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Pre-electrohydrodynamic relaxation phenomenon in nematic liquid crystals
Volume 25, number 3
.._
. .
: CHEVICAL PtiSrCS
. ’ iN’NEMATIC
LEmRS
LIQUID
:
, 1 April 1974,. : ,
‘.
CRYSTALS
:
D.S..PARMAR and A.& JAL.ALGDDIN Department of Phvsik, Aiigarh Muslim Universiv, Alig$ 202001, India
Received 24 January 1974
Study of electrohydcodynamic instabilities in thicker nematic liquid crystal samples (800-1200 pm) of MBBA is reported. An initial rise in the intensity of transmitted light immediately after the application of an electric field has been found to precede the attenuation of the transmitted beam due to the gradual development of hydrodynamic instability in the sample. The dependence of the relative dominance of the two relaxation phenomenon on the applied electric field ‘intensity has been studied.
It is well known that there exists a threshold voltage ofabout 5V for the initiation of electrohydrodjmamic phenomenon in a thin (10-I 00 pm) layer of nematic liquid crystal sandwiched between planar electrodes. Above this voltage, a stationary domainlike pattern is obtained [l-4]. With further increase in the voltage the laminar flow pattern gradually changes into a regime of turbulent flow in which the liquid crystal strongly scatters light [S]. On the basis of the study of molecular structural properties of liquid crystals, it is expected that when an electric field is applied to the sample, the orientation of the molecules far from the electrodes is most likely to be strongly influenced by the field while the molecules closer to the electrodes are assumed to be held in place by the boundaries [6] as shown in fig. la.
E
:
9
t
l
.________-_----_-
-
5
&.
i,k-s&k
__________--______ (b)
.’
Fig. 1. (a) Orientation of the molecules in a thicker &ple. (b) Helfrich type instabili&.
.-
,..
: 1
In isotropic’dielectric liquids, the dc field leads to space charges due to a net injection of charge carriers. These space charges lead to cellular flow as in the classical Benard problem [7]. The same mechanism is present in the case of nematics also. This observation is consistent with that in dc fields, when the cellular flow persists in the isotropic phase [8]. However, space charges can also arise due to the anisotropic conductivity (u,, > ul) of nematics [9]. Detailed calculations on the torques in a nematic liquid crystal in an electric field have been made by Helfrich [lo]. In this theory, spatial variation of the snolecular orientation, given by the director n, are considered for an infinitite nematic. n is supposed to vary in the X direction only (see fig_ lb). The onset of insiability can be predicted from the theories of Helfrich [IO] and Dubois-Violette et al. [l 1); but there are no criteria for determining whether the instability will develop through some relaxation processes or instantaneously. _. In the present paper, we report .m investigation of the rise .time.(Tr) of turbulent electrohydro.. dynaniic flow‘using:tht? transmitted light Me&y through a thick&@OO-1200 grn) sample pf -( I$@-tiethoxybenzylidene)~g-n-butylanilene (MBBA) .liquid crystal s&&he’d betwe+ two planar ti&pafent.blectrod& (GOa .+p&d gl+ $!aies) at a c&ns&t tempe&re of ZS”C’(+matic rari&$the :. .
‘.
Volume
25, number 3
CHEMICAL PHYSICS LETTERS
1 April 1974
sample is 204 1°C). The nematic molecules were aligned parallel to SnO2 coated glass electrodes by rubbing with cheesecloth. In view of the greater thickness of the sample a higher voltage was required for introducing efectrohydrodynamic effects. When a dc electric field is applied to the sample, it shows a peculiar behaviour with regard to the rise time T,, when measured on an oscilloscope screen with the help of the experimental arrangement outlined in fig. 2. A light beam from a source was made to fall onto the sample through an optical system consisting of condensers, Polaroids and lenses. The transmitted light was focussed on a photomultiplier (RCA 93 1A)_ ne output of the photomultiplier was fed into an oscilloscope (Philips PM 3230/90) the electron beam of which was triggered only on the application of the electric field to the sample. The sample shows a pe.culiarbehaviour with regard to the rise time T,, as shown in fig. 3. At 950 V, the transmitted light intensity increases first for a short period, T,, (= 50 msec) and then decreases gradually to the equilibrium value in a period Trz 7 350 msec(fig. 3a). Both Trl and Tr2 decrease with the increasing value of the applied field (figs. 3b and 3c) and ultimately the light intensity versus the time curve follows the usual monotonic fall in intensity [8] till the equilibrium value is reached. ‘ihe initial rise time in the intensity of the transmitted light in the present case seems to be due to the dielectric reorientation of the molecules, which are free from the influence of the surface. The
POWER SW,TcH
~UPprY
TRIGGER
SOURCE
\
0sclLLaScapE
Fig. 3. Photomultiplier output showing the variations in the transmitted light intensity. (a) At 95OV, the transmitted light intensity increases for 50 msec (Tr,) and then decreases to an equilibrium value in 350 msec (T,,). (b) At 125OV. Trl = 30 msec, Trz = 3OOxpsec. (c) Electrohydrodynamic instahiity is predominant above 1400V. At 14OOV, Tr, __= U msec, I& = 2XJ m”-
TEFLON SPACER
Fig. 2. Schematic diagram of the experimental setup. 418
.
