The Dielectric Properties of Liquid Crystals

The dielectric constant of an insulating material e, also known as the permittivity, can be defined as the extent to which a material will become electrically polarized in the presence of an electric field. In an isotropic material, we define a single dielectric constant. However, the anisotropic nature of liquid crystal materials, such as the nematic phase, means that the direction of the electric field with respect to the liquid crystal director is important. In this case, we can define two different dielectric constants, ey and e. ey represents the ability of the molecule to polarize along the long axis and to polarize along the short axis. The existence of these two different dielectric constants means that we can define a new quantity, the dielectric anisotropy, 

The dielectric anisotropy Ae can be either positive or negative, with positive Ae materials orienting with their long axis parallel to the E-field and negative Ae materials orienting with their short axis parallel to the E-field. Practically, the magnitude of Ae represents the ease with which the molecules will respond to an applied field the larger the value of Ae, the easier it is to reorient the liquid crystal molecules. 

The dielectric constants for a liquid crystal material can be determined by treating the liquid crystal cell as a parallel plate capacitor filled with a liquid crystal as the dielectric. The capacitance of this cell is given by 

In general, when a liquid crystal molecule is subject to an electric field the molecule will tend to become electrically polarized. This polarization creates a dipole in the molecule that will tend to align with the electric field. In the bulk nematic phase, aligned molecules will reorient together in response to the applied field. This bulk reorientation of the nematic director field is known as the Freedericksz transition. 

FIGURE 2.25 The response of a planar aligned liquid crystal with a positive dielectric anisotropy to the application of a perpendicular electric field. A single column of molecules is shown for clarity. 

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We highlight some aspects of the high-pressure studies on the dielectric properties of liquid crystals reviewed in this chapter. 

The purpose of this Chapter is to describe the dielectric properties of liquid crystals, and relate them to the relevant molecular properties. In order to do this, account must be taken of the orientational order of liquid crystal molecules, their number density and any interactions between molecules which influence molecular properties. Dielectric properties measure the response of a charge-free system to an applied electric field, and are a probe of molecular polarizability and dipole moment. Interactions between dipoles are of long range, and cannot be discounted in the molecular interpretation of the dielectric properties of condensed fluids, and so the theories for these properties are more complicated than for magnetic or optical properties. The dielectric behavior of liquid crystals reflects the collective response of mesogens as well as their molecular properties, and there is a coupling between the macroscopic polarization and the molecular response through the internal electric field. Consequently, the molecular description of the dielectric properties of liquid crystals phases requires the specification of the internal electric field in anisotropic media which is difficult. 

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