Electroconvection

Recent results on standard and nonstandard electroconvection

Standard electroconvection

Electric field-induced patterns in liquid crystals have been observed and studied for about 50 years. During this time, a great variety of structures, detected under different conditions, have been described; theoretical descriptions were also developed parallel with the experiments and a huge number of papers have been published. The non-vanishing interest in the topic is due to several factors. First, most experimentalists working with new (or even well-known) liquid crystals apply sooner or later an electric field for different purposes and, as a response, often (maybe undesirably or unexpectedly) have to face with emergence of patterns. Second, understanding the complexity of the formation mechanism of regular patterns in a viscous, anisotropic fluid is an extremely challenging theoretical task. Third, specialists in display fabrication or in other applications are also interested in the results; either to make use of them or in order to avoid field-induced patterns.

In this review, we attempt to provide a systematic overview of the large amount of published results, focusing on recent achievements, about the three main types of electric field-induced patterns: transient patterns during the Freedericksz transition, flexoelectric domains and electroconvection. As a result of different instability mechanisms, a variety of pattern morphologies may arise. We address the physical background of the mechanisms, specify the conditions under which they may become effective, discuss the characteristics of the patterns, and summarize the possibilities of morphological transitions induced by frequency, voltage or temperature variations. Special emphasis is given to certain topics, which recently have gained enhanced interest from experimental as well as theoretical point of view, like driving with ultra-low frequencies or non-sinusoidal (superposed) waveforms, and the dynamics of defects and embedded colloidal particles. Assisting newcomers to the field, we also mention some, yet unresolved, problems, which may need further experimental and/or theoretical studies.

N. Éber, P. Salamon and Á. Buka: Electrically induced patterns in nematics and how to avoid them, Liquid Crystals Reviews 4 (2), 101-134 (2016). [pdf]

The effect of superposed dc and ac applied voltages on two types of spatially periodic instabilities in nematic liquid crystals, flexoelectric domains (FD), and electroconvection (EC) was studied. The onset characteristics, threshold voltages, and critical wave vectors were determined. We found that in general the superposition of driving with different time symmetries inhibits the pattern forming mechanisms for FD and EC as well. As a consequence, the onset extends to much higher voltages than the individual dc or ac thresholds. A dc-bias-induced reduction of the crossover frequency from the conductive to the dielectric EC regimes and a peculiar transition between two types of flexodomains with different wavelengths were detected. Direct measurements of the change of the electrical conductivity and its anisotropy, induced by the applied dc voltage component, showed that the dc bias substantially affects both parameters. Taking into account the experimentally detected variations of the conductivity in the linear stability analysis of the underlying nematohydrodynamic equations, a qualitative agreement with the experimental findings on the onset behavior of spatially periodic instabilities was obtained.

N. Éber, P. Salamon, B. A. Fekete, R. Karapinar, A. Krekhov, and Á. Buka: Suppression of spatially periodic patterns by dc voltage, Phys. Rev. E 93, 042701 (2016). [pdf]

In contrast to the predictions of the standard theory of electroconvection (EC), our experiments showed that the action of superposed ac and dc voltages rather inhibits pattern formation than favors the emergence of instabilities; the patternless region may extend to much higher voltages than the individual ac or dc thresholds. The pattern formation induced by such asymmetrical voltage was explored in a nematic liquid crystal in a wide frequency range. The findings could be qualitatively explained for the conductive EC, but represent a challenging problem for the dielectric EC.

P. Salamon, N. Éber, B. Fekete, and Á. Buka: Inhibited pattern formation by asymmetrical high-voltage excitation in nematic fluids. Phys. Rev. E, 90, 022505/1-5 (2014) [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.

Theory

Experiment

Theory

Experiment

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]

The behaviour of an electric field induced pattern forming instability, the electroconvection in a nematic liquid crystal, was studied under the influence of superposed dc and ac electric voltages. The onset parameters (threshold voltages and critical wave numbers) were determined. It was found that the superposition of voltages inhibits the pattern forming mechanism; therefore the patternless region extends to much higher voltages than the individual ac or dc thresholds. A dc bias induced reduction of the electrical conductivity and a shift of the crossover frequency from the conductive to dielectric electroconvection regimes were also detected.

