Williams domains electrohydrodynamic instabilities

In nematic liquid crystals, subjected to an external electric field at a certain critical voltage, a periodic distribution of the space charge Q and the electric potential appears, resulting in the corresponding periodic variations of the initial director orientation L and the hydrodynamic fiow with the velocity v. This effect, known as the electrohydrodynamic instability (EHDI), could be visualized optically as a periodic pattern of domains. Fig. 5.5. In a screen, domains become visible as black and white stripes perpendicular to the distortion plane, where periodic director deformation and vortex liquid crystal movement is observed. These stripes are caused by the periodicity of the change in the refractive index for an extraordinary ray due to variations in the director. Fig. 5.6. These spatially periodic variations of the refractive index (domains) were first detected by Zvereva and Kapustin [32]. Then Williams [33] investigated transverse domains in detail, and it is current practice to call this type of instability Williams or Kapustin-Williams [34] domains. 

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. 

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. 

Presumed ferroelectric effects in liquid crystals were reported by Williams at RCA in Princeton, U. S. A., as early as 1963, and thus at the very beginning of the modern era of liquid crystal research [5]. By subjecting nematics to rather high dc fields, he provoked domain patterns that resembled those found in solid ferroelectrics. The ferroelectric interpretation seemed to be strengthened by subsequent observations of hysteresis loops by Kapustin and Vistin and by Williams and Heilmeier [7]. However, these patterns turned out to be related to electrohydrodynamic instabilities, which are well understood today (see, for instance, [8], Sec. 2.4.3 or [9], Sec. 2.4.2), and it is also well known that certain loops (similar to ferroelectric hysteresis) may be obtained from a nonlinear lossy material (see [10], Sec. 2.4.2). As we know today, nematics do not show ferroelectric or even polar properties. In order to find such properties we have to lower the symmetry until we come to the tilted smectics, and further lowering their symmetry by making them chiral. The prime example of such a liquid crystal phase is the smectic C. ... 

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