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The Kerr constants and relaxation times in the isotropic phase of nematic homologous series
Volume 69A, number 4
PHYSICS LETTERS
25 December 1978
THE KERR CONSTANTS AND RELAXATION TIMES IN THE ISOTROPIC PHASE OF NEMATIC HOMOLOGOUS SERIES R. YAMAMOTO, S. ISHIHARA and S. HAYAKAWA Materials Reserach Laboratory, Matsushita Electric Industrial Co., Ltd., Kadoma, Osaka, 571, Japan
and K. MORIMOTO Wireless Research Laboratory, Matsushita Electric Industrial Co., Ltd., Kadoma, Osaka, 571, Japan Received 10 May 1978 Revised manuscript received 3 October 1978
The anisotropy of the refractive index and of the dielectric constant for cyanobiphenyl homologous compounds has been measured. From these results, it is pointed out that the alternation of the Kerr constants and relaxation times with the carbon chain length are due to the variation of the coefficient a of the Landau expansion of the compounds.
The critical behaviour of the Kerr effect for nematic liquid crystals near the isotropic—nematic transitions predicted from the Landau—de Gennes model [1]
for the orientational relaxation times r for electrically induced molecular order and for the anisotropy of the refractive index z~n0and of the dielectric constant
has been studied by many authors [2—8]. From the measurements of electrically and magnetically induced birefringence, Poggi Ct al. [6] have determined the coefficients in the Landau series expansion of the free energy for MBBA and 4’-n-heptyl-4-cyanobiphenyl and found the calculated latent heats to be in good agreement with the experimental value. Hanson et al. [7i have measured the optically induced refractive index and the corresponding relaxation time for p,p’-di-n-alkoxy-azoxybenzene homologous compounds in order to understand the influence of molecular structures. As a result, it has been found that optical Kerr constant drops with the length of the alkoxy chain, mainly owing to a drop in optical polarizability anisotropy. On the other hand, we have shown [8] that the electric Kerr constant for two neinatic homologous series of 4’-n-alkyl- and 4’-nalkoxy-4-cyanobiphenyl in the isotropic phase exhibits the even—odd alternation with the number of the chain carbon atoms. However, a satisfactory explanation of this alternation has not been given yet. We will present here the recent experimental results
~ for cyanobiphenyl homologous compounds and give a brief explanation of the Kerr effect on the basis of the experimental results. The samples used in the work were two nematic homologous series of 4’-n-alkyl-4-cyanobiphenyl (C~H2~÷1—C6H4—C6H4—CN with n = 4—8, nCB) and 4’-n-alkoxy-4-cyanobiphenyl(C0H2~~1O—C6H4— C6H4—CN with n = 3—8, nOCB). Some of these liquid crystals were purchased from E. Merck & Co. and some were presented by the Fuji Color Co. The measurement of r was made with the same arrangement as described in the previous paper [8]. Pulsed voltages with a rapid rise and decay time of iOns were used. The value of r is calculated by using the relation II~ exp (—t/r), where 1~is the transmitted light intensity at the steady state and I is the intensity at a time t after the removal of the applied voltage~ According to the Landau—de Gennes model [1], r is expected to take the form r = r0/T T*, where T’~’~ the second order transition temperature and T0 is temperature independent only at a narrow temperature range. In our experiments, T0 was nearly constant at
276
—
Volume 69A, number 4
PHYSICS LETTERS
25 December 1978
Table 1 Various experimental data of 4’-n-alkyl-4-cyano-biphenyl (nCB). n
~.n
~
0
BATX 2) 108
r.ATX (s K) 106
a (J/em3 K)
V (cP)
(cm K/V 4 5
0.176
11.0 11.0
2.24 1.50
0.570 0.221
0.037 0.061
21 14
6
0.180 0.170
10.8
1.61
0.510
0.053
27
7
0.172
11.6
1.17
0.203
0.080
16
8
0.167
11.7
1.01
0.426
0.090
38
a temperature range of T*< T< T* + 7°C.The measurement of the refractive anisotropy ~n 0 was made with a wedge-shaped cell by the measurement of interference fringes [9]. The cell was prepared by enclosing a liquid crystal between two optically flat glass slides in contact along one edge and separated along another by a tungsten wire of about 0.5 mm diameter. The optical axis was established by rubbing the slide prior to assembly, along the contact edge. Some of the rubbed cells showed a small decrease 3% in the capacitance with a magnetic field of 10 kG applied in the rubbing direction. Therefore, the obtained value of z.~n0may be somewhat smaller than the value in the well-oriented nematic phase because of imperfect alignment of the liquid crystal though no systematic variation in alignment with chain length was found. The parallel plate cell was used to measure the dielectric anisotropy ~e0 ~ er). Alignment of the liquid
On the other hand, the field-induced birefringence i~n(E)is given by ~n(E) = ~n0Q(E). Therefore, from the Kerr law and eq. (2) we get [6]: 2) ~e B ~n(E)/(A ./l’ 0/[12irAa(T— T*)], (3) where B is the Kerr constant and X is the wavelength of the light. The variation of Q with time is given by [1,7] aQ/at = —aF/aQ, (4) ~,.