.. . ... . ; :,_. I ,_ .~. :,
~-
.:
..
..:
Volume
1 April 1974
CHEMICAL PHYSICS LElTERS
25, number 3
lb00 Jc
1401PL
1200
t UJ’~
r’
!I 9 z
BOG,
w p
601!l,
5 P
4oc 1.
20,0.
40
(Q
Fig. 4. The variation
80
of the reorientation
120
160 RISE
rise time CT,,)
200 TIME 3
240 280 IN MSEC-
and electrohydrodynmic
320
360
rise time (Tr2)
400
440
480
with the applied voltage
to
the sample. increasing field aligns the molecules perpendicular to the electrodes which increases the light transmission till the conductivity anisotropy no longer favours instability_ Trr may thus be defined as the orientation rise time. Both Tr, and Trz have been plotted in fig. 4. The initial rise of the light intensity is observed only at low applied voltage. In the voltage range 500-1400 V, Trl accounts for IO-15% of T,_ With further increase in the applied voltage the rate of growth of hydrodynamic instability becomes more rapid and this effect dominates over the initial dielectric reorientation effect. In such case, the initial growth in the intensity due to the phenomenon of dielectric reorientation is compensated, ultimately overshadowed, by a simultaneous fall in the intensity due to the hydrodynamic turbulence. The electrohydrodynamic rise time Trz , when correlated with the applied electric field, is found to follow, within 5%, an empirical equation of the form Tr2 =a
+b+G +c E E,53 ’
(1)
where E is the intensity of the applied electric field and a, b, c and d are numerical constants_ As regards the significance of the terms appearing in eq. (l), Koelmans et al. [S] have reported that in the case of thin films, the electrohydrodynamic rise time is given by Tr, =AqIeE”
,
(2)
when n is the viscosity of the liquid crystal, E its dielectric constant and A is a numerical constant. In the case of thicker samples used in the present work one cannot expect the same relationship to hold, because the electroviscous effects have not been taken into account in eq. (2) Even then at higher fields, when the electrohydrodynamic effect is predominant, the term containing E3 in eq. (1) is negligibly small. However, if n in eq. (2) is considered as a function of E and AE, the electric field gradient throughout the sample thickness [ 121, eq. (2) reduces to eq. (1) at higher voltages by Taylor expansion ofn(E, A.0 The study of the rise time at different temperatures and sample thicknesses is in progress_ -419,
Volume
The
Ahmed
25. number
3
CHEMICAL PHYSICS LETTERS
authors are deeply gratehI to Professor for his kind support and encouragement.
Rais
References
1 April 1974
151 G-H. Heilmeiq L.A. Zanoni and L.A. Barton, Proc. IEEE 56 (1968) 1162. 161 E.J. Kahn, Appl. Phys. Letters 20 (1972) 199. [71 N. Felici, Rev. Gen. Elec. 78 (1969) 717. (8i .H. Koelmans and A.M. van Boxtel, Phys. Letters 32A (1970) 32: Mol. Cryst. Liquid Cryst. 12 (1971) 185. [9] E.F. C&r. Mol. Cryst.
[ I] G. Durand,
M. Veyssie’, F_ Rondelez and L. L&er, Compt. Rend. Acad. Sci. (Paris) 8270 (1970) 97. [2] R. Wiiams, J. Chem. Phys. 39 (1963) 384. [3] P.A. Penz, Phys. Rev. Letters 24 (1970) 1405. [4] Orsay Liquid Crystal Group. Mol. Cryst. Liquid Cryst. 12 (1971) 2.51.
Liquid
Cryst.
7 (1969)
253.
[IO] W. Helfrich, J. Chem. Phys. 51 (1969) 4092. [I 1J E. Dubois-Violette, P.G. de Gennes and 0. Parodi, J. Phys. (Parisj
32 (1971)
305.
