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

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

B. Labroo, V. Razdan, D.S. Parmar, Geoffroy Durand

To cite this version:

B. Labroo, V. Razdan, D.S. Parmar, Geoffroy Durand. AC electric field induced flow and helix

unwinding in focal conic texture of smectic C* liquid crystal. Journal de Physique Lettres, Edp

sciences, 1985, 46 (24), pp.1177-1181. �10.1051/jphyslet:0198500460240117700�. �jpa-00232954�

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 - ¹⁹⁰ 006, ^India (Re~u ^{le 25} septembre 1985, accepte ^{le 31 octobre} 1985)

Résumé.

On soumet

mince (~ 10 03BCm) ^{texture à} conique focale de DOBAMBC

phase smectique ^{C* à}

champ électrique alternatif. Au-delà d’un seuil,

écoulement permanent

^bou- chon » 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

pression critique pompée électriquement

^{coeur des} coniques focales, par l’anisotropie ^de conductivité.

Abstract

A thin (~ 10 03BCm) focal conic texture of DOBAMBC in its Sm C* phase ^{is submitted}

to

AC electric field. Above

field threshold,

^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

DC electric pressure, from the action of the AC field on AC space charges, generated by conductivity anisotropy.

Classification Physics ^Abstracts

46.60

61.30

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 hydro- dynamic ^{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 Indo-French 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 http://dx.doi.org/10.1051/jphyslet:0198500460240117700

L-1178 JOURNAL DE PHYSIQUE - ^LETTRES

The sample used is the widely studied DOBAMBC (p-decyloxy-benzylidene 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 10-50 _{~m range.}

The sample ^is temperature controlled in a Mettler FP 52 hot stage and observed under a pola- rizing microscope. ^{A low} frequency (0-20 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 « dechira-}

lization » 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) ^A typical ^{focal conic texture.} The space charges ^{due to} conductivity anisotropy pile up in the

cones with apex

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}

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.

from the focus C towards the centre of the ellipse T 1. The emission of new stripes ^is exactly ^com- pensated 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.

Voltage flow threshold

frequency ^for

cell of 10 _~m thickness.

L-1180 JOURNAL DE PHYSIQUE - ^LETTRES

constant) and Ja is the anisotropic part ^{of the current} density. ^For f fR, equation (1) ^{results in}

where d-1 stands for the divergence ^and ~a/ ~ is the relative anisotropy ^of conductivity (geome-

trical 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 - ;2013 .2013 ~ ^{2 Q 4~ E 2 ~}

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 ^{Y been observed. For} f > fR, p varies ^{f fR~ p} like ~ 2 2 ~2013 2 ~ ^E2

^{which indicates a}

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 non-} linear 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.

Fig. ^3.

^Flow velocity

voltage,

conditions

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 arran-

gement ^{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 nematic-like.

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

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[2] HANDSCHY, ^{M. A. and} CLARK, ^N. A., Phys. Rev. Lett. 51 (1983) ^471.

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[4] BOULIGAND, Y., ^J. Physique ³³ (1972) ^525.

[5] MARTINOT-LAGARDE, Ph., Paper presented ^{at the York} Conference, ^1984.

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