Low- <i>Q</i> Asymptotic Behavior of the Effective Structure Factor Yields Model-Independent Radius of Interparticle Interaction ( <i>R</i> _<i>i</i> )

Guinier analysis has been extensively used in academic and industrial research settings to obtain the model-independent size of a polymer, protein, or colloid in solution from small-angle scattering data. Using the Guinier model, the radius of gyration (<i>R</i> _<i>g</i> ) is extracted from the form factor at low <i>Q</i>. Here, we develop an analogous approach for analyzing the effective structure factor data at low <i>Q</i> to extract a model-independent radius of interaction potential, <i>R</i> _<i>i</i> . Whereas <i>R</i> _<i>g</i> describes how spread out the scattering length density distribution of particles is from their center of mass, <i>R</i> _<i>i</i> is an effective root-mean-square distance that quantifies how far the interparticle correlation deviates from its ideal gas configuration due to interactions. We demonstrate this novel analysis method by applying it to experimental small-angle neutron scattering data on lysozyme protein solutions. We discuss its broad implications for analysis of low-<i>Q</i> asymptotic X-ray and neutron scattering data, where Guinier analysis is traditionally applied.