Dielectric Anisotropy of Nematics

In the case of liquid crystals (2.5a), (2.5b) could be rewritten for dielectric components e, j, and is, thus denoting r , r L, and rig. A typical example of the frequency dependence of dielectric constants e is given in Fig. 2.3. 

A particularly interesting case occurs when the static value of exceeds that of . In this case, as a result of the low-frequency dispersion in at a certain frequency /o, a change in sign of the dielectric anisotropy of the nematic liquid crystals can occur. Sometimes this frequency is low. 

FIGURE 2.3. Relaxation of s, in a eutectic mixture of phenylbenzoates (2.i) [5] (solid lines) and in mixture WI [6] (dashed lines). 

The dielectric sign inversion frequency fo is strongly temperature dependent [8] 

The process of the relaxation of the liquid crystal orientational polarization also effects the frequency dependence of the electric conductivity [6] 

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The low-frequency dielectric anisotropy of nematic cells is also important (Table 4.2). 

The dielectric constants of an aligned nematic phase are dependent upon both the temperature and the frequency of the applied field at temperatures below the clearing point. The dielectric permitivity, j, measured parallel to all three axes above the clearing point in the isotropic liquid is the same. Therefore, the dielectric anisotropy of the same compound in the liquid state is zero, see Figure 2.10. The sign and magnitude of the dielectric constants and, therefore, the dielectric anisotropy are dependent upon the anisotropy of the induced molecular polarisability, Aa, as well as the anisotropy and direction of the resultant permanent molecular polarisation determined by permanent dipole moments. 

This interpretation was confirmed to some extent by experimental results, since it had been found that nematic mixtures composed of apolar nematic compounds and polar nematic compounds (nitriles) consist of a number of unassociated polar and non-polar monomers as well as associated polar dimers. This not only gives rise to a high value for the observed dielectric anisotropy of the mixture due to the non-associated polar compounds, but also... 

Experimental orientational data have been obtained from proton NMR spectra of 1,4-difluorobenzene, 1,4-dichlorobenzene, 1,4-diboromobenzene and naphthalene dissolved in several nematic solvents at different tempera-tures. The results indicate a relationship between the sign and magnitude of dielectric anisotropies of the nematic solvents and the temperature dependence of the orientational biaxiality ratio of the solutes dissolved in them. ... 

As an example of an application of the mean field method we shall consider the theory of the dielectric anisotropy of the nematic phase. The low frequency dielectric anisotropy of a molecule is determined by two factors (i) the polarizability anisotropy which for the elongated molecules of nematogenic compounds always makes a positive contribution (i.e., a... 

Kang SW, Sprunt S, Chien LC. 2001. Switchable diffraction gratings based on inversion of the dielectric anisotropy in nematic liquid crystals. Appl Phys Lett 78 3782 3784. 

The dielectric anisotropy of the first monomer, the -cyano- -acryloyloxybiphenyl, was measured. The of a 0.10/0.90 molar-fraction mixture of this compound, with a nematic compound having an equal to 0.1, is 2.1. Since the anisotropies are additive, the anisotropy of the considered monomer is approximately equal to 2.0. 

Figure 10.2. Dielectric anisotropy of a nematic liquid crystal.

SSFLCs have a very short switching time (in the order of microseconds) because of the direct coupling force of the spontaneous polarization and an electric field. This response is about a thousand times faster than that of conventional nematic devices, which utilize the dielectric anisotropy of the molecule. 

Three important dielectric effects in nematic liquid crystals are to be discussed. The three cases differ in the geometry of the specimen and the sign of dielectric anisotropy of the material used (Fig. 6a—c). 

The nematic Azomethines and Azoxybenzene derivatives exhibit a negative dielectric anisotropy. If there is no permanent electric dipole perpendicular to the long axis of the molecule (e = 0), or one of the p-positions carries a strong polar group, the dielectric constant ey in the direction of the long axis dominates and the dielectric anisotropy (Ae = ey — becomes positive. The dielectric anisotropy of the Azoxybenzene derivative (b) is at —0.2, whereas that of the Azobenzene analogon (a) is at +0.2. 

In the case of positive dielectric anisotropy of a nematic, even a weak field makes the isotropic phase uniaxial and the N-I phase transition disappears (see Pikin [7], Chap. 4). However, the apparent N-I phase transition temperature may change with the electric or magnetic field. For a>0 and E n, the quadratic-in-field energy terms (Eq. (la) and (lb)) reduce the free energy and stabilize the anisotropic phase. In the... 

For negative dielectric anisotropy of the nematic phase, < 0, the external field may induce a biaxial nematic phase. With increasing field one may reach the tricritical point [18] where the first-order N-I transition becomes a second-order one. 

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