On the Comparative Analysis of Different Phase Coexistences in Mesoporous Materials

Abstract

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.

Development and application of an advanced percolation model for pore network characterization by physical adsorption

“…In the context of these serial models, a model was introduced, where during adsorption and desorption the condensation and desorption effects were modelled in a symmetric fashion, including initiation of condensation, pore blocking and cavitation 65,66 . This approach was extended towards mercury porosimetry and thermoporometry [67][68][69][70][71] and very recent work includes the extension of the theory to bethe lattices, comparing the details of the percolation behavior for linear and branched structures 72 .…”

Advanced NMR Cryoporometry

“…2) by taking account of different thermodynamic pre-factors. In this particular case, they found to exhibit identical transition behaviors [92]. This has far-reaching implications for NMR cryoporometry -the rich spectrum of information already obtained for gas-liquid equilibria can directly be applied to gain deeper insight into solidliquid equilibria of confined molecular ensembles.…”

“…Normalized nitrogen adsorption/desorption (red circles) and water melting/freezing (blue rectangles) in controlled pore class CPG with 12.8 nm pore size plotted on the unified coordinates. Reproduced from 92.…”

“…Indeed, this may happen on heating if the very first liquid bridge is nucleated at a temperature T, which is already higher than the pore equilibrium transition temperature for all remaining pores in the chain. On colling this can also be observed if the pore lengths are sufficiently short, so that thermodynamic fluctuations may facilitate freezing by overcoming the barriers in the free energy [92]. In this regard, as soon as the experimental data are analyzed, L shall be interpreted as the number of different alternating domains, which can be formed in the material under the given experimental conditions.…”

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

“…Hence, besides our present data, we have considered isotherm data by Huber and Tsou (1998), Thommes et al. (2006), Soós et al (2007), and Enninful et al (2022) . The extracted PSDs for each case, as well as the average PSD, are presented in Figure a.…”