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Introduction to Liquid Crystals

Liquid crystals are wonderful materials. In addition to the solid crystalline and isotropic liquid phases, they exhibit many so-called mesophases in which they flow like ordinary liquids yet possess crystalline properties [1]. These mesophases are characterized by many unique physical and optical properties and offer a fertile ground for several areas of fundamental pursuits, as well as applications in display screens of ubiquitous devices, photonics, THz and microwave and biomedical systems [2-8].

1.1. MOLECULAR STRUCTURES AND CHEMICAL COMPOSITIONS

With few exceptions, liquid crystals are composed of organic substances with a typical structure, as depicted in Figure 1.1. They are aromatic and, if they contain benzene rings, they are often referred to as benzene derivatives. In general, aromatic liquid crystal molecules such as those shown in Figure 1.1 comprise a side chain R, two or more aromatic rings A and A´, connected by linkage groups X and Y, and at the other end connected to a terminal group R´.

Examples of side chain and terminal groups are alkyl (CnH2n+1), alkoxy (CnH2n+1O), and others such as acyloxyl, alkyl carbonate, alkoxy carbonyl, and the nitro and cyano groups. The Xs of the linkage groups are simple bonds or groups such as stilbene (-?-), ester (-?-), tolane (--), azoxy (--), Schiff base (-?-), acetylene (?-??-), and diacetylene (-). The names of liquid crystals are often fashioned after the linkage group (e.g. Schiff-base liquid crystal). There are quite a number of aromatic rings. These include saturated cyclohexane or unsaturated phenyl, biphenyl, and terphenyl in various combinations.

The majority of liquid crystals are benzene derivatives; the rest include heterocyclics, organometallics, sterols, and some organic salts or fatty acids. Their typical structures are shown in Figures 1.2-1.4. Heterocyclic liquid crystals are similar in structure to benzene derivatives, with one or more of the benzene rings replaced by a pyridine, pyrimidine, or another similar group. Cholesterol derivatives are the most common chemical compounds that exhibit the cholesteric (or chiral nematic) phase of liquid crystals. Organometallic compounds are special in that they contain metallic atoms and possess interesting dynamical and magneto-optical properties.

Figure 1.1. Molecular structure of a typical liquid crystal.

Figure 1.2. Molecular structure of a heterocyclic liquid crystal.

Figure 1.3. Molecular structure of an organometallic liquid crystal.

Figure 1.4. Molecular structure of a sterol.

All the physical and optical properties of liquid crystals such as dielectric constants, elastic constants, viscosities, absorption spectra, transition temperatures, the existence of mesophases, anisotropies, and optical nonlinearities are governed by the properties of these constituent groups and how they are chemically synthesized together. Since these molecules are quite large and anisotropic, and therefore very complex, it would take a treatise to discuss all the possible variations in the molecular architecture and the resulting changes in their physical properties. Nevertheless, there are some general observations one can make on the dependence of the physical properties on the molecular constituents [2]. For example, the chemical stability of liquid crystals depends very much on the central linkage group. Schiff-base liquid crystals are usually quite unstable. Ester, azo, and azoxy compounds are more stable but are also quite susceptible to moisture, temperature change, and ultraviolet (UV) radiation. Compounds without a central linkage group are among the most stable liquid crystals ever synthesized. The most widely studied one is 5CB (pentyl cyanobiphenyl), whose structure is shown in Figure 1.5. Other compounds such as pyrimide and phenyl cyclohexane are also quite stable.

Figure 1.5. Molecular structure of 5CB (pentyl cyanobiphenyl).

1.2. OPTICAL PROPERTIES

In general, optical properties of liquid crystals fall into two distinct categories: those characteristics of individual constituent molecules and those unique to the bulk crystalline mesophases. Here we discuss optical properties that are largely decided by the individual constituent molecules; optical properties associated with various ordered mesophases of liquid crystals are elaborated in later chapters.

1.2.1. Electronic Optical Transitions and UV Absorption

Since liquid crystal constituent molecules are quite large, their energy level structures are rather complex. In essence, the basic quantum mechanical theory is similar to the one described in Chapter 10 for a multilevel molecule. Generally, the energy levels are referred to as orbitals: p, n, and s orbitals for the ground and low-lying levels and p *, n *, and s * for their excited counterparts. Since most liquid crystals are aromatic compounds, containing one or more aromatic rings, the energy levels or orbitals of aromatic rings play a major role. In particular, the p p * transitions in a benzene molecule have been extensively studied. Figure 1.6 shows three possible p p * transitions in a benzene molecule.

In general, these transitions correspond to the absorption of light in the near-UV spectral region (=200 nm) [2]. These results for a benzene molecule can also be used for interpreting the absorption of liquid crystals containing phenyl rings. On the other hand, in a saturated cyclohexane ring or band, usually only s electrons are involved. The s s * transitions correspond to absorption of light of shorter wavelength (=180 nm) in comparison to the p p * transition mentioned previously.

These optical properties are also related to the presence or absence of conjugation (i.e. alternations of single and double bonds, as in the case of a benzene ring). In such conjugated molecules, the p electron's wave function is delocalized along the conjugation length, resulting in absorption of light in a longer wavelength region compared to, for example, that associated with the s electron in compounds that do not possess conjugation. Absorption data and spectral dependence for a variety of molecular constituents, including phenyl rings, biphenyls, terphenyls, tolanes, and diphenyl-diacetylenes, may be found in [2].

Figure 1.6. The p p* electronic transitions in a benzene molecule.

1.2.2. Visible and Infrared Absorption; Terahertz, Microwave

The spectral transmission dependence of two typical liquid crystals is shown in Figure 1.7a and b. Liquid crystals are quite absorptive in the UV region, as are most organic molecules/liquids. In the visible and near-infrared (IR) regime (i.e. from 0.4 to ~2 µm), there are no absorption bands, and thus liquid crystals are quite transparent in this regime. In the mid-IR (3-5 µm) and IR (9-12 µm), rovibrational transitions begin to dominate, and liquid crystals are quite absorptive in this spectral area (Table 1.1).

Table 1.1 Anisotropic Physical Parameters of a Typical Nematic Liquid Crystals (E7)

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

The absorption coefficient a in the UV (~0.2 µm) regime is on the order of 103 cm-1; in the visible (~0.5 µm) regime, a «100 cm-1; in the near-IR (~3-5 µm and ~9-12 µm) regime, a ~ 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...