where t is the viscosity coefficient. We put eq. (1) for E”~0 into eq. (4) and from the equation aQ/at = —Q/r, we derive the orientational relaxation time r 0.6 0.5
o
0.4
—
0)
crystal was achieved by applying a magnetic field of 10 kG to the cell. The capacitance of the cell was measured at 100 kHz by using a YHP-4072 automatic capacitance bridge. According to the Landau—de Gennes model [11, when an electric field E is applied to a nematic liquid crystal in its isotropic phase, the expansion of the free energy per unit volume in powers of the order parameter Q can be written as [6,7]:
0.3 Q2 0.1
0 30 -~
ao 0
~
3 4~
)<
1.0
(1) where the expansion coefficients a, b, c are assumed to be temperature independent. As a first approximation, from eq. (1) the field-induced order Q(E) can be
expressed as follows: Q(E) E~/[12ira(T -
T*)J.
(2)
0
4
5
3
4
6I 5
7I 6
8(nCB) 7(nOCB)
fl 4’-n-alkoxy-4-cyanobiphenyl (nOCB) with the number of and Fig. 1. Alternation of BAT and rAT for 4’-n-alkyl(nCB) carbon chain atoms n.
277
Volume 69A, number 4
PHYSICS LETTERS
the decrease of Bi~.tTis mainly due to the increase of the coefficient a in the Landau expansion. This is well understood by fig. 2, where the variations of B 1~1Tand 1/a for nCB is shown as a function of n. On the other hand, rLIT tends to become faster in spite of the in-
nCB
>
2.0
30
1.0
20
.2
H
~
0
4
5
6
7
10
crease of the coefficient n. This result is viscosity also supposed to arisev with from increasing the increase of a with increasing n.
~.
In summary, our experimental results show that the even—odd effect in the electric Kerr effect for
8
Fig. 2. Experimental value of B~Tand calculated value of 1/a for 4‘-n-alkyl-4-cyanobiphenyl (nCR).
—
T*)~.
cyanobiphenyl homologs is mainly due to the alternation of the coefficient a in the Landau—de Gennes expansion with the number of the carbon chain atoms. The authors wish to thank Dr. H. Sato of the central research laboratory Matsushita Elec. md. Co., for help-
as follows [1,7]:
r = (v/a) (T
25 December 1978
(5)
ful discussions.
The values of B and ‘r for the same %~T=T— T~’ and other data obtained from our measurements for
References
4’-n-alkyl-4-cyanobiphenyl (nCB) are listed in table 1. The values of a and v were calculated by using eqs. (3) and (5), respectively. The variations of Bz~Tand rL\T for two cyanobiphenyl homologs (nCB and nOCB) are plotted as a function of the number of the chain carbon atoms n in fig. 1. In general, B~Tfor nOCB is larger than that for nCB, while rL~Tfor nOCB is faster then that for nCB. This suggests that nOCB is superior in practical use to nCB. In fig. I, BL~Tdecreases with increasing n, showing the zig-zag behaviour. However, the product of £~.flf3 and &l~ for nCB varies by less than 10% with n (see table 1). Therefore, it is supposed form eq. (3) that
[1] P.G. de Gennes, Mo!. Cryst. Liquid Cryst. 12 (1971)193. [2] M. Schadt and W. Helfrich, Mol. Cryst. Liquid Cryst. 17 (1972) 355. 131 3. Y.R. AppI.Shen, Phys.Phys. 44 (1973) 2971.30 (1973) [4] A.R. G.K.L.Johnston, Wong and Rev. Lett. 895. [5JJ.C. Filippini and Y. Poggi, J. Physique 35 (1974) L-99. 161 Y. Poggi, J.C. Filippini and R. Aleonard, Phys. Lett. 57A (1976) 53. [7] E.G. Hanson, Y.R. Shen and G.K.L. Wong, Phys. Rev. A14 (1976) 1281. [81 R. Yamamoto, S. Ishihara, S. Hayakawa and K. Morimoto, Phys. Lett. 60A (1977) 414. [91 I. Haller, H.A. Huggins and M.J. Freiser, Mo!. Cryst. Liquid Cryst. 16 (1972) 53.
