Types of mesophases for small molecules

There are two principal categories of mesophases, thermotropic and lyotropic. Thermotropic liquid crystals are formed within a particular range of temperature in a molten material, with no solvent present, whereas lyotropic liquid crystals are formed by some substances when they are dissolved in a solvent. Within each of these categories there are three distinct classes of mesophases, which were first identified by Friedel in 1922. The simplest of these to describe are the nematic and smectic classes, illustrated schematically in fig. 12.16. These phases are formed by long thin rigid molecules which tend to line up parallel to each other. 

The word nematic means thread-like and in the nematic phase there is simply a tendency for the rods to become parallel to each other unlike the molecules in a true crystalline phase, they are not exactly parallel and there is no long-range correlation between the positions of adjacent molecules. The average direction of the molecules is called the director and is indicated in fig. 12.16 by the arrow labelled n. 

The word smectic describes the soapy feel of the smectic phase. The dilference between the ordering in this phase and that in the nematic phase is that, in addition to the rods being nearly parallel, there is a very strong tendency for the ends of the molecules to lie in parallel planes, so that the structure becomes layered, as indicated in fig. 12.16. The layered structure is responsible for the soapy feel. As in the nematic phase, the rods are not exactly parallel and there is no long-range correlation between the lateral positions of the rods. There are several varieties of smectic structure. If the director is normal to the planes of the layers, as shown in fig. 12.16, the variety is smectic A if the director is inclined at the same angle for all layers, it is smectic C. 

The third class of liquid crystals is the cholesteric class, which is of rather less importance for synthetic polymers than the other two classes. In this 

In a particular domain of a liquid crystal the axes of the molecules are equally likely to lie anywhere within the range of angles 0 = 0 to from the director. Derive an expression for the order parameter S for the domain and evaluate S for 9o = 20°. 

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