Recent results on flexodomain


A regular domain structure consisting of parallel stripesflexodomains have been induced by low frequency (subHz) electric voltage in a bent core nematic liquid crystal. The wavelength of the pattern is in the range of 1–10 micrometers and thus can conveniently be observed in a polarizing microscope. It also serves as an optical grating and produces a regular system of laser diffraction spots. The pattern was found to emerge and disappear consecutively in each half period of the driving, with the wavelength of the flexodomains changing periodically as the ac voltage oscillates. Analyzing the polarization characteristics of the diffracted light, the polarization of the first order spot was found perpendicular to that of the incident light, in accordance with a recent theoretical calculation.



Ming-Ya Xu, Meng-jie Zhou, Ying Xiang, Péter Salamon, Nándor Éber, and Ágnes Buka: Domain structures as optical gratings controlled by electric field in a bent-core nematic. Optics Express 23(12), 15224 (2015) [pdf]


The effect of superimposed ac and dc electric fields on the formation of electroconvection and flexoelectric patterns in nematic liquid crystals was studied. For selected ac frequencies, an extended standard model of the electrohydrodynamic instabilities was used to characterize the onset of pattern formation in the two-dimensional parameter space of the magnitudes of the ac and dc electric field components. Numerical as well as approximate analytical calculations demonstrate that depending on the type of patterns and on the ac frequency, the combined action of ac and dc fields may either enhance or suppress the formation of patterns. The theoretical predictions are qualitatively confirmed by experiments in most cases. Some discrepancies, however, seem to indicate the need to extend the theoretical description.


Alexei Krekhov, Werner Decker, Werner Pesch, Nándor Éber, Péter Salamon, Balázs Fekete, and Ágnes Buka: Patterns driven by combined ac and dc electric fields in nematic liquid crystals, Phys. Rev. E 89, 052507/1-9 (2014) [pdf]


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 |e1 e3| of the flexoelectric coefficients was also determined by considering elastic anisotropy.



P. Salamon, N. Éber, A. Krekhov and Á. Buka: Flashing flexodomains and electroconvection rolls in a nematic liquid crystal. Phys. Rev. E. 87, 032505/1-10 (2013) [pdf]


In this chapter the influence of flexoelectricity on pattern formation induced by an electric field in nematics will be summarized. Two types of patterns will be discussed in the linear regime, the equilibrium structure of flexoelectric domains and the dissipative electroconvection (EC) rolls. In a separate section, recent experimental and theoretical results on the competition and crossover between the flexoelectric domains and EC patterns will be described.



Á. Buka, T. Tóth-Katona, N. Éber, A. Krekhov and W. Pesch, Chapter 4. The role of flexoelectricity in pattern formation. In eds. Á. Buka and N. Éber, Flexoelectricity in Liquid Crystals. Theory, Experiments and Applications, Imperial College Press, London, 2012. pp. 101–135


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.




[N. Éber,L.O. Palomares, P. Salamon, A. Krekhov and Á. Buka: Temporal evolution and alternation of mechanisms of electric-field-induced patterns at ultralow-frequency driving. Phys. Rev. E 86, 021702/1-9 (2012).] [pdf]




[N. Éber, L.O. Palomares, P. Salamon, A. Krekhov, Á. Buka: Competition between Electric Field Induced Equilibrium and Dissipative Patterns at Low Frequency Driving in Nematics. Invited talk at the 24th International Liquid Crystal Conference, Mainz, August 19th - 24th, 2012] [pdf]


The temporal evolution of electric field induced patterns within the driving period was studied in the nematic Phase 5 in a wide frequency range. The compound exhibits a transition from conductive to dielectric regime of electroconvection (EC) at high frequency. At low frequencies we found that the conductive EC rolls evolve and decay in each half period of driving. Following EC rolls another pattern, flexoelectric domains (FD), also appear as flashes in the same half period. This scenario thus represents a repetitive morphological transition between dissipative (EC) and equilibrium (FD) patterns.



[N. Éber, P. Salamon and Á. Buka: Competition between Electric Field Induced Equilibrium and Non-Equilibrium Patterns at Low Frequency Driving in Nematics. In Proceedings of the 13th Small Triangle Meeting on Theoretical Physics, Stará Lesná, November 14-16, 2011, J. Busa, M. Hnatic and P. Kopcansky (eds.), IEP SAS, Kosice, 2012, pp. 56-63.]  [pdf]




We present in this paper a detailed analysis of the flexoelectric instability of a planar nematic layer in the presence of an alternating electric field (frequency ω), which leads to stripe patterns (flexodomains) in the plane of the layer. This equilibrium transition is governed by the free energy of the nematic, which describes the elasticity with respect to the orientational degrees of freedom supplemented by an electric part. Surprisingly the limit ω 0 is highly singular. In distinct contrast to the dc case, where the patterns are stationary and time independent, they appear at finite, small ω periodically in time as sudden bursts. Flexodomains are in competition with the intensively studied electrohydrodynamic instability in nematics, which presents a nonequilibrium dissipative transition. It will be demonstrated that ω is a very convenient control parameter to tune between flexodomains and convection patterns, which are clearly distinguished by the orientation of their stripes.



[A. Krekhov, W. Pesch, Á. Buka: Flexoelectricity and pattern formation in nematic liquid crystals. Phys. Rev. E 83, 051706 (2011)]  [pdf]





Periodic stripe patterns which form when an electric field is applied to a thin nematic liquid crystal layer with a very low conductivity are discussed. In this case the dielectric electroconvection mode persists down to very low frequencies of the driving voltage. A Lifschitz point, i.e., a transition from normal to oblique rolls is detected in the dielectric regime. A crossover from electroconvection to flexoelectric domains occurs for extremely low frequencies of about 0.1 Hz. The crossover scenario yields pattern morphologies characteristic for both mechanisms, i.e., electroconvection and flexoelectric domains which appear consecutively within one period of the driving voltage. A theoretical description of the onset characteristics of dielectric convection, which is based on an extended model including flexoelectricity, is also presented.

[M. May, W. Schöpf, I. Rehberg, A. Krekhov, A. Buka: Transition from longitudinal to transversal patterns in an anisotropic system. Phys. Rev. E 78, 046215 (2008)]  [pdf]