AC electric field induced flow and helix unwinding in focal conic texture of smectic C* liquid crystal

Transcription

1 AC electric field induced flow and helix unwinding in focal conic texture of smectic C* liquid crystal B. Labroo, V. Razdan, D.S. Parmar, G. Durand To cite this version: B. Labroo, V. Razdan, D.S. Parmar, G. Durand. AC electric field induced flow and helix unwinding in focal conic texture of smectic C* liquid crystal. Journal de Physique Lettres, 1985, 46 (24), pp < /jphyslet: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1985 HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 On A J. Physique Lett. 46 (1985) L1177 L DÉCEMBRE 1985, L1177 Classification Physics Abstracts AC electric field induced flow and helix unwinding in focal conic texture of smectic C* liquid crystal (*) B. Labroo, V. Razdan, D. S. Parmar and G. Durand (**) Department of Physics, University of Kashmir, Srinagar , India (Re~u le 25 septembre 1985, accepte le 31 octobre 1985) 2014 Résumé. soumet une mince (~ 10 03BCm) texture à conique focale de DOBAMBC en phase smectique C* à un champ électrique alternatif. Audelà d un seuil, un écoulement permanent «bouchon» est observé. Il démarre du foyer des ellipses, vers leur centre. A fort champ, les couples de cisaillement visqueux déroulent la texture hélicoïdale. Le seuil d écoulement est lié à une pression critique pompée électriquement au coeur des coniques focales, par l anisotropie de conductivité Abstract thin (~ 10 03BCm) focal conic texture of DOBAMBC in its Sm C* phase is submitted to an AC electric field. Above a field threshold, a DC plug flow of the texture normal to the layers is observed. It always originates from the focus of the ellipses towards their centre and extends to the entire focal domain. At higher field, the associated viscous shear unwinds the helical texture. The flow threshold is explained by the build up at the focus of a DC electric pressure, from the action of the AC field on AC space charges, generated by conductivity anisotropy. Smectic C* liquid crystals are lamellar fluid systems, made of chiral organic rod like molecules, tilted in the lamellae [1]. Their lack of inversion symmetry allows for a macroscopic electric polarization P to build up. Because of the chirality, the smectic layers are twisted relative to each other, so that the C* phase is heli ferroelectric. Much work has been done [2] using DC electric field to unwind the helix and to demonstrate the existence of P. At extremely low frequencies, comparable to an inverse time of defect propagation through the sample, an AC field can also couple with P, unwinding the helical texture as a DC field. For higher frequencies, on the other hand, the AC field can not couple with P, although helix unwinding above a given threshold has indeed been reported [3]. The mechanism of this AC unwinding is not yet understood. Most of these experiments have been performed on uniformly aligned C* texture, which nevertheless always contains some defects in the shape of focal conics [4] disclination lines. In this Letter, we report on the existence, above a given threshold of an AC electrically induced DC hydrodynamic flow in a focal conic texture of a Sm C* liquid crystal. This DC flow extends all over the sample, inducing viscous shear torques which finally unwind the helical texture. (*) Work supported by CSIR, UGC, DST, India and CNRS, France under IndoFrench Scientific and Cultural Exchange Programme. (**) On leave of absence from «Laboratoire de Physique des Solides, Orsay, France». Article published online by EDP Sciences and available at

3 (a) L1178 JOURNAL DE PHYSIQUE LETTRES The sample used is the widely studied DOBAMBC (pdecyloxybenzylidene p amino 2 methyl butyl cinnamate) which presents a Sm A phase below the isotropic transition temperature TA 117 C and a Sm C* phase below = T~ 95 C. The material is placed in between two tin oxide coated transparent glass plates (1 x 1 cm2) with spacer thickness d in the 1050 ~m range. The sample is temperature controlled in a Mettler FP 52 hot stage and observed under a polarizing microscope. A low frequency (020 khz) AC generator can be connected to the glass electrodes in order to apply an AC sinosidal electric field to the sample. The electrode surfaces have been rubbed parallel to induce a planar orientation. The sample is cooled slowly from the isotropic phase. We obtain in the Sm A phase large (500 ~m) oriented regions, separated by well defined focal conics. The ellipses parallel to the plates are found to be at random in the bulk as well as at the surface of the sample. Further cooling (5 C) below T~ results in the well defined parallel stripes characteristic of the helical texture. The apparent periodicity of these «dechiralization» lines [5] is found to be 2.7 ~m i.e., half the pitch Z 5.4 = ~m, in agreement with previous measurements [6]. This indicates that the surface anchoring must be polar [7]. We now apply the electrical field by increasing the voltage V across the sample of thickness 10 J.1m, for a fixed frequency f 200 Hz. Up to Vth 7.7 volts (rms), the texture does not = move but one out of every two stripes appears to get out of the texture by the side, to the focal conic boundaries, or to the place exactly below the remaining stripes, so that the new spatial period is exactly the pitch Z. Above Vth, the parallel stripes start moving with a steady DC velocity v perpendicular to their orientation. Increasing the voltage, v increases until the helical texture unwinds, leaving the appearance of the previous Sm A texture. The observed steady motion of the stripes above Vth is definitely a real hydrodynamic flow of the helical texture since we have observed that some dust particles, trapped in the bulk were moving with the same velocity v. The direction of v is always the same for a given part of the sample, although in a few cases we see two antagonistic superimposed flows. This uniform flow must therefore be a plug flow of the C* bulk texture. The sources for these flows are located in all cases at the focus C of the elliptical focal conic parallel to the plates (Fig. 1). These focal points appear to emit periodically new stripes, i.e., to emit Sm C* layers. The direction of v is always Fig. 1. A typical focal conic texture. The space charges due to conductivity anisotropy pile up in the cones with apex on the hyperbola r 2" The pressure in the liquid core of F, increases as E 2 ~ and above a mechanical breakdown threshold, induces the emission of new layers from the focus C along the arrow direction, towards the centre of the ellipse Fi. (b) Aspect of the plug flow seen from above, from the uniform motion of dechiralization lines.

