Density functional theory model of adsorption deformation

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.

Study on the difference of pore structure of anthracite under different particle sizes using low-temperature nitrogen adsorption method

The low-temperature nitrogen adsorption test was used to study anthracite from Jiulishan coal mine with different particle size ranges of 60-80 mesh, 150-200 mesh, and > 200 mesh. The adsorption isotherm, adsorption capacity, pore volume, pore specific surface area, and average pore diameter of coal samples were analyzed by BET and DFT models in order to study the influence of particle size on the pore structure of anthracite and determine the optimal range of particle size for low-temperature nitrogen adsorption test. The results indicate that the particle size plays a significant effect on the pore structure of anthracite and the adsorption capacity of soft coal is less affected by particle size, while hard coal is substantially affected by particle size. The adsorption capacity of hard coal with particle size of > 200 mesh is increased by 7 times when compared with the particle size of 60-80 mesh, indicating that the gas molecular mobility hindrance decline and pore connectivity improves with the decrease of particle size. The average pore diameter of hard coal decreases continuously from 3.1424 to 2.854 nm, while that of soft coal expands from 2.8947 to 3.2515 nm and then to 3.0362 nm with the decrease of particle size. The effects of particle size on the pore surface area of soft and hard coal are concentrated within the < 10 nm pore aperture. Effect of particle size on hard coal pore volume is mainly focused in the pore size < 10 nm, whereas that of soft coal is primarily concentrated in the pore with aperture ranges of 2-100 nm. When the particle sizes varies from 60-80 mesh to 150-200 mesh, the collapse of large pore of hard coal appears better than that of closed pore. When the particle size of hard coal reaches > 200 mesh, the collapse of closed pores and the damage to small pores are stronger than the collapse of large pores. The fractal dimensions with relative pressure of 0-0.20 and 0.20-0.995 are defined as D₁ and D₂, respectively, and when the fractal dimension D₁ increases, the surface roughness and structural complexity of coal samples increase with the decrease of anthracite particle size, while the fractal dimension D₂ shows the opposite trend, which indicates that anthracite of smaller particle size possess higher adsorption capacity. Therefore, 150-200 mesh is recommended as the preferred anthracite particle size in low-temperature nitrogen adsorption test.

Polar liquids at charged interfaces: A dipolar shell theory

The structure of polar liquids and electrolytic solutions, such as water and aqueous electrolytes, at interfaces underlies numerous phenomena in physics, chemistry, biology, and engineering. In this work, we develop a continuum theory that captures the essential features of dielectric screening by polar liquids at charged interfaces, including decaying spatial oscillations in charge and mass, starting from the molecular properties of the solvent. The theory predicts an anisotropic dielectric tensor of interfacial polar liquids previously studied in molecular dynamics simulations. We explore the effect of the interfacial polar liquid properties on the capacitance of the electrode/electrolyte interface and on hydration forces between two plane-parallel polarized surfaces. In the linear response approximation, we obtain simple formulas for the characteristic decay lengths of molecular and ionic profiles at the interface.

Structural Forces in Ionic Liquids: The Role of Ionic Size Asymmetry

Ionic liquids (ILs) are charged fluids composed of anions and cations of different size and shape. The ordering of charge and density in ILs confined between charged interfaces underlies numerous applications of IL electrolytes. Here, we analyze the screening behavior and the resulting structural forces of a representative IL confined between two charge-varied plates. Using both molecular dynamics simulations and a continuum theory, we contrast the screening features of a more-realistic asymmetric system and a less-realistic symmetric one. The ionic size asymmetry plays a nontrivial role in charge screening, affecting both the ionic density profiles and the disjoining pressure distance dependence. Ionic systems with size asymmetry are stronger coupled systems, and this manifests itself both in their response to the electrode polarization and spontaneous structure formation at the interface. Analytical expressions for decay lengths of the disjoining pressure are obtained in agreement with the pressure profiles computed from molecular dynamics simulations.

Solvation force and adsorption isotherm of a fluid mixture in nanopores of complex geometry based on fundamental measure theory

A novel method based on the fundamental measure theory is developed to calculate the solvation force and adsorption isotherm of a Lennard-Jones fluid mixture in complex geometries. Fast Fourier transform and 3D-voxel discretization are used for accurately computing the confined fluid densities in a closed pore of arbitrary geometry. Given the fluid densities, the solvation force distribution at the solid surface can be calculated using a new formulation from either mechanical or thermodynamic approach. Understanding the solvation force behavior, which depends on many factors such as pore geometry, confined density distribution, molecule size, is very important to analyze the pore deformation from a poromechanical point of view. Special attention in the numerical simulations is given to the adsorption problem of CH₄and CO₂gas mixture in ellipsoidal pore.

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.

