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Jana Heuer

Introduction

Electro-hydrodynamic convection (EHC) in anisotropic fluids is a standard system for dissipative pattern formation. A large variety of electroconvection patterns in an external electric ac field has been reported. Different combinations of the anisotropies of conductive and dielectric material constants result in distinct types of EHC structures. In the classical EHC studies, liquid crystals with positive conductivity anisotropy and negative or weakly positive dielectric anisotropy have been used. Both the spatial (normal rolls, grid patterns) and temporal properties (stationary, harmonic, subharmonic, travelling patterns) of these systems are multifaceted and have been investigated thoroughly in the course of the last 30 years. Beside the rich experimental results, an extensive model based on the Carr-Helfrich mechanism has been developed that yields not only a linear stability analysis but also a weakly nonlinear description. It explains the temporal behaviour of the electroconvection system.

Setup The experimental observation is performed with a µm thin transparent glass cell wherein the nematic liquid crystal is sandwiched. Applying an electric AC field normal to the cell will lead to an accelaration of the charges that exist due to impurity. In the inhomogenous director field these carges will separate into charge clouds. The flow field driven by this ionic flow couples to the director deflection. Thus, convection rolls arise that are visible by means of the shadowgraph method in the polarazing microscope. The pattern appears above a certain threshold voltage with different wave numbers that depend on the excitation frequency.

Description of the formation of convection rolls, java applet

phase1 (a): oblique conduction rolls
(b): normal conduction rolls
(c): normal dielectric rolls
(d)-(f): higher instabilites
(g): ground state, no convection rolls

EHC patterns near the threshold voltage:

rollslowfreq

At higher voltages the pattern becomes more complex:

rollshighfreq

R. Williams: Domains in liquid crystals, J. Chem. Phys. 39, 384 (1963).
E. F. Carr: Influence of electric and magnetic fields on the dielectric constant and loss of the liquid crystal Anisaldazine, J. Chem. Phys. 38, 1536 (1963).
W. Helfrich: Conduction-induced alignment of nematic liquid crystals - basic model and stability considerations, J. Chem. Phys. 51, 4092 (1969).
E. Dubois-Violette, P. G. de Gennes, O. Parodi: Hydrodynamic instabilities of nematic liquid crystals under a.c. electric fields, J. Phys. (France) 32, 305 (1971).
L. Kramer, W. Pesch: Electrohydrodynamic instabilities in nematic liquid crystals in Pattern Formation in Liquid Crystals, p. 221, editors A. Buka, L. Kramer (Springer, NY, 1996).
S. Rasenat, G. Hartung, B. L. Winkler, I. Rehberg: The shadowgraph method in convection experiments, Exp. Fluids 7, 412 (1989).
H. Amm, M. Grigutsch, R. Stannarius: Spatio-temporal analysis of electroconvection in nematics, Z. Naturforschung 53a, 117 (1998).

Unusual electroconvection of bent-core nematics

The current research turns the attention to materials were the signs of the conductivity and dielectric anisotropy are changed. Here the observed patterns differ significantly from the classical types. Partially these patterns can be described within the Carr-Helfrich mechanism but in some cases novel or adapted models have to be discussed.

bananas We describe a novel mechanism that leads to patterns that are qualitatively different from those of the conventional EHC. In this context we investigate a bent-core (banana-shaped) liquid crystal with a positive dielectric and a negative conductivity anisotropy. The orientation and optical behaviour of the observed patterns are no longer describable within the classic model. In contrast to the common EHC, the pattern evolves from a distorted ground state above the so-called splay Fréedericksz transition. Moreover the convection rolls are oriented along the initial director easy axis. The usual stripe patterns are perpendicualr to this axis or slightley tilted. Because of these qualitative differences we derived a new basic mechanism that adapts the Carr-Helfrich theory and is based on a twist instability coursing a modulation in the cell plane after the splay Fréedericksz transition. Our model predicts qualitatively the correct threshold behaviour and optical characteristics of the observed unusual electroconvection patterns.

phasebent rollsbent

D. Wiant, J. T. Gleeson, N. Éber, K. Fodor-Csorba, A. Jákli, T. Tóth-Katona: Nonstandard electroconvection in a bent-core nematic liquid crystal, Phys. Rev. E 72, 041712 (2005).
Á. Buka, B. Dressel, W. Otowski, K. Camara, T. Toth-Katona, L. Kramer, J. Lindau, G. Pelzl, W. Pesch: Electroconvection in nematic liquid crystals with positive dielectric and negative conductivity anisotropy, Phys. Rev. E 66, 051713 (2002).
E. Kochowska, S. Németh, G. Pelzl, Á. Buka: Electroconvection with and without the Carr-Helfrich effect in a series of nematic liquid crystals, Phys. Rev. E 70, 011711 (2004).
T. Tóth-Katona, A. Cauquil-Vergnes, N. Éber and Á. Buka: Non-standard electroconvection with Hopf-bifurcation in a nematic with negative electric anisotropies, www.e-lc.org, 12/6 (2006).

M.-G. Tamba, W. Weissflog, A. Eremin, J. Heuer, R. Stannarius: Electro-optic characterization of a nematic phase formed by bent core mesogens, Eur. Phys. J. E 22, 85 (2007).
R. Stannarius, J. Heuer: Electroconvection in nematics above the splay Fréedericksz transition, submitted.

Subharmonic patterns

In EHC experiments different regimes can be observed that are distinguishable clearly due to their spatio-temporal behaviour. Their occurance depends on the excitation wave form and the excitation frequency. The classic EHC studies, using sinus and square waves, described two dynamic pattern regimes: Conduction rolls are stationary whereas dielectric patterns change temporally with the period of the excitation. We found a new regime with a dynamics that leads to a system response with the double period of the excitating electric field. Necessarily for the occurrence of these novel patterns are certain asymmetries of the applied wave form. Antisymmetry, time reversal symmetry and dichotomy of the exciation wave suppress the subharmonic regime.

E.g. sawtooth excitation: Space-time plots of the three pattern regimes:
phasesub spacetime

T. John, J. Heuer, and R. Stannarius: Influence of excitation wave forms and frequencies on the fundamental time symmetry of the system dynamics, studied in nematic electroconvection, Phys. Rev. E 71, 056307 (2005).
R. Stannarius, J. Heuer, and T. John: Fundamental relations between the symmetry of excitation and the existence of spatiotemporal subharmonic structures in a pattern-forming dynamic system, Phys. Rev. E 72, 066218 (2005).
C. Bohley, J. Heuer, R. Stannarius: Optical properties of electrohydrodynamic convection patterns: rigorous and approximate methods, J. Opt. Soc. Am. A 22, 2818 (2005).
J. Heuer, T. John, and R. Stannarius: Reentrant EHC Patterns Under Superimposed Square Wave Excitation, Mol. Cryst. Liq. Cryst. 449, 11 (2006).

 

 

Last modified April 18, 2007, jana.heuer@gast.uni-magdeburg.de