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FREEDERICKSZ TRANSITION IN PRETILTED NEMATIC CELLS IN THE MAGNETIC FIELD
NORMAL TO THE DIRECTOR
H. Onnagawa, M. Kuwahara, K. Miyashita
To cite this version:
H. Onnagawa, M. Kuwahara, K. Miyashita. FREEDERICKSZ TRANSITION IN PRETILTED NE- MATIC CELLS IN THE MAGNETIC FIELD NORMAL TO THE DIRECTOR. Journal de Physique Colloques, 1979, 40 (C3), pp.C3-519-C3-524. �10.1051/jphyscol:19793104�. �jpa-00218705�
FREEDERICKSZ TRANSITION IN PRETILTED NEMATIC CELLS IN THE MAGNETIC FIELD NORMAL TO THE DIRECTOR
H. ONNAGAWA, M. KUWAHARA and K. MIYASHITA
Department of Electronic Engineering, Toyama University, Takaoka, Toyama 933, Japan
Abstract. — Threshold phenomenon of molecular orientational deformation is presented for pretilted nematic cells in magnetic field. The direction of the magnetic field is normal to the director of nematic molecules in the plane containing both the director and the line normal to the cell sur- faces. Experimental result of capacitance vs. magnetic field strength characteristic curves are analyzed on the base of continuum theory and related to two types of molecular orientation patterns. The experimental results are in good agreement with the theoretical curves based on the assumption of rigid boundary coupling.
1. Introduction. — Molecular orientational defor- mation of nematic liquid crystal by external magnetic field has widely been studied experimentally as well as theoretically [1], [2], [3]. Rapini and Papoular [4]
treated theoretically the case of tilt alignment in the magnetic field parallel to cell surfaces. Recently, from the viewpoint of display characteristics of liquid crystal devices, large numbers of efforts have been done and some of them have succeeded to control the tilt angle of nematic molecules to cell surfaces in the absence of external field [5], [6], [7], [8], [9], [10].
However, threshold phenomenon of pretilted nematic cells has not yet been studied so satisfactorily, though some papers have discussed the effective value of threshold field strength for pretilted nematic cells in external magnetic or electric field which is parallel or perpendicular to cell surfaces and is not normal to the director [4], [10].
This paper reports on theoretical and experimental results of molecular orientational deformation in the magnetic field which is in the plane containing both the director of nematic molecules and the line normal to the cell surfaces. In section 2, molecular orienta- tional deformation in the magnetic field normal to the director is treated theoretically, and is predicted that two types of orientational deformations may occur.
The typical curves of capacitance TO magnetic field strength characteristics are calculated for each type
of deformation. Experimental procedure is written in section 3. Experimental results of capacitance vs magnetic field strength and observations of transmitted light patterns of the cells in the magnetic field through crossed polarizers. These experimental results are compared with the theoretical results based on the continuum theory on the assumption of rigid boundary coupling in section 4.
2. Theoretical. — The generalized case in which both the directions of molecular orientation and magnetic field are arbitrary in a plane T has already been discussed [11]. This section is devoted mainly to discuss the threshold phenomenon and related matters for uniformly pretilted nematic cell in the magnetic field normal to the director. Figure 1 shows the relation between the molecular orientation angle cpM in the midplane and the magnetic field strength H, where <p0 is the pretilt angle of nematic molecules and 6 is the angle of the magnetic field to the line normal to cell surface (*). Two types of orientational defor- mation patterns may exist at 60 = <pa + n/2, and corresponding threshold magnetic field strengths are not equal if two elastic constants for splay K11
and bend K33 are not equal. Curves I and II in figure 1 (*) Figure 3 in ref. [11] by the authors should be replaced by figure 1 in this paper.
JOURNAL DE PHYSIQUE Colloque C3, supplément au n° 4, Tome 40, Avril 1979, page C3-519
Résumé. — Nous présentons des seuils de déformation d'orientation moléculaire pour des cellules contenant des nématiques préinclinés, placées dans un champ magnétique. La direction du champ magnétique est normale à l'orientation du directeur, dans le plan contenant à la fois le directeur et la normale aux lames définissant la cellule.
Nous analysons nos résultats caractéristiques, de capacité fonction du champ magnétique, sur la base de la théorie continue, en relation avec deux types d'orientation moléculaire. Les résultats expérimentaux sont en bon accord avec les courbes théoriques calculées d'après l'hypothèse d'un ancrage rigide aux parois.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19793104
C3-520 H. ONNAGAWA. M. KUWAHARA AND K. MIYASHITA
HIHc
FIG. 1. - Calculated cp, vs H/H, relation at 6, = cp,
+
n/2.Free energy of pretilted nematic cell takes a maximum vaIue with respect to cp, at a given value of H/H, on the broken lines. Dotted lines show minor discontinuous change of molecular alignment.
