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Electric field quenching of thermal fluctuations of orientation in a nematic liquid crystal
Solid State Communications,
Vol. 10, pp. 8 15—818, 1972. Pergamon Press.
Printed in Great Britain
ELECTRIC FIELD QUENCHING OF THERMAL FLUCTUATIONS OF ORIENTATION IN A NEMATIC LIQUID CRYSTAL* J.L. Martinand and G. Durand Commissariat
a l’Entrgie
Atomique, C.E.N de Fontenay-aux-Roses, B.P no. 6, 92
—
Fontenay-aux-Roses
(Received 9 February 1971 by P.G. de Gennes)
Using Kayleigh scattering and light beating spectroscopy, we observe the thermally excited angular fluctuations of the di-rector in the nematic phase of MBBA (p-methoxybenzylidene-p-n-butyl-aniline) in presence of a stabilizing a.c. electric field. Both the intensity and damping time of these fluctuations are found to decrease when increasing the field intensity, allowing the measurement of the bend Frank elastic constant.
IN NEMATIC liquid crystals (NLC), the angular fluctuations of the molecular orientation gives rise to a strong depolarized Rayleigh scattering, the dynamics of which has been recently studied by light beating spectroscopy.”2 De Gennes has shown3 that the application of a stabilizing field should freeze the amplitude of these fluctuations, quenching the scattered intensity, and allowing a determination of the Frank elastic constants, The stabilizing field increases also the restoring torque to equilibrium for these angular fluctuations, so that the damping time associated with the two modes of angular fluctuations should decrease essentially as the intensity of the fluctuations, and give rise to the same information. In this letter we report measurements of the electric field dependence of the intensity and spectrum of Rayleigh scattered light in nematic p-methoxy-benzylidene-p-n-butylaniline (MBBA) from which we derive essentially the bend elastic constant K 33.
the director and ~a = — .~.. The two modes of angular fluctuations are defined in reference (3). For MBBA (where E,~ < 0) an electric field applied perpendicular to the director should not affect the mode 2 fluctuations, where the director twists around the field direction, but is expected to quench the mode 1 fluctuations; e.g. combination of bend and splay. The variation of the damping time T, of the mode 1 for the case of pure bend is expected to be: 1/7~=
+
Al
(1)
the bracket < > indicates a time iverage, A is a constant (A > 0 for MBBA) of the form: .
A
=
.
.
(— Ea/4n~)(c~/c.~.,) ~Kq2}~
(2)
for the case of pure bend fluctuations, the wave vector q of the fluctuations is parallel to the director (that implies small scattering angles), and K is the Frank elastic constant K~. The
ç~/e~~ for A comes from the effect of the
The theory of the effect of a stabilizing electric field on the damping time r can be derived from reference (4). Let us call Efi E,~,the dielectric constants parallel and perpendicular to ‘K
1/Ti)ct1
transverse field induced by the bend deformation (see reference (5)). The corresponding prediction for the variation of intensity I from reference (3) is essentially the same as equation (1), replacing rbyl.
Work supported by DRME under contract 70/634
t Associated with C.N.R.S.
815
816
ORIENTATION IN A NEMATIC LIQUID CRYSTAL
Our experimental set up has been described in reference (1). The sample is a MBBA monocrystal of 50 ±2~m thickness (optically two tin-oxide coated semi-transparent glass measured under a microscope) placed between slides. The sample is nematic at room temperature (24 ±1°C). The NCL is orientated parallel to the plates by the well known rubbing technique. The stabilizing electric field is a 5kHz a.c. field, normal to the director, for which the amplitude is maintained for below the threshold for the dielectric electrohydrodynamical 6 The scattering angle, and then q, instability. are small enough to observe an appreciable quenching effect from the field. The thickness of the sample is chosen to minimize both spurious boundary friction and multiple scattering, The resulting current fluctuations of the photomultiplier are analysed with a correlator (Hewlett—Packard 3721A). We observe independently the two modes of angluar fluctuations by using the polarization selection rules demonstrated in reference (3).
We first observe the depolarized scattering from mode 2. The spectrum is found to be purely homodyne. Within our experimental accuracy we see no apparent variation its exponential 2>, as ofexpected. The decay time~T2value vs.. Taking the known values linearly with and
ut
(Hz)
Vol. 10, No. 9
*
+
1/1(arbuiits)o
+
o
~0
ioo
200
300
400 (E2>(esu)
FIG. 1. Linear increase of the damping rate (~) and the inverse intensity (o) of thermal hand fluctuations in room temperature MBBA vs. the mean square amplitude of a stabilizing 5kHz a.c. electric field. in good agreement with other independent measurements. The uncertainty on K 33 comes partly from the difficulty of thickness measuremerits and partly from the residual dispersion of the experimental data, which is probably related to some aging of the sample. From the known (equation IV 25a of reference (4)) forexpression the zero field intercept (1/~
2/~
?7B (19 ±3)10_2 poise in good agreement withinthe measurements 7 Note that absence of field, of the Gähwiller. data for (l/r,) 0 show some dispersion, probably related to defects in the sample which are removed by the application of the field.
