Due to their unique syrnrnetry properties ferroelectric liquid crystals show .... thickness, d is smaller than the helical pitch, p (surface stabilized structure), then.
Mal. Ctyst. Liq. Cry51 , 1991, Vol. 201, pp. 115-124 Reprints available directly from the publisher Photocopying prmitted by License only Q 1991 Gordon and Breach Science Publ~shcrsS.A. Printed in the United States of America
Mechano-Electrical Effects on Planar Sg Liquid Crystals A. JAKLI and L. BATA Central Research lnsttiuie for Physics, H-1525 Budapest. P. 0.Box 49 (Received Junt. 6, 1'289; in fiiul furm .411gusr 10, I W ) )
Shear flow induced voltages (mcchano-clectrical responses) were detected and analyzed in two planar
:S liquid crystal samples Frequency spectra, temperature dnd shear rate dcpcndrfices were measured. Resonances observed in the frequency spectra are In accordance with the resonances were found in the electromechanical responses of these materials. The origin of the mechano-electrical effect i s interpreted in the frame of s h e a ~flow :ilignment mechanism.
Key words: liquid crysfals (61301, Jerrorlectricity (77801,elrctricnl properties (7390), electrical resonances (7785), pi~;oclettricity (7740)
INTRODUCTION L
Due to their unique syrnrnetry properties ferroelectric liquid crystals show piezoelectric behaviours. As it was found S:. liquid crystals convert alternating electric fields into mechanical vibrations,'-had vice versa, due to mechanical deformations electric polarization appears o n the ~ a r n p l e s . ~ . ~ The former one is called electrvmrchanical effect and was observed on planar S: liquid crystals. Due to alternating electric fields the bounding plates vibrate relative to each other. Both responses measured at the frequency of ~ h capplied AC field and the first harmonics may have several resonances in the kilohertz frequency range. One of these resonances appears only in focal conic textures (defects are present at the cover plates), while others exist even in homogeneous planar samples4 (layers are nearly perpendicular to cover plates without any defect on sirfaces). It is suggrsted, that the resonances are the consequence of chevron structure of SF. liquid crystals." The latter effect (hereafter we call it mechano-electrical cffect) first was found by Pieranski nf nl.%n homeotropic S: sample (smectic layers were parallel to cover plates), and was measured at low frequencies (f < 200 Hz). Later similar effect was reported without any details7 also on planar S:- samples. . In this paper we describe our detailed investigations on the mechano-electrical effect.The frequency spectra of induced voltages due to unit amplitude vibrations of the upper bounding plate were determined in two planar aligned S: samples.
Temperature and shear ampjitude dependences are mentioned too. Origin of this effect is explained in the frarrlc: of flow alignment mechanism, and the observed data are compared to the calculated forrnutae.
EXPERIMENTS 4
The investigations are carried out on sandwich cells with boundary area of A! = 6 cm2 of two planar aligned S: liquid crystal samples. The liquid crystal films were planarly iiligned by means of a periodic shear1(' supplied by an excited membrane of a loudspeaker. while samples were cooled down into their S, phase. I n order to study the effect of shear flow a vibrarion of rhe upper platc w35 maintained at St- phase of the sample with thc help of n vibrating lnltdspeaker membrane. For measuring thc resulting amplitude, a Briiel & Kjaer accelerometer (BK 4375) was fixed on the top plale. The signal of accelerometer was preamplified with a DK 2645 charge amplifier, and was analyzed by an ITIIACO (Model 3962) lock-in amplifier. '1.0 avoid higher harmonics the lock-in together with a sharp band pass filter was tuned on the frequency of the vibrating loudspeaker. The oxillation amplitude ofthe upper plate was determined by measuring the acceleration and dividing it by o2(w = 2.r~- vibration freque~lcy).Bounding plates were coated by SnO, transparent electl-odcs. The electrodes were connected to the input of the lock-in. (The input impedance of the lock-in can be regarded as a paralleI KC elemenr with RI = 10 Ma and Cl = 44 pF.) The loudspeaker was excited by the internal oscillator of the lock-in. Frequency was changed in steps from f = 100 Hz up lo f = 10 kHz. Measurcmcnts were controlled by a personal computer. Samples were thermostatted with rhe accuracy of *0.3"C, and visually observed by a polarizing micr~scope.The sample thickness and parallelism were set by fixing the lower plate to micrometer screws. The parallelism and sample thickness were checked with tht: help of n laser beam and by capacitance measurements rcspectively. By this method the accuracy of parallelism and sample thickness were better than l o a d rad and .t2 pm respectively. The block scheme uf the cxpcrimental arrangement is presenled in Figurt: 3 . Experimerlis werc carried out on two room temperature SF liquid crystal mixtures. 1.) A binant mixture FK4. Its phase sequence is the following:
T = 23°C its pitch is p = 5 prn and its spontaneous polarization is7 Po = 1.2 10-j Wm2. 2.) A thermochromic frrrmclcctric liquid crystalH called N202 with a high spoa-
at
.