N. Éber, P. Salamon, B. Fekete, T. Tóth-Katona, R. Karapinar, M. Sacks, and Á. Buka: Electroconvection in a Nematic Liquid Crystal under Superposed AC and DC Electric Voltages, In. Proceedings of the 15^th Small Triangle Meeting on Theoretical Physics, Stará Lesná, October 27-30, 2013, J. Buša, M. Hnatič and P. Kopčanský (eds.), IEP SAS, Košice, 2014, pp. 46-51. [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 13^th 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]

The temporal evolution of the spatially periodic electroconvection (EC) patterns has been studied within the period of the driving ac voltage by monitoring the light intensity diffracted from the pattern. Measurements have been carried out on a variety of nematic systems, including those with negative dielectric and positive conductivity anisotropy, exhibiting 'standard EC' (s-EC), those with both anisotropies negative exhibiting 'nonstandard EC' (ns-EC), as well as those with the two anisotropies positive. Theoretical predictions have been confirmed for stationary s-EC and ns-EC patterns. Transitions with Hopf bifurcation have also been studied. While traveling had no effect on the temporal evolution of dielectric s-EC, traveling conductive s-EC and ns-EC patterns exhibited a substantially altered temporal behavior with a dependence on the Hopf frequency. It has also been shown that in nematics with both anisotropies positive, the pattern develops and decays within an interval much shorter than the period, even at relatively large driving frequencies.

[T. Tóth-Katona, N. Éber, and Á. Buka: Temporal response to harmonic driving in electroconvection. Phys. Rev. E 83, 061704/1-8 (2011)] [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]

We reexamine the influence of the flexoelectricity on the electroconvection (EC), the effect which has previously been studied in the conductive EC regime only. Now we extend our studies to the dielectric EC, and to the parameter range for which the standard model of EC excludes the existence of the instability. First, we demonstrate that inclusion of flexoelectricity into the standard model of EC provides a finite EC threshold even for this "forbidden" material parameter range (in accordance with the experiments). Second, we show that flexoelectricity considerably decreases the threshold voltage for the dielectric regime. Finally, we present a novel frequency dependence of the threshold voltage for all EC patterns in the case when the period of the driving frequency becomes comparable with the director relaxation time.

[T. Tóth-Katona, N. Éber, Á. Buka: Flexoelectricity in electroconvection. Mol. Cryst. Liq. Cryst. 511, 11-24 (2009)] [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]

An unexpected type of behavior in electroconvection (EC) has been detected in nematic liquid crystals (NLCs) under the condition of comparable time scales of the director relaxation and the period of the driving ac voltage. The studied NLCs exhibit standard EC (s-EC) at the onset of the instability, except one compound in which nonstandard EC (ns-EC) has been detected. In the relevant frequency region, the threshold voltage for conductive s-EC bends down considerably, while for dielectric s-EC it bends up strongly with the decrease of the driving frequency. We show that inclusion of the flexoelectric effect into the theoretical description of conductive s-EC leads to quantitative agreement, while for dielectric s-EC a qualitative agreement is achieved. The frequency dependence of the threshold voltage for ns-EC strongly resembles that of the dielectric s-EC.

[T. Tóth-Katona, N. Éber, Á. Buka, A. Krekhov: Flexoelectricity and competition of time scales in electroconvection, Phys. Rev. E. 78, 036306 (2008)] [pdf]

A systematic overview of various electric-field induced pattern forming instabilities in nematic liquid crystals is given. The standard hydrodynamic description of nematics predicts the occurrence of striped patterns (rolls) in various wavenumber ranges, which depend on the anisotropy of the dielectric permittivity and that of the electrical conductivity as well as on the initial director orientation (planar or homeotropic). We discuss in detail three basic configurations with emphasis on the characterization of the threshold voltage and the critical wavenumber of the resulting patterns. Some features of the weakly nonlinear behavior are also addressed. Experimental exploration of additional pattern types, not captured by the standard model of electroconvection, is also presented. The impact of flexoelectricity as a possible explanation of the nonstandard EC patterns is discussed.

