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Updated: Feb 24, 2026

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Published on: March 2, 2020
Low‑Q Asymptotic Behavior of the Effective Structure Factor Yields Model-Independent Radius of Interparticle
Chelsea E R Edwards1, Wellington C Leite2, Yun Liu1,3
1NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States.
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 (R g ) 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, R i . Whereas R g describes how spread out the scattering length density distribution of particles is from their center of mass, R 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-Q asymptotic X-ray and neutron scattering data, where Guinier analysis is traditionally applied.
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