Dielectric Properties of Anisotropic Fluids

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. 

At frequencies above the dielectric relaxation frequency, another diffraction with a threshold makes its appearance (see Fig. 4). This is the chevron regime, which is not hydrodynamic in origin but depends on interaction between the anisotropic dielectric properties of the fluid and the field. It represents a sinusoidal modulation of the... 

Liquid crystals are anisotropic fluids and the discussion of their dielectric properties is based on the fundamental ideas obtained for isotropic liquids. We recall the relevant results. 

From the point of view of physics, LCs are partially oriented fluids that exhibit anisotropic optical, dielectric, magnetic, and mechanical properties. The most important property of LCs is the reorganization of their supramolecular structures on external stimuli such as electric and magnetic fields, temperatnre, and mechanical stress, which lead to changes in their optical properties. In particular, electric tiled-induced control of optical properties of LCs (electro-optical effects based on the Freedericksz transition ) is at the heart of the multi-billion dollar liquid crystal display (LCD) industry. Most current LCD technologies rely on nematic " and to a lesser extent on ferroelectric LCs, while the recently discovered bent-core and orthoconic LCs still require significant investment into fundamental research and development. These and other applications and technologies continne to drive the search for new liquid crystal materials, and provide impetus to continue fundamental studies on new, often exotic, classes of compounds. 

Liquid crystals are anisotropic fluids with optical properties similar to those of bire-fringent crystals. They are often inhomogeneous and, as a consequence, the dielectric tensor is a function of position. The inhomogeneity may be a property of the phase, such as the helical structure of chiral phases, or it may be the result of deformations. 

The combination of molecular order and fluidity in a single phase results in several remarkable properties unique to liquid crystals. By now, it is quite evident that the constituent molecules of liquid crystal mesophases are structurally very anisotropic. Because of this shape anisotropy, all the molecular response functions, such as the electronic polarizability, are anisotropic. The long range order in the liquid-crystal phases prevents this molecular anisotropy from being completely averaged to zero, so that all the macroscopic response functions of the bulk material, such as the dielectric constant, are anisotropic as well. We have, therefore, a flexible fluid medium whose response to external perturbations is anisotropic. 

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