Liquid crystal structure, disclinations

The introduction of the disclinations into a liquid crystal structure usually leads to an increase of the free energy of the system. Therefore, defects are not stable, and one generally is able to decrease the number of disclinations by annealing (see Figure 6.2b), or other ways. There are, however, a few cases where disclinations are energetically favorable, and the ordered array of disclinations or defect walls are necessary conditions for the existence of the phase. The existence of these defect phases reflects the fine balance between competing factors. 

Equation 19 introduced above is useful for discussing a process of structural re-formation of a nematic polymeric liquid crystals. The analysis in terms of Eq 19 makes it possible to evaluate the orientational relaxation time t in a force-free state of a nematic liquid crystal despite actual existence of wall and disclination effects. Figure 9 gives an example of computer-fitting for the experimental result shown in Fig. 4 (t = 6.9 sec 1) ... 

The study of defects in liquid crystal systems is rooted in the understanding of defects in the solid state. For instance, crystals are rarely perfect and usually contain a variety of defects, e.g., point defects, line defects, or dislocations, and planar defects such as grain boundaries. In addition to these typical imperfections of the solid state, liquid crystals can also exhibit defects known as disclinations. These defects are not usually found in solids and result from the fact that mesophases have liquid-like structures that can give rise to continuous but sharp changes in the orientations of the molecules, i.e., sharp changes in orientation occur in the director field. 

Zimmer JE, White JL, Disclination structures in the carbonaceous mesophase. Advances in Liquid Crystals, Vol 5, Academic Press, New York, 157, 1982. 

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. 

Fig. 8.13 Two disclinations fixed by their end at the two glasses limiting a layer of a nematic liquid crystal. They interact with each other by the elastic force proportional to 1/Pi2 (a). The structure of the director field n(r) near the two disclinations of positive and negative strength and four dark brushes corresponding to the j = 1 disclinations (b)...

Fig. 8.21 Structure of the director field around different singular lines (disclinations) in a cholesteric liquid crystal x , X and x, Signs (—) and (+) correspond to different Volterra...

Intensity fluctuations are also clearly visible. However, the practiced eye will notice that only disclinations of whole number rank are present in the preparation. Focal conic zones remain unchanged, up to some small details. But where only one colour was observed previously, we now often find two colours separated by a thin wall. All these observations are compatible with the simple idea that molecules are tilted relative to the plane of the layer, as shown in Fig. 9.11a. When there is no external field, the tilt direction remains indeterminate, just as we found for the directions of optical axes in nematic phases, which gave rise to their threadlike texture. However, the absence of disclinations of whole number rank is characteristic of a layered structure. The two colours can be understood as being due to occurrence of positive and negative tilts in thin preparations (see Fig. 9.11b). These arguments are corroborated by crystallographic studies. We have thus discovered a second type of layered liquid crystal, called the smectic C phase, or Sc- Note that this tilting does not preclude a liquid-type order within layers (a kind of 2-dimensional nematic phase). 

Figure 13.9 (a) The liquid crystal director configuration of the disclination formed between the doubletwist cylinders, (b) The structure of the disclinations in the simple cubic packing of the double-twist cylinders, (c) The structure of the disclinations in the body-centered cubic packing of the double-twist cylinders. 

Usually the Cano method [8] is used for chiral nematic liquid crystals. It can also be applied to SmC phases, but then the demands on the orientation of the liquid crystal are more extensive as a nearly perfect orientation of the layer normal k as well as of the c-director are required. The presented method utilizes the different thicknesses which occur in a sample if a lens is placed on top of it. A sketch of this is shown in Fig. 4.6a. Due to the anchoring conditions, only helical structures with integer multiples N of the pitch p are allowed and regions with different values of N are separated by disclination lines [14]. Thus, a picture similar to the one shown in Fig. 4.6b occurs [15]. If the radius of curvature Rc of the lens is known, the value of the pitch p can be calculated according to [9]... 

The situation is simpler if the column lattice is helically distorted perpendicular to the column axes blocks of parallel columns are stacked on top of each other with a finite angle between the columns of adjacent blocks (Figure 11.10) [18], The blocks are thus separated by planar tilt grain boundaries, and parallel linear screw disclinations lie within these boundary planes (Figure 11.11). This structure is perfectly analogous to the twist grain boundary phases of chiral smectic liquid crystals. 

J. Bezic and S. Zumer, Chiral nematic liquid crystals in cylindrical cavities A classification of planar structures and models of nonsingular disclination lines, Liq. Cryst. 14, 1695 (1993). 

This simple treatment of liquid crystalline defects is only applicable to nematics, and the detailed appearance of disclination lines will differ from the simple structures described above because of differences between the elastic constants for splay, twist and bend. In smectic phases, defects associated with positional disorder of layers will also be important, and some smectic phase defects such as edge dislocations have topologies similar to those described for crystals. The defect structures of liquid crystals contribute to the characteristic optical tex-... 

Disclinations are rotation defects, and are rare or absent in three-dimensional crystals, owing to their prohibitive energies, but are in general compatible with liquid crystalline structures. They were initially called disinclinations [2, 3, 54], but the term was later simplified to disclination . 

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. 

One well-known characteristic feature of nematic liquid crystals is the thread-like texture that can be observed with a polarizing microscope. The name nematic, derived from the Greek word "thread," reflects that feature. By examining the thin and thick thread-like structures in nematic liquid crystals, Otto Lehman i and Georges FriedeF deduced that this phase involves long-range orientational order. The first step to the interpretation of the threads as disclinations of the director field has been made by Oseen. Later Frank " derived Oseen s theory of curvature elasticity on a more general basis and presented it in a simpler form (see Appendix C.1). 

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