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Understanding and working with liquid crystals requires a multidisciplinary set of skills that brings topics normally associated with physics, chemistry, and condensed matter physics to bear on a single problem. In this book our interest is to emphasize another discipline—that of optics—which, based on what we have discussed so far, has been a driving application for liquid crystals, as they are a primary component of display technologies. The unique properties of liquid crystals revolve around the position and orientation of their molecules, topics closely associated with condensed matter physics. The tools of condensed matter physics, which deals with the physics of the phases of condensed matter and attempts to explain the observed behavior drawing from thermodynamics and statistical mechanics, have evolved over time, in particular, with the acceptance of quantum mechanics. The early studies that led to the acceptance of quantum mechanics often involved studies of crystal structures, and the use of x-ray diffraction led to the understanding of the order structure of crystals being related to the orientation of atoms in a lattice. The positional variations of properties, anisotropies, are modeled to incorporate the uniqueness of each direction using tensor mathematics. Tensor descriptions of systems are not new in the area of condensed matter physics, and, clearly, liquid crystals deal with the more familiar condensed phases of solids and liquids and, in particular, crystals and liquids. The importance of position and orientation in describing the molecules of liquid crystals makes the descriptions common in condensed matter physics useful in modeling the anisotropies of liquid crystals and lead rapidly to the need to delve into the mathematical topic of vectors and tensors for describing liquid crystals.
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