Curves I and I1 are associated with two types of orientational deformations.
correspond to the molecular orientation patterns I and I1 in figure 2a, respectively. The threshold field for each case is defined as H,,, and H,,, as shown in figure 26, and Hc is the threshold field for homeotropic alignment. The value of Hthl/Hc is given as the mini- mum value of the following equation with respect to (0, :
(PM
HIHC = (214 .Jwo F(cp) dip 2 (1)
FIG. 2. -a) Two types of molecular orientational deformation patterns I and I1 correspond to I and I1 in figure 1. b) Definition of threshold fields H,,, and H,,, for K , , / K 3 , . c) H,,,/H,,, vs cp, for
K l 1 / K , , = 1 and 0.7.
where
ppp
The value of Hth,/Hc is the extreme of eq. (1) when cp, approaches to cp, and is written as follows :
Figure 2c shows Hth,/Hth, vs cp, for Kll/K3, = 1 and 0.7. The value of (Hi,, - Hthl)/Hth, is maximum at cp, = 450, however, less than 1
%
for K, ,/K,, = 0.7.Capacitance vs magnetic field strength is written as follows :
where
and and E, in eq. (4) are the dielectric constants parallel and perpendicular to the optic axis of pretilted cell, respectively [ll]. In eq. (3), the magnetic field H is related to cp, by eq. (1). Calculated C vs H curves are shown in figure 3.
FIG. 3. - C vs H relations.
FREEDERICKSZ TRANSITION IN PRETILTED NEMATIC CELLS C3-521
3. Experimental. - Experimental techniques were similar to those reported earlier [ll]. Uniform tilt alignment of high tilt angle (near parallel) has been obtained by oblique evaporation of SiO [5], and low tilt (near homeotropic) alignment has been obtained by coating cell surfaces first with N,N-dimethyl-N- octadecyl
-
3-
aminopropyltrimethoxysilyl chloride (DMOAP) [12] on which SiO has been deposited obliquely. The nematic material used is p-methoxy-.92b ' I I I I I
1 2 3 4 5 6 7 0 9 1 0
H (kOe)
FIG. 4. - Experimental results of C w H relations for 0, and some angles close to 0,. The vertical axis is normalized by the capacitance
at H = 0. a ) rp, = 220, b) rp, = 66.30.
benzylidene-p-n-butylaniline (MBBA) and the conduc- tivity is about 1 x 10-I (Q cm)-
'
parallel to the optic axis at 25 O C . All the cells used in this experiment are optically uniaxial and domain free in the absence of external field. Pretilted cells have been placed in the magnetic field so that the field direction is parallel tor.
4. Experimental results and discussion. - The C vs H characteristics are shown for two cells in figure 4. The pretilt angle of the cells in the figures a and b are 220 and 66.3O, respectively. Each cell shows threshold phenomenon at 8,. The experimental results at angles near O,, however, do not follow the same curves when the field strength is decreased, and the discrepancy is obvious between the experimental results and the theoretical curves based on the conti- nuum theory particularly at 8, as shown in figure 5.
FIG. 5. - Comparison between theoretical and experimental results of C vs H curves for the cell of figure 4a. Solid lines are
theoretical results.
In this calculation, orientational deformation for the curve of 8, is assumed to be the type I in figure 2a.
Figure 6 shows the optical observation of the cell of figure 4a in the magnetic field near 0, through crossed polarizers. In this experiment, the magnetic field is increased from zero to 8 kCX: at each angle 8. It appears that two types of domains coexist near the angle of 8,.
Furthermore, the areal ratio of two types of domains varies as H is decreased as seen in figure 7. This is the reason why C v s H curves at angles near 8, do not follow the same curve when H is decreased. From comparison between the theoretical and experimental
C3-522 H. ONNAGAWA, M. KUWAHARA AND K. MIYASHITA
FIG. 6. - Transmitted light patterns through crossed polarizers for a pretilted nematic cell in the magnetic field in the plane T. Two types of domains coexist near the angles of 6, (cp, = 120, H = 8 kOe).
results, the light and dark regions in figures 6 and 7 correspond to the molecular orientation pattern of I and I1 in figure 2a, respectively. The range of magnetic field direction where two types of orientation coexist is shown for nine cells in table I.
TABLE I
The angle of magnetic Jield where two of molecular orientation patterns coexist.
Cell No.
-
<
cp, )- A6
(*I
-
1 10 - 50 < < 50
2 00 - 20 < < 20
3 17O -1.80< <1.80
4 11.70 -0.30< ~ 0 . 3 0
and curves c and d have been obtained under the condition of the fixed direction of the field at 8,.
