Thermotropic Mesophases Formed by Achiral Rod-Like Molecules

2 Thermotropic Mesophases Formed by Achiral Rod-like Molecules 

This class of materials is of fundamental importance for the further discussion of their electrooptical properties. Traditionally, we divide these mesophases into the nematic and various smectic phases [1-5]. Nematic liquid crystals are characterized by long-range orientational order and the random disposition of the centers of gravity of individual molecules. As for an isotropic liquid, the density does not depend on coordinates 

The direction of preferred orientation of the molecules is usually characterized by a unit vector L, which satisfies the condition L = —L valid for any nonpolar media. This vector is called the director. In nematic liquid crystals the director coincides with the direction of the optical axis z, so that its components are (0,0, Fig. 1.2(a). 

The nematic phase is cylindrically symmetric with respect to the z-axis and, in addition, it possesses a mirror plane perpendicular to z (the point symmetry group is Dooh)- 

The director determines only the direction of the preferred orientation of the molecules, and indicates nothing about the degree of orientational order in the mesophase. The order parameter, 5, which is the first moment P2 in the expansion of the cylindrical distribution function of molecules in the Legendre polynomial series, provides just such a measure of the long-range orientational order 

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