X-ray diffraction from smectic multilayers: crossover from kinematical to dynamical regime

We study X-ray diffraction in smectic liquid crystal multilayers. Such systems are fabricated as freely suspended films and have a unique layered structure. As such, they can be described as organic Bragg mirrors with sub-nanometre roughness. However, an interesting peculiarity arises in the diffraction from these structures: the characteristic shape of diffraction peaks associated with dynamical scattering effects is not observed. Instead, the diffraction can be well described kinematically, which is atypical for Bragg mirrors. In this article we investigate the transition between the kinematical and dynamical regimes of diffraction. For this purpose, we analyse the reflection of synchrotron radiation from a real liquid crystal sample with both kinematical and dynamical theories. On the basis of these theories, we derive a quantitative criterion for the transition from the kinematical to the dynamical regime. This, in turn, allows us to explain the peculiar diffraction behaviour in smectic films with thicknesses exceeding thousands of molecular layers.