Sorption Isotherm Reconstruction and Extraction of Pore Size Distributions for Serially Connected Pore Model (SCPM) Structures Employing Algorithmic and Statistical Models

Abstract

Valiullin et al. [J. Phys. Chem. C 2019, 123, 16239] have developed a statistical theory describing adsorption/desorption hysteresis in one-dimensional pore structures with structural disorder. The theory captures the behavior of such systems based on simple rules for the phase transformations in individual pores together with assumptions about the role of pore connectivity. To test this theory, we have developed an algorithmic method for exact construction of sorption isotherms for chains of pores from single pore isotherms. We show that the predictions of the statistical theory are indeed very accurate. We have used the statistical theory to extract the pore size distribution (PSD) and chain lengths using both adsorption and desorption branches of the isotherm obtained by the algorithmic model on various pore structures. The predicted PSD’s and chain lengths are in excellent agreement with the actual properties of the original structures. We conclude that the statistical theory offers a new direction toward a more accurate characterization methodology of nanoporous materials.

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

“…In this way, the integral transition equations describing both boundary and scanning transitions can be obtained analytically and any state within the hysteresis region becomes fully determined. The validity of the solutions obtained has been proven in several computational studies. , …”

“…The validity of the solutions obtained has been proven in several computational studies. 72,91 By comparing the theoretical results with selected experimental observations, we prove that, regardless of its onedimensional topology, the model provides deeper insight into the collective processes occurring in the pore networks. In particular, we (i) explain why the shapes of the boundary transitions change with decreasing geometric disorder from type H2(a) to H2(b) and further to H1; (ii) quantitatively reproduce the scanning behavior for different disorder strengths and identify the governing mechanisms determining their shapes; (iii) highlight the importance of the macroscopic size of the materials impacting the transition behavior; (iv) identify weak disorder as a source of H1-type hysteresis in the CPG-like materials rendering the transitions being governed by (nearly) infinite avalanches; 41 (v) argue that the interconnectivity of the pore space most significantly affects the boundary desorption and freezing transitions; and (vi) show that the presence of several defects in the pore structure may change the transition mechanism.…”

“…In this regard, eq can be considered to be a generalized version of eq for the collections of interconnected pore chains. The accuracy of the equations derived was proven with the help of the algorithmic simulations and numerical solutions of the mean field theory …”

“…The accuracy of the equations derived was proven with the help of the algorithmic simulations and numerical solutions of the mean field theory. 91 One of the important distinctions of the SKV theory as compared to IPM is the fact that it provides the most natural basis for unraveling the scanning behavior. Notably, even though the most complete spectrum of information is encoded in the scanning curves, their poor understanding and lack of tractable theoretical models have left this rich information source unused.…”

Characterization of Hierarchically Ordered Porous Materials by Physisorption and Mercury Porosimetry—A Tutorial Review

“…A recently developed statistical theory describes hysteresis and hysteresis scanning curves in 1D pore structures with structural disorder. [ 114,115 ] A quantitative description of scanning curves has been suggested by percolation models and methods based on molecular simulation (e.g., [ 110,111 ] and references therein).…”