A Poromechanical Model for Sorption Hysteresis in Nanoporous Polymers

Sorption hysteresis in nanoporous polymer is an intriguing phenomenon that involves coupling between sorption and deformation. Based on the mechanism revealed at the microscopic level by use of molecular simulation, a poromechanical model is developed capturing all relevant physics and yielding a quantitative description. In this model, the coupling between sorption and deformation is described by a poromechanics framework. More in detail, an upscaling process from the molecular mechanism is implemented to model the hysteresis through the state change of each element upon deformation. We provide two solutions of the model: a numerical one based on the finite element method and an analytical one based on uniform strain assumption. The results from both solutions agree well with the molecular simulation and experimental results, therefore capturing and describing adequately sorption hysteresis. The developed model illustrates that water forms different structural distributions upon adsorption and desorption. A parametric study shows that sorption hysteresis is influenced by material properties. We find that a softer material with stronger adsorbent-adsorbate interaction tends to exhibit more profound sorption hysteresis. The developed model, which relies on the concepts of sorption-deformation coupling and multiscale modeling from atomistic simulations to domain dependent theory, paves the way for a new direction of modeling sorption hysteresis.

Stress or Strain Does Not Impact Sorption in Stiff Mesoporous Materials

The present paper investigates strain-induced sorption in mesoporous silicon. Contrarily to a previous report based on indirect evidence, we find that external mechanical strain or stress has no measurable impact on sorption isotherms, down to a relative accuracy of 10^-3. This conclusion is in agreement with the analysis of the sorption-induced strain of porous silicon and holds for other stiff mesoporous materials such as porous silicas.

In situ visualization of loading-dependent water effects in a stable metal-organic framework

Competitive water adsorption can have a significant impact on metal-organic framework performance properties, ranging from occupying active sites in catalytic reactions to co-adsorbing at the most favourable adsorption sites in gas separation and storage applications. In this study, we investigate, for a metal-organic framework that is stable after moisture exposure, what are the reversible, loading-dependent structural changes that occur during water adsorption. Herein, a combination of in situ synchrotron powder and single-crystal diffraction, infrared spectroscopy and molecular modelling analysis was used to understand the important role of loading-dependent water effects in a water stable metal-organic framework. Through this analysis, insights into changes in crystallographic lattice parameters, water siting information and water-induced defect structure as a response to water loading were obtained. This work shows that, even in stable metal-organic frameworks that maintain their porosity and crystallinity after moisture exposure, important molecular-level structural changes can still occur during water adsorption due to guest-host interactions such as water-induced bond rearrangements.

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.

Unusual hygroscopic nature of nanodiamonds in comparison with well-known porous materials

Nanodiamond aggregates have interparticle pores of 4.5 nm on average, exhibiting porous nature involved in their water storage. This work studies the hygroscopic nature of porous nanodiamond aggregates by water absorption based on liquid water droplets. Nanodiamond aggregates show hydrophobicity from the water vapor adsorption. Surprisingly, porous nanodiamond aggregates quickly absorb water droplets at the bulk scale. The volume of absorbed liquid water is comparable to that of the water-absorbing clay Montmorillonite and higher than those of zeolites ZSM-5 and molecular sieve 5A. This hygroscopic nature of nanodiamonds is ascribed to the micro- and mesoporous structure of their aggregates and the special core-shell structure of each nanodiamond particle (wrapped by graphene-like carbon). The absorption rate of liquid water in the porous nanodiamonds is influenced by the surface wettability, while the hygroscopic capacity depends mainly on the hierarchical porosity.

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.

Capillary Stress and Structural Relaxation in Moist Granular Materials

A numerical and theoretical framework to address the poromechanical effect of capillary stress in complex mesoporous materials is proposed and exemplified for water sorption in cement. We first predict the capillary condensation/evaporation isotherm using lattice-gas simulations in a realistic nanogranular cement model. A phase-field model to calculate moisture-induced capillary stress is then introduced and applied to cement at different water contents. We show that capillary stress is an effective mechanism for eigenstress relaxation in granular heterogeneous porous media, which contributes to the durability of cement.

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.

Method To Detect Ethanol Vapor in High Humidity by Direct Reflection on a Xerogel Coating

A simple double thin-film coating-based device is proposed to quantify the ethanol content in humid air featuring a 10 ppm resolution and spanning a dynamic range from 0 to 1000 ppm. The transduction involves the measurement of the direct optical reflection intensity, changing upon refractive index variations induced by water and ethanol adsorption within the coatings. The first thin-film coating is a microporous methyl-functionalized, silica xerogel material more sensitive to alcohol, and the second one is a microporous pure silica xerogel material more sensitive to water. The precision of the sensor is achieved through a mathematical treatment applied on the time resolved adsorption period. Reflection signals of both the ethanol- and water-sensitive coatings are taken into account in the treatment to correct for differences in ambient conditions (temperature, relative humidity, presence of volatile organic compounds) within the same chamber previous to data analysis, which corresponds to realistic operating conditions. As the adsorption mechanism is governed by molecular dynamic equilibrium, these sensors are fast and instantaneously regenerated in ambient air. The sensor is easy to assemble and was reusable for a period exceeding 1 year (maximal tested time).