From the zero delay value of the autocorrelation oscillator function and the joint of the local intensity, wemeasurement derive for each value of E, the intensity 1~ of the bend fluctuations. The data (see Fig. 1) show a decrease of l~similar to that of ‘r, ,but their greater dispersion does not allow us to improve the
K 33
=
(7,2 ±1)1U~dyne
(3)
1)0 = K33 q (where 77B is the bend viscosity) and the previously determined K 33 we can now compute the bend viscosity
estimated value of K33. I~can decrease so
Vol. 10, No.9
ORIENTATION IN A NEMATIC LIQUID CRYSTAL
much that for high values of (not shown on Fig. 1) we should observe in principle the double scattering from mode 2. In this high field regime, we do observe a signal of damping time TD ~ /2 superposed to the weak mode 1 signal. As we are in a heterodyne regime we identify this signal as being due to double scattering from mode 2. In fact, if we turn the analyser by an angle of about 10°we can make the single scattering signal from mode 2 leak through: this signal appears now with its damping time T
T
T~
In conclusion using quasielastic Rayleigh scattering we have observed the predicted quenching of thermally excited angular fluctuations in NLC due to the application of a stabilizing a.c. electric field. The effect is visible not only by a decrease of intensity, but also by a shortening of the associated damping time of the fluctuations. For many practical reasons (defects, multiple scattering ) damping time measurements are found to be -
.
.
much easier and more accurate than intensity
2.
Comparing the intensity ‘D of the double scattering signal to I~in a 75~msample, we estimate that the critical length for which ‘D = (I~)~is about five to ten times the thickness of our sample. 12 Note that this ratio is the same for all small scattering angles. 2 ) Because ofare double ‘r (
817
the data of Fig. 1 have
been restricted 1to values of’
measurements. We believe that they constitute a valuable method for measuring Frank elastic constants. We have here demonstrated the
method by measuring the bend elastic constant. The splay and twist constants can be determined using the homeotropic geometry. Another possibility is to to the use director, a stabilizing magnetic field parallel which, in the same geometry, quenches now the two modes of angular fluctuations; we have in fact observed these effects. Full account of this study will be published elsewhere.
Acknov~1edgements — We acknowledge useful discussions with other members of the Orsay Group.
REFERENCES
1.
ORSAY LIQUID CRYSTAL GROUP, Phys. Rev. Lett. 22, 1361 (1969)..
2. 3.
HALLER I. and LITSTER J.D., Phys. Rev. Lett. 25, 1550 (1970). DE GENNES P.G., Cr. hebd. sêanc. Ac. Sci., Paris 266B, 15 (1968).
4.
GROUPE D’ETUDE DES CRISTAUX LIQUIDES (Orsay), Chem. Phys., 51, 816 (1969).
5.
DUBOIS—VIOLETTE E., DE GENNES P.G. and PARODI 0., J. Phys. 32. 305 (1971).
6. 7.
For a review of these effects, see for instance ORSAY LIQUID CRYSTAL GROUP, Mol. Cryst. Liq. Cryst., 12, 251 (1971). GAHWILLER Ch., Phys. Lett. 36A, 311 (1971).
8. 9.
BRUNET—GERMAIN, Cr. hebd. séanc. Acad. Sci., Paris 271B, 1075 (1970). WILLIAMS C. and CLADIS P.E., Solid State Comrnun., to be published.
10. GASPAROUX H. and PROST J., J. Phys. 32, 953 (1971). 11. DIGUET D., RONDELEZ F. and DURAND G., Cr. hebd. sêanc. Acad. Sci., Paris 271B, 954 (1970). 12. For a previous discussion, see LEGER QUERCY L., 3~cycle thesis, Orsay (1971).
818
ORIENTATION IN A NEMATIC LIQUID CRYSTAL
Vol. 10, No.9
Utilisant Ia spectroscopie par battements lumineux, nous observons La diffusion Rayleigh due aux fluctuations thermiques angulaires du directeur dans la phase nématique du MBBA (p-méthoxybenzylidénep-n-butylaniline) en presence d’un champ Clectrique alternatif stabilisant. L’intensité et Ic temps d’amortissement dCcroissent tous deux lorsqu’on augmente l’intensitC du champ, cc qul perniet la mesure de La constante élastique de Frank pour La flexion.
