Search

We investigate flexodomains, which are observed in planar layers of certain nematic liquid crystals, when a dc voltage $U$ above a critical value ${U}_{c}$ is applied across the layer. They are characterized by stationary stripelike spatial variations of the director in the layer plane with a wave number $p(U)$. Our experiments for different nematics demonstrate that $p(U)$ varies almost linearly with $U$ for $Ug{U}_{c}$. That is confirmed by a numerical analysis of the full nonlinear equations for the director field and the induced electric potential. Beyond this numerical study, we demonstrate that the linearity of $p(U)$ follows even analytically, when considering a special parameter set first used by Terent'ev and Pikin [Sov. Phys. JETP 56, 587 (1982)]. Their theoretical paper serves until now as the standard reference on the nonlinear analysis of flexodomains, since it has arrived at a linear variation of $p(U)$ for large $U\ensuremath{\gg}{U}_{c}$. Unfortunately, the corresponding analysis suffers from mistakes, which in a combination led to that result.

~Received 19 March 1998! The response of a homeotropically aligned nematic liquid crystal layer to oscillatory rectilinear shear ~Couette flow ! was investigated for frequencies f between 0.01 and 200 Hz and layer thickness d between 10 and 130 mm. Below the onset of instability the cell was placed between crossed polars and light transmission was studied using a parallel light beam. The experimental results for the transmitted light intensity agree quantitatively with numerical solutions of the nematodynamic equations for different cell thicknesses, oscillation frequencies, and amplitudes. For frequencies between 25 and 150 Hz the critical oscillation amplitude for the onset of a spatial pattern, observed in polarized white light, could be reached. The pattern consisted of stationary rolls perpendicular to the direction of the oscillation. The experimentally obtained frequency dependence of the critical shear amplitude for the roll instability for different cell thicknesses is compared with an existing theory and the results of numerical calculations. @S1063-651X~98!09411-2# Nematic liquid crystals ~NLCs! exhibit interesting flow phenomena due to the coupling between the local molecular orientation ~director n ˆ! and the velocity field v. The flow properties of NLCs are characterized by Leslie viscosity coefficients a 1 ,...,a6 , two of which a 2(,0) and a 3 are important in describing the coupling between flow and director orientation @1‐4#. In the case of steady, plane, parallel shear flow, e.g., along the x axis with a velocity field v x(z )( v y 5 v z 50) and in the absence of other torques, the director will tend to align in the flow plane ( x-z plane! at a fixed angle u fl 56arctan(a3 /a2) 1/2 with the x axis if a 3,0 ~the 6

Pattern forming instabilities induced by ultralow frequency sinusoidal voltages were studied in a rodlike nematic liquid crystal by microscopic observations and simultaneous electric current measurements. Two pattern morphologies, electroconvection (EC) and flexodomains (FD), were distinguished, both appearing as time separated flashes within each half period of driving. A correlation was found between the time instants of the EC flashes and those of the nonlinear current response. The voltage dependence of the pattern contrast $C(U)$ for EC has a different character than that for the FD. The flattening of $C(U)$ at reducing the frequency was described in terms of an imperfect bifurcation model. Analyzing the threshold characteristics of FD, the temperature dependence of the difference $|{e}_{1}\ensuremath{-}{e}_{3}|$ of the flexoelectric coefficients was also determined by considering elastic anisotropy.

The nonlinear response of a nematic slab subjected to a rectilinear low-frequency oscillatory Couette and Poiseuille flow is investigated theoretically. We find that under Poiseuille flow and with appropriate alignment conditions by surface anchoring and/or magnetic field a state with slow, spontaneous director rotation appears. This may provide a model for the slow director rotations observed in high-frequency Couette flow. \textcopyright{} 1996 The American Physical Society.

The temporal evolution of patterns within the driving period of the ac voltage was studied in the 10-mHz-250-Hz frequency range. It was shown that the stationary electroconvection pattern of the conductive regime transforms into a flashing one at ultralow frequencies, existing only in narrow time windows within the period. Furthermore a transition between electroconvection and flexoelectric domains was detected which is repeating in each half period. The two patterns are well separated in time and in Fourier space. Simultaneous current measurements uncovered that the electric properties of the polyimide orienting layers influence the redistribution of the applied voltage. The experimental findings are in good qualitative agreement with the theoretical predictions based on an extended standard model including flexoelectricity.

We consider instabilities, either homogeneous or periodic in space, which develop in a nematic liquid crystal layer under rectilinear oscillatory Couette flow for planar surface alignment of the director perpendicular to the flow plane. On the basis of a numerical and analytical linear stability analysis we determine the critical amplitude of the oscillatory flow, the wave number, and the symmetry of the destabilizing mode and present a comprehensive phase diagram of the flow instabilities. In particular it is found that by varying the frequency of the Couette flow the instability changes its temporal symmetry. This transition is shown to be related to the inertia effects of the nematic fluid, which become more important with increasing flow frequency. We also show that an electric field applied perpendicularly to the nematic layer can induce an exchange of instabilities with different spatial and temporal symmetries. The theoretical results are compared with experiments, when available.

We study theoretically the slow director precession and nonlinear waves observed in homeotropically oriented nematic liquid crystals subjected to circular or elliptical Couette and Poiseuille flow and an electric field. From a linear analysis of the nematodynamic equations it is found that in the presence of the flow the electric bend Fréedericksz transition is transformed into a Hopf-type bifurcation. In the framework of an approximate weakly nonlinear analysis we have calculated the coefficients of the modified complex Ginzburg-Landau equation, which slightly above onset describes nonlinear waves with strong nonlinear dispersion. We also derive the equation describing the precession and waves well above the Fréedericksz transition and for small flow amplitudes. Then the nonlinear waves are of diffusive nature. The results are compared with full numerical simulations and with experimental data.

When a binary fluid mixture enters the two-phase region by crossing its critical point it immediately becomes unstable. Even arbitrarily small composition fluctuations tend to grow and the fluid decomposes into two discrete phases which form an irregular labyrinthine pattern whose characteristic length scale is initially determined by the wave vector with the fastest growth rate. At a later stage of this spinodal decomposition, the pattern coarsens. Close to the critical point, but still in the one-phase regime, the restoring forces vanish, the diffusion dynamics shows a critical slowing down, the amplitude of the fluctuations of the order parameter grows, and the mixture becomes increasingly susceptible to external fields. The influence of external fields on the demixing process has received growing attention because of the possibility of controlling the demixing morphology. Polymer blends are ideal candidates for such experiments due to their high viscosity, their large correlation length, and the resulting slow dynamics. It has been found that thin films of incompatible polymers, which had been spin coated from a common solvent, resemble the structure of the underlying prepatterned surface [1]. Small filler particles can trigger com