Small-angle scattering analysis of empty or loaded hierarchical porous materials

Small-angle scattering (SAXS or SANS) is one of the few experimental methods available for the nanometer-scale study of physicochemical phenomena inside porous solids. Its potential, however, is often limited by the lack data analysis methods to convert scattering data into real-space structural information. This is notably the case for most porous materials of practical interest, which exhibit a hierarchical structure with micro, meso, and macropores, with often a secondary material confined in the pores, such as in supported catalysts, as well as fuel-cell and battery materials. Here, we discuss a general SAXS data analysis methodology for this type of material. Assuming that each structural level is statistically independent from the others and has a distinct characteristic length scale, compact mathematical expressions are derived for the scattering of the entire hierarchical structure [J.Phys.Chem.C, in press]. The method is illustrated with the SAXS analysis of SBA-15 micro- and meso-porous silica loaded with copper nitrate, as well as to supported catalysts obtained after calcining that material. The SAXS analysis shows that the nitrate permeates both the micro and mesopores, while the metallic copper obtained after calcination is found only in the mesopores. Moreover, the spatial distribution of the metal depends on the specifics of the calcination, as confirmed by electron tomography [Angew.Chem. 54 (2015) 11804]. The general methodology will be of interest to anyone interested in the quantitative analysis of small-angle scattering data from empty or loaded porous solids, and from any type of hierarchical material