samples with cylindrical pores and slit pores. Meanwhile, we precisely analyzed the PSDs of shale rocks based on the developed adsorption equations as capillary condensation volume is involved in the total adsorbed amount. Thus, the PSDs of shale rocks with cylindrical pore and slit pore were analyzed by the new adsorption equation.

A molecular simulation study into the stability of hydrated graphene nanochannels used in nanofluidics devices

Graphene-based nanochannels are a popular choice in emerging nanofluidics applications because of their tunable and nanometer-scale channels. In this work, molecular dynamics (MD) simulations were employed both to (i) assess the stability of dry and hydrated graphene nanochannels and (ii) elucidate the properties of water confined in these channels, using replica-scale models with 0.66-2.38 nm channel heights. The use of flexible nanochannel walls allows the nanochannel height to relax in response to the solvation forces arising from the confined fluid and the forces between the confining surfaces, without the need for application of arbitrarily high external pressures. Dry nanochannels were found to completely collapse if the initial nanochannel height was less than 2 nm, due to attractive van der Waals interactions between the confining graphene surfaces. However, the presence of water was found to prevent total nanochannel collapse, due to repulsive hydration forces opposing the attractive van der Waals force. For nanochannel heights less than ∼1.7 nm, the confining surfaces must be relaxed to obtain accurate hydration pressures and water diffusion coefficients, by ensuring commensurability between the number of confined water layers and the channel height. For very small (∼0.7 nm), hydrated channels a pressure of 231 MPa due to the van der Waals forces was obtained. In the same system, the confined water forms a mobile, liquid monolayer with a diffusion coefficient of 4.0 × 10^-5 cm² s^-1, much higher than bulk liquid water. Although this finding conflicts with most classical MD simulations, which predict in-plane order and arrested dynamics, it is supported by experiments and recently published first-principles MD simulations. Classical simulations can therefore be used to predict the properties of water confined in sub-nanometre graphene channels, providing sufficiently realistic molecular models and accurate intermolecular potentials are employed.

Models of adsorption-induced deformation: ordered materials and beyond

Adsorption-induced deformation is a change in geometrical dimensions of an adsorbent material caused by gas or liquid adsorption on its surface. This phenomenon is universal and sensitive to adsorbent properties, which makes its prediction a challenging task. However, the pure academic interest is complemented by its importance in a number of engineering applications with porous materials characterization among them. Similar to classical adsorption-based characterization methods, the deformation-based ones rely on the quality of the underlying theoretical framework. This fact stimulates the recent development of qualitative and quantitative models toward the more detailed description of a solid material, e.g. account of non-convex and corrugated pores, calculations of adsorption stress in realistic three-dimension solid structures, the extension of the existing models to new geometries, etc. The present review focuses on the theoretical description of adsorption-induced deformation in micro and mesoporous materials. We are aiming to cover recent theoretical works describing the deformation of both ordered and disordered porous bodies.

Peculiarities of Thermodynamic Behaviors of Xenon Adsorption on the Activated Carbon Prepared from Silicon Carbide

An activated carbon prepared from silicon carbide by thermochemical synthesis and designated as SiC-AC was studied as an adsorbent for xenon. The examination of textural properties of the SiC-AC adsorbent by nitrogen vapor adsorption measurements at 77 K, powder X-ray diffraction, and scanning electron microscopy revealed a relatively homogeneous microporous structure, a low content of heteroatoms, and an absence of evident transport macropores. The study of xenon adsorption and adsorption-induced deformation of the Si-AC adsorbent over the temperature range of 178 to 393 K and pressures up to 6 MPa disclosed the contraction of the material up to -0.01%, followed by its expansion up to 0.49%. The data on temperature-induced deformation of Si-AC measured within the 260 to 575 K range was approximated by a linear function with a thermal expansion factor of (3 ± 0.15) × 10-6 K-1. These findings of the SiC-AC non-inertness taken together with the non-ideality of an equilibrium xenon gaseous phase allowed us to make accurate calculations of the differential isosteric heats of adsorption, entropy, enthalpy, and heat capacity of the Xe/SiC-AC adsorption system from the experimental adsorption data over the temperature range from 178 to 393 K and pressures up to 6 MPa. The variations in the thermodynamic state functions of the Xe/SiC-AC adsorption system with temperature and amount of adsorbed Xe were attributed to the transitions in the state of the adsorbate in the micropores of SiC-AC from the bound state near the high-energy adsorption sites to the molecular associates.