[ 121 s. !.A and D. Jones, Appl. Phys. Letters
16 (1970)
484.
.._
. .
: CHEVICAL PtiSrCS
. ’ iN’NEMATIC
LEmRS
LIQUID
:
, 1 April 1974,. : ,
‘.
CRYSTALS
:
D.S..PARMAR and A.& JAL.ALGDDIN Department of Phvsik, Aiigarh Muslim Universiv, Alig$ 202001, India
Received 24 January 1974
Study of electrohydcodynamic instabilities in thicker nematic liquid crystal samples (800-1200 pm) of MBBA is reported. An initial rise in the intensity of transmitted light immediately after the application of an electric field has been found to precede the attenuation of the transmitted beam due to the gradual development of hydrodynamic instability in the sample. The dependence of the relative dominance of the two relaxation phenomenon on the applied electric field ‘intensity has been studied.
It is well known that there exists a threshold voltage ofabout 5V for the initiation of electrohydrodjmamic phenomenon in a thin (10-I 00 pm) layer of nematic liquid crystal sandwiched between planar electrodes. Above this voltage, a stationary domainlike pattern is obtained [l-4]. With further increase in the voltage the laminar flow pattern gradually changes into a regime of turbulent flow in which the liquid crystal strongly scatters light [S]. On the basis of the study of molecular structural properties of liquid crystals, it is expected that when an electric field is applied to the sample, the orientation of the molecules far from the electrodes is most likely to be strongly influenced by the field while the molecules closer to the electrodes are assumed to be held in place by the boundaries [6] as shown in fig. la.
E
:
9
t
l
.________-_----_-
-
5
&.
i,k-s&k
__________--______ (b)
.’
Fig. 1. (a) Orientation of the molecules in a thicker &ple. (b) Helfrich type instabili&.
.-
,..
: 1
In isotropic’dielectric liquids, the dc field leads to space charges due to a net injection of charge carriers. These space charges lead to cellular flow as in the classical Benard problem [7]. The same mechanism is present in the case of nematics also. This observation is consistent with that in dc fields, when the cellular flow persists in the isotropic phase [8]. However, space charges can also arise due to the anisotropic conductivity (u,, > ul) of nematics [9]. Detailed calculations on the torques in a nematic liquid crystal in an electric field have been made by Helfrich [lo]. In this theory, spatial variation of the snolecular orientation, given by the director n, are considered for an infinitite nematic. n is supposed to vary in the X direction only (see fig_ lb). The onset of insiability can be predicted from the theories of Helfrich [IO] and Dubois-Violette et al. [l 1); but there are no criteria for determining whether the instability will develop through some relaxation processes or instantaneously. _. In the present paper, we report .m investigation of the rise .time.(Tr) of turbulent electrohydro.. dynaniic flow‘using:tht? transmitted light Me&y through a thick&@OO-1200 grn) sample pf -( I$@-tiethoxybenzylidene)~g-n-butylanilene (MBBA) .liquid crystal s&&he’d betwe+ two planar ti&pafent.blectrod& (GOa .+p&d gl+ $!aies) at a c&ns&t tempe&re of ZS”C’(+matic rari&$the :. .
‘.
Volume
25, number 3
CHEMICAL PHYSICS LETTERS
1 April 1974
sample is 204 1°C). The nematic molecules were aligned parallel to SnO2 coated glass electrodes by rubbing with cheesecloth. In view of the greater thickness of the sample a higher voltage was required for introducing efectrohydrodynamic effects. When a dc electric field is applied to the sample, it shows a peculiar behaviour with regard to the rise time T,, when measured on an oscilloscope screen with the help of the experimental arrangement outlined in fig. 2. A light beam from a source was made to fall onto the sample through an optical system consisting of condensers, Polaroids and lenses. The transmitted light was focussed on a photomultiplier (RCA 93 1A)_ ne output of the photomultiplier was fed into an oscilloscope (Philips PM 3230/90) the electron beam of which was triggered only on the application of the electric field to the sample. The sample shows a pe.culiarbehaviour with regard to the rise time T,, as shown in fig. 3. At 950 V, the transmitted light intensity increases first for a short period, T,, (= 50 msec) and then decreases gradually to the equilibrium value in a period Trz 7 350 msec(fig. 3a). Both Trl and Tr2 decrease with the increasing value of the applied field (figs. 3b and 3c) and ultimately the light intensity versus the time curve follows the usual monotonic fall in intensity [8] till the equilibrium value is reached. ‘ihe initial rise time in the intensity of the transmitted light in the present case seems to be due to the dielectric reorientation of the molecules, which are free from the influence of the surface. The
POWER SW,TcH
~UPprY
TRIGGER
SOURCE
\
0sclLLaScapE
Fig. 3. Photomultiplier output showing the variations in the transmitted light intensity. (a) At 95OV, the transmitted light intensity increases for 50 msec (Tr,) and then decreases to an equilibrium value in 350 msec (T,,). (b) At 125OV. Trl = 30 msec, Trz = 3OOxpsec. (c) Electrohydrodynamic instahiity is predominant above 1400V. At 14OOV, Tr, __= U msec, I& = 2XJ m”-
TEFLON SPACER
Fig. 2. Schematic diagram of the experimental setup. 418
.
