Unbiased Quantitative Analysis of Scattering Length Density Profiles in Dilute Solutions via Small-Angle Scattering

We present an alternative method for quantitatively analyzing particle density profiles in dilute solutions using small-angle scattering. Our technique utilizes an orthonormal basis function expansion, allowing for the extraction of characteristic mass distributions in self-assembled structures without the need for a predefined structural model. Through computational benchmarking, we demonstrate its efficacy by accurately reconstructing the density profiles of soft ball systems with varying levels of fuzziness based on their scattering signatures. We further illustrate the method's versatility by fitting small-angle neutron scattering data from L64 Pluronic micelles at different temperatures. This straightforward and analytical approach enhances scattering analysis by eliminating reliance on presumptive structural models, paving the way for detailed quantitative descriptions of complex nanoscopic structures in various soft matter systems.