# Guinier plot

A Guinier analysis attempts to extract the size-scale for a structure by fitting the scattering to an equation of the form:

$I(q) = I_0 \exp \left( - \frac{R_g^2}{3} q^{2} \right)$
$\ln(I(q)) = \ln(I_0) - (R_g^2/3)q^{2}$

Thus a plot of ln(I) vs. q2 can be used to highly the scaling of the scattering. A straight-line in such a plot is indicative of Guinier scaling. Such an analysis is typically only done with the low-q portion of the data. Linear (Guinier) scaling suggests that the system is essentially monodisperse; it can thus be used as a means of quality control before further data analysis (e.g. Form factor).

## Rule of thumb

The larger one's particles are, the smaller the minimum q must be. One also only expects the Guinier scaling to be maintained up to a certain maximum q:

• For spherical particles, $\scriptstyle q_{\mathrm{max}} < 1.3 R_g$
• For elongated particles, $\scriptstyle q_{\mathrm{max}} < 0.8 R_g$