An exact inversion method for extracting orientation ordering by small- angle scattering

GR Huang and JM Carrillo and YY Wang and C Do and L Porcar and B Sumpter and WR Chen, PHYSICAL CHEMISTRY CHEMICAL PHYSICS, 23, 4120-4132 (2021).

DOI: 10.1039/d0cp05886f

We outline a nonparametric inversion strategy for determining the orientation distribution function (ODF) of sheared interacting rods using small-angle scattering techniques. With the presence of direct inter-rod interaction and fluid mechanical forces, the scattering spectra are no longer characterized by the azimuthal symmetry in the coordinates defined by the principal directions of simple shear conditions, which severely compounds the reconstruction of ODFs based on currently available methods developed for dilute systems. Using a real spherical harmonic expansion scheme, the real-space ODFs are uniquely determined from the anisotropic scattering spectra and their numerical accuracy is verified computationally. Our method can be generalized to extract ODFs of uniaxially anisotropic objects under different flow conditions in a properly transformed reference frame with suitable basis vectors.

Return to Publications page