Reconstruction of Three-Dimensional Anisotropic Structure from Small-Angle Scattering Experiments
Guan-Rong Huang1,2*, Yangyang Wang4, Bin Wu3, Zhe Wang3, Changwoo Do3, Gregory S. Smith3, Lionel Porcar5, Wei-Ren Chen2,3
1Physics Division, National Center for Theoretical Sciences, Hsinchu City, Taiwan
2Shull Wollan Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA
3Biology and Soft Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA
4Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA
5Institute of Laue-Langevin, Grenoble, France
* Presenter:Guan-Rong Huang,
When subjected to flow, the structures of many soft-matter systems become anisotropic due to the symmetry breaking of the spatial arrangements of constituent particles at the microscopic level. At present, it is common practice to use various small-angle scattering techniques to explore flow-induced microstructural distortion. However, there has not been a thorough discussion in the literature on how a three-dimensional anisotropic structure can be faithfully reconstructed from two-dimensional small-angle scattering spectra. In this work, we address this issue rigorously from a mathematical perspective by using real spherical harmonic expansion analysis. We first show that, except for cases in which mechanical perturbation is sufficiently small, the existing small-angle scattering techniques generally do not provide complete information on structural distortion. This limitation is caused by the linear dependence of certain real spherical harmonic basis vectors on the flow-vorticity and flow-velocity gradient planes in the Couette shear cell. To circumvent the constraint imposed by this geometry, an alternative approach is proposed in which a parallel sliding plate shear cell is used with a central rotary axis along the flow direction. From the calculation of rotation of the reference frame, we demonstrate the feasibility of this experimental implementation for a fully resolved three-dimensional anisotropic structure via a case study of sheared polymers.

Keywords: Small-angle Scattering/Diffraction, Anisotropic Structure