Superionic Liquids in Conducting Nanoslits: Insights from Theory and Simulations

Mapping the theory of charging supercapacitors with nanostructured electrodes on known lattice models of statistical physics is an interesting task, aimed at revealing generic features of capacitive energy storage in such systems. The main advantage of this approach is the possibility to obtain analytical solutions that allow new physical insights to be more easily developed. But how general the predictions of such theories could be? How sensitive are they to the choice of the lattice? Herein, we address these questions in relation to our previous description of such systems using the Bethe-lattice approach and Monte Carlo simulations. Remarkably, we find a surprisingly good agreement between the analytical theory and simulations. In addition, we reveal a striking correlation between the ability to store energy and ion ordering inside a pore, suggesting that such ordering can be beneficial for energy storage.

Adsorption-induced deformation of mesoporous materials with corrugated cylindrical pores

Mesoporous materials play an important role both in engineering applications and in fundamental research of confined fluids. Adsorption goes hand in hand with the deformation of the absorbent, which has positive and negative sides. It can cause sample aging or can be used in sensing technology. Here, we report the theoretical study of adsorption-induced deformation of the model mesoporous material with ordered corrugated cylindrical pores. Using the classical density functional theory in the local density approximation, we compared the solvation pressure in corrugated and cylindrical pores for nitrogen at sub- and super-critical temperatures. Our results demonstrate qualitative differences between solvation pressures in the two geometries at sub-critical temperatures. The deviations are attributed to the formation of liquid bridges in corrugated pores. However, at super-critical temperatures, there is no abrupt bridge formation and corrugation does not qualitatively change solvation pressure isotherms. We believe that these results could help in the analysis of an adsorption-induced deformation of the materials with distorted pores.

Water Adsorption in Soft and Heterogeneous Nanopores

ConspectusLiquids under confinement differ in behavior from their bulk counterparts and can acquire properties that are specific to the confined phase and linked to the nature and structure of the host matrix. While confined liquid water is not a new topic of research, the past few years have seen a series of intriguing novel features for water inside nanoscale pores. These unusual properties arise from the very specific nature of nanoporous materials, termed "soft porous crystals"; they combine large-scale flexibility with a heterogeneous internal surface. This creates a rich diversity of behavior for the adsorbed water, and the combination of different experimental characterization techniques along with computational chemistry at various scales is necessary to understand the phenomena observed and their microscopic origins. The range of systems of interest span the whole chemical range, from the inorganic (zeolites, imogolites) to the organic (microporous carbons, graphene, and its derivatives), and even encompass the hybrid organic-inorganic systems (such as metal-organic frameworks).The combination of large scale flexibility with the strong physisorption (or even chemisorption) of water can lead to unusual properties (belonging to the "metamaterials" category) and to novel phenomena. One striking example is the recent elucidation of the mechanism of negative hydration expansion in ZrW₂O₈, by which adsorption of ∼10 wt % water in the inorganic nonporous framework leads to large shrinkage of its volume. Another eye-catching case is the occurrence of multiple water adsorption-driven structural transitions in the MIL-53 family of materials: the specific interactions between water guest molecules and the host framework create behavior that has not been observed with any other adsorbate. Both are counterintuitive phenomena that have been elucidated by a combination of experimental in situ techniques and molecular simulation.Another important direction of research is the shift in the systems and phenomena studied, from physical adsorption toward studies of reactivity, hydrothermal stability, and the effect of confinement on aqueous phases more complex than pure water. There have been examples of water adsorption in highly flexible metal-organic frameworks being able to compete with the materials' coordination bonds, thereby limiting its hydrothermal stability, while tweaking the functional groups of the same framework can lead to increased stability while retaining the flexibility of the material. However, this additional complexity and tunability in the macroscopic behavior can occur from changes in the confined fluid rather than the material. Very recent studies have shown that aqueous solutions of high concentration (such as LiCl up to 20 mol L^-1) confined in flexible nanoporous materials can have specific properties different from pure water and not entirely explained by osmotic effects. There, the strong ordering of the confined electrolyte competes with the structural flexibility of the framework to create an entirely new behavior for the {host, guest} system.

