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Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals
ISSN: 1058-725X (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/gmcl19
Trifluorinated Liquid Crystals for TFT Displays
D. Demus , Y. Goto , S. Sawada , E. Nakagawa , H. Saito & R. Tarao
To cite this article: D. Demus , Y. Goto , S. Sawada , E. Nakagawa , H. Saito & R. Tarao (1995) Trifluorinated Liquid Crystals for TFT Displays, Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals, 260:1, 1-21, DOI: 10.1080/10587259508038680 To link to this article: https://doi.org/10.1080/10587259508038680
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Mol. C y s t . Liq. C y s t . 1995, Vol. 260, pp. 1-21 Reprints available directly from the publisher Photocopying permitted by license only
0 1995 OPA (Overseas Publishers Association) Amsterdam B.V. Published under license by Gordon and Breach Science Publishers SA Printed in Malaysia
TRIFLUORINATED LIQUID CRYSTALS FOR TFT DISPLAYS #
D. DEMUS, Y. GOTO, S . SAWADA, E. NAKAGAWA, H. SAITO
and R. TARAO Chisso Petrochemical Corporation, Research Center,
5-1 Goi Kaigan, Ichihara, Chiba, 290 Japan
ABSTRACT 3,4,5-tri-fluorobenzene derivatives with different core structures have been synthesized and
their physical properties have been determined. Most of the compounds are nematic with broad existence
regions. The materials have large dielectric anisotropy, low viscosity, low optical anisotropy and very good voltage holding ratio and high chemical stability and are valuable components for mixtures to be used in TFT displays. The good voltage holding ratio of the compounds is related to their high electrical resistivity. In order to reproduce the dependence of the resistivity on the dielectric constant, we derived a general formula. Its derivation is based on the interaction of the impurity ions with the induced and permanent dipoles of the liquid crystal molecules. We are able to show, that ion/ion interactions in highly purified liquid crystals may be neglected.
INTRODUCTION
For use in TFT displays the nematic liquid crystals should have high electrical resistivity (high voltage holding ratio), large dielectric anisotropy, low birefringence, low viscosity and very good chemical and thermal stability'. In continuation of former work of the Chisso Research
# Part of a plenary lecture at the 15th International Liquid Crystal Conference, Budapest 1994.
1
2
D. DEMUS ET AL.
Center on 3,4-di-fluorobenzene derivatives', the 3,4,5-trifluorobenzene group was used as new moiety and first results were already mentioned by Yamamoto et a1.3. Here we report in more detail about this substance class, including the materials from Reference 3 as well as additional derivatives and discuss their physical characteristics. Because of the importance of the electrical resistivity for the voltage holding ratio, by considering the intermolecular interactions of ionic impurities with the dipolar liquid crystal molecules, we derived a formula describing the dependence of the resistivity on the dielectric constant of a material. The comparison with experimental data shows that the formula can reproduce the results. Additionally we are able to show, that in liquid crystals of high electrical resistivity the ion/ion interactions may be neglected.
SYNTHESIS
Confirmation of the structures of the products was obtained
by 'H-NMR spectroscopy ( J E O L EX-90 > .Transition tempera-
tures were measured using a Mettler FP5 hotstage and control unit in conjunction with a Nikon OPTIPHOT polarizing microscope. The purities of each compound shown in Tables 1.1, 1.2 and 1.3 were checked by GLC analysis (Shimadzu GCl4APF fitted with a 40m CBPl-M50-025 column) and were found to be 99.9% unless stated otherwise. All the compounds listed in Tables 1.1, 1.2 and 1.3 were synthesized by applying the previously reported catalytic C-C bond formation reactions4. 5'6. We have described the synthetic procedures for two typical 3,4,5-tri-fluorinated compounds shown in Tables 1.1 and 1.2. The other compounds may be prepared by analogous instructions.
