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

TL;DR

This paper investigates the transition from kinematical to dynamical diffraction regimes in smectic liquid crystal multilayers, revealing why these structures predominantly exhibit kinematical diffraction patterns despite their mirror-like layered nature.

Contribution

It provides a quantitative criterion for the crossover between diffraction regimes in smectic multilayers, explaining their unique diffraction behavior.

Findings

Diffraction in smectic multilayers is predominantly kinematical for thick films.

A derived criterion predicts the transition point between regimes.

The study explains the atypical diffraction patterns observed in experiments.

Abstract

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-nanometer roughness. However, an interesting peculiarity arises in the diffraction on 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 analyze the reflection of synchrotron radiation on a real liquid crystal sample with both kinematical and dynamical theories. Furthermore, based on 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 behavior in smectic films with thicknesses exceeding thousands of molecular layers.