Short-pitch helicoidal modes in antiferroelectric liquid crystals and scattering of resonant X rays

Polarization anisotropy of X-ray atomic factors and `forbidden' resonant reflections

“…Another interesting example was found in chiral smectic liquid crystals with an incommensurate spiral structure (Mach et al, 1998;Levelut & Pansu, 1999;Gorkunov et al, 1999;Matkin et al, 2000;Hirst et al, 2002); the issue was recently surveyed by Clegg (2005). The observations of 'forbidden' reflections near the S and Se K edges provided the first direct evidence of distinct periodicities in the structures of several chiral smectic phases.…”

Interlayer Self-Diffusion and Structure of Chiral Smectic Phases Studied by 2H NMR Exchange Experiment

“…Significant experimental and theoretical efforts have been directed to investigate the structure and dynamics of these chiral LC materials. − It is now widely accepted that a typical phase sequence for these chiral materials is Sm −Sm C *− −Sm −Sm upon decreasing temperature and is a result of the relevant interlayer interactions. , Note that certain phases may not exist in some materials. Although a variety of experimental probes has been used to obtain information on the molecular packing in these phases, including resonant X-ray, ,, optical rotatory power, ,, ellipsometry, and dynamic light scattering, only the structures of Sm C * and are well documented. Other chiral subphases are still of much current interest.…”

Specific selective reflections in the ferrielectric phases of chiral smectic liquid crystals

“…Data obtained inevitably mean that the investigated phases have the structure similar to a helix with the pitch close to the integer number of layers [4,7]. It was shown that the observed splitting of the scattered peaks can be treated as a result of the incommensurability of helical structure.…”

“…(7,8) on the helix of polarization, here exist some more reflections, the strongest of them having transferred momentum f ( 3 6 q -m p ) , m = 1 , 2 , 3 , (18) where m = 1 corresponds to type I1 reflections, m = 2 corresponds to type I and m = 3 gives type I11 reflections. In fact, the allowance for higher powers of C-directors and displacement give rise to some more reflections with weaker intensity.…”

“…The variant of the molecular ordering called "clock-wise", that is the helicoidal structure with a very short pitch, becomes probable if the restriction on the tilting direction is not applied and the simplest forms of interlayer interactions are considered [2]. The structures similar to the "clock-wise" arise also in the semi-phenomenological model of short-pitch modes (SPM) first formulated in [3] and developed recently in [4][5][6][7]. This model assumes that the pitch of SPM is close to some integer number of smectic layers.…”