[Á. Buka, N. Éber, W. Pesch, L. Kramer: Isotropic and anisotropic electroconvection. Phys. Reports, 448, 115-132 (2007)] [pdf]

We present experimental measurements near the onset of electroconvection (EC) of homeotropically aligned nematic liquid crystals Phase 5A and MBBA. A voltage of rms value V₀ and frequency f was applied. With increasing V₀, EC occurred after the bend Freedericksz transition. We found supercritical bifurcations to EC that were either stationary bifurcations or Hopf bifurcations to traveling convection rolls, depending on the sample conductances. Results for the onset voltages V_c, the critical wave numbers k_c, the obliqueness angles q_c, and the traveling-wave (Hopf) frequencies at onset w_c over a range of sample conductances and driving frequencies are presented and compared, to the extent possible, with theoretical predictions. For the most part good agreement was found. However, the experiment revealed some unusual results for the orientations of the convection rolls relative to the direction selected by the Freedericksz domain.

[S.-Q. Zhou, N. Éber, Á. Buka, W. Pesch, G. Ahlers: Onset of electro-convection in homeotropically aligned nematic liquid crystal. Phys. Rev. E, 74, 046211 (2006)] [pdf]

The decay of stripe patterns in planarly aligned nematic liquid crystals has been studied experimentally and theoretically. The initial patterns have been generated by the electrohydrodynamic instability and a light diffraction technique has been used to monitor their decay. In our experiments different decay rates have been observed as a function of the pattern wave number. According to our theoretical analysis they belong to a spectrum of decay modes and are individually selected in dependence on the initial conditions. Additional insight has emerged from a refined physical optical description of the diffraction intensity. The results compare well with experiments, which include also controlled modifications of the initial conditions to assess different decay modes.

[W. Pesch, L. Kramer, N. Éber, Á. Buka: The Role of Initial Conditions in the Decay of Spatially Periodic Patterns in a Nematic Liquid Crystal. Phys. Rev. E, 73, 061705 (2006)] [pdf]

A systematic overview of various electric-field induced pattern forming instabilities in nematic liquid crystals is given. Particular emphasis is laid on the characterization of the threshold voltage and the critical wavenumber of the resulting patterns. The standard hydrodynamic description of nematics predicts the occurrence of striped patterns (rolls) in five different wavenumber ranges, which depend on the anisotropies of the dielectric permittivity and of the electrical conductivity as well as on the initial director orientation (planar or homeotropic). Experiments have revealed two additional pattern types which are not captured by the standard model of electroconvection and which still need a theoretical explanation.

[Á. Buka, N. Éber, W. Pesch, L. Kramer: Convective patterns in liquid crystals driven by electric field. In.. Self-Assembly, Pattern Formation and Growth Phenomena in Nano-Systems, Eds. A. A. Golovin, A. A. Nepomnyashchy, NATO Science Series II, Mathematica, Physics and Chemistry, Vol. 218, Springer, Dordrecht, 2006, pp. 55-82] [pdf]

Nonstandard electroconvection

N. Éber, P. Salamon and Á. Buka: Electrically induced patterns in nematics and how to avoid them, Liquid Crystals Reviews 4 (2), 101-134 (2016). [pdf]

A regular domain structure consisting of parallel stripes – flexodomains – 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]

Electric-field-induced patterns of diverse morphology have been observed over a wide frequency range in a recently synthesized bent-core nematic (BCN) liquid crystal. At low frequencies (up to ∼25 Hz), the BCN exhibited unusual polarity-dependent patterns. When the amplitude of the ac field was enhanced, these two time-asymmetrical patterns turned into time-symmetrical prewavylike stripes. At ac frequencies in the middle-frequency range (∼50–3000 Hz), zigzag patterns were detected whose obliqueness varied with the frequency. Finally, if the frequency was increased above 3 kHz, the zigzag pattern was replaced by another, prewavylike pattern, whose threshold voltage depended on the frequency; however, the wave vector did not. For a more complete characterization, material parameters such as elastic constants, dielectric permittivities, and the anisotropy of the diamagnetic susceptibility were also determined.

Ying Xiang, Meng-jie Zhou, Ming-Ya Xu, Péter Salamon, Nándor Éber, and Ágnes Buka: Unusual polarity-dependent patterns in a bent-core nematic liquid crystal under low-frequency ac field, Phys. Rev. E 91, 042501 (2015) [pdf].