278
PHYSICS LETTERS
25 December 1978
THE KERR CONSTANTS AND RELAXATION TIMES IN THE ISOTROPIC PHASE OF NEMATIC HOMOLOGOUS SERIES R. YAMAMOTO, S. ISHIHARA and S. HAYAKAWA Materials Reserach Laboratory, Matsushita Electric Industrial Co., Ltd., Kadoma, Osaka, 571, Japan
and K. MORIMOTO Wireless Research Laboratory, Matsushita Electric Industrial Co., Ltd., Kadoma, Osaka, 571, Japan Received 10 May 1978 Revised manuscript received 3 October 1978
The anisotropy of the refractive index and of the dielectric constant for cyanobiphenyl homologous compounds has been measured. From these results, it is pointed out that the alternation of the Kerr constants and relaxation times with the carbon chain length are due to the variation of the coefficient a of the Landau expansion of the compounds.
The critical behaviour of the Kerr effect for nematic liquid crystals near the isotropic—nematic transitions predicted from the Landau—de Gennes model [1]
for the orientational relaxation times r for electrically induced molecular order and for the anisotropy of the refractive index z~n0and of the dielectric constant
has been studied by many authors [2—8]. From the measurements of electrically and magnetically induced birefringence, Poggi Ct al. [6] have determined the coefficients in the Landau series expansion of the free energy for MBBA and 4’-n-heptyl-4-cyanobiphenyl and found the calculated latent heats to be in good agreement with the experimental value. Hanson et al. [7i have measured the optically induced refractive index and the corresponding relaxation time for p,p’-di-n-alkoxy-azoxybenzene homologous compounds in order to understand the influence of molecular structures. As a result, it has been found that optical Kerr constant drops with the length of the alkoxy chain, mainly owing to a drop in optical polarizability anisotropy. On the other hand, we have shown [8] that the electric Kerr constant for two neinatic homologous series of 4’-n-alkyl- and 4’-nalkoxy-4-cyanobiphenyl in the isotropic phase exhibits the even—odd alternation with the number of the chain carbon atoms. However, a satisfactory explanation of this alternation has not been given yet. We will present here the recent experimental results
~ for cyanobiphenyl homologous compounds and give a brief explanation of the Kerr effect on the basis of the experimental results. The samples used in the work were two nematic homologous series of 4’-n-alkyl-4-cyanobiphenyl (C~H2~÷1—C6H4—C6H4—CN with n = 4—8, nCB) and 4’-n-alkoxy-4-cyanobiphenyl(C0H2~~1O—C6H4— C6H4—CN with n = 3—8, nOCB). Some of these liquid crystals were purchased from E. Merck & Co. and some were presented by the Fuji Color Co. The measurement of r was made with the same arrangement as described in the previous paper [8]. Pulsed voltages with a rapid rise and decay time of iOns were used. The value of r is calculated by using the relation II~ exp (—t/r), where 1~is the transmitted light intensity at the steady state and I is the intensity at a time t after the removal of the applied voltage~ According to the Landau—de Gennes model [1], r is expected to take the form r = r0/T T*, where T’~’~ the second order transition temperature and T0 is temperature independent only at a narrow temperature range. In our experiments, T0 was nearly constant at
276
—
Volume 69A, number 4
PHYSICS LETTERS
25 December 1978
Table 1 Various experimental data of 4’-n-alkyl-4-cyano-biphenyl (nCB). n
~.n
~
0
BATX 2) 108
r.ATX (s K) 106
a (J/em3 K)
V (cP)
(cm K/V 4 5
0.176
11.0 11.0
2.24 1.50
0.570 0.221
0.037 0.061
21 14
6
0.180 0.170
10.8
1.61
0.510
0.053
27
7
0.172
11.6
1.17
0.203
0.080
16
8
0.167
11.7
1.01
0.426
0.090
38
a temperature range of T*< T< T* + 7°C.The measurement of the refractive anisotropy ~n 0 was made with a wedge-shaped cell by the measurement of interference fringes [9]. The cell was prepared by enclosing a liquid crystal between two optically flat glass slides in contact along one edge and separated along another by a tungsten wire of about 0.5 mm diameter. The optical axis was established by rubbing the slide prior to assembly, along the contact edge. Some of the rubbed cells showed a small decrease 3% in the capacitance with a magnetic field of 10 kG applied in the rubbing direction. Therefore, the obtained value of z.~n0may be somewhat smaller than the value in the well-oriented nematic phase because of imperfect alignment of the liquid crystal though no systematic variation in alignment with chain length was found. The parallel plate cell was used to measure the dielectric anisotropy ~e0 ~ er). Alignment of the liquid
On the other hand, the field-induced birefringence i~n(E)is given by ~n(E) = ~n0Q(E). Therefore, from the Kerr law and eq. (2) we get [6]: 2) ~e B ~n(E)/(A ./l’ 0/[12irAa(T— T*)], (3) where B is the Kerr constant and X is the wavelength of the light. The variation of Q with time is given by [1,7] aQ/at = —aF/aQ, (4) ~,.
