Stochastic analysis of capillary condensation in disordered mesopores

Two-Step Wetting of Nanoporous Carbons: Small-Angle Scattering Analysis of Capillary Rise

Numerous applications of nanoporous materials require their pores to be filled with liquids. In spite of its huge technological importance, the conditions for the wetting of nanometer-sized pores and its phenomenology are still poorly understood. We report on capillary rise experiments with water in carbon xerogels, with synchrotron small-angle scattering used to follow the process in situ at the nanometer scale. The data reveal a two-step wetting process whereby water permeates first into molecular-sized micropores, which is followed by the imbibition of larger mesopores. A Cassie-Baxter analysis shows that the presence of water in the micropores is central, as it turns the mesopores from being hydrophobic to hydrophilic. Based on the so-calculated contact angles, the mesopore wetting kinetics are found to be quantitatively described by a classical Washburn model. Modeling of the experimental water profile ahead of the Washburn front reveals strong surface barriers opposing water transfer from the mesopores to the micropores.

Confinement induced change of microemulsion phase structure in controlled pore glass (CPG) monoliths

We use small-angle neutron scattering (SANS) to investigate the structure and phase behavior of a complex fluid within meso- and macroporous matrices. Specifically, bicontinuous microemulsions of the temperature-dependent ternary system C10E4-water-n-octane are investigated in controlled pore glass (CPG) membranes with nominal pore diameters of 10 nm, 20 nm, 50 nm, and 100 nm. The scattering data were analyzed using the Teubner-Strey model and a multiphase generalization of clipped Gaussian-field models. The analysis indicates changes in the phase structure of the bicontinuous microemulsion in the membranes with the smallest pores. This is attributed to a shift in the ternary phase diagram toward a three-phase structure at lower surfactant concentrations. This effect is likely related to a larger internal surface area in the membranes with smaller pores, which enhances surfactant adsorption onto the pore walls.

Small-Angle Scattering Indicates Equilibrium Instead of Metastable Capillary Condensation in SBA-15 Mesoporous Silica

Questions about the origin of the adsorption/desorption hysteresis in mesoporous materials are as old as sorption experiments themselves. The historical conception that underlines most existing methods to extract pore size distributions from sorption data assumes that adsorption is a metastable process and that desorption takes place at thermodynamic equilibrium. In this work, we measure nitrogen and argon sorption on a series of 14 SBA-15 ordered mesoporous silicas and use small-angle X-ray scattering to independently determine their pore sizes. We find that capillary condensation systematically occurs close to thermodynamic equilibrium according to a Derjaguin-Broekhoff-de Boer calculation. Our analysis suggests that many earlier works have significantly underestimated the actual pore size in SBA-15 materials. It also highlights the critical role of the reference isotherm used to calibrate the fluid-solid interaction in the models.

Inelastic neutron scattering analysis with time-dependent Gaussian-field models

Converting neutron scattering data to real-space time-dependent structures can only be achieved through suitable models, which is particularly challenging for geometrically disordered structures. We address this problem by introducing time-dependent clipped Gaussian field models. General expressions are derived for all space- and time-correlation functions relevant to coherent inelastic neutron scattering for multiphase systems and arbitrary scattering contrasts. Various dynamic models are introduced that enable one to add time-dependence to any given spatial statistics, as captured, e.g., by small-angle scattering. In a first approach, the Gaussian field is decomposed into localized waves that are allowed to fluctuate in time or to move either ballistically or diffusively. In a second approach, a dispersion relation is used to make the spectral components of the field time-dependent. The various models lead to qualitatively different dynamics, which can be discriminated by neutron scattering. The methods of this paper are illustrated with oil/water microemulsion studied by small-angle scattering and neutron spin-echo. All available data-in both film and bulk contrasts, over the entire range of q and τ-are analyzed jointly with a single model. The analysis points to the static large-scale structure of the oil and water domains while the interfaces are subject to thermal fluctuations. The fluctuations have an amplitude of around 60 Å and contribute to 30% of the total interface area.

Stochastic models of dense or hollow nanoparticles and their scattering properties

A family of stochastic models of disordered particles is proposed, obtained by clipping a Gaussian random field with a function that is space dependent. Depending on the shape of the clipping function, dense or hollow particles can be modelled. General expressions are derived for the form factor of the particles, for their average volume and surface area, and for their density and surface-area distributions against the distance to the particle centre. A general approximation for the form factor is also introduced, based on the density and surface-area distributions, which coincides with the Guinier and Porod expressions in the limits of low and high scattering vector magnitude q. The models are illustrated with the fitting of small-angle X-ray scattering (SAXS) data measured on Pt/Ni hollow nanoparticles. The SAXS analysis and modelling notably capture the collapse of the particles' porosity after being used as oxygen-reduction catalysts.

