Lattice symmetry of the cholesteric blue phases

Abstract

The cholesteric blue phases (BP I and BP II) can be modeled as cubic lattices of disclinations in a cholesteric matrix. In an earlier paper we presented results of free-energy calculations for three models with 0 (F4232), 0 (I432), and 0 (I4&32) space-group symmetry. In the present paper calculations for a fourth model, also of 0 symmetry, are presented (we differentiate these models as 0 '+' and 0 ' ', respectively). For a number of cholesterol derivatives we assign the 0 ' ' structure to the BP I, and the 0 structure to BP II, on the following evidence: For the case of equal elastic constants the calculations show a crossover of the free energy, the 0 structure being lowest at the higher temperatures, and 0 ' ' at lower temperatures. (However, the crossover may disappear for other values of the elastic constants. ) The assignment is consistent with the observed BP I and BP II lattice constants in terms of cholesteric pitch. There is excellent agreement between calculated and observed intensities of the Bragg reAections. Some details of the observed Braggdiffraction spectra are also discussed.

DNA liquid crystalline blue phases. Electron microscopy evidence and biological implications

“…As regards the second blue phase, it could be either BPI or BPII (cubic arrays of double twist tubes, body centred cubic and simple cubic, respectively [21,28,29]). As already pointed out, a precise determination of the lattice parameters would require further 3D reconstruction from the electron microscopy Downloaded by [Duke University Libraries] at 09:05 05 January 2015 data, together with diffraction studies of the samples over a large range of wavelengths.…”

Numerical calculations of the phase diagram of cubic blue phases in cholesteric liquid crystals

“…Blue phases provide a particularly fascinating example of liquid crystal ordering as they correspond to complicated director fields which, even in equilibrium, are threaded by a regular network of disclinations [8][9][10][11][12][13]. Identifying their structure presented a considerable theoretical challenge the resolution of which is clearly summarised in the review by Wright and Mermin [4].…”

“…The nomenclature used here refers to the symmetry group which characterises the lattice of disclinations formed in the blue phases following [4,11,12] been proposed as a model for BP II. The defect structure in each phase in shown in Figure 1.…”

Self-Organized 3D Photonic Superstructure: Blue Phase Liquid Crystal

“…BPs have also been discovered in smectics [59], discotics [60] and metallomesogens [61]. [13,[63][64][65], and the corresponding wavelength λ with respect to the lattice plane (hkl) can be estimated by the following equation [66]:…”

“…The manner of DTC packing varies as phase transition. On the aspect of lattice structure, BPI is body-centered cubic with I4 1 32 (O 8 ) symmetry, whereas BPII belongs to simple (primitive) cubic space group P4 2 32 (O 2 ) [6,11,13,14]. The schematic depictions of the cylinder arrangement and disclination network in BPI as well as in BPII are presented respectively in Fig.…”