Lateral disorder in Langmuir monolayers: Theoretical derivations and grazing-incidence x-ray diffraction

Recent studies of the self-assembly of Langmuir monolayers have revealed novel forms of lateral molecular ordering. Such studies typically involve the use of grazing-incidence synchrotron radiation scattering, and the lateral order manifests itself as distinct diffraction patterns. As the molecular organization becomes more intricate, the corresponding diffraction pattern becomes more complicated. At this point, standard analysis, such as identifying peak positions and solving the crystal structure, is insufficient to describe the system. In such cases, a physics-based simulation of the diffraction is required. In this article, we present a versatile theoretical framework for simulating complex structural molecular ordering in Langmuir monolayers. We begin by applying the formalism to a simple case of solid-state monolayers and extend the analysis to describe the structural organization in the collapsed state. The applicability of the method is validated through comparison with experimental data collected at the bending magnet synchrotron beamline.