Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2025-01-05T13:33:34.489Z Has data issue: false hasContentIssue false
  • English
  • Français

Pattern Formation During the Growth of Liquid Crystal Phases

Published online by Cambridge University Press:  29 November 2013

Patrick Oswald ,
John Bechhoefer  and
Francisco Melo
Get access

Extract

Liquid crystals, discovered just a century ago, have wide application to electrooptic displays and thermography. Their physical properties have also made them fascinating materials for more fundamental research.

The name “liquid crystals” is actually a misnomer for what are more properly termed “mesophases,” that is, phases having symmetries intermediate between ordinary solids and liquids. There are three major classes of liquid crystals: nematics, smectics, and columnar mesophases. In nematics, although there is no correlation between positions of the rodlike molecules, the molecules tend to lie parallel along a common axis, labeled by a unit vector (or director) n. Smectics are more ordered. The molecules are also rodlike and are in layers. Different subtypes of smectics (labeled, for historical reasons, smectic A, smectic B,…) have layers that are more or less organized. In the smectic A phase, the layers are fluid and can glide easily over each other. In the smectic B phase, the layers have hexagonal ordering and strong interlayer corrélations. Indeed, the smectic B phase is more a highly anisotropic plastic crystal than it is a liquid crystal. Finally, columnar mesophases are obtained with disklike molecules. These molecules can stack up in columns which are themselves organized in a two-dimensional array. There is no positional correlation between molecules in one column and molecules in the other columns.