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.

Water Adsorption Property of Hierarchically Nanoporous Detonation Nanodiamonds

The detonation nanodiamonds form the aggregate having interparticle voids, giving a marked hygroscopic property. As the relationship between pore structure and water adsorption of aggregated nanodiamonds is not well understood yet, adsorption isotherms of N₂ at 77 K and of water vapor at 298 K of the well-characterized aggregated nanodiamonds were measured. HR-TEM and X-ray diffraction showed that the nanodiamonds were highly crystalline and their average crystallite size was 4.5 nm. The presence of the graphitic layers on the nanodiamond particle surface was confirmed by the EELS examination. The pore size distribution analysis showed that nanodiamonds had a few ultramicropores with predominant mesopores of 4.5 nm in average size. The water vapor adsorption isotherm of IUPAC Type V indicates the hydrophobicity of the nanodiamond aggregates, with the presence of hydrophilic sites. Then the hygroscopic nature of nanodiamonds should be associated with the surface functionalities of the graphitic shell and the ultramicropores on the mesopore walls.

Fluids in porous media. IV. Quench effect on chemical potential

It appears to be a common sense to measure the crowdedness of a fluid system by the densities of the species constituting it. In the present work, we show that this ceases to be valid for confined fluids under some conditions. A quite thorough investigation is made for a hard sphere (HS) fluid adsorbed in a hard sphere matrix (a quench-annealed system) and its corresponding equilibrium binary mixture. When fluid particles are larger than matrix particles, the quench-annealed system can appear much more crowded than its corresponding equilibrium binary mixture, i.e., having a much higher fluid chemical potential, even when the density of each species is strictly the same in both systems, respectively. We believe that the insight gained from this study should be useful for the design of functionalized porous materials.

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.

Thermodynamics of the Flexible Metal-Organic Framework Material MIL-53(Cr) From First Principles

We use first-principles density functional theory total energy and linear response phonon calculations to compute the Helmholtz and Gibbs free energy as a function of temperature, pressure, and cell volume in the flexible metal-organic framework material MIL-53(Cr) within the quasiharmonic approximation. GGA and metaGGA calculations were performed, each including empirical van der Waals (vdW) forces under the D2, D3, or D3(BJ) parameterizations. At all temperatures up to 500 K and pressures from -30 MPa to 30 MPa, two minima in the free energy versus volume are found, corresponding to the narrow pore (np) and large pore (lp) structures. Critical positive and negative pressures are identified, beyond which there is only one free energy minimum. While all results overestimated the stability of the np phase relative to the lp phase, the best overall agreement with experiment is found for the metaGGA PBEsol+RTPSS+U+J approach with D3 or D3(BJ) vdW forces. For these parameterizations, the calculated free energy barrier for the np-lp transition is only 3 to 6 kJ per mole of Cr₄(OH)₄(C₈H₄O₄)₄.

Converting Water Adsorption and Capillary Condensation in Usable Forces with Simple Porous Inorganic Thin Films

This work reports an innovative humidity-driven actuation concept based on conversion of chemical energy of adsorption/desorption using simple nanoporous sol-gel silica thin films as humidity-responsive materials. Bilayer-shaped actuators, consisting of a humidity-sensitive active nanostructured silica film deposited on a polymeric substrate (Kapton), were demonstrated as an original mean to convert water molecule adsorption and capillary condensation in usable mechanical work. Reversible solvation stress changes in silica micropores by water adsorption and energy produced by the rigid silica film contraction, induced by water capillary condensation in mesopores, were finely controlled and used as energy sources. The influence of the film nanostructure (microporosity, mesoporosity) and thickness and the polymeric substrate thickness on actuation force, on movement speed and on displacement amplitude are clearly evidenced and discussed. We show that the global mechanical response of such silica-based actuators can easily be adjusted to fabricate tailor-made actuation systems triggered by humidity variation. This study provides insight into hard ceramic stimulus-responsive materials that seem to be a promising alternative to traditional soft organic materials for surface-chemistry-driven actuation systems.

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.

Adsorption deformation of microporous composites

We study here the behavior of flexible adsorbent materials, or soft porous crystals, when used in practical applications as nanostructured composites such as core-shell particles or mixed matrix membranes. Based on simple models and the well-established laws of elasticity, we demonstrate how the presence of a binder results in an attenuation of the adsorption-induced stress and deformation. In the case where the adsorbent undergoes adsorption-induced structural transitions, such as the gate opening phenomenon occurring in some metal-organic frameworks, we show that the presence of the binder will result in shifts of the adsorption-induced transition pressures.

