Dielectric microscopic anisotropy

With this background, we have proposed and developed a new purely electrical method for imaging the state of the polarizations in ferroelectric and piezoelectric material and their crystal anisotropy. It involves the measurement of point-to-point variations of the nonlinear dielectric constant of a specimen and is termed scanning nonlinear dielectric microscopy (sndm) [1-7]. This is the first successful purely electrical method for observing the ferroelectric polarization distribution without the influence of the screening effect from free charges. To date, the resolution of this microscope has been improved down to the subnanometer order. 

Our purpose is to demonstrate how it is possible to describe the anomalous dielectric relaxation from microscopic models of the underlying processes. Moreover, we shall illustrate how the effects of the inertia of the molecules and an external potential arising from crystalline anisotropy or indeed any other mechanism could be included. 

There is a very interesting example of the flexoelectric torque acting on the director in the bulk. In a typical planar nematic cell the director is strongly anchored at both interfaces, n = (1,0,0) and the electric field is directed along z. The conductivity is low and the dielectric anisotropy is either zero or small negative, such that the dielectric torque may only weakly stabilize the initial planar structure. Upon the dc field application, a pattern in the form of stripes parallel to the initial director orientation in the bulk nollx is observed in the polarization microscope. The most interesting feature of these domains is substantial field dependence of their spatial period as shown in Fig. 11.30 [34]. 

An optically isotropic liquid crystal (LC) refers to a composite material system whose refractive index is isotropic macroscopically, yet its dielectric constant remains anisotropic microscopically [1]. When such a material is subject to an external electric field, induced birefringence takes place along the electric field direction if the employed LC host has a positive dielectric anisotropy (Ae). This optically isotropic medium is different from a polar Uquid crystal in an isotropic state, such as 5CB (clearing point = 35.4°C) at 50 C. The latter is not switchable because its dielectric anisotropy and optical anisotropy (birefringence) both vanish in the isotropic phase. Blue phase, which exists between cholesteric and isotropic phases, is an example of optically isotropic media. 

The anchoring energy was shown to depend on cell thickness [61] (see also [3, 59]). The thinner the cell the higher the anchoring energy. It is a type of the nonlocality effect discussed in [1]. One of the possible microscopic reasons for the effect is the field of the space charge of the ions adsorbed at opposite interfaces. Such a field can stabilize or destabihze the director in the surface layers in accordance with a sign of the dielectric anisotropy and initial orientation of the nematic [62]. In any case, it results in an increase of an apparent value of Ws in thin cells. 

As noted earlier, Qa/9 may be equally well-defined in terms of other macroscopic properties such as the refractive index or dielectric tensor. However, the simple relation [Eq. (3.6)] cannot be expected to hold for the dielectric anisotropy Ae and electric polarizability aij. This is due to complicated depolarization effects caused by the relatively large near-neighbor electrostatic interaction. The internal field corrections [3.3] are necessary in the electric case. It has been shown that Qa can be used to describe orientational order both in uniaxial and biaxial phases. Furthermore, measurement of Qa/3 is particularly useful when description of flexible molecules using microscopic order parameters becomes problematic. Experimentally, both magnetic resonance and Raman scattering techniques [3.3] may be employed to monitor the orientational order of individual molecules and to determine microscopic order parameters. 

As can be seen in TABLE 1, not all substances have a nematic phase but some of these compounds can also be important components of practical mixtures. That means, from an application point of view, it is necessary to characterise those non-nematic or non-liquid-crystalline substances by an effective or virtual dielectric anisotropy. Mainly for this reason, the dielectric properties are usually measured in mixtures, containing the corresponding substances at a fixed concentration, and the value characteristic of the component is obtained by extrapolation. This provides the main reasons for the scatter in the data, some of which can be attributed to the different host mixtures used. In this connection, too, dipole-dipole association is an important factor to make the microscopic investigation of the dielectric property of a nematic phase precise. The extrapolation conditions are noted in TABLE 1 and details can be found in the appropriate references. 

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