Evaluation of Small-Angle X-Ray Scattering of Polymers

The influence of the particle factor and lattice factor on the positions of the small-angle reflections of polymer crystalline samples is investigated. Since a single-crystal cake or a polymer solid crystallized from melt supposedly consists of stacks of nearly parallel plate-like lamellae, one may describe the scattering behavior of polymer crystals based on a periodic step function with fluctuating periods (linear paracrystal). In this model the particle factor as well as the lattice factor may shift the scattering maxima out of the positions given by the Bragg equation. Good agreement with the observation that the first order leads to a larger spacing than the second one may be obtained by introduction of an unsymmetrical distribution function for the lamellar thickness.