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

Chelsea E.R. Edwards; Wellington C. Leite; Yun Liu

doi:10.1021/acsmeasuresciau.5c00099

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

Chelsea E.R. Edwards
, Wellington C. Leite
, Yun Liu

Biological Labeling and Scattering

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	35-45
Number of pages	11
Journal	ACS Measurement Science Au
Volume	6
Issue number	1
DOIs	https://doi.org/10.1021/acsmeasuresciau.5c00099
State	Published - Feb 18 2026

Funding

This project was supported by C.E.R. Edwards’s appointment to the National Research Council (NRC) Research Associateship Program (RAP) at the National Institute of Standards and Technology (NIST), administered by the Fellowships Office of the National Academies of Sciences, Engineering, and Medicine (NASEM). Y. Liu acknowledges the support by the Center for High Resolution Neutron Scattering, a partnership between the National Institute of Standards and Technology and the National Science Foundation under Agreement No. DMR-2010792. The authors thank Drs. John Barker, Ryan Murphy, and Susana Teixeira at the NIST Center for Neutron Research for helpful discussions about SANS data quality, background subtraction, and the current limits of accurate low-concentration measurements and Dr. Alexandros Chremos of the NIST Chemical Informatics Group for helpful feedback on the manuscript. Certain commercial equipment, instruments, or materials (or suppliers, or software, etc.) are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose. This research used resources at the High Flux Isotope Reactor, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. SANS studies were performed using the Bio-SANS instrument of the Center for Structural Molecular Biology (FWP ERKP291), a DOE Office of Biological and Environmental Research (OBER) Structural Biology Resource. The beam time was allocated to proposal number IPTS-33061.

Keywords

colloidal solutions
Guinier analysis
neutron scattering
particle interactions
radius of gyration
small-angle scattering
structure factor

Access to Document

10.1021/acsmeasuresciau.5c00099

Cite this

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title = "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.",

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author = "Edwards, \{Chelsea E.R.\} and Leite, \{Wellington C.\} and Yun Liu",

note = "Publisher Copyright: Not subject to U.S. Copyright. Published 2025 by American Chemical Society",

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AU - Edwards, Chelsea E.R.

AU - Leite, Wellington C.

AU - Liu, Yun

N1 - Publisher Copyright: Not subject to U.S. Copyright. Published 2025 by American Chemical Society

PY - 2026/2/18

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N2 - 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.

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KW - colloidal solutions

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