These results a
-
d have been measured for the cell of figure 4b. Solid lines are the results of numerical analysis on the assumption of rigid boundary coupling.The experimental results a and b are in good agreement with the theoretical results. Agreement between the theory and the experiment, however, is not so good for the region near the threshold field of curve a, because of the occurrence of counter type of orien- tational deformation associated with the local varia- tion of cp, which has hardly been recognized optically.
In the case of parallel or homeotropically aligned cells, C vs H curves are well in quantitative agreement
5 - 9 00 - 0.30 < < 0.30
(*) A 0 = 0 - (cp, C 90°).
Either one of these two orientations can be sup-
pressed as follows. At first, magnetic field must be
-
/ .\strengthened at 8 = 8,
+ P,
whereI p I
> 5O. ThenP
may be reduced to zero, while holding the strong magnetic field. If
P
< 0, the type I occurs as shown infigure 8a. If
p
> 0, however, the type I1 will result (a) I13 (bl[IIJ
(Fig. 8b). The characteristic curves a and b of figure 9 FIG, 8. -The method for the appearance of only one type of
have been obtained with the method above mentioned, orientational deformation at 8,.
FREEDERICKSZ TRANSITION IN PRETILTED NEMATIC CELLS C3-523
FIG. 7. - The areal ratlo of two types of domains vanes as the magnetic field strength IS decreased at 0, (cp, = 1 2 O , 0 = 102" 10 mm cp).
FIG. 9. - Experimental and theoretical results of C vs. H relation at 0, for the cell of figure 4b. Curves a and b have been obtained with the method shown in figure 8, and curves c and d have been obtained under the condition of fixed direction of magnetic field at 6,. Solid
lines are theoretical results.
FIG. 10. - C I T H curves at 0, near the threshold fieid for /3 < 0 (I) and /3 > 0 (11).
C3-524 H. ONNAGAWA, M. KUWAHARA AND K. MlYASHlTA
with experimental results in spite of coexistence of reverse tilt domains. The reason is that there is no difference between C vs H curves for two types of orientation patterns of these cells. Figure 10 shows C vs H curves for
p
< 0 andp
> 0 in the region near threshold. No significant difference can be obtained between H,,, and H,,, within experimental accuracy.5. Conclusion. - It has been clarified that two types of molecular orientational deformations result if magnetic field is applied normal to the director of nematic molecules of uniaxially pretilted cell in the plane containing both the director and the line normal
to the cell surfaces. Theoretically, threshold field strength for each type of deformation are not equal if the elastic constants for splay and bend are not equal. However, the difference for MBBA which has the value of K l l / K , ,
-
0.7 at 25 OC [13], is estimated to be less than I%
of the threshold field strength, therefore, it is reasonable that the difference has not been detected experimentally.Acknowledgment. - The authors wish to thank Dr. M. Wada and Dr. T. Uchida for their helpful discussion and encouragement.
References
[I] RAPINI, A,, PAPOULAR, M. and PINCUS, P., C. R. Hebd. Sean.
Acad. Sci. 267B (1968) 1230.
[2] GRULER, H., SCHEFFER, T. J. and MEIER, G., Z. Naturforsch.
27a (1972) 966.
[3] TSUCHIYA, H. and NAKAMURA, K., Mol. Cryst. Liquid Cryst.
29 (1974) 89.
[4] RAPINI, A. and PAPOULAR, M., J. Physique Colloq. 30 (1969) C4-54.
[5] JANNING, J. L., Appl. Phys. Lett. 21 (1972) 173.
[6] URBACH, W., BOIX, M. and GWON, E., Appl. Phys. Lett. 25 (1974) 479.
[7] MEYERHOFER, D., Appl. Phys. Lett. 29 (1976) 691.
[8] GOODMAN, L. A., MCGINN, J. T., ANDERSON, C. H. and DIGERONIMO, F., Proc. S.I.D. 18 (1977) 11.
[9] CAABICOVSKY, R. and KOCMANN, G., Proc. S.I.D. 18 (1977) 23.
[lo] GUYON, E. and URBACH, W., .Nonemissive Electrooptic Dis- plays, eds. Kmetz, A. R. and Willisen, F. K. (Plenum, New York) 1975, p. 121.
[ l l ] ONNAGAWA, H. and MIYASHITA, IS., Japan. J . Appl. Phys.
13 (1974) 1741.
[I21 KAHN, F. J., TAYLOR, G. N. and SCHONHORN, H., Proc.
ZEEE 61 (1973) 823.
[13] HALLER, I., J. Chem. Phys. 57 (1972) 1400.