Application of Consistency Criteria To Calculate BET Areas of Micro- And Mesoporous Metal–Organic Frameworks

Abstract

Metal–organic frameworks (MOFs) can exhibit exceptionally high surface areas, which are experimentally estimated by applying the BET theory to measured nitrogen isotherms. The Brunauer, Emmett, and Teller (BET)-estimated nitrogen monolayer loading is thus converted to a “BET area,” but the meaning of MOF BET areas remains under debate. Recent emphasis has been placed on the usage of four so-called “BET consistency criteria.” Using these criteria and simulated nitrogen isotherms for perfect crystals, we calculated BET areas for graphene and 25 MOFs having different pore-size distributions. BET areas were compared with their corresponding geometrically calculated, nitrogen-accessible surface areas (NASAs). Analysis of simulation snapshots elucidated the contributions of “pore-filling” and “monolayer-formation” to the nitrogen adsorption loadings in different MOF pores, revealing the origin of inaccuracies in BET-calculated monolayer loadings, which largely explain discrepancies between BET areas and NASAs. We also find that even if all consistency criteria are satisfied, the BET calculation can significantly overestimate the true monolayer loading, especially in MOFs combining mesopores (d ≥ 20 ?) and large micropores (d = 10–20 ?), due to the overlap of pore-filling and monolayer-formation regimes of these two kinds of pores. While it is not always possible to satisfy all consistency criteria, it is critical to minimize the deviation from these criteria during BET range selection to consistently compare BET areas of different MOFs and for comparing simulated and experimental BET areas of a given MOF. To accurately assess the quality of a MOF sample, it is best to compare experimental BET areas with simulated BET areas rather than with calculated NASAs.