Liquid Crystals. Iam-Choon Khoo

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ampersand c period circ semicolon"/>. In the case of smectic‐A, which possesses rotational symmetry around ModifyingAbove n With ampersand c period circ semicolon, ModifyingAbove p With ampersand c period circ semicolon must therefore be vanishing. In the case of smectic‐C, there is a reflection symmetry (mirror symmetry) about the plane defined by the ModifyingAbove n With ampersand c period circ semicolon and ModifyingAbove z With ampersand c period circ semicolon axes, so ModifyingAbove p With ampersand c period circ semicolon is also vanishing. This reflection symmetry is broken if a chiral center is introduced to the molecule, resulting in a smectic‐C* system.

      By convention, ModifyingAbove p With ampersand c period circ semicolon is defined as positive if it is along the direction of ModifyingAbove z With ampersand c period circ semicolon times ModifyingAbove n With ampersand c period circ semicolon, and negative otherwise. Figure 1.13c shows that since ModifyingAbove n With ampersand c period circ semicolon precesses around ModifyingAbove z With ampersand c period circ semicolon, ModifyingAbove p With ampersand c period circ semicolon also precesses around ModifyingAbove z With ampersand c period circ semicolon. If, by some external field, the helical structure is unwound and ModifyingAbove n With ampersand c period circ semicolon points in a fixed direction, as in Figure 1.12d, then ModifyingAbove p With ampersand c period circ semicolon will point in one direction. Clearly, this and other director axis reorientation processes are accompanied by a considerable change in the optical refractive index and other properties of the system, and they can be utilized in practical electro‐ and opto‐optical modulation devices. More detailed discussions of smectic liquid crystals are given in Chapter 4.

      1.3.4. Functionalized and Discotic Liquid Crystals

      In general, temperature ranges for the various mesophases of single constituent liquid crystals are quite limited. Therefore, while many fundamental studies are still conducted on such liquid crystalline materials, industrial applications employ mostly mixtures, composites, or specially doped liquid crystals with large operating temperature range and tailor‐made physical and optical properties.

Schematic illustration of a shuttlecock-shaped liquid crystal formed by incorporating fullerene C60 into various liquid crystals was reported.

      Besides these molecular synthesis techniques, there are other ways to dramatically improve the performance characteristics of liquid crystals. In the following sections, we describe three well‐developed methods, focusing our discussion on nematic liquid crystals as they exemplify the unique characteristics of liquid crystals widely used in optical and photonic applications.

      1.4.1. Mixtures

Schematic illustration of phase diagram of the mixture of two liquid crystals.

      If

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