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Figure 1.7. Transmission spectra of nematic liquid crystals: (a) 5CB; (b) N‐(4‐methoxybenzylidene)‐4‐butylaniline (MBBA).

      The absorption coefficient α in the UV (~0.2 μm) regime is on the order of 10³ cm⁻¹; in the visible (~0.5 μm) regime, α ≪10⁰ cm⁻¹; in the near‐IR (~3–5 μm and ~9–12 μm) regime, α ~ 10² cm⁻¹. There are, of course, large variations among the thousands of liquid crystals that have been synthesized. It is possible to identify liquid crystals with the desirable absorption/transparency for a wavelength of interest. For example, the terahertz and microwave regime, [5, 6] have identified/synthesized liquid crystals (LC’s) with relatively low absorption coefficient α ~ 10⁰ cm⁻¹; low absorption is important since applications in such long‐wavelength regimes require much thicker interaction length (cell thickness).

A unique advantage of liquid crystals is the sizeable birefringence throughout the entire visible–IR‐terahertz‐microwave spectrum. At the 20–60 GHz region, [6] has shown that for a typical liquid crystal such as E7, ε_e = 3.17 (refractive index n_e = 1.78) and ε₀ = 2.72 (refractive index n₀ = 1.65), i.e. a birefringence Δn ~ 0.13.

1.3. LYOTROPIC, POLYMERIC, AND THERMOTROPIC LIQUID CRYSTALS

      There are several distinct types of liquid crystals: lyotropic, polymeric, thermotropic, and discotic. These materials exhibit liquid crystalline properties as a function of different physical parameters and environments such as temperature, molecular constituents’ structure, and concentration.

      1.3.1. Lyotropic Liquid Crystals

      Lyotropic liquid crystals are obtained when an appropriate concentration of material is dissolved in some solvent. The most common systems are those formed by water and amphiphilic molecules (molecules that possess a hydrophilic part that interacts strongly with water and a hydrophobic part that is water insoluble) such as soaps, detergents, and lipids. Here the most important variable controlling the existence of the liquid crystalline phase is the amount of solvent (or concentration). There are quite a number of phases observed in such water‐amphiphilic systems, as the composition and temperature are varied; some appear as spherical micelles, and others possess ordered structures with 1‐, 2‐, or 3‐D positional order.

Examples of these kinds of molecules are soaps (Figure 1.8) and various phospholipids like those present in cell membranes. Lyotropic liquid crystals are of interest in biological studies [7].

Figure 1.8. Chemical structure and cartoon representation of sodium dodecyl sulfate (soap) forming micelles.

      1.3.2. Polymeric Liquid Crystals

Polymeric liquid crystals are basically the polymer versions of the monomers discussed in Section 1.1. A good account of polymeric liquid crystals may be found in [9]. There are three common types of polymers, as shown in Figure 1.9a–c, which are characterized by the degree of flexibility. The vinyl type (Figure 1.9a) is the most flexible, the Dupont Kevlar polymer (Figure 1.9b) is semirigid, and the polypeptide chain (Figure 1.9c) is the most rigid. Mesogenic (or liquid crystalline) polymers are classified in accordance with the molecular architectural arrangement of the mesogenic monomer. Main‐chain polymers are built by linking rigid mesogenic groups in a manner depicted schematically in Figure 1.10a; the link may be a direct bond or some flexible spacer. Liquid crystal side‐chain polymers are formed by pendant side attachment of mesogenic monomers to a conventional polymeric chain, as depicted in Figure 1.10b.

Figure 1.9. Three different types of polymeric liquid crystals: (a) vinyl type; (b) Kevlar polymer; (c) polypeptide chain.

Figure 1.10. Polymeric liquid crystals: (a) main chain; (b) side chain.

      1.3.3. Thermotropic Liquid Crystals: Smectic, Nematic, Cholesteric, and Blue‐phase Liquid Crystals

      Although the molecular structures of thermotropic liquid crystals are quite complicated, they are often represented as “rigid rods” that interact with one another to form distinctive ordered structures (or phases) as a function of ascending temperature: crystals, smectic, nematic, cholesteric (including blue‐phase), and the isotropic liquid phase. In smectic liquid crystals, there are several subclassifications in accordance with the positional and directional arrangement of the molecules.

      As explained in greater detail in the following chapters, these mesophases are defined and characterized by many physical parameters such as long‐ and short‐range order, orientational distribution functions, and so on. Here we continue to use the rigid‐rod model and pictorially describe these phases in terms of their molecular arrangement.

Figure 1.11a depicts the collective arrangement of the rodlike molecules in the

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