Scattering functions of core-shell-structured hard spheres with Schulz-distributed radii.

The scattering intensity of polydisperse systems of core-shell and layered hard spheres is considered. The Percus-Yevick solution for the partial structure factors is cast in a form suitable for numerical and analytical treatment. Closed-form, analytical expressions are given for an effective hard-sphere model of the scattering intensity of particles with an internal layered structure and a size polydispersity governed by a Schulz distribution. A similar model for polydisperse hard spheres of core-shell structure but with a monodisperse shell thickness is also presented. The models are tested against small-angle X-ray scattering experiments on a hard-sphere-like microemulsion system.