Instabilities in nematics

Various other instances of hydrodynamic and electrohydrodynamic instabilities in nematic and, to a lesser extent, smectic liquid crystals have been investigated. No attempt is made here to review this work. For the present discussion, it is sufficient to note that (a) most of the work has dealt with oriented layers having anisotropic properties, and (b) some interesting instabilities arise in oriented layers which do not occur for isotropic materials. An example of the latter is cellular convection in a fluid layer confined between horizontal plates maintained at different temperatures. With an isotropic fluid, convection can arise only if the lower plate is hotter than the upper plate. Then, fluid near the lower plate is less dense and tends to rise while fluid near the upper plate is denser and tends to sink. With an oriented layer, however, convection can arise even when the upper plate is hotter if the anisotropy of thermal conduction properties is of a particular type (8). 

Abstract A systematic overview of various electric-field induced pattern forming instabilities in nematic liquid crystals is given. Particular emphasis is laid on the characterization of the threshold voltage and the critical wavenumber of the resulting patterns. The standard hydrodynamic description of nematics predicts the occurrence of striped patterns (rolls) in five different wavenumber ranges, which depend on the anisotropies of the dielectric permittivity and of the electrical conductivity as well as on the initial director orientation (planar or homeotropic). Experiments have revealed two additional pattern types which are not captured by the standard model of electroconvection and which still need a theoretical explanation. 

L. Kramer and W. Pesch, Electrohydrodynamic Instabilities in Nematic Liquid Crystals. In Pattern Formation in Liquid Crystals, editors A. Buka and L. Kramer, pages 221-255, Springer, 1996. 

A.N. Trufanov, M.I. Barnik and L.M. Blinov, A Novel Type of the Electrohydrodynamic Instability in Nematic Liquid Crystals, m Advances in Liquid Crystal Research and Application, editor L. Bata, pages 549-560, Akademiai Kiado - Pergamon Press (1980). 

Hydrodynamic instabilities 3.11.1 Homogeneous instability in shear flow The anisotropic properties of nematics give rise to certain novel instability mechanisms that are not encountered in the classical problem of hydro-dynamic instability in ordinary liquids. Theoretical work on electro-hydrodynamic instability stimulated systematic studies on two other types of convective processes, viz, thermal and hydrodynamic instabilities, and it was soon established that the basic mechanisms involved in all three cases are closely similar. " In this section we shall examine the problem of hydrodynamic instabilities in nematics. 

The studies outlined here are the most important ones that established the fundamental of principles of thermal instability in nematics. A number of theoretical and experimental investigations on these and other geometries have since been reported. A particularly interesting study is that of Lekkerkerker who predicted that a homeotropic nematic heated from below (which, it will be recalled, is stable against stationary convection) should become unstable with respect to oscillatory convection. The phenomenon was demonstrated experimentally by Guyon et... 

For a concise review of instabilities in nematics and cholesterics, see S. Chandrasekhar and U. D. Kini in Polymer Liquid Crystals, (eds. A. Cferri, W. R. Krigbaum and R. B. Meyer), Chapter 8, Academic, New York... 

N.V. Madhusudana, V.A. Raghunathan and K.R. Sumathy, Plexoelectric origin of oblique-roll electrohydrodynamic instability in nematics, Pramana-J. Phys. 28(3), L311-L316, (1987). 

M. Monkade, Ph. Martinot-Lagarde and G. Durand, Electric polar surface instability in nematic liquid crystals, Europhys. Lett. 2(4), 299-305, (1986). doi 10.1209/0295-5075/2/4/007... 

V.A. Raghunathan and N.V. Madhusudana, A new threshold flexoelectric instability in nematic liquid crystals. Mol. Cryst. Liq. Cryst. Lett. 6, 103-111, (1989). 

Besides the elastic and the electric torques the so-called flexoelectric (or flexo) torques on the director play an important role as well. Their effect on pattern-forming instabilities in nematics is the main issue of this chapter. Flexotorques originate from the fact that typically (in some loose analogy to piezoelectricity) any director distortion is accompanied by an electric flexopolarization Pa (characterized by the two ffexocoefScients ei, 63). From a microscopic point of view, finite ei and 03 naturally arise when the nematic molecules have a permanent dipole moment. But also for molecules with a quadrupolar moment, finite ei and 63 are possible (see also Chapter 1 in this book ). Flexopolarization has to be incorporated into the free energy P n) for finite E. It is not surprising that this leads to quantitative modifications of phenomena, which exist also for ci = 63 = 0. Though, for example, the Freedericksz threshold field Ep is not modified, the presence of flexoelectricity leads to considerable modifications of the Freedericksz distorted state for E > Ep- ... 

E.I. Rjumtsev and S.G. Polushin, Electrohydrodynamic instabilities in nematic liquid crystals with large positive dielectric anisotropy, Liq. Cryst. 13(5), 623-628, (1993). doi 10.1080/02678299308026335... 

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...

Dubois-Violette, E., Durand, G., Guyon, E., Manneville, P., Pieranski, P. Instabilities in nematic liquid crystals. In Liebert, L. (ed.) Liquid Crystals, pp. 147-208. (Ehrenreich, H., Seitz, F., Turnbull, D. (eds.) series Solid State Physics), Academic Press, New-York, (1978). 

E. Dubois-Violette, S. Durand, E. Guyon, P. Manneville, and P. Pieranski, "Instabilities in Nematic Liquid Crystals," in Liquid Crystals, L.Liebert,... 

FIGURE 5.5. Electrohydrodynamic instability in nematic liquid crystals (a) the onset of the instabihty (b) the vortex motion of a Hquid crystal and (c) the picture of black-and-white stripes in the screen plane. 

Electrohydrodynamic Instability in Nematics with Oblique Director Orientation at the Boundaries... 

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. 

Let us note that (5.61) is a complementary model to the above given (5.39) and both of them could describe the appearance of electrohydrody-namic instability in nematics. Comparing the term... 

Classification of Threshold Conditions for Different Instabilities in Nematics... 

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. 

A.N. Trufanov, Investigation of mechanisms of electrohydrodynamic instabilities in nematic liquid crystals. Doctor Thesis, Institute of Crystallography, Moscow, 1981. 

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