Soft-mode turbulence in electrohydrodynamic convection of a homeotropically aligned nematic layer

Abstract

The experimental study of electroconvection in a homeotropically aligned nematic ͑MBBA͒ is reported. The system undergoes a supercritical bifurcation ''rest state-spatiotemporal chaos.'' The chaos is caused by longwavelength modulation of the orientation of convective rolls. For the first time the observations both below and beyond the Lifshitz point are accompanied by quantitative analysis of temporal autocorrelation functions of turbulent modes. The dependence of the correlation time on the control parameter is obtained. A secondary bifurcation from normal to abnormal rolls is discussed. ͓S1063-651X͑97͒51412-7͔PACS number͑s͒: 47.27.Cn, 47.52.ϩj, 47.65.ϩa, 61.30.Gd Being a rich pattern-forming system, ac-driven electrohydrodynamic convection ͑EHC͒ in a nematic layer attracts a good deal of attention of both theoreticians and experimentalists ͓1,2͔. The system consists of a thin layer of a nematic liquid crystal sandwiched between two parallel electrodes. The convection occurs when the applied to the layer ac voltage V exceeds a certain threshold V c ͓3͔. There are two conventional realizations of EHC, namely planar, where the director n lies in plane of the electrodes (x-y plane͒, and homeotropic, where the director is perpendicular to the electrodes. It is clear that in the planar alignment the nonconvective state is anisotropic in the x-y plane, contrary to the homeotropic geometry, where spatially uniform distribution of the director parallel to the z axis yields isotropy in the x-y plane.In EHC most attention has been paid to the planar orientation; the homeotropic alignment has not been studied in detail yet. Meanwhile, in the homeotropic case EHC instability is usually preceded by Fréedericksz transition: beyond a certain threshold voltage V F the director tilts with respect to the z axis ͓3͔. Thus, at VϾV F the director has a nonzero projection on the x-y plane (n ʈ ), which therefore brings about spontaneous breaking of isotropy in this plane. Since orientation of n ʈ is not imposed by any external factor, the system is degenerate with respect to arbitrary rotations in the x-y plane. In other words, at the threshold of homeotropic EHC the system has additional ͑compared to the planar alignment͒ continuous one-parameter group of symmetry, which provides grounds for qualitatively different dynamics.Theoretical analysis of pattern formation at small values of the normalized control parameter ͓ϵ(V 2 ϪV c 2 )/V c 2 Ӷ1] shows that planar and homeotropic EHC do differ dramatically ͓4,5͔. In particular, in the planar case at small one can have steady stable normal rolls ͑the pattern's wave vector k is parallel to undistorted n͒ at the frequency of the applied ac-voltage f lying beyond the so-called Lifshitz point ͑LP͒, and oblique rolls ͑a certain finite angle between k and n͒ below LP ͓1,2͔.Contrary to this, in the homeotropic case while beyond LP the governing equations also have steady solutions of the normal-roll type; all of them are unstable under very general conditions ͓5͔. The instability occurs due ...

Compressed exponential relaxation as superposition of dual structure in pattern dynamics of nematic liquid crystals

“…There are two types of SMT pattern; oblique rolls in f < f L and normal rolls in f > f L , where f L denotes the Lifshitz frequency [9,10]. The interaction between the convective and Goldstone modes are different between oblique and normal rolls [45,46]; the convective wave vector in SMT tend to become parallel to the C-director in the normal roll and oblique in the oblique roll.…”

“…With further increasing V , the electrohydrodynamic convection occurs at the electroconvective threshold voltage V c . The nonlinear coupling between the convective mode q(x, y) and the Nambu-Goldstone one C(x, y) induces spatially and temporally disordered pattern called soft-mode turbulence (SMT) [9][10][11]. SMT is regarded as an experimentally observed spatiotemporal chaos.…”

“…An experimentally obtained spatiotemporal chaos in homeotropically aligned nematic liquid crystals is soft-mode turbulence (SMT) [9][10][11], induced by nonlinear coupling between the local convective mode and global Nambu-Goldstone one (see Appendix for details). SMT has a characteristic spatial structure.…”

Square Patterns and their Dynamics in Electroconvection

“…The time evolution of the patterns was studied as a function of frequency and the dimensionless control parameter For quantitative characterization of the pattern dynamics a local autocorrelation function C(x,t) of the intensity along the line I(x,t) was computed according to the formula ( ) ∝ ε at small ω, which indicates a direct transition to STC from the homogeneous state [15]. At higher ω (above ω*) the structure is stationary at onset up to ε = 0.05.…”

“…Consequently one obtains spatio-temporal chaos (STC), often called soft mode turbulence [6], already at the onset of EC. This type of chaotic behavior has been devoted considerable attention to in recent years, both theoretically [5] and experimentally [7][8] [9].…”