Vol. 10, pp. 8 15—818, 1972. Pergamon Press.
Printed in Great Britain
ELECTRIC FIELD QUENCHING OF THERMAL FLUCTUATIONS OF ORIENTATION IN A NEMATIC LIQUID CRYSTAL* J.L. Martinand and G. Durand Commissariat
a l’Entrgie
Atomique, C.E.N de Fontenay-aux-Roses, B.P no. 6, 92
—
Fontenay-aux-Roses
(Received 9 February 1971 by P.G. de Gennes)
Using Kayleigh scattering and light beating spectroscopy, we observe the thermally excited angular fluctuations of the di-rector in the nematic phase of MBBA (p-methoxybenzylidene-p-n-butyl-aniline) in presence of a stabilizing a.c. electric field. Both the intensity and damping time of these fluctuations are found to decrease when increasing the field intensity, allowing the measurement of the bend Frank elastic constant.
IN NEMATIC liquid crystals (NLC), the angular fluctuations of the molecular orientation gives rise to a strong depolarized Rayleigh scattering, the dynamics of which has been recently studied by light beating spectroscopy.”2 De Gennes has shown3 that the application of a stabilizing field should freeze the amplitude of these fluctuations, quenching the scattered intensity, and allowing a determination of the Frank elastic constants, The stabilizing field increases also the restoring torque to equilibrium for these angular fluctuations, so that the damping time associated with the two modes of angular fluctuations should decrease essentially as the intensity of the fluctuations, and give rise to the same information. In this letter we report measurements of the electric field dependence of the intensity and spectrum of Rayleigh scattered light in nematic p-methoxy-benzylidene-p-n-butylaniline (MBBA) from which we derive essentially the bend elastic constant K 33.
the director and ~a = — .~.. The two modes of angular fluctuations are defined in reference (3). For MBBA (where E,~ < 0) an electric field applied perpendicular to the director should not affect the mode 2 fluctuations, where the director twists around the field direction, but is expected to quench the mode 1 fluctuations; e.g. combination of bend and splay. The variation of the damping time T, of the mode 1 for the case of pure bend is expected to be: 1/7~=
+
A
(1)
the bracket < > indicates a time iverage, A is a constant (A > 0 for MBBA) of the form: .
A
=
.
.
(— Ea/4n~)(c~/c.~.,) ~Kq2}~
(2)
for the case of pure bend fluctuations, the wave vector q of the fluctuations is parallel to the director (that implies small scattering angles), and K is the Frank elastic constant K~. The
ç~/e~~ for A comes from the effect of the
The theory of the effect of a stabilizing electric field on the damping time r can be derived from reference (4). Let us call Efi E,~,the dielectric constants parallel and perpendicular to ‘K
1/Ti)ct1
transverse field induced by the bend deformation (see reference (5)). The corresponding prediction for the variation of intensity I from reference (3) is essentially the same as equation (1), replacing rbyl.
Work supported by DRME under contract 70/634
t Associated with C.N.R.S.
815
816
ORIENTATION IN A NEMATIC LIQUID CRYSTAL
Our experimental set up has been described in reference (1). The sample is a MBBA monocrystal of 50 ±2~m thickness (optically two tin-oxide coated semi-transparent glass measured under a microscope) placed between slides. The sample is nematic at room temperature (24 ±1°C). The NCL is orientated parallel to the plates by the well known rubbing technique. The stabilizing electric field is a 5kHz a.c. field, normal to the director, for which the amplitude is maintained for below the threshold for the dielectric electrohydrodynamical 6 The scattering angle, and then q, instability. are small enough to observe an appreciable quenching effect from the field. The thickness of the sample is chosen to minimize both spurious boundary friction and multiple scattering, The resulting current fluctuations of the photomultiplier are analysed with a correlator (Hewlett—Packard 3721A). We observe independently the two modes of angluar fluctuations by using the polarization selection rules demonstrated in reference (3).
