Cellulosic nanowhiskers. Theory and application of light scattering from polydisperse spheroids in the Rayleigh-Gans-Debye regime

Mathematical treatment of light scattering within the Rayleigh-Gans-Debye limit for spheroids with polydispersity in both length and diameter is developed and experimentally tested using cellulosic nanowhiskers (CNW). Polydispersity indices are obtained by fitting the theoretical formfactor to experimental data. Good agreement is achieved using a polydispersity of 2.3 for the length, independent of the type of acid used. Diameter polydispersities are 2.1 and 3.0 for sulfuric and hydrochloric acids, respectively. These polydispersities allow the determination of average dimensions from the z-average mean-square radius (< S-2 >(z)) and the weight-average molecular weight (M.) easily obtained from Berry plots. For cotton linter hydrolyzed by hydrochloric acid, the average length and diameter are 244 and 22 nm. This compares to average length and diameter of 272 and 13 nm for sulfuric acid. This study establishes a new light-scattering methodology as a quick and robust tool for size characterization of polydisperse spheroidal nanoparticles.