Low-Q Asymptotic Behavior of the Effective Structure Factor from Small-Angle Scattering Yields Model-Independent Radius of Interparticle Potential (Ri)

Published

November 7, 2025

Author(s)

Chelsea Edwards, Wellington Leite, Yun Liu

Abstract

Guinier analysis has been extensively used in academic and industrial research settings since the 1940s 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, based on a concentration-independent Rg. Whereas Rg describes how spread out the scattering length density distribution of particles is from their center of mass, Ri is an effective mean-squared distance that quantifies how far the inter-particle correlation is deviant from its ideal gas due to interactions. We demonstrate this novel analysis method by applying it to experimental small-angle neutron scattering data on lysozyme protein solutions, and discuss its broad implications for analysis of low-Q asymptotic x-ray and neutron scattering data, where Guinier or Zimm analysis is traditionally applied.

Citation

ACS Measurement Science Au

Volume

6

Issue

1

Pub Type

Journals

Download Paper

https://doi.org/10.1021/acsmeasuresciau.5c00099

Local Download

Citation

Edwards, C. , Leite, W. and Liu, Y. (2025), Low-Q Asymptotic Behavior of the Effective Structure Factor from Small-Angle Scattering Yields Model-Independent Radius of Interparticle Potential (Ri), ACS Measurement Science Au, [online], https://doi.org/10.1021/acsmeasuresciau.5c00099, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=960254 (Accessed February 20, 2026)