>'-
MECHANO-ELECTRICAL EFFECTS OF FLC-5
,
.
FIGURE 1 Block-diagram of the txper~rnentalarrangement The planar SF llquid crystal film 1s sheared by means of a vibration of the upper bounding plate. The vtbration is ensured by a v~bratlng membrane of a loudspeakcr (LS) which ts cxc~tedby the appropriately amplified (V A , ) slpnal of the ~nternaloscillator of the h k - i n . The ~nducedvoltages U" and the acceleration of the movlng plate wcrc detected on evaporated SnO, electroder by a BK 4375 Bruel & Kjaer accelerometer ( A ) , and were analyzed simultaneuusly by a Ithaco L o c k - ~ nAmplifier. The Iwk-in was controlled and I ~ Ssignals wzrc processed by a personal computer. The sample parailel~srnand th~cknesswere set by tizing the lower platc tu mtcrometer screws. The sample was thermostatted (TH).
taneous polarization (Po= 7(1 . Urn2)and with pitch in the light wavelength regime (p = 0.3 prn)l2 at room temperature. The phase sequence of N l U 2 is: Iso -- S , - Sc - Cr
EXPERIMENTAL RESULTS
In Figure 2 we plotted the frequency spectrum of the mechano-electrical response of a planar aligned FK4 sample (T= 25°C).Induced voltages at constant vibrational amplitude were observed in the lack-in input. The sample thickness was d = 19 Fm,and the sample impedances (the sample is a parallel RC element) were R, = 20 Mfl and C, = 1.13 nF. The continuous line is a fit on measured data. Measuring errors are indicated in the spectrum. At low frequencies (f < 0.5 kHz) the errors came from the measurement error of vibrational srnplitude~,4+~ while at high frequencies (f > 4-5 kHz) the induced voltages were within the measuring error. In the frequency interval 0.5 kHz < f < 5 kHz the measuring error everywhere was smaller than 520%. At this regime two main resonances were found at f, = 2.9 kHz and fi = 1.5kHz frequencies which correspond to the resonances found in electromechanical responses of the same materiaL4 Spectrum of N202 is similar to that of FK4. At T = 25°C for a d = 15 pm sample thickness sandwich cell (its electrical parameters are R, = 2 MR and C, =
FIGURE 2 Frequency spectrum uf mcchanv-electricalr e s p n e ni a pcriudjcally shedrcd planar al~gned FK4 S: liquid crystal sarnplc. r means thc ratio of the induced volteges and the amplitudes of upper hounding plate vibration. IriduaJ volldecs wcrc dcfeaed in thc Iwk-in inpul (whiuh impendanccs are R, = LU hiIl and C, = 40 pF). The s~rnplrparameters were: T = ZS'C, d = 19 km. R, = 20 M i l ,
r.=
1.13 nF.
O.588 nF) the frequency dependence of mechano-electrical response is plotted in Figure 3. The Iargest resonance was found at the same frequency as in its electromechanical response4 (f, = 3.9 kHz). We also Iound othcr s~nallerresonances which were nut present at the electromechanical effect. Comparing the maxirnurrl amplitudes of FK4 to that of N202 we can see that in FK4 induced voltages are about two orders of magnitude larger than in N202. If seems tu be ill contradiction with the fact that Po (FK4) is about two orders of magnitude smaller than P, (N202). For the shear amplitude dependences simple linear functions were found. Examples (NZ02sample, T = 22°C d = 15 pm at frequencies f = 3.8 kHz and f = 1.0 kHz) are plotted in Figure 4. We could nor see any deviance frnm the linear behaviour, and did not observe any harmonics. Temperature dependence of mechano-electrical effect was found to be similar to that measured by Pieranski et. al."in homeotropic samples ar significantly smalier shear frequencies. This Icmperature dependence is also similar to that measured in electromechanical effect~.~-'.*.' The ternperaturc dependzn~y:of induced voltages C/"(kV) i3 plotted in Figure 5 . The acceleration of the upper plate was kept constanr (a = 5 mis) at frequency of J = 4.02 kHz while the temperature was cunslantly T = 23°C.
d
MECHANO-ELECIRICAL EFFECTS OF FLC-s
FlGURE 3 Frequency spctrurn of mechano-electrical response of a periudically shearcd planar N202 l~quidcrystal samplc. I n the vertical axis the ratio of the induced voltages and shear amplitude of upper bounding plate (T)are plotted. Induced voltages were detected in the lock-in Input (R, = 10 Mil, C, = 40 pF). The sample paramerers are the followings; T = 25'C, d = 15 prn, R, = ? MI1 and C, = 0.588 nF.
