Small-angle scattering: the Guinier technique underestimates the size of hard globular particles due to the structure-factor effect

The straightforward calculation of small-angle scattering intensity by hard spheres at different concentrations is performed. For the same system of hard spheres, the scattering intensities were found both using the product of the form factor and the structure factor {based on the work of Kinning & Thomas [Macromolecules, (1984), 17, 1712–1718]} and using the correlation function {based on the work of Kruglov [J. Appl. Cryst. (2005), 38, 716–720] and Hansen [J. Appl. Cryst. (2011), 44, 265–271; J. Appl. Cryst. (2012), 45, 381–388]}. All three intensities are in agreement at every concentration. The values of the radii of gyration found from the Guinier plot are shown to be noticeably underestimated compared to the true radius of gyration of a single sphere. Presented are the calculated correction factors that should be applied to the experimentally found radius of gyration of spheres. Also, the concentration effects are shown to have an even greater impact on the radius of gyration of prolate particles that is found from the Guinier plot.