Static light scattering of triaxial nanoparticle suspensions in the Rayleigh-Gans-Debye regime: application to cellulose nanocrystals

A simple method has been developed to measure the dimensions of triaxial nanoparticles through light scattering data. The application of Debye's expansion of the form factor has been extended beyond the second moment of the difference of distances (radius of gyration). Analytical expressions have been derived for the fourth and sixth moments that are valid for all nanoparticle shapes. The moments provide information about the aspect ratio of the nanoparticles regardless of the geometry. If a shape is assumed, simple algebraic expressions for the moments can be obtained for monodisperse and polydisperse samples, which can be used to solve for specific nanoparticle dimensions. The methods described here have been applied to static light scattering measurements of dilute aqueous suspension of triaxial cellulose nanocrystals isolated from cotton. When the polydispersity is included, the dimensions determined from light scattering data (6.4 x 28 x 152 nm) are in close agreement with atomic force microscopy measurements. This methodology can be easily applied to nanoparticles of complex shapes and extended to other scattering techniques; it would be especially useful for polymer based nanoparticles and biological macromolecules.