4 Voltage FLOW AND HELIX UNWINDING IN Sm C* L1179 from the focus C towards the centre of the ellipse T 1. The emission of new stripes is exactly compensated by the absorption of stripes moving along the hyperbola T2 which points towards the focus. From above the plates it seems that the end of the hyperbola close to the focus acts as a directive electric pump towards the centre of the ellipse (Fig. 1 b). Inside a given elliptical focal conic, this flow extends far away from the focus of the ellipse. More generally, most of the ellipses are incomplete and thus these flows extend to all regions of the sample, with various velocities v, inducing flow and back flow for mass conservation. This total extension of the flow demonstrates that the stabilizing forces responsible for the observed threshold cannot be attributed to any larger anchoring to the surface plates. In fact the layers appear to be very mobile indicating that close to the plates, because of a large layer dislocation density (or because of a large decrease of the smectic ordering), the material must be considered in a fluid nematic phase, rather than in a smectic one. For one given source of flow, we have measured the frequency dependence of Vth. The data plotted in figure 2 shows that Vth is frequency independent, from f 0 to f = fr ~ 700 Hz, above which it increases linearly. A measurement of the resistance R and capacitance C of our sample at the same temperature gives (2 ~crc) 1 ~ 800 Hz comparable to fr which must then be considered as the dielectric relaxation frequency of our material. We conclude that AC space charges must play a role in the threshold mechanism. The layer emission from the focus of the ellipses can be visualized as a local DC mechanical breakdown of the focal conic texture under the action of the AC field acting on some AC space charges. To explain this breakdown, we propose the following mechanism : Electrical conductivity (1 is known to be anisotropic in smectic materials [8], being larger parallel to the layers than across the layers. In the focal conic texture of figure la, the layers which converge towards the hyperbola F2 close to the focus of the ellipse Fl, form cones with apex on the hyperbola r 2. Under the action of E, space charges of opposite sign pile up inside these cones. The charge density p can be estimated using the charge conservation equation where ~ ~ E = T 8 2 7rfR, is the mean charge relaxation frequency (8 is the mean dielectric Fig. 2. flow threshold versus frequency for a cell of 10 ~m thickness.