Adsorption-Induced Expansion of Graphene Oxide Frameworks: Observation by in Situ Neutron Diffraction

We have investigated adsorption-induced deformation in graphene oxide framework materials (GOFs) using neutron diffraction at sample pressures up to 140 bar. GOFs, made by the solvothermal reaction of graphite oxide and benzene-1,4-diboronic acid, are a suitable candidate for deformation studies due to their narrow (∼1 nm), monodispersed, slit-shaped pores whose width can be measured by diffraction techniques. We have observed, in situ, a monotonic expansion of the slit width with increasing pressure upon adsorption of xenon, methane, and hydrogen under supercritical conditions. The expansion of ∼4% observed for xenon at a pressure of 48 bar is the largest deformation yet reported for supercritical adsorption on a carbonaceous material. We find that the expansion of the three gases can be mapped onto a common curve based solely on their Lennard-Jones parameters, in a manner similar to a law of corresponding states.

In Situ Small-Angle Neutron Scattering Investigation of Adsorption-Induced Deformation in Silica with Hierarchical Porosity

Adsorption-induced deformation of a series of silica samples with hierarchical porosity has been studied by in situ small-angle neutron scattering (SANS) and in situ dilatometry. Monolithic samples consisted of a disordered macroporous network of struts formed by a 2D lattice of hexagonally ordered cylindrical mesopores and disordered micropores within the mesopore walls. Strain isotherms were obtained at the mesopore level by analyzing the shift of the Bragg reflections from the ordered mesopore lattice in SANS data. Thus, SANS essentially measured the radial strain of the cylindrical mesopores including the volume changes of the mesopore walls due to micropore deformation. A H₂O/D₂O adsorbate with net zero coherent neutron scattering length density was employed in order to avoid apparent strain effects due to intensity changes during pore filling. In contrast to SANS, the strain isotherms obtained from in situ dilatometry result from a combination of axial and radial mesopore deformation together with micropore deformation. Strain data were quantitatively analyzed with a theoretical model for micro-/mesopore deformation by combining information from nitrogen and water adsorption isotherms to estimate the water-silica interaction. It was shown that in situ SANS provides complementary information to dilatometry and allows for a quantitative estimate of the elastic properties of the mesopore walls from water adsorption.

Study of the pore structure and size effects on the electrochemical capacitor behaviors of porous carbon/quinone derivative hybrids

We demonstrate the hybridization of a redox-active quinone derivative, 2,5-dichloro-1,4-benzoquinone (DCBQ), and porous carbons with different pore structures for aqueous electrochemical capacitor electrodes. The hybridization is performed in the gas phase, which enables accurate porous carbon/DCBQ weight ratios. This method is advantageous over conventional liquid phase adsorption, in terms of facile optimization of the porous carbon/DCBQ weight ratio to obtain high-performance aqueous electrochemical capacitor electrodes, dependent on the kind of porous carbons; moreover, complete adsorption in the liquid phase cannot be achieved by the conventional liquid phase adsorption method. Their electrochemical capacitor performances are evaluated using an aqueous 1 M H₂SO₄ electrolyte, and the adsorbed DCBQ undergoes redox reactions inducing pseudocapacitance within the pores of porous carbons. To study the effect of the pore size on the electrochemical capacitor behavior, two kinds of activated carbon (AC) with different pore sizes are examined: the microporous AC and the AC with both micro- and mesopores. Additionally, we examine ordered microporous carbon with a uniform pore size of 1.2 nm and a three-dimensionally (3D) ordered and mutually connected pore structure. The results reveal that mesopores facilitate proton conduction inside the DCBQ-constrained carbon pores, whereas the 3D-ordered and mutually connected micropores balance high volumetric capacitance enhancement with excellent rate capability. Such high proton conduction inside such constrained spaces can be explained only by the Grotthuss mechanism.

We investigated the redox reaction of a quinone derivative within the pores of porous carbons, which is affected by the pore sizes and structures of the porous carbons.

Exploring the thermodynamic criteria for responsive adsorption processes

We describe a general model to explore responsive adsorption processes in flexible porous materials. This model combines mean field formalism of the osmotic potential, classical density functional theory of adsorption in slit pore models and generic potential functions which represent the Helmholtz free energy landscape of a porous system. Using this model, we focus on recreating flexible adsorption phenomena observed in prototypical metal-organic frameworks, especially the recently discovered effect of negative gas adsorption (NGA). We identify the key characteristics required for the model to generate unusual adsorption processes and subsequently employ an extensive parametric study to outline conditions under which gate-opening and NGA are observed. This powerful approach will guide the design of responsive porous materials and the discovery of entirely new adsorption processes.

