Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-08T05:28:38.808Z Has data issue: false hasContentIssue false
  • English
  • Français

Pattern Formation in Electrohydrodynamic Convection

Published online by Cambridge University Press:  29 November 2013

Walter Zimmermann
Get access

Extract

One hundred years after their discovery, we meet liquid crystals everywhere in our daily life. Their most widely known application is the liquid crystal displays (LCDs) in watches, pocket calculators, or gasoline pumps. Applications aside, liquid crystals show many exciting properties, making them highly interesting for fundamental research. For example, electrohydrodynamic convection (EHC) in nematic liquid crystals, which is studied in cells of a configuration similar to liquid crystal displays, serves with its characteristic properties as a model System for investigating central questions of pattern formation and chaos.

Today's liquid crystal displays work on the principle described in 1971 by Martin Schadt and Wolfgang Helfrich (Figure 1). In nematic liquid crystals, organic molecules orient on average along a macroscopic direction, described by the director field n(r), that has neither head nor tail (n = −n). Nematics are therefore anisotropic and for energetic reasons, n(r) orients parallel (perpendicular) to an electric field when the dielectric permittivity (ε∥) along n is larger (smaller) than the perpendicular (ε⊦ one. For positive εa = ε∥ − ε⊦, when an electric field is applied perpendicular to the direction of n, a reorientation of n takes place together with a corresponding change in the optical property of the cell. The controlled change by an electric field in the optic axis (orientation) in well-defined areas of the display then allows the representation of numbers, etc.

Type
Complex Materials
Information
MRS Bulletin , Volume 16 , Issue 1 , January 1991 , pp. 46 - 56
Copyright
Copyright © Materials Research Society 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Kelker, H. and Hatz, R., Handbook of Liquid Crystals (Verlag Chemie, Weinheim 1980); E. Kaneko, Liquid Crystal TV Displays: Principle and Applications of Liquid Crystal Displays (KTK Scientific Publishers, Tokyo, 1987).Google Scholar
2.Blinov, L.M., Electro-Optical and Magneto-Optical Properties of Liquid Crystals (Wiley, New York).Google Scholar
3.Velarde, M.G. and Normand, C., Scientific American 243 (1980) p. 92; H.L. Swinney and J.P. Gollub, Hydrodynamic Instabilities and the Transition to Turbulence (Springer, Berlin, 1981).Google Scholar
4.Rasenat, S., Hartung, G., Winkler, B.L., and Rehberg, I., Experiments in Fluids 7 (1989) p. 412.CrossRefGoogle Scholar
5.Joets, A., Ribotta, R. in Cellular Structures in Instabilities, Lecture Notes in Physics, Vol. 210, edited by Wesfreid, J.E. and Zaleski, S. (Springer, 1984) p. 294; A. Joets and R. Ribotta, J. de Physique 47 (1986) p. 595.CrossRefGoogle Scholar
6.Juárez, W. de la Torre and Rehberg, I., Phys. Rev. A42 (1990) p. 2096.CrossRefGoogle Scholar
7.Zimmermann, W. and Kramer, L., Phys. Rev. Lett. 55 (1985) p. 402.CrossRefGoogle Scholar
8.Bodenschatz, E., Zimmermann, W., and Kramer, L., J. de Physique 49 (1988) p. 1875.CrossRefGoogle Scholar
9.Bodenschatz, E., Kaiser, M., Kramer, L., Pesch, W., Weber, A., and Zimmermann, W., in New Trends in Nonlinear Dynamics, edited by Coullet, P. and Huerre, P., NATO ASI Series, Plenum Press (1990).Google Scholar
10.Peach, M. and Koehler, J.S., Phys. Rev. 80 (1950) p. 436 (Letter).CrossRefGoogle Scholar
11.Yamazaki, H., Kai, S., and Hirakawa, K., J. Phys. Soc. Jpn. 56 (1987) p. 1.CrossRefGoogle Scholar
12.Bodenschatz, E., Pesch, W., and Kramer, L., Physica D 27 (1987) p. 249.Google Scholar
13.Goren, G., Procaccia, I., Rasenat, S., and Steinberg, V., Phys. Rev. Lett. 63 (1989) p. 1237; S. Rasenat, V. Steinberg, and I. Rehberg (to be published in Phys. Rev. A).CrossRefGoogle Scholar
14.Kramer, L., Bodenschatz, E., and Pesch, W., Phys. Rev. Lett. 64 (1990) p. 2588.CrossRefGoogle Scholar
15.Kai, S. and Zimmermann, W., Prog. Theor. Phys. 99 (1990) p. 458.CrossRefGoogle Scholar
16.Nasuno, N. and Kai, S. (submitted to Euro-phys. Lett., 1990).Google Scholar
17.Rasenat, S., Braun, E., and Steinberg, V. (submitted for publication).Google Scholar
18.Kaiser, M., Pesch, W., and Bodenschatz, E., to be published in Physica D, 1990.Google Scholar
19.Hirakawa, K. and Kai, S., Mol. Cryst. Liq. Cryst. 40 (1977) p. 261.CrossRefGoogle Scholar
20.Kai, S., Zimmermann, W., Andoh, M., and Chizumi, N., Phys. Rev. Lett. 64 (1990) p. 1111; S. Kai, W. Zimmermann, and M. Andoh, Modern Physics Lett. B 4 (1990) p. 767 (brief review).CrossRefGoogle Scholar
21.Kai, S., Chizumi, N., and Kohno, M., Phys. Rev. 40 (1989) p. 6554.CrossRefGoogle Scholar
22.Lowe, M., Gollub, J., and Lubensky, T.C., Phys. Rev. Lett. 51 (1983) p. 786; M. Lowe and J.P. Gollub, Phys. Rev. (1985) p. 3893; Phys. Rev. Lett. 55 (1985) p. 2575.CrossRefGoogle Scholar
23.Zimmermann, W.et al. (submitted for publication).Google Scholar
24.Joets, A. and Ribotta, R., Phys. Rev. Lett. 60 (1989) p. 2164.CrossRefGoogle Scholar
25.Rehberg, I., Rasenat, S., and Steinberg, V., Phys. Rev. Lett. 62 (1989) p. 756.CrossRefGoogle Scholar
26.Riecke, H., Crawford, J.C., and Knobloch, E., Phys. Rev. Lett. 61 (1988) p. 1942; D. Walgraef, Europhys. Lett. 7 (1988) p. 485.CrossRefGoogle Scholar
27.Rehberg, I., Rasenat, S., Fineberg, J., Juárez, M. de la Torre, Steinberg, V., Phys. Rev. Lett. 61 (1988) p. 2449.CrossRefGoogle Scholar
28.Brand, H.R., Kai, S., and Wakabayashi, S., Phys. Rev. Lett. 54 (1985) p. 555.CrossRefGoogle Scholar
29.Dubois-Violette, Elisabeth, CRAS B273 (1971) p. 923.Google Scholar