An analytical scattering function for polydisperse spherical core-shell particles with Schulz-Flory size distributions of both core size and shell thickness

The scattering function for polydisperse core-shell particles with Schulz-Flory size distributions of both the core radius and the shell thickness is analytically calculated. The results of the analytical solution are compared with the results of a numerical integration over both size distributions, as well as with available analytical solutions for homogeneous spheres. The CPU time required for the calculation of the scattering function can be reduced by several orders of magnitude compared with numerical integration. This is of tremendous importance in nonlinear curve fitting requiring repeated calculation of the theoretical function in an iterative process.