Rigid Sphere Molecular Model Enables an Assessment of the Pore Curvature Effect upon Realistic Evaluations of Surface Areas of Mesoporous and Microporous Materials

A gas adsorption rigid spheres model (RSM) was incorporated into the CPSM model (corrugated pore structure model) to correlate the pore surface areas obtained from the BET and CPSM methods. The latter is a method simulating the gas sorption hysteresis loop and enables the evaluation of surface areas S CPSM through the integration of the pertinent pore size distributions. Thus, S CPSM values are inherently influenced by pore curvature. The new CPSM−RSM version estimates surface areas S CPSMfs that are independent of pore curvature and can be compared with the pertinent S BET values. The RSM exploits the fact that a curved pore surface accommodates fewer molecules, assumed to behave as rigid spheres, than an equal flat one. Thus, the RSM accounts for a higher molecular surface coverage A c (nm2/molec.) in pores with marked curvature than that (i.e., A f) on a flat surface. The ratio A c/A f for nitrogen adsorbed on single pore sizes varies in the range A c/A f = 1.44−1.03 for pore sizes D = 1.5−15 nm, respectively. Also for D = 1.5−5.0 nm the S CPSMfs and S BET values are lower by ∼10−45% than the S CPSM estimates. From the application of the CPSM−RSM model on several porous materials exhibiting all known types of sorption hysteresis loops, it was confirmed that S BET ≈ S CPSMfs (±5%) and (S CPSM − S BET)/S BET = 3−68% for the materials examined. In conclusion, the BET method may produce quite conservative surface area estimates for materials exhibiting pore structures with appreciable pore curvature, whereas the CPSM−RSM model can reliably predict both S CPSM and S CPSMfs = S BET values.