Models liquid crystal cubic phase

The distribution of defects in mesophases is often regular, owing to their fluidity, and this introduces pattern repeats. For instance, square polygonal fields are frequent in smectics and cholesteric liquids. Such repeats occur on different scales - at the level of structural units or even at the molecular level. Several types of amphiphilic mesophase can be considered as made of defects . In many examples the defect enters the architecture of a unit cell in a three-dimensional array and the mesophase forms a crystal of defects [119]. Such a situation is found in certain cubic phases in water-lipid systems [120] and in blue phases [121] (see Chap. XII of Vol. 2 of this Handbook). Several blue phases have been modeled as being cubic centred lattices of disclinations in a cholesteric matrix . Mobius disclinations are assumed to join in groups of 4x4 or 8x8, but in nematics or in large-pitch cholesterics such junctions between thin threads are unstable and correspond to brief steps in recombinations. An isotropic droplet or a Ginsburg decrease to zero of the order parameter probably stabilizes these junctions in blue phases. 

Also the above-described SmQ phase was object of molecular simulation studies by using the molecule shown in Fig. 10.42 [99]. Figure 10.43 shows the structure of the SmQ phase, which is also known as the r l phase. This structure is based on a model according to Levelut et al. (Fig. 10.40 in [100]), in which the local liquid crystal molecular alignment direction is tilted in respect to the layers of smectic blocks. In the case of a 45° tilt, this leads to a cubic phase with a threefold symmetry. 

Figure 2 Phase diagram of a binary amphiphile-water mixture obtained from a Ginzburg- Landau model with a vector order parameter for the amphiphile orientation (50,51]. The phases L and L2 are micellar liquids, is a lamellar phase. H and H denote hexagonal and inverse hexagonal phases, respectively, I is an fee crystal of spherical micelles, and V is a simple cubic bicontinuous phase. (From Ref. 51.)...

There is ample evidence that small cycloalkanes and many of their derivatives with similar sphere-like shapes can exist as plastic crystals [21,22]. They are not birefringent and exhibit fewer X-ray diffraction lines in the plastic phases than in the corresponding (lower temperature) normal crystalline phases. Many plastic phases have cubic lattices like those of the closely related smectic D phases [33] which are comprised of aggregates of rod-like molecules. In both cases, more than one molecule can constitute the unit cell or fundamental lattice unit so that several molecules may tumble in a correlated motion. A similar microscopic model explains the lack of optical birefringence in the related cholesteric blue liquid crystalline phases from some chiral... 

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