Pore-blocking and pore-assisting factors during capillary condensation and evaporation

Domain theory for capillary condensation hysteresis

“…For instance, Bock et al have shown that such a chemical heterogeneity leads to a very complex phase diagram of the confined fluid, even though the pore size is constant. 57,58 Following the previous work by Cordero et al, 59 the adsorbed volume for model B was calculated as follows. Upon adsorption, a porous domain k is filled if one of the following conditions is fulfilled: ͑a͒ if its two neighbors k + 1 and k − 1 are empty, then k of smaller diameter will be filled at a pressure given by the modified Kelvin equation with a cylindrical meniscus; and ͑b͒ if k +1 or k − 1 is filled, then k will be filled when the hemispherical meniscus at the opening between k + 1 and k or k − 1 and k can propagate into the empty cavity k. The latter condition, called advanced condensation 48 or pore assisting factor, 59 occurs when x reaches the pressure given by the modified Kelvin equation with a hemispherical meniscus.…”

“…7 in the case of connected porous materials where each cavity is isolated from the rest of the porosity by several constrictions 5,61 ͑see also Ref. 59 for a complete study of the effect of the number of connections on the scanning curves͒. Each adsorption ͑de-sorption͒ scanning curve first exhibits a nearly flat portion AB until it increases ͑decreases͒ sharply toward the closure point of the hysteresis loop.…”

Phase transitions in disordered mesoporous solids

“…Ink-bottle pore systems of different complexity, representing the elementary units of statistically disordered materials, were investigated using different computer simulation approaches 6 , 31 , 32 . Long linear chains 33 and networks 34 – 36 of pores with different pore sizes were also addressed in numerical simulations and some important insights into, e.g., behavior of the scanning curves were obtained. Theoretical models of capillary phenomena were mostly concerned with the percolation theories in which the connectivity effects were modeled with the help of the loopless Bethe lattices 14 , 37 , 38 .…”

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

“…At the same time, it is commonly accepted that there are physical mechanisms giving rise to interference between the phase states in adjacent pores with different pore sizes (Cordero et al, 2002; Ravikovitch and Neimark, 2002; Morishige and Tateishi, 2003; Libby and Monson, 2004; Rigby and Fletcher, 2004; Morishige et al, 2006; Casanova et al, 2007; Khokhlov et al, 2007; Rasmussen et al, 2010; Reichenbach et al, 2011; Nguyen et al, 2013b; Kondrashova and Valiullin, 2015; Mitropoulos et al, 2015; Rigby et al, 2017). One of them is pore blocking, namely metastability arising from the fact that the invasion of the gas or ice phase is delayed until it can pass a bottleneck on its way.…”

“…Using 3-D electron tomography, such defects were directly visualized in a material with similar pore morphology, SBA-15 (Gommes, 2012). By using numerical analysis of computer generated 3-D disordered network models in combination with advanced sorption and pore blocking, it was shown that, accounting for geometric disorder, leads to qualitatively correct shapes of the sorption isotherms and, most importantly, of the scanning curves (Liu et al, 1993; Cordero et al, 2002; Esparza et al, 2004). Later, by considering truly SCPM, namely computer generated chains of disordered tubular pores, and by modeling either only pore blocking (Coasne et al, 2005) or both pore blocking and advanced sorption (Morishige, 2017), it was shown that already this simplistic model is capable of reproducing all important features of the three-dimensional models.…”