Mechanical Characterization of Hierarchical Structured Porous Silica by in Situ Dilatometry Measurements during Gas Adsorption

Mechanical properties of hierarchically structured nanoporous materials are determined by the solid phase stiffness and the pore network morphology. We analyze the mechanical stiffness of hierarchically structured silica monoliths synthesized via a sol-gel process, which possess a macroporous scaffold built of interconnected struts with hexagonally ordered cylindrical mesopores. We consider samples with and without microporosity within the mesopore walls and analyze them on the macroscopic level as well as on the microscopic level of the mesopores. Untreated as-prepared samples still containing some organic components and the respective calcined and sintered counterparts of varying microporosity are investigated. To determine Young's moduli on the level of the macroscopic monoliths, we apply ultrasonic run time measurements, while Young's moduli of the mesopore walls are obtained by analysis of the in situ strain isotherms during N₂ adsorption at 77 K. For the latter, we extended our previously reported theoretical approach for this type of materials by incorporating the micropore effects, which are clearly not negligible in the calcined and most of the sintered samples. The comparison of the macro- and microscopic Young's moduli reveals that both properties follow essentially the same trends, that is, calcination and sintering increase the mechanical stiffness on both levels. Consequently, stiffening of the monolithic samples can be primarily attributed to stiffening of the backbone material which is consistent with the fact that the morphology on the mesopore level is mainly preserved with the post-treatments applied.

Poroelasticity of Methane-Loaded Mature and Immature Kerogen from Molecular Simulations

While hydrocarbon expulsion from kerogen is certainly the key step in shale oil/gas recovery, the poromechanical couplings governing this desorption process, taking place under a significant pressure gradient, are still poorly understood. Especially, most molecular simulation investigations of hydrocarbon adsorption and transport in kerogen have so far been performed under the rigid matrix approximation, implying that the pore space is independent of pressure, temperature, and fluid loading, or in other words, neglecting poromechanics. Here, using two hydrogenated porous carbon models as proxies for immature and overmature kerogen, that is, highly aliphatic hydrogen-rich vs highly aromatic hydrogen-poor models, we perform an extensive molecular-dynamics-based investigation of the evolution of the poroelastic properties of those matrices with respect to temperature, external pressure, and methane loading as a prototype alkane molecule. The rigid matrix approximation is shown to hold reasonably well for overmature kerogen even though accounting for flexibility has allowed us to observe the well-known small volume contraction at low fluid loading and temperature. Our results demonstrate that immature kerogen is highly deformable. Within the ranges of conditions considered in this work, its density can double and its accessible porosity (to a methane molecule) can increase from 0 to ∼30%. We also show that these deformations are significantly nonaffine (i.e., nonhomogeneous), especially upon fluid adsorption or desorption.

Binary gas mixture adsorption-induced deformation of microporous carbons by Monte Carlo simulation

Considering the thermodynamic grand potential for more than one adsorbate in an isothermal system, we generalize the model of adsorption-induced deformation of microporous carbons developed by Kowalczyk et al. [1]. We report a comprehensive study of the effects of adsorption-induced deformation of carbonaceous amorphous porous materials due to adsorption of carbon dioxide, methane and their mixtures. The adsorption process is simulated by using the Grand Canonical Monte Carlo (GCMC) method and the calculations are then used to analyze experimental isotherms for the pure gases and mixtures with different molar fraction in the gas phase. The pore size distribution determined from an experimental isotherm is used for predicting the adsorption-induced deformation of both pure gases and their mixtures. The volumetric strain (ε) predictions from the GCMC method are compared against relevant experiments with good agreement found in the cases of pure gases.

