Coupling between adsorption and mechanics (and vice versa)

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.

Adsorption-Induced Deformation of Zeolites 4A and 13X: Experimental and Molecular Simulation Study

Gas adsorption in zeolites leads to adsorption-induced deformation, which can significantly affect the adsorption and diffusive properties of the system. In this study, we conducted both experimental investigations and molecular simulations to understand the deformation of zeolites 13X and 4A during carbon dioxide adsorption at 273 K. To measure the sample's adsorption isotherm and strain simultaneously, we used a commercial sorption instrument with a custom-made sample holder equipped with a dilatometer. Our experimental data showed that while the zeolites 13X and 4A exhibited similar adsorption isotherms, their strain isotherms differed significantly. To gain more insight into the adsorption process and adsorption-induced deformation of these zeolites, we employed coupled Monte Carlo and molecular dynamics simulations with atomistically detailed models of the frameworks. Our modeling results were consistent with the experimental data and helped us identify the reasons behind the different deformation behaviors of the considered structures. Our study also revealed the sensitivity of the strain isotherm of zeolites to pore size and other structural and energetic features, suggesting that measuring adsorption-induced deformation could serve as a complementary method for material characterization and provide guidelines for related technical applications.

Elastic Properties of Confined Fluids in Nanopores: An Acoustic-Propagation Model

Following the compressibility route in statistical mechanics, the local isothermal modulus is derived for nanoconfined fluids. Based on this inhomogeneous modulus, an acoustic-propagation model (APM) is first proposed for averaged isothermal modulus in the pore. By utilizing the density profiles obtained from classical density functional theory, the inhomogeneous modulus of supercritical methane in the graphite slit pore is calculated. It is found that the profile of the modulus in the pore is out of phase with that of density. Further, employing the proposed APM method, the averaged isothermal modulus is calculated, and the effects of pressure, pore size, and temperature on the averaged modulus are investigated. It is found that (i) averaged modulus obtained from APM method still satisfies the Tait-Murnaghan (TM) equation, (ii) the averaged modulus is proportional to the reciprocal pore width for wider pores, while it oscillates with the reciprocal pore width for narrower pores, and (iii) the reciprocal modulus is proportional to temperature, while the linearization coefficient is insensitive to the pore size. These findings bear important implications for understanding the elasticity in fluid-saturated nanoporous media and may shed light on the capture or storage of special gases in the fields of geochemistry and geophysics.

Effect of Adsorbent Properties on Adsorption-Induced Deformation

Adsorption-induced adsorbent deformation is of fundamental importance to geoscientists and engineers. To gain insight into the deformation behaviors of different materials, we presented grand canonical Monte Carlo (GCMC) simulations of methane adsorption-induced deformation in slit pores. Adsorption isotherms and deformation behaviors of the pores were obtained for adsorbents with variations in solid density and affinity. The results showed that the adsorption-induced deformation depends on adsorbate loading, pore width, solid density, and affinity. The deformation at a given adsorption loading could be comparable between different solid densities or affinities because solid density or affinity is related to the solvation pressure as the driving force behind the deformation and also the resistance of the deformation. The interaction of these two effects controls the deformation behavior. We expect that our results will help to understand the adsorption-induced deformation in solids with heterogeneous properties and estimate deformation using the gas adsorption data.

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.

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.

Experimental Method for the Determination of the Saturation Vapor Pressure above Supercooled Nanoconfined Liquids

For sorption studies, the saturation vapor pressure p ₀ above an adsorbate is of great significance. For example, it is needed for the determination of the pore size distribution, the Laplace pressure, and the chemical potential. Above the bulk triple point, T ₃ ^bulk, this pressure is identical with the saturation vapor pressure above the bulk liquid. However, below T ₃ ^bulk, the correct value of p ₀(T) is controversial. Nanoconfined fluids exhibit a shift of the freezing and melting temperatures in comparison to the bulk state. Thus, the adsorbed fluid is supercooled in a certain temperature range below T ₃ ^bulk. Here, we show that it is possible to determine the appropriate saturation vapor pressure above the nanoconfined supercooled liquid experimentally. For this purpose, we have performed sorption measurements with liquid argon in nanoporous Vycor glass in the temperature range of the supercooled liquid and at temperatures above the bulk triple point. In order to determine the unknown and temperature-dependent saturation vapor pressure of the supercooled confined adsorbate, p ₀(T), we use the Kelvin equation relating this quantity to the pore radius, r _P(p ₀), that is independent of temperature. The knowledge of the absolute values for the liquid-vapor surface tension of the supercooled adsorbate, γ_lv(T), is not required. However, we presuppose that its dependence on the unknown vapor pressure, γ_lv(p ₀), is bulk-like. Our results indicate that the saturation vapor pressure above the supercooled nanoconfined liquid corresponds to that above supercooled bulk argon (i.e., to the pressure obtained by an extension of the usual vaporization curve to T < T ₃ ^bulk). We expect that this method can be used for the determination of p ₀ above other supercooled adsorbates.

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.

Wood–Moisture Relationships Studied with Molecular Simulations: Methodological Guidelines

This paper aims at providing a methodological framework for investigating wood polymers using atomistic modeling, namely, molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) simulations. Atomistic simulations are used to mimic water adsorption and desorption in amorphous polymers, make observations on swelling, mechanical softening, and on hysteresis. This hygromechanical behavior, as observed in particular from the breaking and reforming of hydrogen bonds, is related to the behavior of more complex polymeric composites. Wood is a hierarchical material, where the origin of wood-moisture relationships lies at the nanoporous material scale. As water molecules are adsorbed into the hydrophilic matrix in the cell walls, the induced fluid–solid interaction forces result in swelling of these cell walls. The interaction of the composite polymeric material, that is the layer S2 of the wood cell wall, with water is known to rearrange its internal material structure, which makes it moisture sensitive, influencing its physical properties. In-depth studies of the coupled effects of water sorption on hygric and mechanical properties of different polymeric components can be performed with atomistic modeling. The paper covers the main components of knowledge and good practice for such simulations.