TRIFLUORINATED LIQUID CRYSTALS
3
Synthesis of compound:3cF3
l-(trans-4-(trans-4-propylcyclohexyl)cyclohexyl)-3,4,5trifluorobenzene
PBr, I PPh,
C 3 H : W - H C-3H*:Br
I) Li 2) ZnBr2/ sonic
cis-4-(trans-4-Propylcyclohexyl)cyclohexylbromide (lOg,O.O35mol) and zinc bromide (3.92g,O.O175mol) in 20ml of a mixture to1uene:tetrahydorofurane (5:l) were placed in the reaction flask under an argon atomsphere. The lithium wire (0.486g,O.O7mol) was placed in the flask under the ultrasonic probe. The flask was cooled in an ice bath below 5OC. Stirring with a magnetic bar ensured a homogenous temperature. The energy level of the sonication was adjusted to the minimum giving the cavitation noise, and a black color was immediately developed. After 30 min irradiation a solution of l-bromo-3,4,5-trifluorobenzene (3.7g, 17.5mmol) and dichloro-(l,l'-bisdiphenylphosphinoferrocene)palladium ( 1 1 ) (70mg) and 15ml tetrahydorofuran was added dropwise within a few minutes. The reaction mixture was stirred at room temperature for 18h. The mixture was poured into saturated aqueous NH4C1
and the product was extracted with toluene (twice). The combined extracts were washed with water and dried (MgS04). The solvent was removed in vacuo and the residue was purified by column chromatography [silicagel: hexane:ethyl acetate 10:1] to yield a colorless solid which was recrystallized from ethanol yielding colorless crystals. Yield :6.129,(52%). 1 ~ - N M R(CDC13) 6 0.5-2.1 (26H,m), 2.37(1H,m), 6.79(2H,m)
4
D. DEMUS ET AL
Synthesis of compound:3eF3
4'-(trans-4-propylcyclohexyl)-3,4,5-trifluorobiphenyl
Butyl-lithium (1.5 mol/l in hexane; 24ml) was added dropwise to a stirred, cooled(-78O C) solution of l-bromo-4(trans-4-propylcyclohexyl)benzene (log, 0.036mol) in dry tetrahydorofurane (30ml) under dry nitrogen. The reaction mixture was maintained under this condition for 3h and then a previously cooled solution of triisopropyl borate (13.6g, 0.072mol) in dry tetrahydorofurane (301111)was added dropwise at -78O C. The reaction mixture was allowed to warm to room temperature over night and then stirred for lh in 10% hydrochloric acid(35%). The product was extracted with ether(twice) and the combined ether extracts were washed with water and dried (MgS04). The solvent was removed in vacuo to yield colorless crystals of 4-(trans-4-propylcyclo hexy1)phenylboronic acid (7.9g, 89%). A solution of 4-(trans-4-propylcyclohexyl)phenylboronic acid (7.9g, 0.032mol) in ethanol (20ml) was added to a stirred mixture l-bromo-3,4,5-trifluorobenzene (6.75g, 0.032mol), tetrakistriphenylphosphinepalladium(0) (1.22g, 1.06mmol) in benzene ( 2 0 m l ) and aqueous sodium carbonate (2mol/l, 64ml) at room temperature under dry nitrogen. The stirred mixture was heated under reflux for 20h. The product was extracted with ether (twice) and the combined ether extracts were washed with water and dried (MgS04). The solvent was removed in vacuo and the residue was purified by column chromatography [silicagel: petroleum fraction (b.p. 40-60C):dichloromethane 5:1] to yield a color-
TRIFLUORINATED LIQUID CRYSTALS
5
less solid which was recrystallized from ethanol yielding colorless crystals. Yield : 6.82g, (64%). 'H-NMR ( CDC13 ) 6 0.82-2.0( 16H,m ) , 2.51 ( lH,m ) , 7.15 ( 2H,m ) , 7.27 (2H,d,J=8.4Hz), 7.42 (2H,d,J=8.4Hz)
PROPERTIES
In Tables 1.1 - 1.3 3,4,5-tri-fluorobenzenederivatives with different core structures are presented. The two ring compounds do not possess nematic phases, but all three ring compounds are nematic, partially in very broad temperature intervals. The comparison with mono- or di-fluorinated compounds (Figure 1) shows that the length-to-breadth ratio of the trifluorinated species is slightly reduced, which explains the reduced clearing temperatures (Table 2).
DIPOLE 1 DEBYE
2,078
3,320
3.899
4,287 FIGURE 1 . Substituted (trans-4-(trans-4-propylcyclohexyl)
cyclohexy1)benzenes. Substituents are from top to bottom: mono-fluoro, di-fluoro, tri-fluoro, cyano. See Color PlateI.
