Abstract
A systematic overview of various electric-field induced pattern forming instabilities in nematic liquid crystals is given. Particular emphasis is laid on the characterization of the threshold voltage and the critical wavenumber of the resulting patterns. The standard hydrodynamic description of nematics predicts the occurrence of striped patterns (rolls) in five different wavenumber ranges, which depend on the anisotropies of the dielectric permittivity and of the electrical conductivity as well as on the initial director orientation (planar or homeotropic). Experiments have revealed two additional pattern types which are not captured by the standard model of electroconvection and which still need a theoretical explanation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M.C. Cross and P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
P.G de Gennes and J. Prost, The Physics of Liquid Crystals, Clarendon Press, Oxford, 1993.
S. Chandrasekhar, Liquid Crystals, University Press, Cambridge, 1992.
Physical Properties of Liquid Crystals: Nematics, editors: D.A. Dunmur, A. Fukudaand G.R. Luckhurst, Inspec, London, 2001.
Pattern Formation in Liquid Crystals, editors: A. Buka and L. Kramer, Springer, New York, 1996.
W. Pesch and U. Behn, Electrohydrodynamic Convection in Nematics. In Evolution of Spontaneous Structures in Dissipative Continuous Systems, editors: F.H. Busse and S.C. Müller, pages 335–383, Springer, New York, 1998.
L. Kramer and W. Pesch, Electrohydrodynamics in Nematics. In Physical Properties of Liquid Crystals: Nematics, editors: D.A. Dunmur, A. Fukuda and G.R. Luckhurst, pages 441-454, Inspec, London, 2001.
W. Pesch and L. Kramer, General Mathematical Description of Pattern-Forming Instabilities. In Pattern Formation in Liquid Crystals, editors: A. Buka and L. Kramer, pages 69-90, Springer, New York, 1996.
L.M. Blinov and V.G. Chigrinov, Electrooptic Effects in Liquid Crystal Materials, Springer, New York, 1994.
H. Pleiner and H. Brandt, Hydrodynamics and Electrohydrodynamics of Liquid Crystals. In Pattern Formation in Liquid Crystals, editors: A. Buka and L. Kramer, pages 15–68, Springer, New York, 1996.
M. Born and E. Wolf, Principles of Optics, Pergamon, Oxford, 1996.
S. Rasenat, G. Hartung, B.L. Winkler and I. Rehberg, Exp. Fluids 7, 412 (1989).
S. P. Trainoff and D. Canell, Physics of Fluids 14, 1340 (2002).
N. Éber, S.A. Rozanski, Sz. Németh, Á. Buka, W. Pesch and L. Kramer, Phys. Rev. E 70, 61706 (2004).
E. Bodenschatz, W. Pesch and G. Ahlers, Annu. Rev. Fluid Mech. 32, 709–778 (2000).
L. Kramer and W. Pesch, Electrohydrodynamic Instabilities in Nematic Liquid Crystals. In Pattern Formation in Liquid Crystals, editors: A. Buka and L. Kramer, pages 221–255, Springer, 1996.
E.F. Carr, Mol. Cryst. Liq. Cryst. 7, 253 (1969).
W. Helfrich, J. Chem. Phys. 51, 4092 (1969).
E. Bodenschatz, W. Zimmermann and L. Kramer, J. Phys. (Paris) 49, 1875 (1988).
See equation (6.5) on p. 221 in [16]. Note that there I h=0.97267 has been replaced by one and that α 3/q2-α2 has been approximated by α2.
Numerical codes for the linear analysis of the full standard model can be obtained upon request from the authors.
A. Joets and R. Ribotta, J. Phys. (Paris) 47, 595 (1986).
S. Kai, N. Chizumi and M. Kokuo, Phys. Rev. A 40, 6554 (1989).
M. Dennin, M. Treiber, L. Kramer, G. Ahlers and D. Cannell, Phys. Rev. Lett. 76, 319 (1995).
S. Rasenat, V. Steinberg and I. Rehberg, Phys. Rev. A 42, 5998 (1990).
M. Treiber and L. Kramer, Phys. Rev. E 58, 1973 (1989).
M. Treiber and L. Kramer, Mol. Cryst. Liq. Cryst. 261, 951 (1995).
I. Rehberg, S. Rasenat and V. Steinberg, Phys. Rev. Lett. 62, 756 (1989).
M. Treiber, N. Éber, Á. Buka and L. Kramer, J. Phys. II (Paris), 7, 649 (1997).
Á. Buka, B. Dressel, W. Otowski, K. Camara, T. Tóth-Katona, L. Kramer, J. Lindau, G. Pelzl and W. Pesch, Phys. Rev. E 66, 051713/1–8 (2002).