.. . ... . ; :,_. I ,_ .~. :,
~-
.:
..
..:
Volume
1 April 1974
CHEMICAL PHYSICS LElTERS
25, number 3
lb00 Jc
1401PL
1200
t UJ’~
r’
!I 9 z
BOG,
w p
601!l,
5 P
4oc 1.
20,0.
40
(Q
Fig. 4. The variation
80
of the reorientation
120
160 RISE
rise time CT,,)
200 TIME 3
240 280 IN MSEC-
and electrohydrodynmic
320
360
rise time (Tr2)
400
440
480
with the applied voltage
to
the sample. increasing field aligns the molecules perpendicular to the electrodes which increases the light transmission till the conductivity anisotropy no longer favours instability_ Trr may thus be defined as the orientation rise time. Both Tr, and Trz have been plotted in fig. 4. The initial rise of the light intensity is observed only at low applied voltage. In the voltage range 500-1400 V, Trl accounts for IO-15% of T,_ With further increase in the applied voltage the rate of growth of hydrodynamic instability becomes more rapid and this effect dominates over the initial dielectric reorientation effect. In such case, the initial growth in the intensity due to the phenomenon of dielectric reorientation is compensated, ultimately overshadowed, by a simultaneous fall in the intensity due to the hydrodynamic turbulence. The electrohydrodynamic rise time Trz , when correlated with the applied electric field, is found to follow, within 5%, an empirical equation of the form Tr2 =a
+b+G +c E E,53 ’
(1)
where E is the intensity of the applied electric field and a, b, c and d are numerical constants_ As regards the significance of the terms appearing in eq. (l), Koelmans et al. [S] have reported that in the case of thin films, the electrohydrodynamic rise time is given by Tr, =AqIeE”
,
(2)
when n is the viscosity of the liquid crystal, E its dielectric constant and A is a numerical constant. In the case of thicker samples used in the present work one cannot expect the same relationship to hold, because the electroviscous effects have not been taken into account in eq. (2) Even then at higher fields, when the electrohydrodynamic effect is predominant, the term containing E3 in eq. (1) is negligibly small. However, if n in eq. (2) is considered as a function of E and AE, the electric field gradient throughout the sample thickness [ 121, eq. (2) reduces to eq. (1) at higher voltages by Taylor expansion ofn(E, A.0 The study of the rise time at different temperatures and sample thicknesses is in progress_ -419,
Volume
The
Ahmed
25. number
3
CHEMICAL PHYSICS LETTERS
authors are deeply gratehI to Professor for his kind support and encouragement.
Rais
References
1 April 1974
151 G-H. Heilmeiq L.A. Zanoni and L.A. Barton, Proc. IEEE 56 (1968) 1162. 161 E.J. Kahn, Appl. Phys. Letters 20 (1972) 199. [71 N. Felici, Rev. Gen. Elec. 78 (1969) 717. (8i .H. Koelmans and A.M. van Boxtel, Phys. Letters 32A (1970) 32: Mol. Cryst. Liquid Cryst. 12 (1971) 185. [9] E.F. C&r. Mol. Cryst.
[ I] G. Durand,
M. Veyssie’, F_ Rondelez and L. L&er, Compt. Rend. Acad. Sci. (Paris) 8270 (1970) 97. [2] R. Wiiams, J. Chem. Phys. 39 (1963) 384. [3] P.A. Penz, Phys. Rev. Letters 24 (1970) 1405. [4] Orsay Liquid Crystal Group. Mol. Cryst. Liquid Cryst. 12 (1971) 2.51.
Liquid
Cryst.
7 (1969)
253.
[IO] W. Helfrich, J. Chem. Phys. 51 (1969) 4092. [I 1J E. Dubois-Violette, P.G. de Gennes and 0. Parodi, J. Phys. (Parisj
32 (1971)
305.
[ 121 s. !.A and D. Jones, Appl. Phys. Letters
16 (1970)
484.