A Model-free Method for Profiling Size Dispersity in Soft Condensed Matter Using Small-angle Scattering

Guan-Rong Huang^1*, Chi-Huan Tung², Lionel Porcar³, Yangyang Wang⁴, Yuya Shinohara⁵, Changwoo Do⁶, Wei-Ren Chen⁶

¹Materials and Optoelectronic Science, National Sun Yat-sen University, Kaoshiung, Taiwan
²Chemical Engineering, National Tsing Hua University, Hsinchu, Taiwan
³D22, Institut Laue-Langevin, Grenoble, France
⁴Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Tennessee, USA
⁵Materials Science and Technology Division, Oak Ridge National Laboratory, Tennessee, USA
⁶Neutron Scattering Division, Oak Ridge National Laboratory, Tennessee, USA

* Presenter:Guan-Rong Huang, email:huangrn@mail.nsysu.edu.tw

In this work, we propose a model-free approach for determining the size polydispersity of soft condensed matter through small-angle scattering. We outline a strategy that utilizes the method of central moment expansion to extract the mean and fluctuation of particle size and skewness of the size distribution function (SDF) from spectral analysis in a bias-free manner. With the polydispersity being moderate, we can reconstruct the SDF using the maximum entropy principle. We demonstrate the validity of our analytical approach by numerically benchmarking a model study over a wide range of size non-uniformity. Our results show that this method is effective for quantifying the size distribution of general soft matter systems.

Keywords: Size Distribution Function, Small-angle Scattering, Central Moment Expansion