Gas Sorption Characterization of Porous Materials Employing a Statistical Theory for Bethe Lattices.

In the present work, a recently developed statistical theory for adsorption and desorption processes in mesoporous solids, modeled by random Bethe lattices, has been applied to obtain pore size distributions and interpore connectivity from sorption isotherms in real random porous materials, employing a robust and validated methodology. Using the experimental adsorption-desorption N2 isotherms at 77.4 K on Vycor glass, a porous material with random pore structure, we demonstrate the solution of the inverse problem resulting in extracted pore size distribution and interpore connectivity, notably different from the predictions of earlier theories. The results presented are corroborated by the analysis of 3D digital images of reconstructed Vycor porous glass, showing excellent agreement between the predictions of geometric analysis and the new statistical theory.

Free energy landscape within the hysteresis regime for fluids confined in disordered mesoporous solids.

Adsorption/desorption and melting/freezing in structurally disordered nanoporous solids exhibit strongly non-equilibrium behavior as revealed by the formation of a hysteresis region populated by the multitude of different states. Many questions concerning the free energy spectrum of these states, including the existence of the equilibrium transition, if any, their accessibility in the experiments, and internal relaxation dynamics toward the global energy minimum, still remain poorly addressed. By using a serially connected pore model with the statistical disorder as a minimal model of the pore networks, we explore the system free energies along the solid-liquid and liquid-gas transitions in the pore systems. The rigorous results obtained with this model shed light on the occurrence and nature of the equilibrium transition line in porous solids with arbitrary pore topology. We discuss further the free energies along the experimentally measured boundary and scanning transitions and how close the equilibrium states can be approached in these experiments.

Connecting dynamic pore filling mechanisms with equilibrium and out of equilibrium configurations of fluids in nanopores.

In the present study, using dynamic mean field theory complemented by grand canonical molecular dynamics simulations, we investigate the extent to which the density distributions encountered during the dynamics of capillary condensation are related to those distributions at equilibrium or metastable equilibrium in a system at fixed average density (canonical ensemble). We find that the states encountered can be categorized as out of equilibrium or quasi-equilibrium based on the magnitude of the driving force for mass transfer. More specifically, in open-ended slit pores, pore filling via double bridging is an out of equilibrium process, induced by the dynamics of the system, while pore filling by single bridge formation is connected to a series of configurations that are equilibrium configurations in the canonical ensemble and that cannot be observed experimentally by a standard adsorption process, corresponding to the grand canonical ensemble. Likewise, in closed cap slits, the formation of a liquid bridge near the pore opening and its subsequent growth while the initially detached meniscus from the capped end remains immobilized are out of equilibrium processes that occur at large driving forces. On the other hand, at small driving forces, there is a continuous acceleration of the detached meniscus from the capped end, which is associated with complete reversibility in the limit of an infinitesimally small driving force.

Diffusion and Molecular Exchange in Hollow Core-Shell Silica Nanoparticles.

The diffusion behavior of small molecules in hollow core-shell nanocapsules was studied using pulsed field gradient NMR. By purposefully selecting the liquid saturating the hollow core and the porous shell and the solvent between the nanocapsules, two different situations corresponding to the excluded and admitted molecular exchange between the intra- and intercapsule liquids at the external boundary of the nanoparticles were covered. In the former case, corresponding to the reflective boundary condition for the molecules approaching the nanocapsule boundary, restricted diffusion in the complex pore space formed by the hollow core and the mesoporous shell was observed. The time-dependent diffusivities measured in the experiment were inter-related with the geometry of the intraparticle pore space. The thus assessed structural information was found to be in a good agreement with that provided by electron microscopy. In the case of the molecular exchange occurring between the two pools of molecules in the nanocapsules and between them, the diffusive dynamics of only the molecules remaining in the nanocapsules during the entire observation times was studied.

Diffusion in hierarchical mesoporous materials: applicability and generalization of the fast-exchange diffusion model.

