Expression of the anisotropy factor of fractal aggregates to enable their characterization using photon density wave spectroscopy

This work aims at expanding the applicability of photon density wave spectroscopy (PDWS) to in-situ characterization of dispersed aggregates of spherical primary particles. For this purpose, an approximate optical model within the Rayleigh-Debye-Gans-theory was developed that links the experimentally determined reduced scattering coefficients μs′ with the fractal dimension D and the radius of gyration aG,Agg of the dispersed aggregates. The model includes an analytical expression for the anisotropy factor gAgg of fractal aggregates that has not been suggested before to our best knowledge. PDWS measurements of suspensions of aggregated amorphous silica and titania nanoparticles were performed and the obtained D and aG,Agg were used to calculate the hydrodynamic radii of the investigated aggregates. The latter were referenced by dynamic light scattering experiments. In contrast to the other reference techniques, PDWS and gravimetric analyses were performed without dilution of the investigated samples. The samples differed in solvent, primary particle size, aggregate size, and aggregate density.