Liquid Crystals

Liquid crystals (LCs) represent a state of matter intermediate between crystalline solids, which are characterized by a regular periodic arrangement of atoms or molecules, and isotropic liquids, which lack any type of order. They exhibit varying degree of orientational and/or translational order in specific spatial directions. For example, in the LC phase known as the smectic-A (SmA), with molecules arranged in stacked layers, one-dimensional translational order similar to a crystal exists in the stacking direction. However, within the layers, the molecular arrangement is liquid-like. Such a phase that is ‘‘liquid’’ in the two in-plane directions and ‘‘crystal’’ in the third, is one example of a large number of LC phases. LC phases are formed by materials made of anisotropic molecules or other entities, such as aggregates of molecules in surfactant solutions known as micelles. LC phases formed by surfactant solutions are known as lyotropic liquid crystals and their discussion is beyond the scope of this article. The simplest of the LC phases, the nematic (N) phase, is formed when the molecules are oriented, on average, parallel to a common direction represented by an apolar unit vector, n, referred to as the ‘‘director.’’ The structure of the phases with degrees of order higher than the N phase is different for different molecular shapes. Different nomenclatures are introduced here to describe them. For the purpose of this article, the N phases are described first, followed by other phases exhibited by rod-like, disk-like, and then bent-core (banana) shaped molecules. Although more than 50....