Competition of periodic and homogeneous modes in extended dynamical systems

Spatiotemporal complexity of electroconvection patterns in nematic liquid crystals

We investigate a number of complex patterns driven by the electroconvection instability in a planarly aligned layer of a nematic liquid crystal. They are traced back to various secondary instabilities of the ideal roll patterns bifurcating at onset of convection, whereby the basic nematohydrodynamic equations are solved by common Galerkin expansion methods. Alternatively these equations are systematically approximated by a set of coupled amplitude equations. They describe slow modulations of the convection roll amplitudes, which are coupled to a flow field component with finite vorticity perpendicular to the layer and to a quasihomogeneous in-plane rotation of the director. It is demonstrated that the Galerkin stability diagram of the convection rolls is well reproduced by the corresponding one based on the amplitude equations. The main purpose of the paper is, however, to demonstrate that their direct numerical simulations match surprisingly well new experiments, which serves as a convincing test of our theoretical approach.

Instabilities Across the Isotropic Conductivity Point in a Nematic Phenyl Benzoate under AC Driving

We characterize the sequence of bifurcations generated by ac fields in a nematic layer held between unidirectionally rubbed ITO electrodes. The material, which possesses a negative dielectric anisotropy epsilona and an inversion temperature for electrical conductivity anisotropy sigmaa, exhibits a monostable tilted alignment near TIN, the isotropic-nematic point. On cooling, an anchoring transition to the homeotropic configuration occurs close to the underlying smectic phase. The field experiments are performed for (i) negative sigmaa and homeotropic alignment, and (ii) weakly positive sigmaa and nearly homeotropic alignment. Under ac driving, the Freedericksz transition is followed by bifurcation into various patterned states. Among them are the striped states that seem to belong to the dielectric regime and localized hybrid instabilities. Very significantly, the patterned instabilities are not excited by dc fields, indicating their possible gradient flexoelectric origin. The Carr-Helfrich mechanism-based theories that take account of flexoelectric terms can explain the observed electroconvective effects only in part.

Three-dimensional imaging of dielectric patterns in electrohydrodynamic convection of a nematic liquid crystal

The transition from surface to bulk normal dielectric rolls in a nematic liquid crystal is imaged by fluorescence confocal polarizing microscopy. The three-dimensional director structure and the liquid flow are scanned in both the layer plane and the transverse plane. Two systems of small-scale convective flow are formed, one at each electrode. Strong anchoring makes director oscillations difficult and charges accumulate by the Carr-Helfrich mechanism. The middle region is a structureless convection where the director oscillates with the frequency of the applied voltage. The small-scale flow eventually fills the cell from one electrode to the other as one system of thin and elongated rolls. The true dielectric mode is not a director pattern, rather a surface flow instability.

Competing modes of instability in an electrically driven nematic liquid crystal with a small positive dielectric anisotropy

Competing modes of electric-field-driven bifurcation have been examined in a planarly aligned nematic liquid crystal with a small positive dielectric anisotropy and large electrical conductivity. The line of bifurcation into the electroconvective state is linear in frequency not only up to the codimension-2 (C2) point but well beyond. This contrasts with the recent theoretical prediction of the absence of further bifurcations within the Freedericksz state, above the C2 frequency. Further, in the frequency regime beyond C2, within the space-filling electroconvective state, a strongly localized dynamical state (SLDS) appears at a voltage threshold which again is linear in frequency. Occurrence of the SLDS through a secondary forward bifurcation is significant in view of the reported observations on the so-called worms, an instability belonging to the SLDS, as the first form of convection seen at the primary subcritical bifurcation.

Dynamics of laser-induced electroconvection pulses

We first report that, for planar nematic 4-methoxy-benzilidene-4-butylaniline (MBBA), the electroconvection threshold voltage has a nonmonotonic temperature dependence, with a well-defined minimum, and a slope of about -0.12 V/degrees C near room temperature at 70 Hz. Motivated by this observation, we have designed an experiment in which a weak continuous-wave absorbed laser beam with a diameter comparable to the pattern wavelength generates a locally supercritical region, or pulse, in dye-doped MBBA. Working 10-20 % below the laser-free threshold voltage, we observe a steady-state pulse shaped as an ellipse with the semimajor axis oriented parallel to the nematic director, with a typical size of several wavelengths. The pulse is robust, persisting even when spatially extended rolls develop in the surrounding region, and displays rolls that counterpropagate along the director at frequencies of tenths of Hz, with the rolls on the left (right) side of the ellipse moving to the right (left). Systematic measurements of the sample-voltage dependence of the pulse amplitude, spatial extent, and frequency show a saturation or decrease when the control parameter (evaluated at the center of the pulse) approaches approximately 0.3. We propose that the model for these pulses should be based on the theory of control-parameter ramps, supplemented with new terms to account for the advection of heat away from the pulse when the surrounding state becomes linearly unstable. The advection creates a negative feedback between the pulse size and the efficiency of heat transport, which we argue is responsible for the attenuation of the pulse at larger control-parameter values.

Competition between electroconvection and Fréedericksz distortions in nematic liquid crystals with slightly positive dielectric anisotropy

Planar electroconvection in nematic liquid crystals with positive dielectric anisotropy is theoretically studied in the nonlinear regime. The system is characterized by a competition between the nonequilibrium electroconvection instability and the equilibrium Fréedericksz distortions. Near a resulting multicritical bifurcation point a splay-roll instability and a bistability between the convective and the homogeneous states occur.