Effects of Enhanced Flexibility and Pore Size Distribution on Adsorption-Induced Deformation of Mesoporous Materials

Here, we present a new model of adsorption-induced deformation of mesoporous solids. The model is based on a simplified version of local density functional theory in the framework of solvation free energy. Instead of density, which is treated as constant here, we used film thickness and pore radius as order parameters. This allows us to obtain a self-consistent system of equations describing simultaneously the processes of gas adsorption and adsorbent deformation, as well as conditions for capillary condensation and evaporation. In the limit of infinitely rigid pore walls, when the film becomes several monolayers thick, the model reduces to the well-known Derjaguin-Broekhoff-de Boer theory for pores with cylindrical geometry. We have investigated the effects of enhanced flexibility of the solid as well as the influence of pore size distribution on the adsorption/deformation process. The formulation of the theory allows to determine the average pore size and its width from the desorption branch of the strain isotherm only. The model reproduces the nonmonotonic behavior of the strain isotherm at low relative pressure. Furthermore, we discuss the effect of rigidity of the adsorbent on the pore size distribution, showing qualitatively different results of the adsorption isotherms for rigid and highly flexible materials, in particular, the shift of evaporation pressure to lower values and the absence of a limiting value of the loading at high relative pressure. We also discuss the results of the theory with respect to experimental data obtained from the literature.

Extraordinary water adsorption characteristics of graphene oxide

The laminated structure of graphene oxide (GO) confers unique interactions with water molecules which may be utilised in a range of applications that require materials with tuneable hygroscopic properties. The precise role of the expandable interlayer spacing and functional groups in GO laminates has not completely been understood to date. Herein, we report the experimental and theoretical investigations on the adsorption and desorption behaviour of water in GO laminates as a function of relative pressure. We observed that GO imparts high water uptake capacity of up to 0.58 gram of water per gram of GO (g g-1), which is significantly higher than silica gel as a conventional desiccant material. More interestingly, the adsorption and desorption kinetics of GO is five times higher than silica gel. The observed extraordinary adsorption/desorption rate can be attributed to the high capillary pressure in GO laminates as well as micro meter sized tunnel-like wrinkles located at the surface.

Heat of adsorption, adsorption stress, and optimal storage of methane in slit and cylindrical carbon pores predicted by classical density functional theory

Temperature, pressure and pore-size dependences of the heat of adsorption, adsorption stress, and adsorption capacity of methane in simple models of slit and cylindrical carbon pores are studied using classical density functional theory (CDFT) and grand-canonical Monte-Carlo (MC) simulation. Studied properties depend nontrivially on the bulk pressure and the size of the pores. Heat of adsorption increases with loading, but only for sufficiently narrow pores. While the increase is advantageous for gas storage applications, it is less significant for cylindrical pores than for slits. Adsorption stress and the average adsorbed fluid density show oscillatory dependence on the pore size and increase with bulk pressure. Slit pores exhibit larger amplitude of oscillations of the normal adsorption stress with pore size increase than cylindrical pores. However, the increase of the magnitude of the adsorption stress with bulk pressure increase is more significant for cylindrical than for slit pores. Adsorption stress appears to be negative for a wide range of pore sizes and external conditions. The pore size dependence of the average delivered density of the gas is analyzed and the optimal pore sizes for storage applications are estimated. The optimal width of slit pore appears to be almost independent of storage pressure at room temperature and pressures above 10 bar. Similarly to the case of slit pores, the optimal radius of cylindrical pores does not exhibit much dependence on the storage pressure above 15 bar. Both optimal width and optimal radii of slit and cylindrical pores increase as the temperature decreases. A comparison of the results of CDFT theory and MC simulations reveals subtle but important differences in the underlying fluid models employed by the approaches. The differences in the high-pressure behaviour between the hard-sphere 2-Yukawa and Lennard-Jones models of methane, employed by the CDFT and MC approaches, respectively, result in an overestimation of the heat of adsorption by the CDFT theory at higher loadings. However, both adsorption stress and adsorption capacity appear to be much less sensitive to the differences between the models and demonstrate excellent agreement between the theory and the computer experiment.

