New insight into ordered cage-type mesostructures and their pore size determination by electron tomography

In this work, a new approach based on electron tomography (ET) has been developed to measure the pore size, through which new insight into cage-type ordered mesostructures and their pore size determination has been obtained. It is demonstrated that the accurate pore diameter, especially for cage-type cubic mesoporous materials, can be determined only through our ET approach by considering that the pore geometry is a real 3D space. We use the established ET method to revisit the applicability of different models for the pore size calculation in nitrogen adsorption analysis. Different from the overwhelming understanding that the nonlocal density functional theory (NLDFT) and Derjaguin-Broekhoff-de Boer (BdB) model are recommended to calculate the pore size of cage-type cubic mesoporous materials while the Barret-Joyner-Halenda (BJH) model should not be used, a new understanding is gained through this study. The choice of a suitable model for pore size determination depends on the precise pore structure. For a cage-type cubic mesoporous material with fcc symmetry and a large entrance connecting the cages, the BJH model is more accurate while the other two methods overestimate the pore size (by up to 40%). The DFT model is more appropriate when the pore shape is a perfect sphere than the BJH model, which underestimates the pore size, and the BdB model, which overestimates the pore size. It is our opinion that the unique ET approach should be used to revisit a vast number of large-pore cubic mesoporous materials to provide genuine structural information.