Williams domains

When the rms (root mean square) voltage reaches a critical threshold ( 5 V), a periodic distortion of nematic alignment is 

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The experimental arrangement for observing the Williams domains is shown in fig. 3.10.1. The nematic film of negative dielectric anisotropy (e.g., PAA or MBBA) is aligned with the director parallel to the glass... 

Fig. 3.10.2. Electrohydrodynamic alignment patterns in nematic liquid crystals, (a) Williams domains in a 38 //m thick sample of p-azoxyanisole. 7.8 V, 100 Hz. (Penz. ) (Z>) Chevron pattern of oscillating domains in MBBA. Sample thickness 100 fjm. Distance between bright lines 5 /im. 260 V, 120 Hz. (Orsay Liquid...

Fig. 3.10.3. (a) Plow and (b) orientation patterns of Williams domains. The periodic orientation pattern and the consequent refractive index variation has a focussing action for light polarized in the plane of the paper. This gives rise to the bright domain lines as indicated by the stars above and below the sample. (After... 

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. )...

Fig. 11. 33 Carr-Helfrich EHD instability in nematic liquid crystals (a) onset of the instability showing a competition of the elastic and hydrodynamic torques (b) photo of Williams domains observed at a voltage 7.5 V in a 20 pm thick cell filled with liquid crystal MBBA...

This accumulation of charge also sets up the flow pattern shown in Figure 10.16. If the electric field is not too strong, these convection cells are quite stable (Williams domains). At larger electric fields, however, the flow becomes turbulent, with a complex, fluctuating director configuration (dynamic scattering). 

If a monochromatic beam, for example, from a laser, is transmitted through a cell showing domain structure, a different pattern appears on a screen placed behind the cell. The diflEraction pattern takes the form of a chain of reflections arranged in the plane perpendicular to the domains [40, 41]. The angular distribution of the maxima and minima is described by the usual equation for diffraction from a grating with period w w is the period of the Kapustin-Williams domains) ... 

The threshold voltages for the Kapustin-Williams domains, calculated from (5.29) and (5.30) for doped MBBA and their dependence on the dielectric anisotropy, are shown in Fig. 5.7 (curve 2). As will be seen below, (5.29) and (5.30) significantly underestimate the value of Uth- This is a consequence of the unidimensionality of the model or, in other words, a consequence of not allowing for the boundary conditions. 

FIGURE 5.7. Experimental dependences of the threshold voltage for Ka-pustin-Williams domains with a planar initial orientation (a) on the anisotropy of the electrical conductivity and (b) on the dielectric anisotropy for doped MBBA (circles) and for mixture A of azoxy compoimds (crosses). Calculation is according to a two-dimensional theory (curve 1) and a one-dimensional theory (curve 2). The threshold of the Prederiks effect for doped MBBA is shown in curve 3, which represents the theory, while the squares represent the experimental measurements [31]. 

The threshold voltage Uth and the f)eriod Wth of the Kapustin-Williams domains are found from the linearized system of equations of nematody-namics in an electric field, as a condition of nontriviality of the fluctuations amplitudes 0 , v , t , where... 

The threshold of the instability in a nematic, with Ae > 0 when there is a planar initial orientation, is calculated in [54, 55]. In [31] it was also shown that the threshold voltage C/th of the Kapustin-Williams domains in homogeneous orientation is proportional to the following nematic viscoelastic parameters ... 

The Kapustin-Williams domains have not been directly observed experimentally with homeotropic orientation. For Ae < 0 they are only observed for a voltage exceeding the Frederiks threshold, i.e., essentially with a quasi-planar orientation. In the region Ae 0, when the threshold of reorientation is high, a different, very specific, instability is observed, namely, a lattice with a small period (wave vector qx y 57r/d) [31], as shown in Fig. 5.6(b). 

FIGURE 5.8. Experimental dependences on Ae of (1) the threshold for the (bend) Prederiks effect Ub (4) the threshold of an electrohydrodynamic instabihty with a homeotropic initial orientation (3) the threshold of the Kapustin-Williams domains with planar initial orientation. The calculation of Uthr using the Helfrich s one-dimensional model for a homeotropic orientation (5.30) is shown in curve 2 [31]. 

Finally, we remember that the Kapustin-Williams domains take place due to the effect of the positive conductive anisotropy of the nematic liquid crystal cr /a and disappear in the region or /a < 0 (Fig. 5.7(a)). The considerable decrease in the threshold voltage of the Kapustin-Williams domains for the large conductive anisotropy c7 /(jj proved to be a useful tool for developing liquid crystal mixtures for a dynamic scattering display with low controlling voltages [56]. 

The two-dimensional model [66] of this domain structure shows that its threshold considerably depends on the value of the Leslie viscosity coefficient as and the dielectric anisotropy Ae. Unlike the Kapustin-Williams domains, this instability could also be observed for negative conductivity anisotropy. There remains only one specific point where the instability ceases to exist, namely, the conductivity isotropy point. Act = 0. 

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 Kapustin-Williams domains were also investigated for an electric field applied parallel to the substrates (perpendicular to the light beam). 

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