Adsorption-Induced Deformation of Hierarchically Structured Mesoporous Silica-Effect of Pore-Level Anisotropy

The goal of this work is to understand adsorption-induced deformation of hierarchically structured porous silica exhibiting well-defined cylindrical mesopores. For this purpose, we performed an in situ dilatometry measurement on a calcined and sintered monolithic silica sample during the adsorption of N₂ at 77 K. To analyze the experimental data, we extended the adsorption stress model to account for the anisotropy of cylindrical mesopores, i.e., we explicitly derived the adsorption stress tensor components in the axial and radial direction of the pore. For quantitative predictions of stresses and strains, we applied the theoretical framework of Derjaguin, Broekhoff, and de Boer for adsorption in mesopores and two mechanical models of silica rods with axially aligned pore channels: an idealized cylindrical tube model, which can be described analytically, and an ordered hexagonal array of cylindrical mesopores, whose mechanical response to adsorption stress was evaluated by 3D finite element calculations. The adsorption-induced strains predicted by both mechanical models are in good quantitative agreement making the cylindrical tube the preferable model for adsorption-induced strains due to its simple analytical nature. The theoretical results are compared with the in situ dilatometry data on a hierarchically structured silica monolith composed by a network of mesoporous struts of MCM-41 type morphology. Analyzing the experimental adsorption and strain data with the proposed theoretical framework, we find the adsorption-induced deformation of the monolithic sample being reasonably described by a superposition of axial and radial strains calculated on the mesopore level. The structural and mechanical parameters obtained from the model are in good agreement with expectations from independent measurements and literature, respectively.

Multicomponent adsorption in mesoporous flexible materials with flat-histogram Monte Carlo methods

We demonstrate an extensible flat-histogram Monte Carlo simulation methodology for studying the adsorption of multicomponent fluids in flexible porous solids. This methodology allows us to easily obtain the complete free energy landscape for the confined fluid-solid system in equilibrium with a bulk fluid of any arbitrary composition. We use this approach to study the adsorption of a prototypical coarse-grained binary fluid in "Hookean" solids, where the free energy of the solid may be described as a simple spring. However, our approach is fully extensible to solids with arbitrarily complex free energy profiles. We demonstrate that by tuning the fluid-solid interaction ranges, the inhomogeneous fluid structure inside the pore can give rise to enhanced selective capture of a larger species through cooperative adsorption with a smaller one. The maximum enhancement in selectivity is observed at low to intermediate pressures and is especially pronounced when the larger species is very dilute in the bulk. This suggest a mechanism by which the selective capture of a minor component from a bulk fluid may be enhanced.

Postextraction Separation, On-Board Storage, and Catalytic Conversion of Methane in Natural Gas: A Review

In today's perspective, natural gas has gained considerable attention, due to its low emission, indigenous availability, and improvement in the extraction technology. Upon extraction, it undergoes several purification protocols including dehydration, sweetening, and inert rejection. Although purification is a commercially established technology, several drawbacks of the current process provide an essential impetus for developing newer separation protocols, most importantly, adsorption and membrane separation. This Review summarizes the needs of natural gas separation, gives an overview of the current technology, and provides a detailed discussion of the progress in research on separation and purification of natural gas including the benefits and drawbacks of each of the processes. The transportation sector is another growing sector of natural gas utilization, and it requires an efficient and safe on-board storage system. Compressed natural gas (CNG) and liquefied natural gas (LNG) are the most common forms in which natural gas can be stored. Adsorbed natural gas (ANG) is an alternate storage system of natural gas, which is advantageous as compared to CNG and LNG in terms of safety and also in terms of temperature and pressure requirements. This Review provides a detailed discussion on ANG along with computation predictions. The catalytic conversion of methane to different useful chemicals including syngas, methanol, formaldehyde, dimethyl ether, heavier hydrocarbons, aromatics, and hydrogen is also reviewed. Finally, direct utilization of methane onto fuel cells is also discussed.

Deformation of Microporous Carbons during N2, Ar, and CO2 Adsorption: Insight from the Density Functional Theory

Using the nonlocal density functional theory, we investigate adsorption of N2 (77 K), Ar (77 K), and CO2 (273 K) and respective adsorption-induced deformation of microporous carbons. We show that the smallest micropores comparable in size and even smaller than the nominal molecular diameter of the adsorbate contribute significantly to the development of the adsorption stress. While pores of approximately the nominal adsorbate diameter exhibit no adsorption stress regardless of their filling level, the smaller pores cause expansive adsorption stresses up to almost 4 GPa. Accounting for this effect, we determined the pore-size distribution of a synthetic microporous carbon by simultaneously fitting its experimental CO2 adsorption isotherm (273 K) and corresponding adsorption-induced strain measured by in situ dilatometry. Based on the pore-size distribution and the elastic modulus fitted from CO2 data, we predicted the sample's strain isotherms during N2 and Ar adsorption (77 K), which were found to be in reasonable agreement with respective experimental data. The comparison of calculations and experimental results suggests that adsorption-induced deformation caused by micropores is not limited to the low relative pressures typically associated with the micropore filling, but is effective over the whole relative pressure range up to saturation pressure.

