Particle size distribution from small-angle scattering data: A histogram technique

A method of reparametrizing small-angle scattered intensity spectra I(q) in terms of the q=0 contributions from populations of spheres of discrete radii I0(r) is described. The minimal assumptions are made that the scattering from a particulate system can be parameterized as a distribution of sizes of solid spheres, and that the particle positions are uncorrelated. The calculated size distribution can be used to define either the multimodal size distributions of spherical particles or the shape of monodisperse, nonspherical particles. In any case, its usefulness is limited at high concentrations where the particle–particle correlation function has significant structure. The applicability of this technique is demonstrated with calculated spectra and experimental results from water-in-oil microemulsions.