# Low‑Q Asymptotic Behavior of the Effective Structure Factor Yields Model-Independent Radius of Interparticle Interaction (R i )

## TL;DR

This paper introduces a new method to determine interparticle interaction radius from low-Q scattering data, similar to Guinier analysis for particle size.

## Contribution

A novel model-independent method to extract the radius of interparticle interaction (Ri) from low-Q scattering data is introduced.

## Key findings

- The new method successfully analyzes experimental neutron scattering data on lysozyme solutions.
- Ri quantifies deviations in interparticle correlations from ideal gas behavior due to interactions.

## 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.