INTERPRETATION Presented mechano-electrical effect shuold be explained by the same mechanism which was considered by Pieranski er al. ? because the relative positions of shear, induced polarization and helical axis are the same (they are perpendicular to each other) both in measurement of Pieranski et al. and our cases. Accordingly we describe the mechanism resulting the observed effect as follows. Shear distorts the original director structure which, as C-director, c and polarization, P, are rigidly coupled, results in a net polarization current flow through on elec~rodes. Considering our geometry (see Figure 6) the schematic of the mechanism is the
A JAKLI AND L. BATA
FIGURE 4 Shear amplirude dependencr of mechano-electrical reqwnse of a planar aligncd N2M l~quidcrystal sample T = ? P C . Other sample parameters are the same as in Figure 3. Crobses: f = 3.8 kHz; open c~rclcs:f = 1.0 kHz.
Here v , ( x ) is the shear flow velocity in the sample c, is the v component of the Cdirector, c ( c is the projection of the director into ~ h csmectic layer). Po is the spontaneous polarization ( P J P , = n x c; o is the smectic Iayer normal). As flow takes place inside smectic layers. where mechanical behaviour of the material is nematic-like, describing dynamics of flow alignment we can use a nematic like description. Till this point our description is identical to that of Pieranski et a/.,6 however the form of the relevant torque balance equation should be different, because the structure of a planar film is different from that of a horneotropic. In planar film the director configuration is affected by the covcr plates. I n this respect two main director structures are to be considered, a. When the sample thickness, d is smaller than the helical pitch, p (surface stabilized structure), then the sample is uniform in z direction, that is the azimuthal angle cp, is constant. b. In case of thick samples (d >> p ) the director structure is helical. and the z dependence of the azimuthal angle reads: (p, = q r (here q = 2 alp).
-
MECHANO-ELECTRICAL EFFECTS OF FLC-5
FIGURE 5 Temperature dependence of ~nducedvoltages due to cunhtant amplitude periodic shears. The shcar irequrncy is f = 4.02 kH7, the acceleration is a = 5 rnis. Other sample pararnecers are identical lo thar uscd in Figure 3.
FIGURE h Sample geometry and the coordinate system during studying rnechanu-electrical responses. Top cover plate is vibrating in 1. direction causing a shear flow w ~ r hvclocity v , insidc brneclic layers. This flow is coupled to direc~orrotations, which results In an induced net polarization in x direciion.
Dynamics of flow alignment should be described by solving the torque balance equation. a. For surface stabilized samples the director field is uniform, so elastic torques can he neglected. Therefore, the torque balance reads:
= a, - cos2q, - oil . sin2y, is the relevant shear viscosity and y, a, is the rotational viscosity" (a,,a, are Leslie coefficients).
where p(cp,,) or,
-
=
122
A . JAKLI
AND L.BATA '
The shear is a harmonic function of time and maintained by the oscillation of the cover plate, so:
Supposing that due to shear the variation of azimuthal angle is small, Equation (2) and Equation (3) provides that in uniform samples the shear induced azimuthal angle variation cp";eads:
d
b. In case of thick samples we should consider the sparial detivatives in the z direction too. As v, does not depend on z, viscous torques are identical to the left hand side of Equation ( I ) , except we have to consider the I dependence of p(., Now the elastic torque, M" arising during the process is not zero and from Leslie continuum theoryg it has the form:
where k(z) = 9 - (cosJqz - sin3qz)
-
-
6 (cos qz - sin q z )
(6)
is in the order of unity. Disregarding the x dependences, furthermore using Equation (2) and Equation (3) the torque balance can be written as
from which for the variation of the azimuthal angle cp;
we
where T = y l l ( K f i Z ) . The average polarization (P,) induced on electrodes reads
Electric charge Q appears on electrodes is:
get that
-
MECHANO-ELECTRICAL EFFECTS OF FLC-s
123
Here flefl is an effective surface area. By definition it is equal the area af a monodomain sample where the director flipping in whole takes place collectively with the same phase. So, if the sample is a monodomain is equai the whole sample area; however if it consists of more domains, then < a, and gives the resulting area of different domains (let's say there are two domains with area 0' and f'l-, then = St+ - R - ) . Because Q ( r ) = Q,el", the induced electric current. I (the sample can be tegarded as an electric current generator) reads: 1 = u Q,. Induced voltage Win measured on parallel RC circuit bujlt from sample impedances R,, C, and input impedances of lock-in R,, C, reads:
-
L
As the lock-in and the sample are electrically parallel, in this equation
R =
R, . and C
R, + R,
=
Ci
+
CC,
Above equations together with our experimental data and sample parameters allow us to calculate effective surface areas of measured samples. Hence pitch of N202 i s p e 0.3 prn
