Application of the Alinaghipour–Falamaki Theory to Mesoporous Materials: Algorithm and Computational Code

The Brunauer-Emmett-Teller (BET) technique, despite its widespread use, often yields overestimated specific surface area (SSA) values because it neglects surface curvature. The recently developed Alinaghipour-Falamaki (AF) theory [Alinaghipour and Falamaki, <i>PCCP</i> <b>2023</b>, 25, 8424-8438] introduces curvature correction and achieves realistic SSA predictions for monosized dense particles and mesoporous materials with narrow pore size distributions. However, its applicability to materials with distributed or complex pore structures remained limited. In this work, we extend the AF theory by integrating it with a modified Barrett-Joyner-Halenda model and propose a new approach for directly determining the surface energy parameter from the desorption isotherm. The resulting algorithm, implemented in an open-source code named <b>HAF-BET</b>, enables accurate SSA and surface energy parameter calculations for mesoporous materials with arbitrary pore size distributions and geometries. When applied to reference materials with known geometrical surface areas, the HAF-BET algorithm achieved average errors of 13% for cylindrical and 22% for spherical pores, significantly outperforming the conventional BET and Shimizu-Matubayasi methods (errors exceeding 45%) [Shimizu and Matubayasi, <i>Langmuir</i> <b>2022</b>, 38, 7989-8002]. Across 51 additional mesoporous samples, HAF-BET consistently produced SSA and surface energy values that were 34 and 56% lower, respectively, than those predicted by the BET method, confirming its reliability. Developed primarily for cylindrical mesopores, the algorithm also proves effective for other curved mesoporous materials, producing SSA values approximately 28% lower than those obtained by the BET method and thus serving as a reliable, curvature-aware alternative for surface area estimation of all mesoporous materials with curved surfaces.