X-Ray Observation of a Stacked Hexatic Liquid-CrystalBPhase

Abstract

X-ray studies have been performed on a new liquid-crystal material which exhibits a noncrystalline B phase. Using free-standing liquid-crystal film techniques, we find that this B phase has short-range in-plane positional correlations but long-range, threedimensional, sixfold bond-orientational order. We interpret our results in terms of a system of interacting two-dimensional hexatic layers.

X-ray cross-correlation analysis and local symmetries of disordered systems: General theory

“…This probably explains why the observed Fourier components, especially in the intensity, but also in the CCF, are weak when compared to the extremely marked ones observed in hexatic liquid crystals, which are stacks of two-dimensional manifolds. [3][4][5] The same difference in the performance of high-order CCFs was observed in the scattering of the coherent laser light on 2D and 3D colloid systems. 6,21 It is tempting to speculate that the subset of LSs with an approximate lineup of a symmetry axis, in a three-dimensional system, is always "dilute," in the sense that it is constituted by a small fraction of the total number of molecules or clusters.…”

“…This leads us to investigate the relationship to pure 2D systems. In fact, extremely marked effects, unveiled by previous x-ray studies, performed with x-ray beams with a limited degree of coherence, of bondorientational order in liquid crystals [3][4][5] ͑especially hexatic ones͒ and dynamical light scattering experiments 6 performed with coherent laser beams on ordered 2D colloid systems, are strongly related to the recent results of Wochner et al Our aim is to provide a sound basis to the statement that the angular intensity correlations deliver information on local bond arrangements in a disordered ͑or partially ordered͒ system. In the dilute limit ͑where local entities containing specific bond angles are separated by distances much larger than the bond lengths͒ the angular correlation function can be explicitly related to a bond-orientational order parameter, which generalizes the order parameter proposed for hexatic liquid crystals 7 by Bruinsma and Nelson.…”

“…͑1͔͒ investigated by Wochner et al 1 does not really contain additional information with respect to the Fourier analysis of the dependence of the intensity. Examples [3][4][5] of analysis of the periodicity in the angular dependence of the intensity can be found in studies of hexatic liquid crystal phases, 7 performed with x-ray beams with the limited degree of coherence. In the next section, we present detailed derivations of the CCF, based on the kinematical x-ray scattering theory.…”

Volume and X-ray diffraction study of terephthal-bis-4,n-decylaniline (TBDA)

“…Molecules are tilted towards the long and the short side of the local rectangular cell for SF and S, [7] respectively. A similar mesophase, in which however the molecules are perpendicular with respect to the plane of the layers, has also been identified; this is a hexatic modification of SB [8].…”

The global phase diagram of the Gay–Berne model

“…Birgenau and Lister 22 were the first to suggest the existence of the SmB phase, carrying over to liquid crystals in three dimensions the concepts introduced by Halperin and Nelson 23 on two-dimensional melting. Hexatic order in liquid crystals was later observed unambiguously by Pindak et al 24 Careful high-resolution x-ray diffraction experiments and the use of freely suspended films 25 showed that most of the phases previously labeled as SmB did not have hexatic order but were crystalline phases. This crystal phase has been typically referred to as crystalline smectic B or crystal B phase ͑the former terminology is, however, misleading as the phase is not a true smectic liquid crystal͒.…”