Defects in Liquid Crystals

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. 

There is only the orientational order in nematics so that only disclinations may appear with no dislocations. In the other kinds of liquid crystals, 

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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. 

Note 1 Disloeations and diselinations are major types of defects in liquid crystals. 

Now we briefly discuss the topological homotopy theory that classifies defects in liquid crystals and judges the stability of the defects according to the symmetry of liquid crystals. 

The singularities in the liquid crystals cause the deformation of the director field of liquid crystals and thus affect the symmetry of liquid crystals. This idea provides an approach to analyze the characteristics of the defects. The order vectors (or scalars, or tensors) of various liquid crystals are not the same. The director n is the order vector of the nematic liquid crystals, but the order for the cholesteric liquid crystals is a symmetric matrix, i.e., a tensor. Because the order vector space is thus a topological one, any configuration of the director field of liquid crystals is thus represented by a point in the order vector space. The order vector space (designated by M) is associated with the symmetry of liquid crystals. The topologically equivalent defects in liquid crystals constitutes the homotopy class. The complete set of homotopy classes constitutes a homotopy group, denoted Hr(M). r is the dimension of the sub-space surrounding a defect, which is related to the dimension of the defect (point, line or wall) d, and the dimension of the liquid crystal sample d by... 

Chandrasekhar S and Ranganath G S 1986 The structure and energetics of defects in liquid crystals Adv. Phys. 35 507-96... 

M. Kleman, Defects in liquid crystals. Rep. Prog. Phys. 52, 555 (1989)... 

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. 

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). 

O.D. Lavrentovich, P. Patsini, C. Zannoni, and S. Zumer (eds.). Defects in Liquid Crystals Computer Simulations, Theory and Experiments, Kluwer, Dordrecht (2001). 

In this chapter we will discuss possible realizations of liquid crystalline ordering in conductive polymers. Section II presents basic properties of conducting polymers with a brief description of charge transport mechanisms in those systems. Section III discusses structural types and defects in liquid crystals, and Section IV covers some experimental results of the structural analysis of mesophases in polymers with flexible side chains and polymer/surfactant systems. Sections III and IV are presented to emphasize the properties important to conducting polymers. In Section V experimental data on liquid crystallinity in conductive polymers will be reviewed. Conclusion will be given in Section VI,... 

M.V. Kurik and O.D. Lavrentovich, Defects in liquid crystals Homotopy theory and experimental studies, Uspekhi Fiz. Nauk 154, 381 (1988) Sov. Phys. Uspekhi 31, 196 (1988)). 

E. Bodenschatz, M. Kaiser, L. Kramer, W. Pesch, A. Weber, W. Zimmermann Patterns and defects in liquid crystals, in P. Coullet, P. Huerre (eds) New Trends in Nonlinear Dynamics and Pattern Farming Phenomena The Geometry of Nonequilibrium, Plenum Press, NATO ASl Series, (1990) W. Pfesch, W. Decker, Q. Rng, M. Kaiser, L. Kramer, A. Weber Weakly nonlinear analysis of pattern formation in nematic liquid crystals, in J. M. Coron, E Helein, J. M. Ghidaglia (eds) Nematics Mathematical and Physical Aspects, Kluwer Academic Publishers, Dordrecht, NATO ASl Series, p. 291 (1991)... 

Ordered media are never perfect, but present deformations and even defects. In liquid crystals, the order is defined by several parameters, mainly the local mean direction of approximately parallel molecules, usually represented by a unit vector n chosen parallel either to the long axis if the molecule is elongated, or normal to the molecules if the molecule is discoidal. A second local variable is the order parameter, which corresponds to a more or less accurate alignment of molecules. The orientation of n is often chosen arbitratily (+n equivalent to -n), since there are no polarities in the distribution of molecules, even if the chemical formula is arrowed , as in the classical example of 4-methyloxy-4 -n-butylbenzyli-dene aniline (MBBA) molecules. Both the parallel and the antiparallel alignment occur in equal proportions. In this case, n is called a director, with only the direction of the molecules being defined, with no preferred orientation. 

Brinkman WF, Cladis PE (1982) Defects in liquid crystals. Phys Today 35(5) 48-54 Chandrasekhar S (1977) Liquid crystals. Cambridge University Press, Cambridge Chen YD, Fuh AYG, Cheng KT (2012) Particular thermally induced phase separation of liquid crystal and poly(N-vinyl carbazole) films and its application. Opt Express 20 16777-16785 Cho JD, Lee SS, Park SC, Kim YB, Hong JW (2013) Optimization of LC droplet size and electro-optical properties of acrylate-based polymer-dispersed liquid crystal by controlling photocure rate. J Appl Polym Sci 130 3098-3105... 

G.R. Luckhurst [ in L amics and Defects in Liquid Crystals A Festschrift in Honour of Alfred Saupe Eds. P.E. Cladis, P. Palffy-Muhoray (Gordon and Breach Science Publishers, Amsterdam, 1998) ]... 

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