Type
Complex Materials
Information
MRS Bulletin , Volume 16 , Issue 1 , January 1991 , pp. 38 - 45
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.de Gennes, P.-G., The Physics of Liquid Crystals (Oxford University Press, 1975). P.E. Cladis, Wim van Saarloos, D.A. Huse, J.S.Patel, J.W. Goodby, P.L. Finn, “Dynamical Test of Phase Transition Order,” Phys. Rev. Lett. 62 (1989) p. 1764. M.A. Anisimov, P.E. Cladis, E.E. Gorodetskii, D.A. Huse, V.E. Podneks, V.G. Taratuta, W. van Saarloos, V.P. Voronov, “Experimental Test of Fluctuation induced First-order Phase Transition: the Nematic-smectic A Transition, Phys. Rev. A 41 (1990) p. 6749.Google Scholar
2.Kléman, M., Points. Lignes. Parois. Tome I and II (Les Editions de Physique, 1977).Google Scholar
3.Oswald, P., “Quelques Aspects de la Plasticif des Smectiques” in Systèmes à Mémoire: une approche multidisciplinaire, edited by Delacour, J. and Lévy, J.-C.S. (Masson, 1989). G. Durand, “Plastic Behavior and Polymorphism of Smectic Liquid Crystal”, J. Chim. Phys. 80 (1983) p. 119.Google Scholar
4.Joets, A., Ribotta, R., in Partially Integrable Nonlinear Evolution Equations, edited by Conte, R.et al. (Kluwer Academie Publishers, Dordrecht, 1990) p. 279. G. Goren, I. Procaccia, S. Rasenat, V. Steinberg, “Interactions and Dynamïcs of Topological Defects: Theory and Experiments near the Onset of Weak Turbulence,” Phys. Rev. Lett. 63 (1989) p. 1237. J.M. Dreyfus, E. Guyon, “Convective Instabilities in Nematics Caused by an Elliptical Shear, J. Physique France 42 (1981) p. 283. E. Guazzelli, E. Guyon, J.E. Wesfreid, “Dislocations in a Roll Hydrodynamic Instability in Nematics: Static Limit,” Phil. Mag. A 48 (1983) p. 709.Google Scholar
5.Srajer, G., Fraden, S., Meyer, R.B., “Field-induced Nonequilibrium Periodic Structures in Nematic Liquid Crystals: Nonlinear Study of the Twist Frederiks Transition,” Phys. Rev. A 39 (1989) p. 4828. D.W. Allender, B.J. Frisken, P. Palffy-Muhoray, “Theory of an Electric Field Induced Periodic Phase in a Nematic Film,” Liq. Cryst. 5 (1989) p. 735.CrossRefGoogle ScholarPubMed
6.Oswald, P., Bechhoefer, J., Libchaber, A., Lequeux, F., “Pattern Formation behind a Moving Cholesteric Smectic-A Interface, Phys. Rev. A 36 (1987) p. 5832. F. Lequeux, P. Oswald, J. Bechhoefer, “Influence of Anisotropic Elasticity in a Cholesteric Liquid Crystal Contained between Two Plates,” Phys. Rev. A 40 (1989) p. 3974. P. Ribiere, P. Oswald, “Nucleation and Growth of Cholesteric Fingers under Electric Field,” J. Physique France 51 (1990) p. 1703.CrossRefGoogle ScholarPubMed
7.Horvath, V.K., Kertesz, J., Vicsek, T., “Viscous Fingering in Smectic Liquid Crystal,” Eur. Phys. Lett. 4 (1987) p. 1133. A. Buka, P. Palffy-Muhoray, Z. Racz, “Viscous Fingering in Liquid Crystals,” Phys. Rev. A 36 (1987) p. 3984. L. Lam, H.C. Morris, R.F. Shaos, S.L. Yang, Z.C. Liang, S. Zheng, H. Liu, “Dynamics of Viscous Fingers in Hele-Shaw Cells of Liquid Crystals: Theory and Experiment,” Liq. Cryst. 5 (1989) p. 1813.CrossRefGoogle Scholar
8.Mullins, W.W., Sekerka, R.F., “Stability of Planar Interface during Solidification of a Dilute Binary Alloy,” J. App. Phys. 35 (1964) p. 444. In exceptionally pure materials, the instability can also be caused by the release of latent heat at the interface.CrossRefGoogle Scholar
9.Langer, J.S., “Instabilities and Pattern Formation in Crystal Growth,” Rev. Mod. Phys. 52 (1980) p. 1.CrossRefGoogle Scholar
10.Wollkind, D.J., Segel, L.A., “A Nonlinear Stability Analysis of the Freezing of a Dilute Binary Alloy,” Phil. Trans. Roy. Soc. London 268 (1970) p. 351. B. Carol, C. Caroli, B. Roulet, “On the Emergence of One-dimensional Front Instabilities in Directional Solidification and Fusion of Binary Mixture,” J. Physique France 43 (1982) p. 1767.Google Scholar
11.Dynamics of Curved Fronts, edited by Pelcé, P. (Academie Press, 1988).Google Scholar
12.Oswald, P., Bechhoefer, J., and Libchaber, A., “Instabilities of a Moving Nematic-isotropic Interface, Phys. Rev. Lett. 58 (1987) p. 2318.CrossRefGoogle Scholar
13.Bechhoefer, J., Simon, A., Libchaber, A., and Oswald, P., “Directional Solidification of Liquid Crystals,” in Random Fluctuations and Pattern Growth: Experiments and Models, edited by Stanley, H.E. and Ostrowsky, N. (Kluwer Académie Publishers, Dordrecht, 1988) p. 93.CrossRefGoogle Scholar
14.Bechhoefer, J., Simon, A., Libchaber, A., and Oswald, P., “Destabilization of a Flat Nematic Interface,” Phys. Rev. A 40 (1989) p. 2042.CrossRefGoogle Scholar
15.Simon, A., Bechhoefer, J., and Libchaber, A., “Solitons and the Eckhaus Instability in Directional Solidification,” Phys. Rev. Lett. 61 (1988) p. 2574.CrossRefGoogle Scholar