Adsorption-Induced Surface Stresses of the Water/Quartz Interface: Ab Initio Molecular Dynamics Study

Adsorption-induced deformation is expansion or contraction of a solid due to adsorption on its surface. This phenomenon is important for a wide range of applications, from chemomechanical sensors to methane recovery from geological formations. The strain of the solid is driven by the change of the surface stress due to adsorption. Using ab initio molecular dynamics, we calculate the surface stresses for the dry α-quartz surfaces, and investigate how these stresses change when the surfaces are exposed to water. We find that the nonhydroxylated surface shows small and approximately isotropic changes in stress, while the hydroxylated surface, which interacts more strongly with the polar water molecules, shows larger and qualitatively anisotropic (opposite sign in xx and yy) surface stress changes. All of these changes are several times larger than the surface tension of water itself. The anisotropy and possibility of positive surface stress change can explain experimentally observed surface area contraction due to adsorption.

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.

Multiscale adsorption and transport in hierarchical porous materials

This review presents the state-of-the-art of multiscale adsorption and transport in hierarchical porous materials.

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.

Chemical reduction of the elastic properties of zeolites: a comparison of the formation of carbonate species versus dealumination

The decrease in elastic moduli (Young's, bulk, and shear modulus), the variations in their asymmetries, the Poisson's ratio and the linear compressibility due to carbonate formation in NaX, have been compared to those produced by dealumination of the zeolite HY framework, from the Al-Si-Al fragment positioned in joined 4R rings. All these systems have been considered at the density functional theory (DFT) level using periodic boundary conditions. The representativeness of the models has been checked by comparison of the calculated IR spectra of carbonate and hydrocarbonate species in NaX and of hydroxyl groups in HY with the experimental equivalents. The correlation between the destabilization energy of the systems and the displacement of Na or K cations coordinated to the carbonate or hydrocarbonate species, expressed in terms of Me-O bond elongation, has been confirmed for either one or two carbonate and hydrocarbonate species per unit cell (UC). Finally, a similar reduction in elasticity in FAU zeolites has been observed, due either to carbonate/bicarbonate formation in NaX or as a step in HY dealumination.

Adsorption stress changes the elasticity of liquid argon confined in a nanopore

Knowledge of the elastic properties of a fluid is crucial for predicting its flow under high pressure, particularly in porous media. However, when a fluid is confined to a nanopore, many of its thermodynamic properties change as compared to bulk. Here we study the effect of confinement on the bulk modulus of liquid argon adsorbed in mesopores using classical density functional theory. We show that, at pressures lower than the saturation pressure, high adsorption stress in the pore causes the lowering of the fluid bulk modulus, a phenomenon which was recently observed experimentally [ Schappert, K.; Pelster, R. Europhys. Lett. 2014 , 105 , 5600 ]. Furthermore, we find that the pore size has a strong effect on the fluid bulk modulus, so that even at saturation, the elastic properties of nanoconfined fluid differ from the bulk values. We show that this difference is also due to the adsorption stress. Our results provide a basis for a new method for characterization of porous materials and have implications for modeling fluids in nanoporous geological formations, such as coal or shale.

Effect of pore structure of nanometer scale porous films on the measured elastic modulus

The impact of pore structure of nanoporous films on the measured elastic modulus is demonstrated for silica-based nanoporous low-k films that are fabricated using an alternative manufacturing sequence which allows a separate control of porosity and matrix properties. For this purpose, different experimental techniques for measuring the elastic properties were compared, including nanoindentation, laser-induced surface acoustic wave spectroscopy (LAwave), and ellipsometric porosimetry (EP). The link between the elastic response of these nanoporous materials and their internal pore structure was investigated using positronium annihilation lifetime spectroscopy (PALS), EP, and diffusion experiments. It is shown that the absolute value of the Berkovich indentation modulus is very sensitive to the local pore structure and stiffness of the substrate and can be influenced by densification and/or anisotropic elasticity upon indentation, while on the other hand spherical indentation results are less sensitive to the local pore structure. The comparison of Berkovich and spherical indentation results combined with finite element simulations can potentially reveal changes in the internal structure of the film. For nanoporous films with porosity above the percolation threshold, the elastic modulus results obtained with LAwave and EP agree very well with spherical indentation results. On the other hand, below the percolation threshold, the elastic modulus values determined by these techniques deviate from the spherical indentation results. This was explained in terms of specific technique related effects that appear to be sensitive to the specific arrangement and morphology of the pores.

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.

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.