Development and application of a novel model based on percolation theory for advanced pore network characterization by physical adsorption

Physical adsorption is one of the most widely used techniques to characterize porous materials because of being reliable and able to assess micro- and mesopores within one approach. However, challenges persist in characterizing disordered and hierarchically structured porous materials. This study introduces a pore network model aiming to enhance the textural characterization of nanoporous materials. Our model, based on percolation theory on a Bethe lattice, includes all mechanisms known to contribute to adsorption hysteresis in mesoporous pore networks during capillary condensation and evaporation. The model accounts for delayed and initiated condensation during adsorption as well as equilibrium evaporation, pore blocking and cavitation during desorption. Coupled with dedicated non-local-density functional (NLDFT) kernels, the proposed method provides a unified framework for modeling the entire experimental adsorption-desorption isotherm, including desorption hysteresis scans. Hence, our model unveils key pore network characteristics like the effective connectivity, but also has the potential to determine pore size distributions of mesoporous materials by taking quantitatively pore network effects into account. The applicability of the method is demonstrated on a selected set of nanoporous silica materials exhibiting distinct types of hysteresis loops (types H1, H2a, H1/H2a and H5) including ordered mesoporous silica networks, i.e, KIT-6 silica, hybrid SBA-15/MCM-41 silica with plugged pores, but also two disordered silica pore networks, i.e., a hierarchical meso-macroporous monolith and porous Vycor glass. For all materials, good correlation is found between simulated and experimental primary adsorption and desorption isotherms as well as desorption scans allowing for a determination of key pore network characteristics such as pore connectivity and pore size distributions.The versatility and enriched textural insights provided by the proposed novel network model allows for a comprehensive characterization previously inaccessible, and hence will contribute to a further advancement in the textural characterization of novel nanoporous materials for optimizing important applications such as catalysis, separation processes, gas-and energy storage.