Small-angle scattering from spherical core–shell particles: an analytical scattering function for particles with Schulz–Flory size distribution

Abstract

The scattering function for Schulz–Flory distributed spherical core–shell particles is derived analytically. A constant ratio of core to shell radii is assumed. The analytical expression, which does not require any numerical integration, provides a fast way to model experimental data by nonlinear least-squares fitting. The asymptotic behavior for large momentum transfers coincides with the different power laws expected for homogenous spheres and thin spherical shells. In the second part, the derived expression is applied to describe experimental small-angle X-ray scattering data from core–shell particles with different particle sizes, polydispersity and ratio of core to shell radii. For large particles, a resolution correction by numerical convolution with a Gaussian resolution function is applied.