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

On the Low-Pressure Hysteresis (LPH) in Gas Sorption Isotherms of Porous Carbons

This study investigates the origin of low-pressure hysteresis (LPH) in the adsorption and desorption of three different probe molecules: carbon dioxide, nitrogen, and argon, across various adsorption temperatures (from cryogenic to room temperature), and within five different carbon materials: synthetic carbons (pristine and one post-synthetically oxidized) and natural coal. Significant attention is dedicated to elucidating LPH in oxidized samples outgassed at various temperatures (120-350 °C). Experimental results show that insufficient outgassing temperature can lead to unreliable data due to artificial LPH and significantly underestimated textural properties, primarily caused by porosity blockage from substances like moisture. Conversely, in samples where heteroatoms have a stabilizing effect on texture, such as natural coal, careful consideration of outgassing temperature is crucial due to the risk of thermal degradation. Other factors contributing to LPH are adsorption temperature, and especially, kinetic limitations at cryogenic temperatures for cellulose-based carbons. Minor factors responsible for LPH are the physical state of the sample (monolith vs powder) and the flexibility of the porous system, both studied by carbon dioxide sorption. This study constitutes an important piece in the evaluation of LPH, providing practical recommendations and underlining the importance of experimental design, with implications for further research in this complex field.

Design and Synthesis of N-Doped Porous Carbons for the Selective Carbon Dioxide Capture under Humid Flue Gas Conditions

The design of novel porous solid sorbents for carbon dioxide capture is critical in developing carbon capture and storage technology (CCS). We have synthesized a series of nitrogen-rich porous organic polymers (POPs) from crosslinking melamine and pyrrole monomers. The final polymer's nitrogen content was tuned by varying the melamine ratio compared to pyrrole. The resulting polymers were then pyrolyzed at 700 °C and 900 °C to produce high surface area nitrogen-doped porous carbons (NPCs) with different N/C ratios. The resulting NPCs showed good BET surface areas reaching 900 m² g^-1. Owing to the nitrogen-enriched skeleton and the micropore nature of the prepared NPCs, they exhibited CO₂ uptake capacities as high as 60 cm³ g^-1 at 273 K and 1 bar with significant CO₂/N₂ selectivity. The materials showed excellent and stable performance over five adsorption/desorption cycles in the dynamic separation of the ternary mixture of N₂/CO₂/H₂O. The method developed in this work and the synthesized NPCs' performance towards CO₂ capture highlight the unique properties of POPs as precursors for synthesizing nitrogen-doped porous carbons with a high nitrogen content and high yield.

Full-scale pore characteristics in coal and their influence on the adsorption capacity of coalbed methane

Coalbed methane (CBM) is primarily stored and transported through the pores in the coal matrix, making it essential to study the development of different scales of pores in coal to better understand the evaluation and exploration of CBM. In this study, four coal samples of varying ranks (R_o,max = 0.68%-2.86%) were selected, and different scale pores were obtained through low-pressure CO₂ and Ar adsorption (LP-CO₂/ArGA) and mercury intrusion porosimetry (MIP) experiments. A full-scale pore evaluation model was established, and the impact of pores on methane adsorption and restriction was analyzed and discussed through high-pressure adsorption experiments. Our results show that (1) at high pressures (> 100 MPa), the MIP technique caused pore compression and overestimated the pore size below 30 nm by up to 47.2%; (2) to obtain a comprehensive pore evaluation, we developed an accurate model that combines LP-CO₂/ArGA with NLDFT and BJH and NLDFT models to determine micropore (0.3-1.5 nm) and mesopore (1.5-30 nm) parameters. By combining this model with MIP test results, we can obtain a full-scale pore size in the range of 0.3 nm-200 μm; (3) coal rank affected the development of full-scale pore characteristics. As coal rank increased, the specific surface area (SSA) of micropores and adsorption capacity of methane first decreased, then increased. Micropores were found to be the most important storage space for CBM and control gas adsorption, with a microporous SSA and PV to total SSA and total PV ratio of 97.93% and 63.69%, respectively. (4) We also observed a significant linear relationship between the fractal dimension of micropores and the Langmuir volume (V_L) based on fractal theory. As the fractal dimension increased, V_L also increased (R² = 0.8581), indicating that V_L is controlled by the complexity of micropores, which is consistent with the comprehensive evaluation index (D_t) and V_L (R² = 0.8744). Based on our predicted model, V_L can be estimated using the SSA of micropores and D_t. Our findings shed light on the relationship between pore morphology and CBM occurrence and have practical implications for fields such as catalytic synthesis, E-CBM, and gas purification.

