DYNAMICS OF ELECTROHYDRODYNAMIC INSTABILITIES IN NEMATIC LIQUID CRYSTALS

Abstract

We explore the problem of electrohydrodynamic instabilities in nematic liquid crystals in the parallel (planar) orientation, in the context of the one-dimensional time-dependent model proposed by Dubois-Violette, de Gennes and Parodi. In the first part of the paper, we solve the equations of motion analytically in the case of an applied electric field E whose time variation is a square wave of frequency v. Our solution covers the entire range of material parameters, includ- ing explicitly the case of either positive or negative dielectric anisotropy, and is valid for 0 5 v 5 10 kHz for typical materials. One result is a determination of the instability threshold curve, showing in particular that the conduction-regime threshold is a smooth closed curve in the E - v plane whose shape depends on the dielectric relaxation time z, the viscoelastic relaxation time TH, and the Helfrich gain parameter (2. We treat the case of any sample thickness d and show that for samples so thin that TH (GC d2) <: zl2/(c2 - 1) the conduction-regime threshold loop shrinks and disappears, the dielectric regime then extending down to v = 0. We also treat in a very simple analysis the case of non-linearities and saturation when the applied field is above threshold. We are thus able to account for the variable grating mode (which has been experimentally observed), in which the domain width is inversely proportional to the applied field over a factor of at least ten in domain width. We calculate also the growth (or decay) rate s of an oscillation near threshold, whose slowly varying amplitude goes as exp st ; s is of order z-l(ElE~ - 1) where ET is the threshold field. The fact that our results are based on analytic rather than numerical simulation techniques allows us to give a physical interpretation to the predictions.