Liquid crystals are ubiquitous. They are in silk, snail slime, and crude oil. They are in mantles of neutron stars, and provide models for cosmic strings. They are in our food (gluten) and drinks (milk). The behavior of hair cells in the inner ear and the function of DNA are affected by them. The insulating coating of the axons of nerve cells is a liquid crystal called myelin. Liquid crystals are very responsive to excitations, which has led to many useful applications, such as liquid crystal displays. A great deal is known and understood about liquid crystalline materials (Chandrasekhar, 1992; de Gennes and Prost, 1993).

Liquid crystalline materials are orientationally ordered soft matter (Palffy-Muhoray, 2007). These materials are composed of large organic molecules, which have a long and rigid core, typically consisting of several linked benzene rings, terminated by a flexible alkyl chain. Such a molecular structure is then often modeled by disk-like or rod-like entities, depending on the cylindrical aspect ratio. Such model molecules have a head–tail symmetry. Thus, at high densities, liquid crystals can naturally create local orientational order. Onsager (1949) showed that hard rods tend to align at volume fractions larger than about four times their breadth-to-length ratio. Many liquid crystal phases can exist, depending on the temperature and solvent concentration. Some of these phases are shown in Fig. 11.1.

An isotropic disordered liquid phase exists at high temperatures. As the temperature is lowered, there is a competition between the positional and orientational entropies: the former favors a random location for a rod and the latter a random orientation.