Tensorial x-ray structure factor in smectic liquid crystals

Abstract

The amplitudes and the polarizations of the different resonant reflections characterizing the modulation of the orientational order in smectic liquid crystals are derived from the molecular tensorial structure factor. In the case of a commensurate helicoidal modulation, our conclusions are consistent with the previous predictions of Dimitrienko. We have extended Dimitrienko's prediction to incommensurate helicoidal structures and to commensurate but nonhelicoidal modulations. We have compared the estimated values for different models of modulations with the same period, with the experimental data obtained on different smectic-C variants. These comparisons enable us to discriminate between the different models.