Christian Balzer

Deformation of porous carbons upon adsorption.

N2 and CO2 sorption measurements with in situ dilatometry implemented in a commercial volumetric sorption instrument were performed at 77 and 273 K, respectively. The resolution of the linear deformation was about ±0.2 μm. To separate effects due to microporosity, external surface area and mesopores synthetic porous carbons (xerogels) with different external surface areas and microporosities were applied as a model system. The experimental data show that the relative length change of the monolithic carbon xerogels investigated passes different stages during ad- and desorption, which are connected to micropore-, multilayer- and mesopore-sorption. The length change observed in the range of micropore and surface adsorption was found to be nonmonotonic and to take negative as well as positive values, with the maximum swelling observed being on the order of 4‰. With respect to the length change, the micropore structure seems to have the most significant impact on the overall length change, while the external surface is only of minor importance. Quantiative analysis of the deformation according to the models of Bangham and Scherer for the length change in the range of multilayer- and mesopore-adsorption allows extracting the macrosopic as well as the skeletal Youngs modulus.

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.

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 samples 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.

Relationship Between Pore Structure and Sorption-Induced Deformation in Hierarchical Silica-Based Monoliths

Abstract Experimental results on sorption-induced deformation during n-pentane desorption were obtained by in-situ dilatometry and in-situ small angle X-ray scattering (SAXS). The sample investigated was a silica-based monolith with hierarchical pore structure comprising a macroporous network of struts, each strut containing well-defined cylindrical mesopores ordered on a 2D hexagonal lattice. In-situ dilatometry and in-situ SAXS measurements revealed strain isotherms of similar shape, which are qualitatively in good agreement with recent theoretical predictions. From the relative pressure range of the liquid filled mesopores a pore load modulus of 1.5 GPa is determined. The relative pressure region of mono- and multilayer formation, however, reveals differences between the two independent methods. In particular, the net strain at saturation pressure is considerably larger for in-situ dilatometry. We attribute this observation to the different sensitivity of the two methods to anisotropic deformation in the hierarchical solid framework. While in-situ SAXS measures the mesopore lattice strain and is therefore exclusively sensitive to radial deformation of the struts, dilatometry measures the linear deformation of the isotropic macroscopic sample, being sensitive to the volumetric strain of the whole network.

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.

Setting Directions: Anisotropy in Hierarchically Organized Porous Silica

Structural hierarchy, porosity, and isotropy/anisotropy are highly relevant factors for mechanical properties and thereby the functionality of porous materials. However, even though anisotropic and hierarchically organized, porous materials are well known in nature, such as bone or wood, producing the synthetic counterparts in the laboratory is difficult. We report for the first time a straightforward combination of sol-gel processing and shear-induced alignment to create hierarchical silica monoliths exhibiting anisotropy on the levels of both, meso- and macropores. The resulting material consists of an anisotropic macroporous network of struts comprising 2D hexagonally organized cylindrical mesopores. While the anisotropy of the mesopores is an inherent feature of the pores formed by liquid crystal templating, the anisotropy of the macropores is induced by shearing of the network. Scanning electron microscopy and small-angle X-ray scattering show that the majority of network forming struts is oriented towards the shearing direction; a quantitative analysis of scattering data confirms that roughly 40% of the strut volume exhibits a preferred orientation. The anisotropy of the materials macroporosity is also reflected in its mechanical properties; i.e., the Youngs modulus differs by nearly a factor of 2 between the directions of shear application and perpendicular to it. Unexpectedly, the adsorption-induced strain of the material exhibits little to no anisotropy.