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directionally correlated; they are aligned in a general direction defined by a unit vector ñ, the so‐called director axis, which may be regarded as the crystal axis. Nevertheless, the molecules are positionally random and exhibit flow very much like liquids; X‐ray diffraction from nematics does not exhibit any diffraction peak.

Schematic illustration of self-organization of the rod-shaped LC molecules via local and long-range order giving rise to various ordered phases of liquid crystal. Schematic illustration of arrangement of dipoles in the centrosymmetric bulk crystal such as nematics. Schematic illustration of molecular arrangements of liquid crystals.

      The smectic‐C phase is different from the smectic‐A phase in that the material is optically biaxial, and the molecular arrangement is such that the long axis is tilted away from the layer normal ModifyingAbove z With ampersand c period circ semicolon (cf. Figure 1.13b).

      Smectic‐C* liquid crystals are interesting in one important aspect; namely, they comprise a system that permits, by the symmetry principle, the existence of spontaneous electric polarization. This can be explained simply in the following way. The spontaneous electric polarization ModifyingAbove p With ampersand c period circ semicolon is a vector and represents a breakdown of symmetry; that is, there is a directional preference. If the liquid crystal properties are independent of the director axis ModifyingAbove n With ampersand c period circ semicolon direction (i.e. plus ModifyingAbove n With ampersand c period circ semicolon is the same as minus ModifyingAbove n With ampersand c period circ semicolon), ModifyingAbove p With ampersand c period circ semicolon, if it exists, must be locally perpendicular to ModifyingAbove n With 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 Скачать книгу