Instabilities in nematic liquid crystals

Emmanuel Plaut

 

      This research represents the continuity of my former activities in Orsay in the team of Roland Ribotta and in the Bayreuther Theoretical Physics Institute. Since my arrival in Nancy, I cooperated with the teams of Werner Pesch in Bayreuth and with the experimental group of James T. Gleeson at Kent State University Physics Department.

      I have been interested by the transition to turbulence in nematic liquid crystal layers submitted to thermal or electrical stress. The dynamics of such anisotropic fluids is rulled by the so-called nematohydrodynamics. The interactions between the scalar fields, the velocity field and the director field (the averaged direction of the rod-like molecules, i.e. the local axis of anisotropy of the fluid) entail new scenarios of instabilities and pattern formation that are quite interesting. I have especially focussed on planar thermoconvection:

(somehow the anisotropic analog system to classical Rayleigh-Bénard convection), and on its electric counterpart, planar electroconvection:

As an example of pattern, let me just show you a `splay bimodal varicose':

Nice, isn't it ? So, if you want to know more, please have a look at my articles...


[1] Optical characterization of the director field in a distorted nematic layer, E. Plaut, A. Joets and R. Ribotta, J. Phys. III France 7, 2459-2474 (1997).

We develop new optical methods using transmitted polarized light for the characterization of the out of plane component nz of the director field in a weakly distorted planar nematic layer. In extraordinary light, we relate the angles of aperture of the caustic surface to the local amplitudes of the nz distortion. In ordinary light, a new type of contrast due to the anisotropic light scattering is shown to give the map of nz2. We apply our methods to the study of the director distortions occuring in the thermal convection.

[2] Cascade of structures in the thermoconvection of a nematic in the director-dominated regime, E. Plaut and R. Ribotta, EuroPhys. Lett. 38, 441-446 (1997).

We report on the first experimental study of the nonlinear evolution of thermoconvection in a planar nematic liquid crystal, in extended geometry and at zero or weak stabilizing magnetic field. As the control parameter is adiabatically increased, we show that the system undergoes a series of bifurcations between stationary convective structures. We stress that this scenario is generic in the convection of a nematic in a regime where the director nonlinear couplings dominate, independently of the basic convective mechanism.

[3] Weakly nonlinear analysis of the secondary bimodal instability in planar nematic convection, E. Plaut and R. Ribotta, Phys. Rev. E 56, R 2375-2378 (1997).

We present a weakly nonlinear analysis of the secondary transition from one to two-mode structures in planar, extended geometry nematic convection. The secondary growth rate being then an explicit function of the nonlinear coupling terms of the basic equations, we can perform a systematic investigation of the physical origin of the secondary mode. This mode turns out to be selected by a nonlinear homogeneous rotation of the director in the horizontal plane.

[4] Spatio-temporal patterns in the Thermoconvection of a planar nematic layer: I. Weakly nonlinear models, E. Plaut and R. Ribotta, Eur. Phys. J. B 5, 265-281 (1998).

We study theoretically the formation of convection patterns in a laterally extended planar nematic layer heated from below, in the linear and weakly nonlinear regimes. By reformulating the viscous coupling terms of the basic nematohydrodynamic equations, a simple interpretation of the flow effects on the director dynamics can be proposed. A detailed linear analysis of the problem is presented. A systematic method to investigate nonlinear mechanisms is developed, and exemplified by the study of the nonlinear saturation in rolls. The extension of the roll amplitude equation with the envelope formalism is used to characterize the dynamics of the roll modulations near threshold. Coupled envelope equations are shown to describe the structure of the point defects in zig-zags observed experimentally. Finally the bifurcation to the bimodal varicose is studied. The secondary wavevector in the bimodal appears to be selected by a rotation of the director in the horizontal plane. Quantitative predictions concerning the amplitude of this rotation are given.

