Development\nand Application of an Advanced Percolation\nModel for Pore Network Characterization by Physical Adsorption

Physical adsorption is one of the\nmost widely used techniques\nto\ncharacterize porous materials because it is reliable and able to assess\nmicro- and mesopores within one approach. Challenges and open questions\npersist in characterizing disordered and hierarchically structured\nporous materials. This study introduces a pore network model aimed\nat enhancing the textural characterization of nanoporous materials.\nThe model, based on percolation theory on a finite-sized Bethe lattice,\nincludes all mechanisms known to contribute to adsorption hysteresis\nin mesoporous pore networks. The model accounts for delayed and initiated\ncondensation during adsorption as well as equilibrium evaporation,\npore blocking, and cavitation during desorption. Coupled with dedicated\nnonlocal-density functional theory kernels, the proposed method provides\na unified framework for modeling the entire experimental adsorption–desorption\nisotherm, including desorption hysteresis scans. The applicability\nof the method is demonstrated on a selected set of nanoporous silica\nmaterials exhibiting distinct types of hysteresis loops (types H1,\nH2a, H1/H2a, and H5), including ordered mesoporous silica networks\n(KIT-6 and SBA-15/MCM-41 hybrid silica with plugged pores) and disordered\nmesoporous silica networks (hierarchical meso-macroporous monolith\nand porous Vycor glass). For all materials, a good correlation is\nfound between calculated and experimental primary isotherms as well\nas desorption scans. The model allows us to determine key pore network\ncharacteristics such as pore connectivity and pore size distributions\nas well as a parameter correlated with the impact of pore network\ndisorder on the adsorption behavior. The versatility and enriched\ntextural insights provided by the proposed novel network model allow\nfor a comprehensive characterization previously inaccessible and hence\nwill contribute to further advancement in the textural characterization\nof novel nanoporous materials. It has the potential to provide important\nguidance for the design and selection of porous materials for optimizing\nvarious applications, including separation processes such as chromatography,\nheterogeneous catalysis and gas and energy storage.