Mesogenic Molecules and Orientational Order

Essentially all of the techniques developed to characterize MLCs can be applied to PLCs with the realization that phenomena that are dependent on reorientation processes in the liquid crystal must be considered on considerably longer time scales in a PLC. Underlying most of the physical measurements performed on liquid crystals is the relationship between the observed anisotropic properties of the mesophase and orientational order of the mesogen. For uniaxial nematic phases and idealized low molar mass mesogens (cylindrical molecules), this relationship is embodied in the following equation ... 

The Hermans orientation function can be given a relatively simple interpretation. A sample with orientation / may be considered to consist of perfectly aligned molecules with mass fraction / and randomly oriented molecules with mass fraction 1 — /. PLCs are often characterized by their order parameter (denoted s), a concept coined by Tsvetkov [16]. This quantity is basically equivalent to the Hermans orientation function. For nematics and smectics the director represents the average mesogen direction and the order parameter can thus only take positive values. For cholesteric phases, on the other hand, the director is chosen perpendicular to the layers and in this case the order parameter takes negative values. 

Of all liquid crystalline phases, the nematic phase is the phase with the highest symmetry, i.e. Dooh, and the least order. As shown in Fig. 3.3a, b, the mesogens solely possess orientational order. Positional order of the mass centers does not occur in this phase. Nematic phases are usually built up by either rod-like or disc-like mesogens. For thermotropic liquid crystals these mesogens are therefore calamitic or discotic molecules, respectively. In both cases the phase is simply denoted with the abbreviation N. For lyotropics, the notation typically distinguishes between nematic phases Nc, which are formed by rod-like micelles, and nematic phases Np, which are composed of disc-like micelles. 

Thennotropic liquid crystal phases are fonned by anisotropic molecules witli long-range orientational order and in many types of stmcture witli some degree of translational order. The main types of mesogen are Arose tlrat are rodlike or calamitic and Arose Arat are disclike or discotic. 

The mesophases of calamitic mesogens are classified in two groups nematic and smectic. The nematic mesophase (N) is characterized by an orientational order of the molecules that are aligned along a preferred direction (defined by a director n) (Figure 8.2). The molecules can slide and move in the nematic mesophase (while roughly keeping their molecular orientation) and rotate around their main axis. This is the less ordered mesophase and it is usually very fluid. 

The liquid crystal phases of calamitic mesogens fall into two types - nematic (N) and smectic (Sm). The nematic phase is the most disordered of the liquid crystal phases and possesses only orientational order, so that the long axes of the molecules are correlated in one direction (known as the director, n) while being positioned randomly (Fig. 2A). There are several smectic phases and these differ from the nematic phase in possessing partial posi-... 

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