Carbonaceous Materials Porosity Investigation in a Wet State by Low-Field NMR Relaxometry

The porosity of differently wetted carbonaceous material with disordered mesoporosity was investigated using low-field 1H NMR relaxometry. Spin−spin relaxation (relaxation time T2) was measured using the CPMG pulse sequence. We present a non-linear optimization method for the conversion of relaxation curves to the distribution of relaxation times by using non-specialized software. Our procedure consists of searching for the number of components, relaxation times, and their amplitudes, related to different types of hydrogen nuclei in the sample wetted with different amounts of water (different water-to-carbon ratio). We found that a maximum of five components with different relaxation times was sufficient to describe the observed relaxation. The individual components were attributed to a tightly bounded surface water layer (T2 up to 2 ms), water in small pores especially supermicropores (2 < T2 < 7 ms), mesopores (7 < T2 < 20 ms), water in large cavities between particles (20−1500 ms), and bulk water surrounding the materials (T2 > 1500 ms). To recalculate the distribution of relaxation times to the pore size distribution, we calculated the surface relaxivity based on the results provided by additional characterization techniques, such as thermoporometry (TPM) and N2/−196 °C physisorption.

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.

An overview on alumina-silica-based aerogels

Silica aerogels are remarkable materials with excellent physicochemical properties, such as high porosity and surface area, along with low density and thermal conductivity. In addition to their outstanding properties, these materials are quite interesting due to the possibility to change their chemistry according to intended applications. However, they also show some disadvantages, like low mechanical strength and poor dimensional stability under high temperatures (above 600 °C). Although these aerogels are frequently used as thermal insulators, for high temperature environments some of their properties need to be improved. The mixing with other ceramic thermally resistant phases is a viable approach. Thus, this work presents an overview on alumina-silica-based aerogels, describing their synthesis, processing and properties. The improvement on their properties will be discussed as a function of the amount of refractory phase (alumina) in the silica matrix. The introduction of the alumina phase makes them stable until 1200-1400 °C, maintaining low values of thermal conductivity at very high temperature (below 81 mW m^-1 K^-1). Finally, a brief survey on the most promising applications of these materials is presented, with several examples. In catalysis, alumina-silica aerogels have shown equivalent performance when compared to reference catalysts. In the field of thermal insulation, these materials show great potential, especially in high temperatures environments, due to their thermal dimensional stability and inherent low thermal conductivity. As adsorbents, higher stability and adsorption capacity were obtained with the incorporation of the alumina phase in silica aerogels, and these materials can be reused for repeated adsorption/desorption cycles. Indeed, a significant improvement of the aerogel performance by the synergetic effect of combining silica and alumina phases is usually obtained, supporting the expectation of the extension of their fields of application.

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.

Structural Flexibility in Activated Carbon Materials Prepared under Harsh Activation Conditions

Although traditionally high-surface area carbon materials have been considered as rigid structures with a disordered three dimensional (3D) network of graphite microdomains associated with a limited electrical conductivity (highly depending on the porous structure and surface chemistry), here we show for the first time that this is not the case for activated carbon materials prepared using harsh activation conditions (e.g., KOH activation). In these specific samples a clear structural re-orientation can be observed upon adsorption of different organic molecules, the structural changes giving rise to important changes in the electrical resistivity of the material. Whereas short chain hydrocarbons and their derivatives give rise to an increased resistivity, the contrary occurs for longer-chain hydrocarbons and/or alcohols. The high sensitivity of these high-surface area carbon materials towards these organic molecules opens the gate towards their application for sensing devices.

Requirements to Determine the Average Pore Size of Nanoporous Media Using Ultrasound

Liquids in nanoporous media are exposed to an adsorption-induced pressure, a consequence of the interaction with the pore surface. The smaller the pore diameter, d P, the higher the pressure at saturation and thus the bulk modulus of the confined liquid. Therefore, it has been proposed to use ultrasonic measurements on saturated nanoporous media for the determination of the average pore size. Here, we discuss the requirements for such an analysis. Although predictions for the size-dependent pore pressure and the liquid's modulus, K iso(d P), are based on isothermal simulations, an experimentalist studying the propagation of ultrasonic waves determines adiabatic moduli, K ad(d P). We show that the quantity relating adiabatic and isothermal moduli, the heat capacity ratio γ = c p/c v = K ad/K iso, exhibits a strong pressure dependence for many bulk liquids. In nanopores, this translates into a size-dependent γ(d P), provided the confinement does not alter the heat capacity ratio. Disregarding this effect in the analysis of ultrasonic data would yield an underestimate of the isothermal modulus and thus an overestimate of the average pore size. For a correct analysis, an experimentalist thus needs to know the size dependence of three quantities: the isothermal modulus, adsorption-induced pressure, and heat capacity ratio.

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.

