Spatial and temporal behavior of pattern formations and defect motions in the electrohydrodynamic instability of nematic liquid crystals.

Abstract

Pattern-formation processes and the associated defect motions are experimentally studied for various rectangular cells with aspect ratios \ensuremath{\Gamma} ranging from 8 to 15 in the electrohydrodynamic instability (EHD). Wave-number selection arises from the competition between the most rapidly growing mode ${k}_{c}$, which dominates initially, and the final stable mode ${k}_{m}$ in the Williams domain (WD) state, which is influenced by the cell boundaries as well as nonlinear effects. Defect motion is associated with such competitive growth into the final stage. The fluctuating Williams domains (FWD's) are strongly related to the oscillatory gliding motion of defects. A temporally nonperiodic change of the number of defects is observed in the FWD state with a power spectrum of 1/f type (defect chaos). For a step change in the external voltage, a clear threshold for the onset of FWD is determined. On the other hand, when the voltage is increased continuously no defect is formed at the threshold for WD, and nondecaying defect motion starts at a certain threshold value. A large hysteresis is observed near the onset of FWD.The step change of the external field leads to defect formation more easily than the continuous change. A detailed phase diagram of stable convective patterns in the plane spanned by the threshold voltage and the applied frequency is presented. The characteristic behavior of defect motions, for example, its oscillatory activity of gliding and climbing motions, is strongly related to the pattern following the second pattern instability. In the case of the strong gliding oscillation, a pattern with temporal order appears above the second threshold. Contrary to this, in the case of the weakly oscillatory motion of defects, a stationary pattern is usually observed above its threshold. The magnetic field suppresses the defect chaos and stabilizes the system, that is, the threshold of the applied electric field for the onset of EHD is raised when the magnetic field is increased. The magnetic field can also change the direction of the roll axis so that it is perpendicular to the external field, which leads more easily to the zigzag and oblique patterns. A detailed phase diagram for the magnetic field effect is also given.