Comparative Gas Sorption and Cryoporometry Study of Mesoporous Glass Structure: Application of the Serially Connected Pore Model

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.

A New Statistical Theory for Constructing Sorption Isotherms in Mesoporous Structures Represented by Bethe Lattices

In the present work, a new statistical theory is developed to describe adsorption and desorption in mesoporous materials (pore sizes ranging from 2 to 50 nm) represented by pore networks in the form of Bethe lattices. The new theory is an extension of a previous theory applied for Statistically Disordered Chain Model (SDCM) structures and incorporates the cooperative effects emerging during phase transitions in pore networks. The theory is validated against simulations and algorithmic models that describe sorption of lattice and real fluids in Bethe lattices. It is seen that the pore network coordination number, or pore connectivity, z, has a significant impact on two important processes observed in pore networks: pore assisting condensation during adsorption and evaporation by percolation during desorption. The inclusion of pore connectivity in the earlier developed framework accounting for cooperativity effects is an important step, rendering the existing models to mimic fluid behavior in real materials more accurately. Hence, the new theory inherently contains all essential elements that may offer the extraction of more reliable pore size distributions utilizing both the adsorption and desorption branches of the isotherm.

On the Comparative Analysis of Different Phase Coexistences in Mesoporous Materials

Alterations of fluid phase transitions in porous materials are conventionally employed for the characterization of mesoporous solids. In the first approximation, this may be based on the application of the Kelvin equation for gas-liquid and the Gibbs-Thomson equation for solid-liquid phase equilibria for obtaining pore size distributions. Herein, we provide a comparative analysis of different phase coexistences measured in mesoporous silica solids with different pore sizes and morphology. Instead of comparing the resulting pore size distributions, we rather compare the transitions directly by using a common coordinate for varying the experiment's thermodynamic parameters based on the two equations mentioned. Both phase transitions in these coordinates produce comparable results for mesoporous solids of relatively large pore sizes. In contrast, marked differences are found for materials with smaller pore sizes. This illuminates the fact that, with reducing confinement sizes, thermodynamic fluctuations become increasingly important and different for different equilibria considered. In addition, we show that in the coordinate used for analysis, mercury intrusion matches perfectly with desorption and freezing transitions.

Impact of Geometrical Disorder on Phase Equilibria of Fluids and Solids Confined in Mesoporous Materials

Porous solids used in practical applications often possess structural disorder over broad length scales. This disorder strongly affects different properties of the substances confined in their pore spaces. Quantifying structural disorder and correlating it with the physical properties of confined matter is thus a necessary step toward the rational use of porous solids in practical applications and process optimization. The present work focuses on recent advances made in the understanding of correlations between the phase state and geometric disorder in nanoporous solids. We overview the recently developed statistical theory for phase transitions in a minimalistic model of disordered pore networks: linear chains of pores with statistical disorder. By correlating its predictions with various experimental observations, we show that this model gives notable insight into collective phenomena in phase-transition processes in disordered materials and is capable of explaining self-consistently the majority of the experimental results obtained for gas-liquid and solid-liquid equilibria in mesoporous solids. The potentials of the theory for improving the gas sorption and thermoporometry characterization of porous materials are discussed.

Synthesis of ordered microporous/macroporous MOF-808 through modulator-induced defect-formation, and surfactant self-assembly strategies

Ordered materials with interconnected porosity allow the diffusion of molecules within their inner porous structure to access the active sites located in the microporous core. As a follow-up of our work on engineering of MOF-808, in this contribution, we study the synthesis of defective MOF-808 using two different strategies: the use of modulators and the surfactant-assisted synthesis to obtain materials with ordered and interconnected pores. The results of the study indicated that (i) the use of modulators of different chain length led to the formation of microporous/mesoporous MOFs through the formation of missing linker defects. However, the use of the acetic acid contributes to the formation of MOFs with larger mesoporous size distributions compared to materials synthesized with formic and propionic acids as modulators, and (ii) the self-assembly of CTAB surfactant produced an ordered microporous/macroporous network which enhanced crystallinity. However, the surface properties of the materials seem to be unaffected by the use of surfactants during synthesis. These results contribute to the development of ordered materials with a broad range of pore size distributions and give rise to new opportunities to extend the applications of MOF-808.