Defect structures cholesteric liquid crystals

We now consider defect structures in the cholesteric liquid crystal. Treating the cholesteric as a spontaneously twisted nematic,... 

Fig. 4.4.2. A spherical drop of a long-pitched cholesteric liquid crystal showing the characteristic /-line (from Robinson ). The structure of this defect was explained...

Cholesteric liquid crystals are compounds that go through a transition phase in which they flow like a liquid, yet retain much of the molecular order of a crystalline solid. Liquid crystals are able to reflect iridescent colors, depending on the temperature of their environment. Because of this property they may be applied to the surfaces of bonded assemblies and used to project a visual color picture of minute thermal gradients associated with bond discontinuities. Cholesteric crystals are potentially a simple, reliable, and economical method for evaluating bond defects in metallic composite structures.f Materials with poor heat-transfer properties are difficult to test by this method. The joint must also be accessible from both sides. ... 

S. V. Shiyanovskii, 1.1. Smalyukh, and O. D. Lavrentovich, Computer simulations and fluorescence con-focal polarizing microscopy of structures in cholesteric liquid crystals, p. 229, in Defects in liquid crystals computer simulations, theory and experiments (Kluwer Academic Publishers, Netherland, 2001). 

In the vicinity of the transition into the isotropic phase, optically isotropic uniform textures are often observed. These so-called blue phases are cubi-cally symmetric defect structures of cholesteric liquid crystals. With decreasing temperature three blue phases occur [13, 14]. All of them are optically active but not birefringent. The observation of the optical Bragg refiections allowed the determination of the structure of these phases. They are formed by a special packing of pieces of the helix into various cubic lattices. An example is shown in Fig. 1.5(b) [15]. Parameters of the lattices are of the order of the helical pitch. Due to the optical Bragg refiection firom the cubic lattice these phases are blue colored. 

A useful structural concept introduced by Kleman and FriedeF postulates a quasi-layered structure and explicitly takes into account the natural twist of the system. Concerning defects, we may think of cholesteric liquid crystals as a smectic with an in-plane nematic behavior, similar to the smectic C phase. Instead of using tire concept of a layered structure to account for the twist, we may also consider tire field of twist axis t in addition to the director field n. The two concepts are essentially equivalent, with the twist field being identical with the layer normal. The twist field accordingly suffices the condition t curti = 0, which means that in this twist field no fwist deformation is allowed. The concept of "layers" or twist-field is an approximation, which may not be valid in the core of the defects. We assume that the core structures of cholesterics (especially those with weak chirality) are similar to that of nematics. 

A very different model of tubules with tilt variations was developed by Selinger et al.132,186 Instead of thermal fluctuations, these authors consider the possibility of systematic modulations in the molecular tilt direction. The concept of systematic modulations in tubules is motivated by modulated structures in chiral liquid crystals. Bulk chiral liquid crystals form cholesteric phases, with a helical twist in the molecular director, and thin films of chiral smectic-C liquid crystals form striped phases, with periodic arrays of defect lines.176 To determine whether tubules can form analogous structures, these authors generalize the free-energy of Eq. (5) to consider the expression... 

We have omitted discussing such interesting properties of liquid-crystal solutions as the Frank elastic constants, the Leslie viscosity coefficients, cholesteric pitch, textured structure (or defects), and rheo-optics. Some of them are reviewed in recent literature [8,167], but the level of their experimental and theoretical studies still remains largely qualitative. 

It should be noted that the appearance of the cholesteric phase of Reinitzer was different from the appearance of the classical cholesteric phase shown in Fig. 1.3b. The phase was opaque and had blue tint. It took a century to decipher its structure it appears to be a blue phase (see Chapter 4) with a structure of liquid lattice consisting exclusively of defects of an initially ideal helical structure. This phase is periodic and shows Bragg diffractiMi of light in all the three principal directions. Therefore, Reinitzer has discovered the first generic photonic crystal At present, a study of photonic crystals, mostly artificial, is one of the hot topics in physics [8]. 

The concept of defects came about from crystallography. Defects are dismptions of ideal crystal lattice such as vacancies (point defects) or dislocations (linear defects). In numerous liquid crystalline phases, there is variety of defects and many of them are not observed in the solid crystals. A study of defects in liquid crystals is very important from both the academic and practical points of view [7,8]. Defects in liquid crystals are very useful for (i) identification of different phases by microscopic observation of the characteristic defects (ii) study of the elastic properties by observation of defect interactions (iii) understanding of the three-dimensional periodic structures (e.g., the blue phase in cholesterics) using a new concept of lattices of defects (iv) modelling of fundamental physical phenomena such as magnetic monopoles, interaction of quarks, etc. In the optical technology, defects usually play the detrimental role examples are defect walls in the twist nematic cells, shock instability in ferroelectric smectics, Grandjean disclinations in cholesteric cells used in dye microlasers, etc. However, more recently, defect structures find their applications in three-dimensional photonic crystals (e.g. blue phases), the bistable displays and smart memory cards. 

Today s challenge is the search for robust cholesteric materials with a low threshold value for lasing, but a high tolerance for pumping. As mentioned above, lasing from cholesteric structures is mostly the domain of low molar mass liquid crystals. That is because it is essential to obtain a monodomain, which is as defect-free as... 

Spherulites showing concentric layers present a disclination radius or diameter, but this structure is due to a topological constraint and does not seem to be linked to liquid crystal growth. Very rapid growth of cholesteric phases often generates screw dislocations of the two types shown in Fig. 24i and j, and this has been filmed by Rault in p-azoxyanisol added to cholesterol benzoate [98, 99]. Slow growth does not result in the production of these defects. 

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. 

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