Two kinds of electroconvection patterns in an ether-bridged bent-core nematic liquid crystal material (BCN), which appear in different frequency ranges, are examined and compared. One is a longitudinal pattern with the stripes parallel to the orientation of the BCN and with a periodicity of approximately the cell thickness, occurring in the high-frequency range of several hundreds Hz; the other one is oblique stripes, which results in a zigzag pattern, and appears in the low-frequency range of several tens Hz. In addition, within an intermediate-frequency range, transformations from oblique to longitudinal and then to normal stripes occur at increased ac voltages. In particular, we investigated the temperature behavior of longitudinal and oblique stripes: When the temperature T increases and approaches the clearing temperature Tc, the contrast of the domains is enhanced and the frequency range of existence becomes wider, while the onset voltages increase only moderately instead of diverging, thus suggesting an isotropic mechanism of pattern formation.

Ying Xiang, Yi-Kun Liu, Ágnes Buka, Nándor Éber, Zhi-Yong Zhang, Ming-Ya Xu, and Everett Wang: Electric-field-induced patterns and their temperature dependence in a bent-core liquid crystal, Phys. Rev. E 89, 012502/1-9 (2014) [pdf]

This article summarizes the results obtained by various experimental methods on the physical properties of a bent-core nematic liquid crystal 4-chloro-1,3-phenylene bis-4-[40-(9-decenyloxy) benzoyloxy] benzoate (ClPbis10BB). The material exhibits unusual properties in all aspects tested. Its bend flexoelectric coefficient is 1000 times larger than in calamitics; it is viscoelastic with a large, shear-rate-dependent viscosity. Its bend and twist elastic constants are abnormally low; thus the nematic phase can be rendered to be a blue fog phase with a small amount of chiral dopant. It shows very high flow birefringence and unusually small leading Landau coefficient. It has two types of isotropic phases; at lower temperature it is probably tetrahedratic that can be transferred into the nematic phase with magnetic field. ClPbis10BB has a frequency-dependent conductivity anisotropy which is characterized by a double sign inversion. It exhibits various electroconvection (EC) patterns which are currently not understood in the frame of the standard theory of EC.

Á. Buka, N. Éber, K. Fodor-Csorba, A. Jákli and P. Salamon: Physical properties of a bent-core nematic liquid crystal and its mixtures with calamitic molecules. Phase Transitions 85, 872-887 (2012) [pdf]

A nematic liquid crystal with high, positive dielectric anisotropy (5CB) has been studied under the influence of the combined action of a dc and an ac electric field. Broad frequency, voltage, and cell thickness ranges were considered. Pattern morphologies were identified; the thresholds and critical wave numbers were measured and analyzed as a function of frequency, dc-to-ac voltage ratio, and thickness. The current-voltage characteristics were simultaneously detected.

[L.E. Aguirre, E. Anoardo, N. Éber and Á. Buka: Regular structures in 5CB liquid crystals under the joint action of ac and dc voltages. Phys. Rev. E 85, 041703/1-9 (2012)] [pdf]

The temporal evolution of the spatially periodic electroconvection (EC) patterns has been studied within the period of the driving ac voltage by monitoring the light intensity diffracted from the pattern. Measurements have been carried out on a variety of nematic systems, including those with negative dielectric and positive conductivity anisotropy, exhibiting "standard EC" (s-EC), those with both anisotropies negative exhibiting "nonstandard EC" (ns-EC), as well as those with the two anisotropies positive. Theoretical predictions have been confirmed for stationary s-EC and ns-EC patterns. Transitions with Hopf bifurcation have also been studied. While traveling had no effect on the temporal evolution of dielectric s-EC, traveling conductive s-EC and ns-EC patterns exhibited a substantially altered temporal behavior with a dependence on the Hopf frequency. It has also been shown that in nematics with both anisotropies positive, the pattern develops and decays within an interval much shorter than the period, even at relatively large driving frequencies.

[T. Tóth-Katona, N. Éber, and Á. Buka: Temporal response to harmonic driving in electroconvection. Phys. Rev. E 83, 061704/1-8 (2011)] [pdf]

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

Two electroconvection (EC) pattern morphologies - a cellular and a subsequent roll pattern - have been detected in the same frequency range in a nematic with positive permittivity and conductivity anisotropies. The frequency dependences of the onset voltages and critical wave numbers have been determined both for homeotropic and planar alignments. It has been proven that both pattern morphologies have a dielectric time symmetry. We also discuss possible sources for the pattern formation in the frame of both the isotropic (Felici-Benard) mechanism, as well as the standard model of EC.

