Dielectric regime

The original, so called 1-d formula of Carr and Helfrich, was later refined and generalized into a 3-d theory capable of calculating the wavevector and describing real, three dimensional patterns (like normal or oblique rolls), other geometries and the dielectric regime [16]. 

The homeotropic geometry also allows for the appearance of structures with a secondary spatial periodicity - chevrons - in the conductive regime at voltages considerably larger than Uc [43]. Such type of chevrons, which are characterized by a periodic arrangement of defect chains, have been observed before exclusively in the dielectric regime. 

The director field oscillates with the driving frequency, similar to the dielectric regime of standard EC. 

At high frequencies - in the dielectric regime - Eqs. (7) and (8) do not apply. For completeness, we mention that independent calculations for this range would invoke a different q-mode (5), the dielectric rolls, with the wavelength that does not scale with d. 

Fig. 3.10.4. Threshold voltage of the AC instabilities versus frequency for MBBA. Sample thickness 100 / m. Region I conducting regime (stationary Williams domains) region II dielectric regime ( chevrons ). Full line is the theoretical The cut-off frequency / = 89 Hz. (After the Orsay Liquid Crystals Group. )...

In this case y/ changes sign with E, but q does not. This corresponds to the dielectric regime in which the director oscillates. 

Fig. 3.10.8. Time dependence of the charge q and the curvature ij/ over one period of the square wave excitation, (a) Conduction regime (cot < 1, T > r). The charges oscillate but the domains are stationary, (b) Dielectric regime (cot P I, T< t). The charges are stationary and the domains oscillate. (After Smith et...

These equations show clearly that the problem falls naturally into two distinct parts. For T>t (3.10.25) has no solution and consequently there is no dielectric regime, while for J < r (3.10.24) has no solution and there is no conduction regime. For T=t, neither equation has a solution (except when CP = 0). 

Equation (3.10.27) can now be integrated but solutions can only be obtained by numerical techniques. Calculations show that in the dielectric regime (a) the threshold field th is independent of the wavevector k, which results in athreshold (as distinct from a voltage threshold as in the conduction regime), (b) varies hnearly as to, (c) for a given H, k varies linearly as to, and ([Pg.194]

If < 2.35, the estimations [69] give a slightly different dependence on the threshold field in the dielectric regime... 

The dependences of the threshold of the Kapustin-Williams domains [68] and the critical frequency [79] on physical parameters are in good agreement with the theoretical estimations (5.43). Only a certain correction of (5.43) is needed to explain the variation of critical frequency for different substances [79]. However, the anisotropic dielectric regime of the electrohydrodynamic instability in homogeneously oriented nematic hquid crystals seems not to have been observed in experiment yet. 

Thus, to date we have three theoretically predicted modes for a high-frequency instability caused by the Carr-Helfrich anisotropic mechanism. They are the conductance and dielectric regimes and the inertia mode. Two of these (the conducting regime and the inertia mode) correspond to the steady-state motion of the liquid and the stationary deviations of the... 

For frequencies above (0 another regime is predicted by the same theory where the director driven by flow is oscillating clockwise and anticlockwise in the ac field. The threshold for this "dielectric regime should also diverge with In experiments,... 

Carr-Helfrich one in nematics and may be studied quantitatively theoretically [280]. At high frequencies, an instability is observed with a characteristic frequency dependence of the threshold field Elayer thickness (fundamental domains). This has been regarded as an analog of the dielectric regime [282], but it can also be interpreted as the electrolytic mode [283] with some specific features. In some special cases a new domain mode is observed [284], which has been referred to the inertial (anisotropic) mode (discussed in Section 9.4.1.3 of this Chapter). 

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