6
D. DEMUS ET AL.
Table 1.1. 3,4,5-F3 Liquid Crystal Compounds
Abbreviation StruCtUal Formula
F
5aF3
wF F
7aF3 C7H15 F
F
4bF3
5bF3
Mesophase("C) C 16.7 I
A E An 7
C 25.6 I
6.8 0.034 -
C 8.4 1 C -0.6 I
5.8 0.024 -
6.8 0.029 -
2cM
C 73.0 (N 48.9) I 8.3 0.068 27.1
3cF3
C 64.7 N 93.7 I 8.3 0.073 25.1
4cF3
C 66.7 N 91.3 I 8.3 0.079 26.6
dF 5cF3 C5H11
F
C 87.3 N 101.21 7.8 0.078 26.6
F
F
2dF3
0.0) I 6.8 0.065 1.6
3dF3
C3H7 -C)CHzCHz w
4dF3
C4H9e C H z C H 2 W
5dF3 C5Hll o C H z C H 2 W
F F
F C 50.7 N 83.4 I 7.8 0.069 28.6 F F
F c 61.5 N 83.2 I 8.8 0.064 25.1
F F
F C 46.5 N 91.1 I 6.3 0.070 30.1 F
2eF3 CZH5 3eF3 4eF3 5eF3 2fF3 3fF3 4fF3
TRIFLUORINATED LIQUID CRYSTALS
7
Table 1.2. 3,4,5-F3 Liquid Crystal Compounds
Mesophase("C)
F
F
C 46.2 1
12.8 0.124 21.6
F
F
C 40.7 (N 33.2) I 12.8 0.137 18.6 F
F
C 37.2 (N 33.2) I 12.3 0.129 21.1 F
F
F
C 30.4 N 58.0 I 11.3 0.134 32.1
F
d
F C 65.1 N 65.8 I
F
F
C 41.8 N 98.3 I
8.3 0.069 23.1 7.3 0.074 31.6
C 57.6 N 96.5 I 7.8 0.074 26.6
5fF3 2gF3 3gF3 C3H7 ~ C H P C H ~ 4gF3 5gF3 C5Hll - C ) C H 2 C H 2
C 54.6 Ss 57.0 F N 103.9 I F
C 43.0 (N37.4) I
F F
F C 48.0 N 51.8 I F F
C 50.9 (N 50.7) I F F
F C 40.2 N 65.2 I F
6.3 0.074 40.1
11.8 0.129 16.1 11.8 0.124 18.1 10.8 0.124 18.6
8
D. DEMUS ET AL.
Table 1. 3. 3,4,5-F3Liquid Crystal Compounds
Abbreviation 2hF3F-H52C
Structual Formula
F
F
Mesophase("C)
A E A n 'I
h a . sl
C 109.3 N 234.0 I 12.8 0.149 56.1
C 105.8 N >250 I 12.6 0.154 57.6
5hF3C 5 H 1 , e F
F
3iF3 C 3 H 7 w C H 2 C H 2
4iF3 C 4 H 9 m C H 2 C H 2
5iF3 C5H11 w C H 2 C H 2
C 87.8 N >250 1 11.3 0.144 51.1
F F C 79.2 N 216.0 I 11.3 0.144 46.6
F
F F C 83.1 N 210.6 I 10.8 0.139 47.1
F
F F C 86.1 N 212.5 I 10.8 0.139 45.1
F
A&, An, q: extrapolated value. Measurement performed using 20wt% solution of 3,4,5-F3 in FB-01 (2cF2 : 3cF2 : 5cF2=1 : 1 : 1 mixture, NI 112.8 "C, A&4.8, An 0.079,q 25.6).
As an exception, 5cF3 measurement was performed using 10wt% solution in FB-01. Temperature of measurement :A&20"C,An 25C 11 2OOC.