See equation (6.29) on p.244 in [16], which has been rewritten. The definition of σ¯α in equation .
Á. Buka, B. Dressel, L. Kramer and W. Pesch, Phys. Rev. Lett. 93(4) 044502/1–4 (2004).
Á. Buka, B. Dressel, L. Kramer and W. Pesch, Chaos 14, 793–802 (2004).
L. Kramer, A. Hertrich and W. Pesch, Electrohydrodynamic Convection in Nematics: the Homeotropic Case. In Pattern Formation in Complex, Dissipative Systems, editor: S. Kai, pages 238–246, World Scientific, Singapore (1992).
A. Hertrich, W. Decker, W. Pesch and L. Kramer, Phys. Rev. E 58, 7355 (1998).
A.G. Rossberg, N. Éber, Á. Buka and L. Kramer, Phys. Rev. E 61, R25 (2000).
S. Kai, K. Hayashi and Y. Hidaka, J. Phys. Chem. 100, 19007 (1996).
Y. Hidaka, J.-H. Huh, K. Hayashi, M. Tribelsky and S. Kai, J. Phys. Soc. Jpn. 66, 3329 (1997).
P. Tóth, Á. Buka, J. Peinke and L. Kramer, Phys. Rev. E 58, 1983 (1998).
H. Richter, N. Kloepper, A. Hertrich and Á. Buka, Europhys. Lett. 30, 37 (1995).
H. Richter, Á. Buka and I. Rehberg, Phys. Rev. E 51, 5886 (1995).
P. Tóth, N. Éber, T.M. Bock, Á. Buka and L. Kramer, Europhys. Lett. 57, 824 (2002).
Á. Buka, P. Tóth, N. Éber and L. Kramer, Physics Reports 337, 157 (2000).
B. Dressel and W. Pesch, Phys. Rev. E. 67, 031707 (2003).
B. Dressel, L. Pastur, W. Pesch, E. Plaut and R. Ribotta, Phys. Rev. Lett. 88, 024503 (2002).
S. Kai and K. Hirakawa, Solid State Commun. 18, 1573 (1976).
P. Petrescu and M. Giurgea, Phys. Lett. 59A, 41 (1976).
A.N. Trufanov, M.I. Barnik and L.M. Blinov, A Novel Type of the Electrohydrodynamic Instability in Nematic Liquid Crystals. in Advances in Liquid Crystal Research and Application, editor: L. Bata, pages 549–560, Akadémiai Kiadó - Pergamon Press (1980).
J.-H. Huh, Y. Yusuf, Y. Hidaka, and S. Kai, Mol. Cryst. Liq. Cryst. 410, 39 (2004).
J.-H. Huh, Y. Hidaka, Y. Yusuf, N. Éber, T. Tóth-Katona, Á. Buka and S. Kai, Mol. Cryst. Liq. Cryst. 364, 111 (2001).
J.-H. Huh, Y. Hidaka, A.G. Rossberg and S. Kai, Phys. Rev. E 61, 2769 (2000).
M. Goscianski and L. Léger, J. Phys. (Paris) 36, N.3, C1–231 (1975).
L.M. Blinov, M.I. Barnik, V.T. Lazareva and A.N. Trufanov, J. Phys. (Paris) 40, N.4, C3–263 (1979).
E. Kochowska, S. Németh, G. Pelzl and Á. Buka, Phys. Rev. E 70, 011711 (2004).
N.V. Madhusudana and V.A. Raghunathan, Mol. Cryst. Liq. Cryst. Lett. 5, 201 (1988).
N.V. Madhusudana and V.A. Raghunathan, Liquid Crystals, 5, 1789 (1989).
M.I. Barnik, L.M. Blinov, A.N. Trufanov and B.A. Umanski, J. Phys. (Paris) 39, 417–422 (1978).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Buka, A., Éber, N., Pesch, W., Kramer, L. (2006). CONVECTIVE PATTERNS IN LIQUID CRYSTALS DRIVEN BY ELECTRIC FIELD. In: Golovin, A.A., Nepomnyashchy, A.A. (eds) Advances in Sensing with Security Applications. NATO Science Series II: Mathematics, Physics and Chemistry, vol 218. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4355-4_02
Download citation
DOI: https://doi.org/10.1007/1-4020-4355-4_02
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-4354-3
Online ISBN: 978-1-4020-4355-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)