Relations between structural parameters and adsorption characterization of templated nanoporous materials with cubic symmetry

A systematic approach is proposed to structural characterization of templated nanoporous materials with cubic symmetry by gas adsorption. We hypothesize that regular structures of these materials can be described in terms of triply periodic minimal surfaces (TPMS), similarly to bicontinuous mesophases observed in oil-water, lipid, block copolymer, and other amphiphilic systems. We relate topological characteristics of TPMS to the pore structure parameters evaluated from adsorption measurements, such as the specific surface area, pore volume, mean pore size, and also pore wall thickness. The relations obtained can be used for discrimination of possible TPMS morphologies. The method developed is used for characterization of newly synthesized MCM-48 mesoporous materials by low-temperature nitrogen adsorption. We show that adsorption data fully support the minimal gyroid model of MCM-48 structure (Ia3d space group) established earlier by the X-ray diffraction (XRD) and transmission electron microscopy studies. The mean pore size of MCM-48 can be accurately described by the hydraulic diameter calculated from the capillary condensation region of nitrogen adsorption isotherms by the nonlocal density functional theory method. Moreover, the adsorption method allows one to estimate the pore wall thickness, which cannot be done by XRD. For a series of high-quality MCM-48 materials reported recently in the literature, the calculated mean wall thickness varied from 0.8 to 1.2 nm. The adsorption method developed is recommended as a complement to X-ray diffraction and electron microscopy techniques for characterization of nanoporous materials.