Liquid crystals (LCs) present a state of matter with properties—as the name suggests—intermediate between those of liquids and crystalline solids. Liquid-crystalline materials, as all liquids, cannot support shear stresses at static equilibrium. Their molecules are characterized by an anisotropy in the shape and/or intermolecular forces. Thus, there is the potential for the formation of a separate phase(s), called a “mesophase(s),” where a partial order arises in the molecular orientation and/or location, which extends over macroscopic distances. This partial long-range molecular order, reminiscent of (but not equivalent to) the perfect order of solid crystals, in addition to the material fluidity, is primarily responsible for the many properties which are inherent characteristics of liquid-crystalline phases, such as a rapid response to electric and magnetic fields, anisotropic optical and rheological properties, etc.—see, for examples, the reviews by Stephen and Straley [1974] and Jackson and Shaw [1991], the monographs by de Gennes [1974], Chandrasekhar [1977], and Vertogen and de Jeu [1988], and the edited volumes by Ciferri et al. [1982] and Ciferri [1991]. The variety of the liquid-crystalline macroscopic properties is such that trying to derive a theory capable of describing the principal liquid-crystalline dynamic characteristics can be a very frustrating task if one does not approach the issue in a systematic fashion. Characteristically, the main two theories that have been advanced over the last thirty years for the description of the liquid-crystalline flow behavior—the Leslie/ Ericksen (LE) theory and the Doi theory—are essentially models developed from a set theoretical frame work—continuum mechanics and molecular theory, respectively. Nevertheless, each one of these theories has a limited domain of application. The description of the dynamic liquid-crystalline behavior through the bracket formalism, as seen in this chapter, leads naturally to a single conformation tensor theory with an extended domain of validity. This conformation theory consistently generalizes both previous theories, which can be recovered from it as particular cases. This offers additional evidence that the wealth of inherent information in LCs can only be appropriately handled when pursued in a systematic, fundamental manner.
Light Propagation in Confined Nematic Liquid Crystals and Device Applications