Revisiting Bangham's law of adsorption-induced deformation: changes of surface energy and surface stress

Adsorption-induced deformation has to be described in terms of the change of the surface stress Δfand not the surface energy Δγ. The former explains both expansion and contraction.

Deformation of Microporous Carbon during Adsorption of Nitrogen, Argon, Carbon Dioxide, and Water Studied by in Situ Dilatometry

Adsorption-induced deformation of a monolithic, synthetic carbon of clearly distinguishable micro- and mesoporosity was analyzed by in situ dilatometry with N2 (77 K), Ar (77 K), CO2 (273 K), and H2O (298 K). A characteristic nonmonotonic shape of the strain isotherm showing contraction of the sample at initial micropore adsorption followed by expansion toward completion of micropore filling was found for all adsorbates. However, the extent of contraction and expansion varied significantly with the adsorbate type. The deformation differences observed were compared with the density ratio of the adsorbates within the micropores and the respective unconfined fluids. In particular, CO2 caused the least contraction of the sample, while in parallel adsorbed CO2 molecules were predicted to be considerably compacted inside carbon micropores compared to bulk liquid CO2. On the contrary, the packing of H2O molecules within carbon micropores is less dense than in the bulk liquid and adsorption of H2O produced the most pronounced contraction. N2 and Ar, both exhibiting essentially the same densities in adsorbed and bulk liquid phase, induced very similar deformation of the sample. These findings support theoretical predictions, which correlate adsorption-induced deformation and packing of molecules adsorbed in micropores. Additionally for the first time, we demonstrated with the N2 strain isotherm the existence of two nonmonotonic stages of subsequent contraction and expansion in the regions of micropore and mesopore filling. This characteristic behavior is expected for any micro- and mesoporous material.

Softening upon Adsorption in Microporous Materials: A Counterintuitive Mechanical Response

We demonstrate here that microporous materials can exhibit softening upon adsorption of guest molecules, at low to intermediate pore loading, in parallel to the pore shrinking that is well-known in this regime. This novel and counterintuitive mechanical response was observed through molecular simulations of both model pore systems (such as slit pore) and real metal-organic frameworks. It is contrary to common belief that adsorption of guest molecules necessarily leads to stiffening due to increased density, a fact that we show is the high-loading limit of a more complex behavior: a nonmonotonic softening-then-stiffening.

Effects of rigid or adaptive confinement on colloidal self-assembly. Fixed vs. fluctuating number of confined particles

The effects of confinement on colloidal self-assembly in the case of fixed number of confined particles are studied in the one dimensional lattice model solved exactly in the grand canonical ensemble (GCE) in Pȩkalski et al. [J. Chem. Phys. 142, 014903 (2015)]. The model considers a pair interaction defined by a short-range attraction plus a longer-range repulsion. We consider thermodynamic states corresponding to self-assembly into clusters. Both fixed and adaptive boundaries are studied. For fixed boundaries, there are particular states in which, for equal average densities, the number of clusters in the GCE is larger than in the canonical ensemble. The dependence of pressure on density has a different form when the system size changes with fixed number of particles and when the number of particles changes with fixed size of the system. In the former case, the pressure has a nonmonotonic dependence on the system size. The anomalous increase of pressure for expanding system is accompanied by formation of a larger number of smaller clusters. In the case of elastic confining surfaces, we observe a bistability, i.e., two significantly different system sizes occur with almost the same probability. The mechanism of the bistability in the closed system is different to that of the case of permeable walls, where the two equilibrium system sizes correspond to a different number of particles.

Theoretical model for fluid-solid coupling in porous materials

This paper introduces a unifying theory for describing complex behavior for porous materials. The key ingredients are the stored energy in solid-fluid interaction as well as the solid-solid and fluid-fluid interactions. A finite element formulation is employed which naturally accounts for the pore-pore network effects and is easily applicable to most pore geometries such as cellular solids and foams. The interactions, built in at the finite element level, give rise to the mechanical response of the macroscopic material unit. Through numerical studies, we show that there is strong coupling between fluid and solid that induces complex mechanical response, i.e., hysteresis and anisotropy. It is demonstrated that hysteresis arises directly from the fluid-solid coupling. We term this type of hysteresis emergent hysteresis.

