Debye-Scherrer rings from block copolymer films with power-like order

The powder-like orientation of lamellar domains in thin films of the diblock copolymer polystyrene-block-poly(methyl methacrylate) is investigated using grazing-incidence small-angle X-ray scattering (GISAXS) and grazing-incidence small-angle neutron scattering (GISANS). Conventional monochromatic GISANS and GISAXS measurements are compared with neutron time-of-flight GISANS. For angles of incidence and exit larger than the critical angle of total external reflection of the polymer, Debye-Scherrer rings are observed. The position of the Debye-Scherrer rings is described quantitatively based on a reduced version of the distorted-wave Born approximation. A strong distortion of the ring shape is caused by refraction and reflections from the film interfaces. Close to the critical angle, the ring shape collapses into a banana shape