Low-Q Asymptotic Behavior of the Effective Structure Factor Yields Model-Independent Radius of Interparticle Interaction (Ri)

Abstract

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 (Rg) is extracted from the form factor at low Q. Here, we develop an analogous approach for analyzing the effective structure factor data at low Q to extract a model-independent radius of interaction potential, Ri. Whereas Rg describes how spread out the scattering length density distribution of particles is from their center of mass, Ri 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-Q asymptotic X-ray and neutron scattering data, where Guinier analysis is traditionally applied.