We first observe the depolarized scattering from mode 2. The spectrum is found to be purely homodyne. Within our experimental accuracy we see no apparent variation its exponential 2>, as ofexpected. The decay time~T2value vs.
ut
(Hz)
Vol. 10, No. 9
*
+
1/1(arbuiits)o
+
o
~0
ioo
200
300
400 (E2>(esu)
FIG. 1. Linear increase of the damping rate (~) and the inverse intensity (o) of thermal hand fluctuations in room temperature MBBA vs. the mean square amplitude of a stabilizing 5kHz a.c. electric field. in good agreement with other independent measurements. The uncertainty on K 33 comes partly from the difficulty of thickness measuremerits and partly from the residual dispersion of the experimental data, which is probably related to some aging of the sample. From the known (equation IV 25a of reference (4)) forexpression the zero field intercept (1/~
2/~
?7B (19 ±3)10_2 poise in good agreement withinthe measurements 7 Note that absence of field, of the Gähwiller. data for (l/r,) 0 show some dispersion, probably related to defects in the sample which are removed by the application of the field.
From the zero delay value of the autocorrelation oscillator function and the joint of the local intensity, wemeasurement derive for each value of E, the intensity 1~ of the bend fluctuations. The data (see Fig. 1) show a decrease of l~similar to that of ‘r, ,but their greater dispersion does not allow us to improve the
K 33
=
(7,2 ±1)1U~dyne
(3)
1)0 = K33 q (where 77B is the bend viscosity) and the previously determined K 33 we can now compute the bend viscosity
estimated value of K33. I~can decrease so
Vol. 10, No.9
ORIENTATION IN A NEMATIC LIQUID CRYSTAL
much that for high values of
T
T~
In conclusion using quasielastic Rayleigh scattering we have observed the predicted quenching of thermally excited angular fluctuations in NLC due to the application of a stabilizing a.c. electric field. The effect is visible not only by a decrease of intensity, but also by a shortening of the associated damping time of the fluctuations. For many practical reasons (defects, multiple scattering ) damping time measurements are found to be -
.
.
much easier and more accurate than intensity
2.
Comparing the intensity ‘D of the double scattering signal to I~in a 75~msample, we estimate that the critical length for which ‘D = (I~)~is about five to ten times the thickness of our sample. 12 Note that this ratio is the same for all small scattering angles. 2 ) Because ofare double ‘r (
817
the data of Fig. 1 have
been restricted 1to values of’
measurements. We believe that they constitute a valuable method for measuring Frank elastic constants. We have here demonstrated the
method by measuring the bend elastic constant. The splay and twist constants can be determined using the homeotropic geometry. Another possibility is to to the use director, a stabilizing magnetic field parallel which, in the same geometry, quenches now the two modes of angular fluctuations; we have in fact observed these effects. Full account of this study will be published elsewhere.
Acknov~1edgements — We acknowledge useful discussions with other members of the Orsay Group.
REFERENCES
1.
ORSAY LIQUID CRYSTAL GROUP, Phys. Rev. Lett. 22, 1361 (1969)..
2. 3.
HALLER I. and LITSTER J.D., Phys. Rev. Lett. 25, 1550 (1970). DE GENNES P.G., Cr. hebd. sêanc. Ac. Sci., Paris 266B, 15 (1968).
4.
GROUPE D’ETUDE DES CRISTAUX LIQUIDES (Orsay), Chem. Phys., 51, 816 (1969).
5.
DUBOIS—VIOLETTE E., DE GENNES P.G. and PARODI 0., J. Phys. 32. 305 (1971).
6. 7.
For a review of these effects, see for instance ORSAY LIQUID CRYSTAL GROUP, Mol. Cryst. Liq. Cryst., 12, 251 (1971). GAHWILLER Ch., Phys. Lett. 36A, 311 (1971).
8. 9.
BRUNET—GERMAIN, Cr. hebd. séanc. Acad. Sci., Paris 271B, 1075 (1970). WILLIAMS C. and CLADIS P.E., Solid State Comrnun., to be published.
10. GASPAROUX H. and PROST J., J. Phys. 32, 953 (1971). 11. DIGUET D., RONDELEZ F. and DURAND G., Cr. hebd. sêanc. Acad. Sci., Paris 271B, 954 (1970). 12. For a previous discussion, see LEGER QUERCY L., 3~cycle thesis, Orsay (1971).
818
ORIENTATION IN A NEMATIC LIQUID CRYSTAL
Vol. 10, No.9
Utilisant Ia spectroscopie par battements lumineux, nous observons La diffusion Rayleigh due aux fluctuations thermiques angulaires du directeur dans la phase nématique du MBBA (p-méthoxybenzylidénep-n-butylaniline) en presence d’un champ Clectrique alternatif stabilisant. L’intensité et Ic temps d’amortissement dCcroissent tous deux lorsqu’on augmente l’intensitC du champ, cc qul perniet la mesure de La constante élastique de Frank pour La flexion.