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

In this work, we introduce a model-free approach for determining the size polydispersity of soft condensed matter through small-angle scattering techniques. 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.