Multimodels computation for adsorption capacity of activated carbon

The pore size distribution of activated carbon is conventionally characterized with nitrogen adsorption measurements at 77 K. The adsorption isotherms are commonly analyzed with a nonlocal density functional theory in combination with a mathematical model for the pore size and geometry. While nonlocal density functional theory is significantly more accurate than the Brunauer–Emmett–Teller theory for gas adsorption, its application to materials characterization is mostly based on a mean-field approximation for van der Waals attractions that is only qualitative in comparison with alternative versions of nonlocal density functional theory or molecular simulations. Toward development of a more reliable theoretical procedure, we compare mean-field approximation-nonlocal density functional theory with three recent versions of non-mean-field methods for gas adsorption at conditions corresponding to experiments for porous materials characterization. The potential applicability of different nonlocal density functional theory methods for pore size distribution predictions is evaluated in terms of the theoretical error bound scale analysis. We find that the weight density approximation is the most reliable for predicting the pore size distribution of amorphous porous materials. In addition to accurate isotherm, weight density approximation yields the theoretical error bound scale for pore size distribution prediction nearly 104 times narrower than that corresponding to mean-field approximation. The new theoretical procedure has been used to analyze the pore size distribution of four activated carbon samples and to predict the adsorption capacities of these materials.

Relationship between Pore-size Distribution and Flexibility of Adsorbent Materials: Statistical Mechanics and Future Material Characterization Techniques

Measurement of the pore-size distribution (PSD) via gas adsorption and the so-called "kernel method" is a widely used characterization technique for rigid adsorbents. Yet, standard techniques and analytical equipment are not appropriate to characterize the emerging class of flexible adsorbents that deform in response to the stress imparted by an adsorbate gas, as the PSD is a characteristic of the material that varies with the gas pressure and any other external stresses. Here, we derive the PSD for a flexible adsorbent using statistical mechanics in the osmotic ensemble to draw analogy to the kernel method for rigid materials. The resultant PSD is a function of the ensemble constraints including all imposed stresses and, most importantly, the deformation free energy of the adsorbent material. Consequently, a pressure-dependent PSD is a descriptor of the deformation characteristics of an adsorbent and may be the basis of future material characterization techniques. We discuss how, given a technique for resolving pressure-dependent PSDs, the present statistical mechanical theory could enable a new generation of analytical tools that measure and characterize certain intrinsic material properties of flexible adsorbents via otherwise simple adsorption experiments.

Experimental method for the determination of adsorption-induced changes of pressure and surface stress in nanopores

The change of surface stress is an important quantity characterising the behaviour of nanoporous systems, however, it is difficult to assess experimentally. In this letter we develop and demonstrate an experimental method for the determination of adsorption-induced changes of the surface stress in nanoporous materials. With the aid of ultrasonic measurements we determine the dependence of the adsorbate's longitudinal modulus [Formula: see text] on the adsorption-induced normal pressure, [Formula: see text], which is exerted by the adsorbate on the porous matrix. From this dependence we deduce the normal pressure at saturation, [Formula: see text], and thereby changes of the surface stress [Formula: see text] at the interface between the solid matrix and the liquid adsorbate. For the model system of argon in nanoporous glass (pore radius [Formula: see text] nm) the ultrasonic method reveals a value for [Formula: see text] that is in very good agreement with the theoretical value known for the argon-silica interface. The disclosure of this experimental method and its application on other systems will enable a better understanding of the behaviour of adsorbates in nanoporous materials.

A carbon nanopore model to quantify structure and kinetics of ion electrosorption with in situ small-angle X-ray scattering

In situ small-angle X-ray scattering was carried out on a custom-built supercapacitor cell and is presented together with a novel data analysis strategy to study the structure and kinetics of ion electrosorption in a nanoporous carbon electrode.

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.

Correlation between the Sorption-Induced Deformation of Nanoporous Glass and the Continuous Freezing of Adsorbed Argon

In this article we study the dependence of the sorption-induced deformation of nanoporous glass on the liquid-solid phase transition of adsorbed argon. During cooling we observe a continuous reduction of the expansion of the porous glass matrix caused by the adsorbate. The contraction is attended by a likewise continuous change of the adsorbed argon's phase state from liquid to solid. This simultaneous behavior evidences that the liquid-solid phase transition leads to a reduction of the pressure the adsorbate exerts on the pore walls. Furthermore, the study shows that small temperature changes can temporarily cause strong deformations of the porous material that decay in long time intervals of up to 1 week. We expect that our observations for the model system of argon and porous glass can be generalized to other systems. Consequently, this study will have implications when considering porous materials for applications, e.g., as a medium for storage.

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.

Controllable synthesis of few-layered and hierarchically porous boron nitride nanosheets

Few-layered porous boron nitride nanosheets prepared using MgB₂ as a dynamic template show good CO₂ adsorption selectivity.