5 L1180 JOURNAL DE PHYSIQUE LETTRES constant) and Ja is the anisotropic part of the current density. For f fr, equation (1) results in where d1 stands for the divergence and ~a/ ~ is the relative anisotropy of conductivity (geometrical factors of the order of unity have been skipped). This AC charge density placed in the AC field E, is submitted to a DC mean force density : The components of g normal to the hyperbola T2 are balanced by the bending forces from the layers inside F2. The components of g parallel to r 2 add up to build a pressure p ; ~ E 2 ~ 2 Q 4~ in the core of the disclination line r 2 which must be considered as a liquid. Above a threshold value of E, this pressure provokes the breakdown of the tubular layers wrapped around the hyperbola r 2 close to the focus of the ellipse T 1. This is the mechanism of layer emission from the focus. The direction of flow is given by the orientation of g along r 2. g drags the layer hyperbola F2 from infmity down to C, the focus of the ellipse T 1. Although the electrical DC force on the layers is localized, the Sm C* layer cohesion is large enough to ensure a plug flow. At threshold the electric pressure p should compare with the elastic constant B associated with large compression. Using al a 0.2, d ~ 10 ~m, e ~ 5, we obtain ~ ~ 108, in reasonable agreement with the known values of B in smectic materials [9]. Using samples of various thicknesses up to 50 ~m, we have indeed verified that the mechanical breakdown of the focal conics correspond to a field threshold Vth increasing linearly with d With f = 0, this mechanism should also work, but the helical texture unwinds from the direct coupling of E with P with a field threshold lower than the one to induce flow; therefore the flow is not visible in absence of stripes, which could explain that it has not yet been observed. For f > fr, p varies like ~ ~2013 E2 which indicates a Y fr~ p ~ linear increase of E2 ~ versus f, as found experimentally (Fig. 2). We have measured (Fig. 3) the field dependence of the velocity v, at a given point of a focal domain by counting the number of stripes passing through the point in unit time. Above Vth, and close to it, v increases linearly with V. This is easily explained by considering that the focal pressure inducing the flow is just the difference between the electrically induced pressure varying like E 2 ~ and the constant mechanical threshold pressure. We do not understand yet the nonlinear behaviour of velocity at higher applied voltage. We have stopped our velocity measurements when our eye could not follow the stripes. The unwinding appears at Y ~ 22 volts, where the extrapolated velocity must be in the range of 200 )mi/s. With an estimated distance in the 1 Jlm range between the plug flow and the electrode, this results in a shear rate 200 Hz. Let us estimate now the critical shear rate which unwinds the helical texture. Assume first that v is parallel to the helical axis. Calling K the curvature elastic constant, 0 the tilt angle of the molecules compared to the layer normal and r~ the viscosity coefficient, the torque density K02 (2 7c/Z)~ must be balanced by the viscous torque density 1102 Vv, where Vv is the velocity gradient. The critical shear rate is thus equal to the helix relaxation rate (KI r~) (2 7r/Z)2. With K ~ 5 x 10 CGS, q = 0.1 poise, we get Vv 500 Hz, a bit larger than the estimated velocity gradient. In fact, for larger fields, we observe that the velocity does not remain parallel to the helical axis. In the viscous torque density, we must drop the angular factor 02 for the components of the velocity normal to the helical axis. This gives ea.sily the missing factor 2.5 and explains the observed shear induced unwinding of the Sm C* helix. In addition q is also adjustable. Finally we have not been able to observe any breakdown or flow in the higher temperature Sm A phase of our material. This is likely due to a stronger anchoring of the smectic layers on the glass electrodes.

6 Flow FLOW AND HELIX UNWINDING IN Sm C* L1181 Fig. 3. velocity versus voltage, same conditions as in figure 2. In conclusion, we have observed an induced DC plug flow in a focal conic texture of a Sm C* liquid crystal under the action of a low frequency AC field. Because of conductivity anisotropy, space charges accumulate close to the focus of the focal conics, 7B, from the local conical arrangement of Sm C* layers. This results in an electrical internal pressure in the core of the focal conic, close to the focus. Above a field threshold, this core explodes, emitting new Sm C* layers from the centre in all ellipses, and absorbing layers from the hyperbola. This pumping action pushes the Sm C* texture in a plug like DC flow, towards the centre of the focal conic. The viscous shear associated to this flow is the mechanism which unwinds the helix at large field. The large mobility of smectic layers indicates that, close to the plates, the Sm C* material must be nematiclike. As neither breakdown nor flow is observed in the Sm A phase, the lack of smectic ordering close to the plate must be characteristic of the Sm C* phase. These flow and the associated viscous shear on the layers explain also probably the regular cross patterns of dechiralization lines recently reported [10] in Sm C* material submitted to AC electric fields. Acknowledgments. We are grateful to Dr. Germain (Orsay) for the synthesis of DOBAMBC. References [1] DOUCET, J., KELLER, P., LEVELUT, A. M. and PORQUET, P., J. Physique 39 (1978) 548. [2] HANDSCHY, M. A. and CLARK, N. A., Phys. Rev. Lett. 51 (1983) 471. [3] PARMAR, D. S., RAINA, K. K. and SHANKAR, J., Mol. Cryst. Liq. Cryst. 103 (1983) 77. [4] BOULIGAND, Y., J. Physique 33 (1972) 525. [5] MARTINOTLAGARDE, Ph., Paper presented at the York Conference, [6] MARTINOTLAGARDE, Ph., DUKE, R. and DURAND, G., Mol. Cryst. Liq. Cryst. 75 (1981) 249. [7] HANDSCHY, M. A., CLARK, N. A. and LAGERWALL, S. T., Phys. Rev. Lett. 51 (1983) 471. [8] DE GENNES, P. G., Physics of Liquid Crystals (Clarendon Press, Oxford) [9] BARTOLINO, R. and DURAND, G., J. Physique 45 (1984) 889. BARTOLINO, R. and DURAND, G., J. Physique Lett. 44 (1983) L79. [10] PARMAR, D. S., RAINA, K. K., RAZDAN, V., LABROO, B. and SHANKAR, J., Communicated for publication.