Orientational correlations in liquid crystalline systems revealed by polarization-analyzed resonant x-ray scattering

The existence of a helical symmetry axis is widespread in systems exhibiting liquid-crystalline order, especially in systems comprised of chiral molecules. Because these systems usually lack three-dimensional positional order, the helical symmetry axis cannot be observed using conventional x-ray scattering. Since the nature of the helical ordering determines the electro-optic response of the liquid crystal phases, it is a crucial structural feature to establish. Important for device applications are the various chiral smectic-C (SmC^*) liquid crystal phases that are composed of fluid-like layers of tilted molecules. The electro-optic response of these phases varies from ferro to ferri to antiferroelectric. To elucidate the structure of the SmC^* phases, we did resonant x-ray scattering at the sulfur K-edge on sulfur containing compounds. Our polarization-analyzed measurements of the resonant diffraction provided unambiguous evidence that the in-plane tilt direction in these phases exhibits a helical interlayer orientational ordering with a short pitch = vd where d is the layer spacing. In the lowest temperature SmC^* phase, which has antiferroelectric ordering, v was close to 2. At higher temperatures, the ferrielectric phases had v = 3, then 4, and finally, an incommensurate value varying between 5 and 8 with increasing temperature.