TRIFLUORINATED LIQUID CRYSTALS
9
Table 2. Relationship between transition temperatures and length to-breadth ratio
Abbreviation Compound 3eF C3H7 m
transition temperatures ("(3
F C 87.6 N 155.2 I
length-to-breadth ratio
3.93
3eF2 c3H7F-
C 45.6 N 123.8 I
3.76
length to-breadth ratio was calculated by MOPAC ver.6
All new compounds possess high dielectric anisotropy, low optical birefringence and low viscosity. The discussion of these data will be performed by use of selected examples and comparison with analogous derivatives of the practical-
. ly important substance classes derived from 3,4-di-fluoro-
benzene2 and 4-cyanobenzene7 A s to be expected, the dielectric anisotropy of the trifluorinated compounds is intermediate between those of the CN-substituted and those of the di-fluorinated compounds (Figure 2). This can be explained by the increased longitudinal component of the dipole in comparison to the monoand di-fluorinated compounds (Figure 1). The temperature dependence of AE is about the same in the substance classes displayed in Figure 2. Compounds with large conjugated core systems, this is biphenyl derivatives (Table 1 ) , have distinctly larger AE than benzene derivatives.
10
D. DEMUS ET AL.
8
.
1
'
1
.
~
-
1
.
1
.
1
.
~:6-
A 4 -.+
&F
2 -
&F
m
-----c
F
C
N
0 ~
'
~
'
~
'
.
l
~
l
=
l
.
TRIFLUORINATED LIQUID CRYSTALS
11
The optical anisotropies of tri-fluorinated compounds are very small and below 0.1, only those of the biphenyl derivatives are slightly higher than 0.1 (Table 1). The order parameters of the tri-fluorinated compounds, because of the diminished length-to- breadth ratio, should be lower than those of the more elongated compounds. This can explain the small optical anisotropies. The temperature dependence of the elastic constants are shown in figure 3. In all cases there is the relation K33 >
Kll > K22 . In comparison to the reference compounds, all
elastic constants of the trifluorinated compounds are
lower. This also holds for K(K = Kii + (K33 - 2 K22)/4 ) .
1.9 F
1.6 -
F
.-
CN
I
.
1.5' '
I
"" "*
-140 -120 -100 -80 -60 -40 -20
T-TC/ "C
Figure 4 Temperature dependence of threshold voltage(Vth)
Figure 4 presents the temperature dependence of the threshold voltages, which were measured in conventional TN cells with An'd = 0 . 5 5 ~ .The tri-fluorinated compounds show the lowest values. This can be explained by the fact that A& of
12
D. DEMUS ET AL.
p/R *
0
20
40
60
80
100
Figure 5 Temperature dependence of specific resistivity(p). them has the largest value, whereas K is the smallest. These findings suggest that the tri-fluorinated compounds are valuable components for mixtures used in displays driven at low voltage. The temperature dependence of the specific resistivity is displayed in Figure 5. The fluorinated substances are superior to the cyano substituted compound, which is specially pronounced at elevated temperatures. There is some experimental evidence, that the electrical resistivity in different substance classes is decreasing with increasing dielectric constant, however, we did not find any explanation of this behaviour. In order to understand this effect, in the following section we derive a formula of the dependence of the resistivity on the dielectric constant.
In Figure 6 the temperature dependence of the voltage holding ratios of the three representative compounds is displayed. We see that the data of the fluorinated compounds
TRIFLUORINATED LIQUID CRYSTALS
13
are superior to those of the cyano compound, which may be explained by the already discussed differences in the specific resistivities.
100
I
I
I
95
VH R/% 90
*
\ F
F
*
85
F
*
CN
4 80
-10
10
30
50
70
90
TI'C Figure 6 Temperature dependence of voltage holding ratio(VHR)
DEPENDENCE OF THE ELECTRICAL RESISTIVITY ON THE DIELECTRIC CONSTANT
In liquid crystals always certain amounts of impurities exist. They can be of different kind: 1. non-polar, non dissociating (e. g. neighboured homologs of a given compound. Such impurities can be determined by calorimetric investigation or chromatographic methods. They only have minor influence on the electrical properties.
2. polar, completely dissociated. For instance small amounts of inorganic salts, acids or bases. Even small amounts of such impurities strongly influence the electri-
14
D. DEMUS ET AL.
cal resistivity of the material, and therefore easily can be determined by resistivity measurements. Because in many cases they are not soluble in non-polar solvents, they can be removed by recrystallization.