16.Simon, A. and Libchaber, A., “Moving Interface: the Stability Tongue and Phenomena Within,” Phys. Rev. A 41 (1990) p. 7090.CrossRefGoogle Scholar
17.Coullet, P., Iooss, G., “Instabilities of One-dimensional Cellular Patterns,” Phys. Rev. Lett. 64 (1990) p. 866.CrossRefGoogle ScholarPubMed
18.Coullet, P., Goldstein, R.E., and Gunaratne, G.H., “Parity-breaking Bifurcations of Modulated Patterns in Hydrodynamic Systems,” Phys. Rev. Lett. 63 (1989) p. 1954.CrossRefGoogle Scholar
19.Rabaud, M., Michalland, S., and Couder, Y., “Dynamical Régimes of Directional Viscous Fingering: Spatiotemporal Chaos and Wave Propagation, Phys. Rev. Lett. 64 (1990) p. 184. G. Faivre, S. de Cheveigne, C. Guthmann, and P. Kurowsi, “Solitary Tilt Waves in Thin Lamellar Eutectics,” Europhys. Lett. 9 (1989) p. 779. K. Kassner and C. Misbah, “Parity Breaking in Eutectic Growth,” Phys. Rev. Lett. 65 (1990) p. 1458.CrossRefGoogle ScholarPubMed
20.Shangguan, D.K. and Hunt, J.D., “Dynamical Study of the Pattern Formation of Faceted Cells,” J. Cryst. Growth 96 (1989) p. 856.CrossRefGoogle Scholar
21.Oswald, P. and Melo, F., “Smectic-A Smectic-B Interface: Faceting and Surface Free Energy Measurement,” J. Physique 50 (1989) p. 3527.CrossRefGoogle Scholar
22.Nozières, P., “Shape and Growth of Crystals,” Lectures given at the Beg Rohu Summer School, 1989.Google Scholar
23.Herring, C., “Some Theorems on the Energies of Crystal Surfaces,” Phys. Rev. 82 (1951) p. 87.CrossRefGoogle Scholar
24.Melo, F. and Oswald, P., “Expérimental Evidence of the Herring Instability at the Smectic-A Smectic-B Interface,” to appear in Annales de Chimie.Google Scholar
25.Bechhoefer, J., Oswald, P., Libchaber, A., and Germain, C., “Observation of Cellular and Dendritic Growth of Smectic-A Smectic-B Interface, Phys. Rev. A 37 (1988) p. 1691.CrossRefGoogle ScholarPubMed
26.Melo, F. and Oswald, P., “Destabilizarion of a Faceted Smectic-A Smectic-B Interface,” Phys. Rev. Lett. 64 (1990) p. 1381.CrossRefGoogle ScholarPubMed
27.Melo, F. and Oswald, P., “Facet Destabilisation and Macrostep Dynamics at the Smectic-A Smectic-B Interface,” to be published in J. Physique France (March 1991).CrossRefGoogle Scholar
28.Bowley, R., Caroli, B., Caroli, C., Graner, F., and Nozières, P., Roulet, B., “On Directional Growth of a Faceted Crystal,” J. Physique France 50 (1989) p. 1377. B. Caroli, C. Caroli, and B. Roulet, “Directional Solidification of Faceted Crystal II. Phase Dynamics of Crenellated Front Patterns,” J. Physique France 50 (1989) p. 3075.CrossRefGoogle Scholar
29.Oswald, P., “Morphological Stability of a Circular Germ in a Discotic Liquid Crystal,” J. Physique 49 (1988) p. 1083.CrossRefGoogle Scholar
30.Oswald, P., “Croissance d'une Phase Discotique,” J. Physique 50 C3 (1989) p. 127.Google Scholar
31.Oswald, P., Malthête, J., and Pelcé, P., “Free Growth of Thermotropic Columnar Mesophase: Supersaturation Effect,” J. Physique 50 (1989) p. 2121.CrossRefGoogle Scholar
32.Brush, L.N., Sekerka, R.F., “A Numerical Study of Two-dimensional Crystal Growth Forms in the Presence of Anisotropic Growth Kinetics,” J. Cryst. Growth 96 (1989) p. 419.CrossRefGoogle Scholar
33.Langer, J.S., “Lectures in the theory of Pattern Formation” in Chance and Matter (Les Houches 1986), edited by Souletie, J., Vannimenus, J., Stora, R. (North Holland, 1987). D.A. Kessler, J. Koplik, and H. Levine, “Pattern Selection in Fingered Growth Phenomena,” Adv. Phys. 37 (1988) p. 255.Google Scholar
34.Oswald, P., “Dendritic Growth of a Discotic Liquid Crystal,” J. Physique 49 (1988) p. 1083.CrossRefGoogle Scholar
35.Amar, M. Ben, private communication.Google Scholar
36.Deutscher, G., “Introduction to Dense Branching Morphology,” in Random Fluctuations and Pattern Groioth: Experiments and Models, edited by Stanley, H.E. and Ostrowsky, N. (Kluwer Académie Publishers, Dordrecht, 1988) p. 117. Y. Couder, “Viscous Fingering in Circular Geometry,” in Random Fluctuations and Pattern Groioth: Experiments and Models, edited by H.E. Stanley and N. Ostrowsky (Kluwer Academie Publishers, Dordrecht, 1988), p. 75.CrossRefGoogle Scholar
37.Grier, D., Ben-Jacob, E., Clarke, R., and Sander, L.M., “Morphology and Microstructure in Electrochemical Deposition of Zinc, Phys. Rev. Lett. 56 (1986) p. 1264. Y. Sawada, A. Dougherty, and J.P. Gollub, “Dendritic Patterns in Electrolytic Métal Deposits,” Phys. Rev. Lett. 56 (1986) p. 1260.CrossRefGoogle ScholarPubMed
38.Brener, E.A., Gellikman, M.B., and Temkin, D.E., “Growth of a Needle-Shaped Crystal in a Channel,” Sov. Phys. JETP 67 (1988) p. 1002.Google Scholar