[P. Kumar, J. Heuer, T. Tóth-Katona, N. Éber, and Á. Buka: Convection-roll instability in spite of a large stabilizing torque. Phys. Rev. E 81, 020702(R) (2010)] [pdf]

[T. Tóth-Katona, N. Éber, Á. Buka: Flexoelectricity in electroconvection. Mol. Cryst. Liq. Cryst. 511, 11-24 (2009)] [pdf]

The onset of electroconvection in binary mixtures of a bent-core and a rod-like nematic has been characterized by measuring the threshold voltage U_c and the critical wave number of the pattern in a wide range of frequencies f. In the mixtures rich in bent-core molecules, a "conductive-prewavy2-patternless-prewavy1" morphological sequence has been detected with an unusual negative slope of U_c(f) at high frequencies. This latter scenario seems to be related to the bent-core component, as it disappears with in creasing the concentration of rod-like molecules. In addition, one of the parameters most relevant for electroconvection, the electrical conductivity, has also been varied by ionic salt doping. It has been found that the above effect of the banana-shaped molecules on the electroconvection scenarios can be suppressed by the conductivity.

[S. Tanaka, H. Takezoe, N. Éber, K. Fodor-Csorba, A. Vajda, and Á. Buka: Electroconvection in nematic mixtures of bent-core and calamitic molecules. Phys. Rev. E 80, 021702 (2009)] [pdf]

For many years it has been commonly accepted that electroconvection (EC) as primary instability in nematic liquid crystals for the "classical" planar geometry requires a positive anisotropy of the electric conductivity, s_a, and a slightly negative dielectric anisotropy, e_a. This firm belief was supported by many experimental and theoretical studies. Recent experiments, which have surprisingly revealed EC patterns at negative conduction anisotropy as well, have motivated the theoretical studies in this paper. It will be demonstrated that extending the common hydrodynamic description of nematics by the usually neglected flexoelectric effect allows for a simple explanation of EC in the "nonstandard" case s_a>0.

[A. Krekhov, W. Pesch, N. Éber, T. Tóth-Katona, Á. Buka: Nonstandard electroconvection and flexoelectricity in nematic liquid crystals. Phys. Rev. E, 77, 021705 (2008)] [pdf]

[Á. Buka, N. Éber, W. Pesch, L. Kramer: Isotropic and anisotropic electroconvection. Phys. Reports, 448, 115-132 (2007)] [pdf]

Electric-field-driven pattern formation has been investigated in a nematic liquid crystal with negative dielectric and conductivity anisotropies. Despite the fact that the standard Carr-Helfrich theory predicts no hydrodynamic instability for such compound, experiments reveal convection patterns which we call nonstandard electroconvection (ns-EC). In this work, we characterize the ns-EC patterns by measuring the frequency, thickness, and temperature dependence of the threshold voltage, wave number, roll orientation, etc., and compare them with the standard-EC (s-EC) characteristics. For the first time, we report traveling rolls in ns-EC, and we give the dependence of the Hopf frequency on the driving frequency, temperature, and sample thickness. Finally, we discuss possible sources for the existence of these patterns.

[T. Tóth-Katona, A. Cauquil-Vergnes, N. Éber, Á. Buka: Non-standard electroconvection with Hopf-bifurcation in a nematic with negative electric anisotropies. Phys. Rev. E, 75, 066210 (2007)] [pdf]

We characterize three nonstandard electrohydro-dynamic instabilities in nematic liquid crystals composed of bent-core molecules. In addition to their shape, another important attribute of this material is that the anisotropy in the electrical conductivity changes sign as the frequency of the applied electric field changes. These instabilities do not appear to fit within the standard model for electroconvection. The first instability creates a pattern with stripes parallel to the initial director orientation, with a wavelength about equal to the separation of the cell plates. The next is the previously reported prewavy instability. The third instability is optically and dynamically identical to the prewavy instability, but is distinguished by different threshold behavior.

[D. B. Wiant, J. T. Gleeson, N. Éber, K. Fodor-Csorba, A. Jákli, T. Toth-Katona: Non-Standard Electroconvection in a Bent Core Nematic. Phys. Rev. E 72, 041712 (2005)] [pdf]