3 . polar, partially dissociated Impurities of this kind may be organic acids, phenols, bases. Their dissociation depends on the dielectric constant (see below). They change the electrical resistivity drastically and can be removed only with large difficulties. The last of these impurities can already exist in the liquid crystal, but also may be formed in the material due to decomposition in electric fields, thermal or photochemical decomposition. Weak electrolytes, this is partially dissociated materials, show a dissociation constant which is dependent on the dielectric constant of the solvent. We consider the most simple dissociation equilibrium
KA + K+ + A-
The standard Gibbs energy of this equilibrium is
and the equilibrium constants are
This means, the total change of the standard Gibbs free energy is divided into a part AGO , which would result from dissociation into non-polar particles (which do not produce strong intermolecular interactions), and a contribution
AG,,~~, which considers the solvation of the dissociation
products (ions) with the solvent (liquid crystal molecules). The molar solvation energy approximately can be
TRIFLUORINATED LIQUID CRYSTALS
15
split into an ion/permanent dipole and an ion/induced dipole contribution:
AGsolv = U(ion/induced dipole) + U(ion/dipole)
(2)
U( ion/induced dipole) = -2 NA aaVeo2p/{2 ( 4 ~ c ~ ~ r ~ ) ) ( 3 )
NA = Avogadro's number aav = average polarizability of the liquid crystal molecule eo = electrical elementary charge E~ = dielectric constant of vacuum r = distance of the particles p = number of nearest neighbours
u( ion/dipole) = - NAeo2p2p/{4nsor43kT}
(4)
p = permanent electrical dipole of the liquid crystal molecule k = Boltzmann's constant
In eq. (4)we introduced the statistical factor 1/2 in comparison to eq. ( 3 ) , because of the direction dependence of the interaction with the highly anisotropic liquid crystal dipole molecules. Adding (3) and (4)according to eq. ( 2 ) , we arrive at
The Onsager theory of dielectric polarization delivers8
E - 1 = (NhF/Eo){a+Fp2/3kT}
(6)
E = average dielectric constant of the liquid crystal N = number density h, F are factors of the Onsager theory describing the reaction field, both are approximately equal to one.
16
D. DEMUS ET AL.
Comparing eqs. ( 5 ) and (6), f o r a given liquid crystal we find
AGsolv = const. ( E -1)
(7)
Starting f r o m eq. (lb) and using well known general relat i o n ~ ~ w,e obtain
Inserting eq. (7) yields
with
C I = -const/RT = NAeo2/ ( 4xrlNhFRT )
The molar conductivity for weak electrolytes is given by:
a = degree of dissociation A T m = conductivity of completely dissociated electrolyte (this is a= 1) The specific resistivity (Qcm) is
c = concentration
The dissociation constant can be expressed in terms of Ostwald I s law9
Kdiss = a2c/(l - a )
(12)
Now we calculate the specific resistivity f r o m eq. (ll),
TRIFLUORINATED LIQUID CRYSTALS
17
inserting A,, from (lo), a from eq. (13) and Kdiss from eq. (9)
with C " = 2/A',K0
We calculated data f o r eq. (141, using the following parameters : T = 300 K r = 0.385'10-9 m (average distance of ions and liquid crystal molecules) KO = 4.10-16
A r m = 5.10-4
p ' = 5-1010 Qm = 5 - 1 0 1 2 Qcm (specific resistivity at complete dissociation) c = 3-10-8 mol/l = 3.10-5 mol m-3 C " = 1019 Qcm = 1017 a m
The calculated data are plotted in comparison to experimental results from many different liquid crystals in Figure 7. Approximately'eq. (14) is able to reproduce the experimental data. In ref. 10 experimental data for the resistivity are presented, which show a similar dependence on the mean dielectric constant. The agreement of calculated and experimental data cannot expected to be very good. In eq. (14) the dissociation constant Kdiss and the molar conductivity, which are material specific constants, are contained. If we consider different liquid crystals, in principle different impurities (with different constants) may be present. The fact that the experimental data accumulate around a common curve points at impurities with similar dissociation and conductivity properties. For synthesis in many cases phenols or carboxylic acids, which can act as dissociating impurities, are used. If their molar mass and the substitution near to the polar group are not too different, similar constants can be expected.
18
D. DEMUS ET AL.
1015 I,
0 TFT
A TN
-
0 STN
Calculated
p/n * cm .
