Defects disclinations, 408-9 dislocations

In order to account for the real 3D structure of cylindrical microdomains, we denote the configurations in Fig. 22a, e and c, g as cylinder-phase defects (cyl-dislocation and +1/2 cyl-disclination), and the configurations in Fig. 22b,f and d,h as matrix defects (m-dislocation and m-disclination). In our systems, cyl-dislocations generally develop during the early stages of film annealing when the overall defect density is high. In well-equilibrated films, cyl-dislocations are less frequent as compared to m-dislocations. 

Generalized line defects, like dislocations and disclinations, are known to produce a markedly anisotropic line broadening, i.e. a line broadening dependent on the observed [hkl direction in the crystalline domain. This is due to the combined effect of the anisotropy of the elastic medium (described by the... 

Nevertheless in polymeric liquid crystals the same types of orientational defects and thus the same types of textures as present in the low mass counterparts have been observed. The textures often formed by polymers are the threaded texture, the schlieren texture and the focal conic texture of smectics. As is for low mass liquid crystals, the texture is a consequence of defects (disclinations and dislocations, refer to Chapter 1) present in the liquid crystal and is characteristic of a specific type of the phase. The texture examination has become a very useful tool in the determination of the type and nature of the polymeric liquid crystals. 

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. 

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. 

As indicated above and illustrated in Fig. 32 i, layers lie horizontally in planes and show some translation dislocations. They are oblique in polygonal fields and generally cross the focal lines at points where they are strongly hat-shaped, whereas elsewhere they are saddle-shaped and dislocations are present, often superimposed on the focal lines. In fans, the layers are vertical and all types of defect (disclinations, focal curves, dislocations) are present. 

As in crystals, defects in liquid crystals can be classified as point, line or wall defects. Dislocations are a feature of liquid crystal phases where tliere is translational order, since tliese are line defects in tliis lattice order. Unlike crystals, tliere is a type of line defect unique to liquid crystals tenned disclination [39]. A disclination is a discontinuity of orientation of tire director field. 

The textures in homeotropic lamellar phases of lecithin are studied in lecithin-water phases by polarizing microscopy and in dried phases by electron microscopy. In the former, we observe the La phase (the chains are liquid, the polar heads disordered)—the texture displays classical FriedeVs oily streaks, which we interpret as clusters of parallel dislocations whose core is split in two disclinations of opposite sign, with a transversal instability of the confocal domain type. In the latter case, the nature of the lamellar phase is less understood. However, the elementary defects (negative staining) are quenched from the La phase they are dislocations or Grandjean terraces, where the same transversal instability can occur. We also observed dislocations with an extended core these defects seem typical of the phase in the electron microscope. 

At the late stage of lamella orientation, classical topological defects (dislocations and disclinations) dominate [40, 41] (Fig. 8h and Fig. 9), and their movement and annihilation can be followed in Fig. 8h-i and Fig. 9. The latter presents an example of the apparent topological defect interactions and their transformations. Displayed are two dislocations of PMMA, which have an attractive interaction due to their opposite core sign. Therefore, in the next annealing step the dislocation is shifted... 

Hahm J, Sibener SJ (2001) Time-resolved atomic force microscopy imaging studies of asymmetric PS-b-PMMA ultrathin films dislocation and disclination transformations, defect mobility, and evolution of nanoscale morphology. J Chem Phys 114(10) 4730-4740... 

Fig. 22 Simulated images (upper panel) and SFM phase images (300 x 300 nm) (lower panel) presenting classical topological defect configurations in lying cylinders (a, e) cyl-dislocation (b, f) m-dislocation (c, g) +1/2 cyl-disclination and (d, h) +1/2 m-disclination. SB films were annealed under 70% of the saturated vapor pressure of chloroform. Reprinted from [36], with permission. Copyright 2008 American Chemical Society...

Detailed analysis of defect configurations in the cylinder phase and of their evolution allowed us to conclude that representative defect configurations provide connectivity of the minority phase in the form of dislocations with a closed cylinder end or of classical disclinations with incorporated alternative, non-bulk structures with planar symmetry. Further, block copolymers show a strong correlation between the defect structure and chain mobility on both short- and long-term time scales. 

These different contrast mechanisms can all be used to reveal the scale of liquid crystalline polymer microstructures. In specimens that exhibit a mosaic texture, and in those that contain predominantly planar defects, domain size is easily defined in terms of areas that uniformly show extinction between crossed polars. However, if the defects are predominantly linear, as in specimens that exhibit schlieren textures, such simple characterization of microstructural scale is no longer possible. Here it is more convenient to look at the length of disclination line per unit volume, which is equivalent to the number of lines intersecting unit area, and analogous to the dislocation density as defined for crystalline solids. Good contrast is essential in order to obtain an accurate count. Technologically, microstructural scale is of growing interest because of its relevance to processability, mechanical properties and optical transparency. 

Figure 4. Isolated topological defects in a triangular lattice, (a) Isolated -1 and +1 disclinations. A vector aligned along a local lattice direction is rotated by 60° upon parallel transport around a unit strength disclination. (6) An isolated dislocation. The heavy line represents a Burgers circuit around the dislocation, and the Burgers vector of the dislocation is the amount by which the circuit fails to close. The core of the dislocation is a tightly bound pair of +1 and -1 disclinations (Reproduced from [78] by permission of Oxford University Press.)...

The local translational and orientational order of atoms or molecules in a sample may be destroyed by singular points, lines or walls. The discontinuities associated with the translational order are the dislocations while the defects associated with the orientational order are the disclinations. Another kind of defect, dispirations, are related to the singularities of the chiral symmetry of a medium. The dislocations were observed long after the research on them began. The dislocations in crystals have been extensively studied because of the requirement in industry for high strength materials. On the contrary, the first disclination in liquid crystals was observed as early as when the liquid crystal was discovered in 1888, but the theoretical treatment on disclinations was quite a recent endeavor. 

The helical structure of the c-director in the smectic C phase makes the defects different from those in the smectic C phase. As the Volterra process produces a screw dislocation, for example, along the z axis and the Burger vector b = d, it must be accompanied by a parallel wedge disclination in the c-director, in the form... 

Crack tips are line defects, but may resemble disclinations more than dislocations if the sides of the crack are inclined to one another rather than parallel. The differences are significant deformation at the crack tip may be very large leading to the generation of dislocations in the plastically deformed region even in brittle ceramics. If this plastic deformation is large, it actually blunts the crack tip and toughens the ceramic. 

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