Bistability in a self-assembling system confined by elastic walls: exact results in a one-dimensional lattice model

The impact of confinement on self-assembly of particles interacting with short-range attraction and long-range repulsion potential is studied for thermodynamic states corresponding to local ordering of clusters or layers in the bulk. Exact and asymptotic expressions for the local density and for the effective potential between the confining surfaces are obtained for a one-dimensional lattice model introduced by J. Pȩkalski et al. [J. Chem. Phys. 138, 144903 (2013)]. The simple asymptotic formulas are shown to be in good quantitative agreement with exact results for slits containing at least 5 layers. We observe that the incommensurability of the system size and the average distance between the clusters or layers in the bulk leads to structural deformations that are different for different values of the chemical potential μ. The change of the type of defects is reflected in the dependence of density on μ that has a shape characteristic for phase transitions. Our results may help to avoid misinterpretation of the change of the type of defects as a phase transition in simulations of inhomogeneous systems. Finally, we show that a system confined by soft elastic walls may exhibit bistability such that two system sizes that differ approximately by the average distance between the clusters or layers are almost equally probable. This may happen when the equilibrium separation between the soft boundaries of an empty slit corresponds to the largest stress in the confined self-assembling system.

Adsorption of n-pentane on mesoporous silica and adsorbent deformation

Development of quantitative theory of adsorption-induced deformation is important, e.g., for enhanced coalbed methane recovery by CO2 injection. It is also promising for the interpretation of experimental measurements of elastic properties of porous solids. We study deformation of mesoporous silica by n-pentane adsorption. The shape of experimental strain isotherms for this system differs from the shape predicted by thermodynamic theory of adsorption-induced deformation. We show that this difference can be attributed to the difference of disjoining pressure isotherm, responsible for the solid-fluid interactions. We suggest the disjoining pressure isotherm suitable for n-pentane adsorption on silica and derive the parameters for this isotherm from experimental data of n-pentane adsorption on nonporous silica. We use this isotherm in the formalism of macroscopic theory of adsorption-induced deformation of mesoporous materials, thus extending this theory for the case of weak solid-fluid interactions. We employ the extended theory to calculate solvation pressure and strain isotherms for SBA-15 and MCM-41 silica and compare it with experimental data obtained from small-angle X-ray scattering. Theoretical predictions for MCM-41 are in good agreement with the experiment, but for SBA-15 they are only qualitative. This deviation suggests that the elastic modulus of SBA-15 may change during pore filling.

Translocation dynamics of freely jointed Lennard-Jones chains into adsorbing pores

Polymer translocation into adsorbing nanopores is studied by using the Fokker-Planck equation of chain diffusion along the energy landscape calculated with Monte Carlo simulations using the incremental gauge cell method. The free energy profile of a translocating chain was found by combining two independent sub-chains, one free but tethered to a hard wall, and the other tethered inside an adsorbing pore. Translocation dynamics were revealed by application of the Fokker-Planck equation for normal diffusion. Adsorption of polymer chains into nanopores involves a competition of attractive adsorption and repulsive steric hindrance contributions to the free energy. Translocation times fell into two regimes depending on the strength of the adsorbing pore. In addition, we found a non-monotonic dependence of translocation times with increasing adsorption strength, with sharp peak associated with local free energy minima along the translocation coordinate.

Understanding adsorption-induced structural transitions in metal-organic frameworks: from the unit cell to the crystal

Breathing transitions represent recently discovered adsorption-induced structural transformations between large-pore and narrow-pore conformations in bi-stable metal-organic frameworks such as MIL-53. We present a multiscale physical mechanism of the dynamics of breathing transitions. We show that due to interplay between host framework elasticity and guest molecule adsorption, these transformations on the crystal level occur via layer-by-layer shear. We construct a simple Hamiltonian that describes the physics of host-host and host-guest interactions on the level of unit cells and reduces to one effective dimension due to the long-range elastic cell-cell interactions. We then use this Hamiltonian in Monte Carlo simulations of adsorption-desorption cycles to study how the behavior of unit cells is linked to the transition mechanism at the crystal level through three key physical parameters: the transition energy barrier, the cell-cell elastic coupling, and the system size.