Adsorption of Diffusing Tracers, Apparent Tortuosity, and Application to Mesoporous Silica

The apparent tortuosity due to adsorption of diffusing tracers in a porous material is determined by a scaling approach and is used to analyze recent data on LiCl and alkane diffusion in mesoporous silica. The slope of the adsorption isotherm at small loadings is written as β = qA/qG, where qA is the adsorption-desorption ratio and qG = ϵ/(as) - 1 is a geometrical factor depending on the range a of the tracer-wall interaction, the porosity ϵ, and the specific surface area s. The adsorption leads to a decrease of effective diffusion coefficient, which is quantified by multiplying the geometrical tortuosity factor τgeom by an apparent tortuosity factor τapp. In wide pores or when the adsorption barrier is high, τapp = β + 1, as obtained in previous works, but in narrow pores there is an additional contribution from frequent adsorption-desorption transitions. These results are obtained in media with parallel pores of constant cross sections, where the ratio between the effective pore width ϵ/s and the actual width is ≈0.25. Applications to mesoporous silica samples are justified by the small deviations from this ideal ratio. In the analysis of alkane self-diffusion data, the fractions of adsorbed molecules predicted in a recent theoretical work are used to estimate τgeom of the silica samples, which is ≫1 only in the sample with the narrowest pores (nominal 3 nm). The application of the model to Li+ ion diffusion leads to similar values of τgeom and to a difference of energy barriers of desorption and adsorption for those ions of ∼0.06 eV. Comparatively, alkane self-diffusion provides the correct order of magnitude of τgeom, with adsorption playing a less important role, whereas adsorption effects on Li+ diffusion are much more important.

Diffusion Anisotropy of Gaseous Helium-3 in Ordered Aerogels at Low Temperatures

We report on the first observation of diffusion anisotropy of gaseous helium-3 entrapped in ordered aerogels at 4.2 K. The origins of ³He diffusion anisotropy in aerogels of different porosity are discussed. The correlations between gas diffusion coefficient and basic parameters of aerogels, such as porosity, fiber diameter, and fiber's degree of alignment, are inspected using simple diffusion simulations within the framework of classical diffusion model in both oriented and chaotic aerogels under conditions of diffuse (Knudsen diffusion) and specular reflections of atoms from the walls. The failure of the two-phase and Knudsen diffusion models at low temperature in isotropic and anisotropic aerogels is observed. The effect of a wall attractive potential on the gas dynamics is suspected to play a crucial role in the gas diffusion and its anisotropy. The rough theoretical estimates of that effect at low temperatures in aerogel space confirm this assumption. The observed peculiar diffusion is universal and is expected to occur with other probe gases at higher temperatures.

The3He nuclear magnetic relaxation in nematically ordered Al2O3aerogels: effects of4He and nitrogen pre-plating

The results of³He gas pulsed NMR spin-lattice relaxation study in high-porosity (84.9%-97.9%) nematically ordered Al₂O₃aerogels at 1.5 and 4.2 K are presented. The linear dependence ofT₁on gas pressure is observed in aerogels that are pre-plated by helium-4. Nitrogen pre-plating prior to helium-4 pre-plating weakly decreases the³He gas spin-lattice relaxation rate. A few possible mechanisms plausibly involved in³He nuclear magnetic relaxation in aerogels are considered. The suggested nuclear spin-lattice relaxation model due to some magnetically 'dirty' aerogel fibers allows to estimate the effective mean free path of³He atoms in aerogel.

Kinetics of Supercritical Drying of Gels

Supercritical drying of gels is considered as the most important step of aerogel production since it enables preservation of the three-dimensional pore structure which lead to unique material properties such as high porosity, low density, and large surface area. An understanding of the kinetics of supercritical drying is necessary to provide insight into material development, scale-up, and optimization of the aerogel manufacturing process. Thus, investigation of supercritical drying is gaining increased attention in recent years. This review paper covers the experimental considerations and techniques to study the kinetics of supercritical drying, fundamental mass transfer mechanisms during the drying process and modeling efforts to predict the drying kinetics for varying operating conditions and gel properties. Transport phenomena involving diffusion, convection, spillage by volume expansion, and axial dispersion are discussed by providing the fundamental equations and empirical correlations to predict transfer coefficients. A detailed review of literature covering experimental and theoretical studies on kinetics of supercritical drying is presented.

Helium-3 gas self-diffusion in a nematically ordered aerogel at low temperatures: enhanced role of adsorption

We performed ³He gas diffusion measurements for the first time in a highly porous ordered Al₂O₃ aerogel sample at a temperature of 4.2 K using a nuclear magnetic resonance field gradient technique. A strong influence of ³He adsorption in the aerogel on self-diffusion is observed. The classical consideration of adsorptive gas diffusion in mesopores leads to anomalously high tortuosity factors. The application of a more sophisticated model than the simple combination of empirical two-phase diffusion and the Knudsen gas diffusion models is required to explain our results. Anisotropic properties of the aerogel are not reflected in the observed gas diffusion even at low gas densities where the anisotropic Knudsen regime of diffusion is expected. The observed gas densification indicates the influence of the aerogel attractive potential on the molecular dynamics, which probably explains the reduced diffusion process. Perhaps this behavior is common for any adsorptive gases in nanopores.

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.