Model-Free Approach for Profiling of Polydisperse Soft Matter Using Small Angle Scattering

A strategy for determining the size polydispersity ofsystems fromtheir small angle coherent scattering is outlined. Using the methodof moment expansion, we show that the various central moments representingthe average particle size, variance of particle size, and skewnessof size distribution function (SDF) for polydisperse systems can beextracted from spectral analysis without bias. When the degree ofpolydispersity is moderate, SDF can be further reconstructed basedon the maximum entropy principle. Numerical benchmarking of a modelstudy over a wide range of size nonuniformity demonstrates the validityof this analytical approach for quantifying the size distributionof general soft matter systems in a model-free manner. Furthermore,the efficacy of this method was validated by successfully applyingit to the fitting of small-angle neutron scattering data obtainedfrom L64 Pluronic micelles using various form factor models. The numericaland experimental verification underscores the reliability and versatilityof this method in accurately characterizing the size distributionof complex soft matter systems.