Threshold electrohydrodynamic instabilities

It has been Icnown for years that a decrease in the phase transition temperature of azobenzene containing LC is induced by trans -cis photoisomerization (23). Smectic LC of 4-alkyl-4 -cyano-biphenyl is subjected to phase transition by photoisomerization of azobenzene leading to a reversible change in the threshold voltage for electrohydrodynamic instability (24). None of them described the concept of image amplification. 

DC and very low frequency AC voltages produce electrohydrodynamic instabilities in the isotropic phase also (T the threshold being... 

In the two-dimensional theory of the threshold for an electrohydrodynamic instability, developed by Pikin [49] and Penz and Ford [50], the velocity of the liquid and the director are regarded as being dependent on both the X- and -coordinates. Solutions are sought which satisfy the conditions of strong molecular anchoring at the electrodes under the following conditions for a planar orientation 6 = 0, = 0, Vz = 0, dvzidz = 0, when... 

A theoretical investigation of the stability of nematic liquid crystals with homeotropic orientation requires a three-dimensional approach. Helfrich s one-dimensional theory predicts the dependence of the threshold of the instability on the magnitude of Ae, as shown by curve 2 in Fig. 5.8, according to which the electrohydrodynamic instability should be observed when either Ae < 0 (and consequently the bend Frederiks effect reorientation will not take place), or when small Ae > 0. In Helfirich s model the destabilizing torque as dvzjdx is responsible for this instability, which replaces the destabilizing torque a dvzjdx in the equation for the director rotations (5.27). Although the torque is small ( a3 -C o 2 ) it is not compensated for (e.g., when Ae = 0) by anything else apart from the elastic torque. 

FIGURE 5.10. Electrohydrodynamic instabilities in nematic liquid crystal with homogeneous initial orientation in the high-frequency regime (a > lJc)- (a) Domains when the voltage is slightly above the threshold voltage and (b) the Chevron pattern. 

FIGURE 5.12. Qualitative dependence of the threshold field Efh for the electrohydrodynamic instability versus reduced frequency u/ujc. 

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. 

The inertia mode has been observed in experiment [44, 93, 94]. Figure 5.16 presents the frequency dependences of the threshold for the appearance of a stationary domain pattern in strongly conducting nematic liquid crystals with Ae < 0 [93]. The domains here have a width exceeding the thickness of the cell wide domains), and are oriented at right angles to the initial orientation of the director. The threshold voltage is practically independent of the thickness of the layer and is proportional to The frequency dependence of the threshold is different for diflFerent samples, which may be caused by the firequency dependence of the electrical conductivity which also includes the dielectric losses. These results correspond to the theoretical predictions for an inertia mode of an electrohydrodynamic instability [92]. 

Electrohydrodynamic instabilities in nematics could be classified according to the dependence of the threshold voltage (or field) on the physical parameters of the liquid crystal, cell geometry, field firequency, etc. Arising domain patterns also differ by the period of the structure and its orientation with respect to the initial director. We hope that this classification proves to be useful, both for finding similar instability phenomena in other liquid crystals (cholesteric, smectic, polymer liquid crystals, etc.) and for practical purposes in avoiding parasitic scattering and hysteresis effects which are undesirable in many applications. 

Let us now briefly describe electrohydrodynamic instabilities in polymer nematics. The first observation of the Kapustin-Williams domains in nematic polymers were reported in [117, 118]. The qualitative picture of the phenomenon is, in fact, the same as that for the conventional nematics (domains perpendicular to the initial director orientation in a planar cell, typical divergence of the threshold voltage at a certain, critical frequency, etc.). The only principal difference is a very slow dynamics of the process of the domain formation (hours for high-molecular mass compounds [117]). The same authors have observed longitudinal domains in very thin samples which may be referred to as the flexoelectric domains [5-14] discussed in Section 5.1.1. 

TABLE 5.1. Electrohydrodynamic instabilities (EHI) in nematics. Threshold conditions and optical patterns. 

Investigation of an electrohydrodynamic instability (Ae < 0) in a planar Grandjean texture shows [17] that, in this case also, the directions of the domains alternate with a transition from one Grandjean zone to another, while the domains are perpendicular to the director of the cholesteric liquid crystal in the middle of the layer in each case. This can be seen in Fig. 6.18. With an increase in d, one-dimensional deformations transform to a two-dimensional grid. The threshold voltages for the formation of a periodic instability and the period of the domains, in this case, oscillate with an increase in thickness (Fig. 6.19). In principle, this can be accounted for by the Helffich-Hurault theory [22, 23], developed with the approximation d Po, in the spirit of (6.20) and (6.21) where the forced pitch P is substituted for the equilibrium pitch Pq-... 

In this section we discuss electrohydrodynamic (EHD) instabilities, that is electric-field-induced phenomena that are caused by the flow of a liquid crystal (see also [8,219]. The reason for the flow is electrical conductivity, which has been disregarded in previous sections. The flow may arise either independently of the anisotropic properties of substance, as in isotropic liquids (isotropic modes of the electrohydrodynamic instability), or may be driven by the conductivity anisotropy, as in liquid crystals (anisotropic modes). The threshold for EHD instabilities depends on many parameters, such as the electrical and viscoelastic properties of substance, the temperature, and the applied field frequency. Due to flow distortion of the director alignment, the instability is usually accompanied by a characteristic optical... 

Figure 28. Threshold voltage as a function of frequency for different electrohydrodynamic instabilities in homogeneously oriented nematics.

Rondelez, Gerritsma, and Arnould have reported the presence of two-dimensional deformations at the threshold voltage for scattering. Electrohydrodynamic instabilities were first predicted for negative... 

In calculating the threshold voltage, Hel-frich assumed that the spatial periodicity of the fluid deformation was proportional to the thickness of the cell. Penz and Ford [19-21] solved the boundary value problem associated with the electrohydrodynamic flow process. They reproduced Helfrich s results and showed several other possible solutions that may account for the higher order instabilities causing turbulent fluid flow. 

Neglecting the frequency response of the electrohydrodynamic flow, Helfrich calculated the threshold voltage for the domain instability. A slightly rewritten form of his expression is... 

Orsay Liquid Crystal Group solved the electrohydrodynamic problem for a variable frequency, sinusoidal voltage source. The fluid instability occurs at the frequency-dependent threshold voltage... 

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