Grazing-incidence small-angle X-ray scattering from thin polymer films with lamellar structures - the scattering cross section in the distorted-wave Born approximation

Grazing-incidence small-angle X-ray or neutron scattering of thin polymer films reveals information about the ordering and preferential orientations of the phase-separated microdomains within the films. The grazing-incidence geometry enhances the surface sensitivity; however, the scattering has to be treated within the framework of the distorted-wave Born approximation. In this work, the case of thin films with lamellar mesostructure is studied, where the orientation of the lamellae is either perpendicular or parallel to the film interfaces. For perpendicular lamellae, Bragg rods are found, which are extended along the film normal, whereas for parallel lamellae, peaks along the film normal appear. The positions of the maxima present in the latter case are explained by accounting for refraction at the film surface and reflection at the film-substrate interface. The results are relevant for thin films of lamellar diblock copolymers.