Transport properties of cyclohexane confined to a silica material with an ordered, bimodal pore structure have been studied by means of pulsed field gradient nuclear magnetic resonance. A particular organization of the well-defined pore structure, composed of a collection of spatially ordered, spherical mesopores interconnected via narrow worm-like pores, allowed for a quantitative analysis of the diffusion process in a medium with spatially ordered distribution of the fluid density for a broad range of the gas-liquid equilibria. The measured diffusion data were interpreted in terms of effective diffusivities, which were determined within a microscopic model considering long-range molecular trajectories constructed by assembling the alternating pieces of displacement in the two constituting pore spaces. It has further been found that for the system under study, in particular, and for mesoporous materials with multiple porosities, in general, this generalized model simplifies to the conventional fast-exchange model used in the literature. Thus, not only was justification of the applicability of the fast-exchange model to a diversity of mesoporous materials provided, but the diffusion parameters entering the fast-exchange model were also exactly defined. The equation resulting in this way was found to nicely reproduce the experimentally determined diffusivities, establishing a methodology for targeted fine-tuning of transport properties of fluids in hierarchical materials with multiple porosities.

Probing pore connectivity in random porous materials by scanning freezing and melting experiments.

Freezing and melting behavior of nitrobenzene confined to pores of Vycor porous glass with random pore structure has been studied by means of nuclear magnetic resonance cryoporometry. The two transitions are found to reveal a broad hysteresis. To get deeper insight into the mechanisms leading to this phenomenon, scanning experiments exploiting temperature reversal upon incomplete freezing or melting have been performed. In this way, it was found that different cooling and warming histories result in different solid-liquid configurations within the pore system. Further evolution of the thus-attained configurations with changing temperature unveiled important information about the transition paths. In particular, these experiments indicated the occurrence of a pronounced pore blocking for freezing, resulting in freezing transitions via invasion percolation. The melting, on the other hand, is found to occur homogeneously over the whole pore network.

The role of mesopores in intracrystalline transport in USY zeolite: PFG NMR diffusion study on various length scales.

PFG NMR has been applied to study intracrystalline diffusion in USY zeolite as well as in the parent ammonium-ion exchanged zeolite Y used to produce the USY by zeolite steaming. The diffusion studies have been performed for a broad range of molecular displacements and with two different types of probe molecules (n-octane and 1,3,5-triisopropylbenzene) having critical molecular diameters smaller and larger than the openings of the zeolite micropores. Our experimental data unambiguously show that, in contrast to what is usually assumed in the literature, the intracrystalline mesopores do not significantly affect intracrystalline diffusion in USY. This result indicates that the intracrystalline mesopores of USY zeolite do not form a connected network, which would allow diffusion through crystals only via mesopores.

NMR magnetization transfer as a tool for characterization of nanoporous materials.

The application of nuclear magnetic resonance magnetization transfer experiments to probe the surface-to-volume ratio and pore morphology of porous materials with characteristic pore sizes of 1-100 nm is described. The method is based on the phenomenon of incomplete freezing of liquids in small pores where a few monolayers adjacent to the pore walls remain liquid. Sufficient difference between the transverse relaxation times in the solid frozen core and liquid surface layer allows the initial preparation and subsequent re-equilibration of a solid-liquid magnetization grating. The method is demonstrated using model nanoporous materials with known characteristics. The ensuing problems of the mechanism of the magnetization transfer through the interface and within the frozen core are discussed and elucidated by pulsed-field-gradient NMR experiments.

Self-diffusion of water and oil in peanuts investigated by PFG NMR.

Pulsed field gradient (PFG) nuclear magnetic resonance (NMR) has been used to study self-diffusion characteristics of water and oil in natural peanuts and in peanuts saturated with water. From the dependence on diffusion time of the echo decay due to diffusion, regions of completely restricted diffusion for the oil molecules were identified. The mean size and size distribution function of these regions were obtained. Combined analysis of diffusion data for peanuts with natural moisture content and for water saturated peanuts shows the cellular nature of these regions. The cell structure, consisting of a cell cavity surrounded by a double membrane was identified.