Determining the Structural Characteristics of Deforming Objects from Their Scattering Signature

There has been much interest in understanding the structural characteristics of deforming materials on different length scales. In the context of scattering, the domain of interest can be splitted into a microscopic region within which the local configurational translation and rotation can be treated in detail, and a larger regime where the description of global shape is appropriate. From a perspective of geometric interpretation at the micro/macroscopic level, a central issue is how to quantitatively determine the structural characteristics from the anisotropic scattering intensity in a model-free manner.
We present a general approach to deal with this problem. In the mean-field limit, we first show that the radius of gyration is the source term of intra-particle structure factor. Using the real spherical harmonic expansion (RSHE), we derive the exact expression of gyration tensor in terms of the anisotropic spatial correlation functions. Meanwhile, we derive the orientational distribution functions to describe the local configurational alignment. Theoretical benchmarks verify that our approach not only facilitates quantitative scattering studies of flowing materials, but also provides insightful information regarding the deformation behavior of materials at the molecular level.