[5] Spatio-temporal patterns in the Thermoconvection of a planar nematic layer: II. Experiments, E. Plaut, L. Pastur and R. Ribotta, Eur. Phys. J. B 5, 283-297 (1998).

We study experimentally the evolution of thermoconvection in a laterally extended planar nematic layer, at zero or weak stabilizing magnetic field. As the applied thermal gradient is increased, a cascade of symmetry breakings occurs, towards structures of increasing spatial complexity, and ultimately towards oscillating states. The patterns are characterized optically, and simple models for the distortion of the vertical (out of plane) component of the director field are proposed.

[6] New symmetry breaking in nonlinear electroconvection of nematic liquid crystals, E. Plaut, W. Decker, A. G. Rossberg, L. Kramer, W. Pesch, A. Belaidi and R. Ribotta, Phys. Rev. Lett. 79, 2367-2370 (1997).

We report on a novel symmetry-breaking bifurcation in nematic liquid crystal convection in planarly aligned cells involving a homogeneous reorientation of the director. The resulting ``abnormal rolls'' explain a number of recent experimental observations in the nonlinear regime.

[7] Extended Weakly Nonlinear Theory of Planar Nematic Convection, E. Plaut and W. Pesch, Phys. Rev. E. 59, 1747-1769 (1999).

We study theoretically convection phenomena in a laterally extended planar nematic layer driven by an ac electric field (electroconvection in the conduction regime) or by a thermal gradient (thermoconvection). We use an order parameter approach and demonstrate that the sequence of bifurcations found experimentally or in the numerical computations can be recovered, provided a homogeneous twist mode of the director is considered as a new active mode. Thus we elucidate the bifurcation to the new ``abnormal rolls'' [E. Plaut et al, Phys. Rev. Lett. 79, 2367 (1997)]. The coupling between spatial modulations of the twist mode and the mean flow is shown to give an important mechanism for the long-wavelength zig-zag nstability. The twist mode is also responsible for the widely observed bimodal instability of rolls. Finally, a Hopf bifurcation in the resulting bimodal structures is found, which consists of director oscillations coupled with a periodic switching between the two roll amplitudes. A systematic investigation of the microscopic mechanisms controlling all these bifurcations is presented. This establishes a close analogy between electro- and thermoconvection. Moreover, a ``director/wavevector frustration'' is found to explain most of the bifurcations.

[8] Competition of periodic and homogeneous modes in extented dynamical systems, B. Dressel, A. Joets, L. Pastur, W. Pesch, E. Plaut and R. Ribotta, Phys. Rev. Lett. 88, 024503-1-4 (2002).

Despite their simple structure, spatially homogeneous modes can participate directly in pattern-formation processes. This is demonstrated by new experimental and theoretical results for thermo-and electro-convection in planar nematic liquid crystals, where two distinct homogeneous modes, twist and splay distortions of the director field, emerge. Their nonlinear excitation is due to certain spontaneous symmetry-breaking bifurcations.

[9]

Electric Nusselt number characterization of electroconvection in nematic liquid crystals, J.T. Gleeson, N. Gheorghiu and E. Plaut, Eur. Phys. J. B 26, 515-520 (2002).

We develop a characterization method of electroconvection structures in a planar nematic liquid crystal layer by a study of the electric current transport. Because the applied potential difference has a sinusoidal time dependence, we define two electric Nusselt numbers corresponding to the in-phase and out-of-phase components of the current. These Nusselt numbers are predicted theoretically using a weakly nonlinear analysis of the standard model. Our measurements of the electric current confirm that both numbers vary linearly with the distance from onset until the occurence of secondary transitions. A systematic comparison between our theoretical and experimental results, using no adjusted parameters, demonstrates moderate agreement, but discrepancies remain. Electric transport measurements during electroconvection represent a quantitative test of the standard model completely independent from optical probes. Thus, the technique described here can be a useful complement to traditional structural measurements.


Emmanuel Plaut
Last modified: Mon Jul 15 20:02:40 CEST 2013