1013
i
l o 1 *r l o 1 ':
.I
- A
0 0
A
wow
0
1o'O- . I . I
I
I
Figure
Coulomb interaction The dissociation produces ions in the liquid crystalline solution. It is well known that ions cause a long-range interaction, which can be calculated according to Coulomb`s law:
zA, zK = charge numbers of the ions
In Reference 11 the following data are given for a typical nematic mixture: p = 1.1012 Qcm , N = 2.1019 m-3
From this we calculate c = 3.3.10`8 mol/l and the average distance rav of two ions is rav = 368-1Om6m With a typical molecular size of a liquid crystal molecule
Mixture
A
SN("C)
2-40
NI(OC)
75.9
q[mPa*s] (20C) 27.5
An (20C)
0.0867
A& (20C)
8.4
P @cm)
>lo14
V90 (volt)
1.51
V50 (volt)
1.81
v10 (volt)
2.22
Cell width (pm) 5.5
Table 3. 3,4,5-F3 LC mixtures for TFT Displays
B
C
D
E
F
G
<-40 83.2 28.1 0.0807 7.5 > 1014 1.62 1.96 2.46 6.3
<-40 81.1 30.4 0.0902 8.4 >lo14 1.62 1.92 2.41 6.3
<-40 91.3 25.8 0.0886 6.1 >lo14 1.73 2.1 1 2.58 5.5
<-40 100.3 26.4 0.0802 6.3 >lo14 1.68 2.07 2.61 5.6
<-40 109.1 32.2 0.0853 7.0 >lo14 1.85 2.22 2.80 5.5
<-40 126.4 34.8 0.0871 6.9 >lo14 2.01 2.39 2.99 5.5
Control
<-40 81.6 25.0 0.0813 4.6 >lo14 1.84 2.17 2.64 6.3
20
D. DEMUS ET AL.
rmin = 2 nm we find, for the relation of the Coulomb interaction with the average neighboured ion and the nearest neighbour, resp.,
This means that for small concentrations there is practically no Coulomb interaction between the ions. Only with p
< lo8 the ratio (16) would exceed 5% .
CONCLUSIONS
All the discussed properties of the tri-fluorinated compounds let expect them to be valuable components for mixtures, specially for use in TFT displays. Table 3 presents some mixtures made from different combinations of trifluorinated compounds and additional components, together with a reference mixture based on di-fluorinated compounds. All mixtures have broad nematic existence regions, low viscosities, low optical anisotropies, low threshold voltages and resistivities above 1014 Qcm. Table 3 proves that outstanding mixtures for TFT displays can be formulated using tri-fluorinated compounds.
REFERENCES
1. B. Bahadur (ed.), Liquid Crystals. Applications and Uses", (World Scientific, Singapore 1990), Vol. 1
2. Y. Goto, T. Ogawa, S. Sawada and S. Sugimori, Mol.
Cryst. Liq. Cryst., 209, 1 (1991)
3 . H. Yamamoto, Y. Kubo, F. Takeshita, K. Terashima, Y. Goto and S . Sawada, _ Pr_ oc_ . _18_th Japan Liquid Crystal Conference 1992, p. 100
4. a ) C. Petrier, J. C. de Souza Barbosa, C. Dupuy and J.
TRIFLUORINATED LIQUID CRYSTALS
21
L. Luche, J. Org. Chem., 50, 5761 (1985); b) C.
Petrier, J. L. Luche and C. Dupuy, Tetrahedron Lett., 1984, 3463 5. N. Miyaura and A. Suzuki, J. Chem. SOC. Chem. Commun., 1979. 866 6 . R. B. Miller and S . Dugar, Organometallics, -3, 1261 (1984) 7. S . Sugimori and Y. Goto, DE 3 223 637 A 8. W. H. de Jeu, Physical Properties of Liquid Crystalline Materials (Gordon & Breach, New York 1980), p. 53 9. Textbooks of Physical Chemistry, e. g. R. A. Alberty, Physical Chemistry ( John Wiley & Sons, New York 7th ed. 1987 ) 10. G. Weber, U. Finkenzeller, T. Geelhaar, H. L Plach, B.
Rieger and L. Pohl, Liq. Cryst., 5 , 1381 (1989)
11. E. de Ley, A . de Meyere, B. Maximus, P. Vetter and H . Pauwels, Proc. SPIE-Int. SOC. Opt. Eng., 1845, 391 (1993)