The three classic states of matter are well known and ubiquitous in everyday life: solid, liquid, and gas. Liquid crystals (LCs), an intermediate state between solid crystal and isotropic liquid, constitute a new fascinating class of condensed soft matter uniquely combining both fluidity and long-range order. The fluid-like mobility enables LCs to be switchable under external stimuli, and crystal-like long-range order bestows anisotropic physical properties on LCs. LCs can be divided into two main classes: thermotropic and lyotropic. Thermotropic LCs consist of individual molecules (or ion pairs) and exhibit phase transitions with the change of temperature. In this case, temperature is the fundamental thermodynamic factor determining mesophase formation. Lyotropic LCs are a special type of solution system that can form mesophases as a function of both temperature and concentration of LC molecules. The building block of a lyotropic phase is an aggregate (called a micelle) formed via self-assembly of many molecules (typically on the order of 100). Examples of LCs can be found both in the natural world and in technological applications. Thermotropic LCs find 189 190 ELECTRIC-AND LIGHT-RESPONSIVE BENT-CORE LIQUID CRYSTALS a wide variety of uses in displays, and an important example of lyotropic LCs is cell membranes formed by amphiphilic lipids. Surfactants in water (i.e., soap water) constitute another useful example of lyotropic LCs. Although the majority of LCs are organic molecules, there exist many LC materials incorporating metals into organic anisotropic molecules [1-3]. These organic-inorganic hybrid LC materials are described as metallomesogens and are recently called metallotropic LCs [4] as distinguished from two main LC classes. In fact, metallomesogens can be classified as either thermotropic or lyotropic LCs depending on their composition and conditions. However, it should be noted that metallomesogens offer a material platform to incorporate magnetic, electronic, optical, redox, and catalytic properties common to inorganic materials into LCs.Although thermotropic LCs have been known to scientists for over 100 years since a discovery by the Austrian botanical physiologist Friedrich Reintizer in 1888, it was only in the late 1960s that they began to be used in display applications. Today, they are best known for their exceptionally successful commercial applications in flat panel display products such as TVs, smart phones, computer displays, and digital projectors. Although today's LC display technology is becoming very advanced, LC materials used in display devices possess the simplest nematic (N) phase and their molecules have been variants on simple rod shapes (Fig. 6.1a). Besides nematic phases, LCs can exhibit other phases: smectic (Sm), columnar (Col), and cubic phases, depending on the orientational or positional orders of their molecules. Nematic phases have only long-range orientational order, smectic mesophases exhibit one-dimensional (1D) positional order and form two-dimensional (2D) layered ...