Capillary bridge formation between hexagonally ordered carbon nanorods

Capillary condensation within the pore space formed by a hexagonal arrangement of carbon nanorods is investigated using a thermodynamic model. Numerical solution of the corresponding non-linear differential equations predicts two characteristic equilibrium phase transitions corresponding to liquid-bridge formation between adjacent rods, and the subsequent filling of the entire pore space with liquid adsorbate at higher relative pressure, respectively. These separate transitions are predicted for a wide range of porosities, as demonstrated for two non-polar fluids, nitrogen and n-pentane, employing experimentally determined reference isotherms to model the fluid–solid interactions. The theoretical predictions are compared to experimental data for nitrogen and n-pentane adsorption in an ordered mesoporous CMK-3 type material, with the necessary structural parameters obtained from small-angle X-ray scattering. Although the experimental adsorption isotherms do not unambiguously show two separate transitions due to a high degree of structural disorder of the mesopore space, their general trends are consistent with the theoretical predictions for both adsorbates.

Gelatin content governs hydration induced structural changes in silica-gelatin hybrid aerogels - Implications in drug delivery

Silica-gelatin hybrid aerogels of varying gelatin content (from 4 wt.% to 24 wt.%) can be conveniently impregnated with hydrophobic active agents (e.g. ibuprofen, ketoprofen) in supercritical CO₂ and used as drug delivery systems. Contrast variation neutron scattering (SANS) experiments show the molecular level hybridization of the silica and the gelatin components of the aerogel carriers. The active agents are amorphous, and homogeneously dispersed in these porous, hybrid matrices. Importantly, both fast and retarded drug release can be achieved with silica-gelatin hybrid aerogels, and the kinetics of drug release is governed by the gelatin content of the carrier. In this paper, for the first time, a molecular level explanation is given for the strong correlation between the composition and the functionality of a family of aerogel based drug delivery systems. Characterization of the wet aerogels by SANS and by NMR diffusiometry, cryoporometry and relaxometry revealed that the different hydration mechanisms of the aerogels are responsible for the broad spectrum of release kinetics. Low-gelatin (4-11 wt.%) aerogels retain their open-porous structure in water, thus rapid matrix erosion dictates fast drug release from these carriers. In contrast to this, wet aerogels of high gelatin content (18-24 wt.%) show well pronounced hydrogel-like characteristics, and a wide gradual transition zone forms in the solid-liquid interface. The extensive swelling of the high-gelatin hybrid backbone results in the collapse of the open porous structure, that limits mass transport towards the release medium, resulting in slower, diffusion controlled drug release. STATEMENT OF SIGNIFICANCE: Developing new drug delivery systems is a key aspect of pharmaceutical research. Supercritically dried mesoporous aerogels are ideal carriers for small molecular weight drugs due to their open porous structures and large specific surface areas. Hybrid silica-gelatin aerogels can display both fast and retarded drug release properties based on the gelatin contents of their backbones. The structural characterization of the aerogels by SANS and by NMR diffusiometry, cryoporometry and relaxometry revealed that the different hydration mechanisms of the hybrid backbones are responsible for the broad spectrum of release kinetics. The molecular level understanding of the functionality of these hybrid inorganic-biopolymer drug delivery systems facilitates the realization of quality-by-design in this research field.

Small-angle scattering by supported nanoparticles: exact results and useful approximations

In functional materials, nanoparticles are often dispersed in a porous support for the purpose of stabilizing them. This makes their characterization by small-angle scattering challenging because the signal comprises contributions from the nanoparticles of interest, from the inert support and from their cross-correlation. Exact analytical expressions for all three contributions are derived in the case of a Gaussian-field model of the porous support, with nanoparticles randomly distributed over the surface. For low nanoparticle loading, the expressions simplify to the addition of properly scaled support and particle scattering. For higher loadings, however, the cross-correlation cannot be ignored. Two approximations are introduced, which capture correlation effects in cases where the pores of the support are much larger or only slightly larger than the nanoparticles. The methods of the paper are illustrated with the small-angle X-ray scattering analysis of hollow metallic nanoparticles supported on porous carbon.