Basic Descriptions of Liquid Crystals

Figture 1.2 A schematic representation of a nematic liquid crystal phase where the short bold lines represent the molecules. A unit vector n, called the director, describes the average direction of the molecular alignment along what is commonly called, in uniaxial nematics, the anisotropic axis. 

It proves convenient to introduce a unit vector n, called the director, to describe the local direction of the average molecular alignment in liquid crystals, as shown in Fig. 1.2. The absence of polarity means that n and —n are indistinguishable, in the sense that the sign of n has no physical significance. 

The word nematic comes from the Greek word urjpa, meaning thread, arising from the thread-like textures often seen in nematic samples. These threads correspond to lines of singularity in the director alignment called disclinations. Such defects will be discussed below in Section 3.8 after a more detailed mathematical description of nematic liquid crystals is given in Chapter 2. 

Before going on to discuss briefly other basic liquid crystal phases, it is worth recording some points about the development of nematic liquid crystals, since a substantial part of this book concerns these substances. The first nematic liquid crystal, p-azoxyanisole (PAA), was synthesised by Gattermann and Ritschke [102], who reported their results in 1890 it was the first liquid crystal not based on a naturally occurring substance and went on to be extensively investigated by Lehmann and others. The first relatively stable room temperature nematic liquid crystal, 4-methoxybenzylidene-4 -butylaniline (MBBA), was synthesised by Kelker and Scheurle [142] in 1969, but, for various reasons, this substance was not considered suitable for some applications. The nematic liquid crystal 4-pentyl-4 -cyanobiphenyl (5CB) is an example of a stable room temperature material designed for use in twisted nematic displays (discussed in Section 3.7) and was synthesised by Gray and co-workers in the early 1970 some details can be found in articles [117, 118). 

Some of the physical parameters for the nematic Uquid crystals PAA, MBBA and 5CB are given in Table D.3 on page 330, which should guide those interested in the theoretical modelling of nematics. In many practical situations, it should be borne in mind that mixtures of nematic materials are often used in displays. 

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The aim of this book is to present a mathematical introduction to the static and dynamic continuum theory of liquid crystals. Before doing so, we outline some points on the discovery and basic description of liquid crystals in Sections 1.1 and 1.2. This is followed by a short summary of the development of the continuum theory of liquid crystals in Section 1.3. The Chapter closes in Section 1.4 with some basic comments on the notation and conventions employed in later Chapters and refers to some sources for those who may require further background on some of these conventions used throughout this book. 

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