Dielectric spectroscopy of liquid crystals

In a simplified picture of the molecular dynamics in the isotropic (liquid) phase and in solid phase, it is commonly assumed that in an isotropic liquid the constituent molecules have freedom of translational and rotational mobility. A solid phase on the other hand, is considered as a state with a high degree of molecular translational and rotational immobilization. Thus at the phase transition, on going from the solid phase to the isotropic phase, molecules are liberated and enabled to move. Traditionally, we refer to this as melting of the translational and rotational degrees of freedom (on going from the solid phase to the isotropic phase, e.g. by warming up a sample) 

The existence of the liquid-crystalline state of matter is not only a function of temperature. A large number of organic materials show liquid crystallinity in properly chosen solvents. Systems which exist in the liquid-crystalline state in a definite range of temperature are called thermotropics, while the second group is known as lyotropics. Both groups show a rich polymorphism. While mesophases of rod-like thermotropic liquid crystals can essentially be subdivided into two 

Some examples of liquid-crystalline monomer materials 

If we approximate the liquid-crystalline molecules by rod-like particles, then the basic thermotropic mesophases can be visualized schematically as in Fig. 4.5. The nematic phase is the least organized of all liquid-crystalline phases and usually appears just below the isotropic phase. In this phase the centers of mass of the elongated molecules have three translational degrees of freedom and thus are distributed randomly as in an ordinary isotropic liquid. However, the long axes of the neighbouring molecules are preferentially aligned with respect to an axis which is called the director, usually denoted by a unit vector n. If the molecules have mirror symmetry, the ordinary nematic phase is observed. It is nearly always characterized by uniaxial symmetry and equivalence of n and — n. For molecules without mirror symmetry, however, the spatial variation of n leads to an helical structure. If one considers a plane perpendicular to the helix axis, then the direction of n is the same in this plane, but it 

In smectic phases there is, in addition to the orientational order, also a positional order in at least one direction. As a result, the centers of mass of molecules are, on average, arranged in equidistant planes, so the smectic phase is frequently visualized as a layered structure, in general with uniform director orientation within each layer (see Fig. 4.5). A number of different smectic phases have been found and the differences between them consist in (i) the orientation of the preferred direction of the molecules (the director) with respect to the layer normal, and (ii) the organization of the centers of molecules in the plane of the layer. 

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