A Novel Approach To Calibrate Mesopore Size from Nitrogen Adsorption Using X-ray Diffraction: An SBA-15 Case Study

Abstract

The mesoporous silicate SBA-15 was prepared with a range of pore sizes by adjusting synthesis conditions, primarily tetraethyl orthosilicate to Pluronic P-123 ratios and calcination temperature. Materials were characterized by SAXS to determine unit cell dimension and diffraction intensities, and by nitrogen adsorption to obtain mesopore diameters using the BJH and DFT methods. We modeled the electron density distribution and then used this to calculate the structure factor and theoretical diffraction intensities. Model results show points where the structure factor equals zero for the 2-D hexagonal system, corresponding to peak extinctions in the SAXS diffraction patterns. We compare model results to experimental data to establish biases in the mesopore diameters determined from nitrogen adsorption. Conventional BJH mesopore determination from the adsorption branch is found to underestimate pore diameters by 15% or ∼0.9 nm, BJH analysis from the desorption branch underestimates pore diameter by 40% or 1.9 nm, and DFT analysis is found to marginally overestimate pore diameter by 10% or 0.7 nm. Our results provide estimates for the biases in pore diameters from BJH analysis larger than bias estimates obtained by other means; more significantly, these results also reveal that DFT analysis overestimates mesopore diameters by 10%.