Reliability of Orientational Order Parameters Determined from Two-dimensional X-ray Diffraction Patterns: A Simulation Study

Molecular Electron Density Distribution and X-Ray Diffraction Patterns of Smectic A Liquid Crystals - A Simulation Study

X-ray diffraction (XRD) is one of the most important methods to assess the long-range translational order in smectic A (SmA) liquid crystals. Nevertheless, the knowledge about the influence of the molecular electron density distribution (MEDD) on the XRD pattern is rather limited because it is not possible to vary the orientational order, the translational order and the MEDD independently in an experiment. We here present a systematic simulation study in which we examine this effect and show that the MEDD indeed has a major impact on the general appearance of the XRD pattern. More specifically, we find that the smectic layer peaks and the intensity ratios thereof strongly depend on the width of the MEDD. The classic approach by Leadbetter et al. to determine the smectic translational order parameter ∑ from XRD intensities works if the MEDD is quite narrow. In all other cases the influence of the MEDD has to be taken into account.

X-ray and Raman scattering study of orientational order in nematic and heliconical nematic liquid crystals

The temperature dependence of the orientational order parameters 〈P_{2}(cosβ)〉 and 〈P_{4}(cosβ)〉 in the nematic (N) and twist-bend nematic (N_{tb}) phases of the liquid crystal dimer CB7CB have been measured using x-ray and polarized Raman scattering. The 〈P_{2}(cosβ)〉 obtained from both techniques are the same, while 〈P_{4}(cosβ)〉, determined by Raman scattering is, as expected, systematically larger than its x-ray value. Both order parameters increase in the N phase with decreasing temperature, drop across the N-N_{tb} transition, and continue to decrease. In the N_{tb} phase, the x-ray value of 〈P_{4}(cosβ)〉 eventually becomes negative, providing a direct and independent confirmation of a conical molecular orientational distribution. The heliconical tilt angle α, determined from orientational distribution functions in the N_{tb} phase, increases to ∼24^{∘} at ∼15 K below the transition. In the N_{tb} phase, α(T)∝(T^{*}-T)^{λ}, with λ=0.19±0.03. The transition supercools by 1.7 K, consistent with its weakly first-order nature. The value of λ is close to 0.25 indicating close proximity to a tricritical point.

Orientational distribution functions and order parameters in "de Vries"-type smectics: A simulation study

Simple smectic A liquid crystal phases with different types of prescribed orientational distribution functions have been simulated and compared in order to study the possibility to distinguish between the Maier-Saupe type and cone-like orientational distributions using the popular method of Davidson et al. [J. Phys. II 5, 113 (1995)]. This method has been used to extract the orientational distribution functions from simulated diffraction patterns, and the results have been compared with actual distribution functions which have been prescribed during simulations. It has been shown that it is indeed possible to distinguish between these two qualitatively different types of orientational distribution already from the shape of the 2D diffraction pattern. Moreover, typical experimental diffraction patterns for "de Vries"-type smectic liquid crystals appear to be close to the ones which have been simulated using the prescribed Maier-Saupe orientational distribution function.