where t is the viscosity coefficient. We put eq. (1) for E”~0 into eq. (4) and from the equation aQ/at = —Q/r, we derive the orientational relaxation time r 0.6 0.5
o
0.4
—
0)
crystal was achieved by applying a magnetic field of 10 kG to the cell. The capacitance of the cell was measured at 100 kHz by using a YHP-4072 automatic capacitance bridge. According to the Landau—de Gennes model [11, when an electric field E is applied to a nematic liquid crystal in its isotropic phase, the expansion of the free energy per unit volume in powers of the order parameter Q can be written as [6,7]:
0.3 Q2 0.1
0 30 -~
ao 0
~
3 4~
)<
1.0
(1) where the expansion coefficients a, b, c are assumed to be temperature independent. As a first approximation, from eq. (1) the field-induced order Q(E) can be
expressed as follows: Q(E) E~/[12ira(T -
T*)J.
(2)
0
4
5
3
4
6I 5
7I 6
8(nCB) 7(nOCB)
fl 4’-n-alkoxy-4-cyanobiphenyl (nOCB) with the number of and Fig. 1. Alternation of BAT and rAT for 4’-n-alkyl(nCB) carbon chain atoms n.
277
Volume 69A, number 4
PHYSICS LETTERS
the decrease of Bi~.tTis mainly due to the increase of the coefficient a in the Landau expansion. This is well understood by fig. 2, where the variations of B 1~1Tand 1/a for nCB is shown as a function of n. On the other hand, rLIT tends to become faster in spite of the in-
nCB
>
2.0
30
1.0
20
.2
H
~
0
4
5
6
7
10
crease of the coefficient n. This result is viscosity also supposed to arisev with from increasing the increase of a with increasing n.
~.
In summary, our experimental results show that the even—odd effect in the electric Kerr effect for
8
Fig. 2. Experimental value of B~Tand calculated value of 1/a for 4‘-n-alkyl-4-cyanobiphenyl (nCR).
—
T*)~.
cyanobiphenyl homologs is mainly due to the alternation of the coefficient a in the Landau—de Gennes expansion with the number of the carbon chain atoms. The authors wish to thank Dr. H. Sato of the central research laboratory Matsushita Elec. md. Co., for help-
as follows [1,7]:
r = (v/a) (T
25 December 1978
(5)
ful discussions.
The values of B and ‘r for the same %~T=T— T~’ and other data obtained from our measurements for
References
4’-n-alkyl-4-cyanobiphenyl (nCB) are listed in table 1. The values of a and v were calculated by using eqs. (3) and (5), respectively. The variations of Bz~Tand rL\T for two cyanobiphenyl homologs (nCB and nOCB) are plotted as a function of the number of the chain carbon atoms n in fig. 1. In general, B~Tfor nOCB is larger than that for nCB, while rL~Tfor nOCB is faster then that for nCB. This suggests that nOCB is superior in practical use to nCB. In fig. I, BL~Tdecreases with increasing n, showing the zig-zag behaviour. However, the product of £~.flf3 and &l~ for nCB varies by less than 10% with n (see table 1). Therefore, it is supposed form eq. (3) that
[1] P.G. de Gennes, Mo!. Cryst. Liquid Cryst. 12 (1971)193. [2] M. Schadt and W. Helfrich, Mol. Cryst. Liquid Cryst. 17 (1972) 355. 131 3. Y.R. AppI.Shen, Phys.Phys. 44 (1973) 2971.30 (1973) [4] A.R. G.K.L.Johnston, Wong and Rev. Lett. 895. [5JJ.C. Filippini and Y. Poggi, J. Physique 35 (1974) L-99. 161 Y. Poggi, J.C. Filippini and R. Aleonard, Phys. Lett. 57A (1976) 53. [7] E.G. Hanson, Y.R. Shen and G.K.L. Wong, Phys. Rev. A14 (1976) 1281. [81 R. Yamamoto, S. Ishihara, S. Hayakawa and K. Morimoto, Phys. Lett. 60A (1977) 414. [91 I. Haller, H.A. Huggins and M.J. Freiser, Mo!. Cryst. Liquid Cryst. 16 (1972) 53.
278