Thermodynamic states and symmetry of liquid crystals

All the diverse types of liquid-crystalline states can be described in a unified manner by analogy with the group-theoretical description of the symmetry and properties of crystals. The symmetry properties of liquid crystals with respect to the orientation of the molecules, and the conditions for the appearance of a modulated orientational structure, are considered. The phase diagrams in liquid crystals are described, and a general scheme of the phase transitions between liquid-crystalline phases is given. The problem of the ferroelectric state in liquids is considered, and the classes of anisotropic liquids that possess ferroelectric and piezoelectric properties are demonstrated. A thermodynamic description is given of the ferroelectric phenomena observed experimentally in smectic liquid crystals. The question of the physical nature of the low-symmetry smectic phases is discussed and the character of the phase transitions in liquid crystals is considered.