Pattern Formation During the Growth of Liquid Crystal Phases
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Figure 1. Nematic-isotropic interface photographed via phase contrast microscopy. The nematic is ai the bottom and the isotropic liquid is at the top. The température gradient is G = 43 Klcm and the thickness is à = 28tx.ni. (a) V = 2.5 fimls; (b) V = 2.7 n-mls; (c)V = 3 ixm/s; (d) V = 4 fimls; (e) V = 5 urn/s; (f) V = 6 fim/s; (g) V = 12 ixm/s; (h) V = 14 fimls.
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Introduction Liquid crystals, discovered just a century ago, hâve wide application to electrooptic displays and thermography. Their physical properties hâve 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:1 nematics, smectics, and columnar mesophases. In nematics, although there is no corrélation between positions of the rodlike molécules, the molécules tend to lie parallel along a common axis, labeled by a unit vector (or director) n. Smectics are more ordered. The molécules are also rodlike and are in layers. Différent subtypes of smectics (labeled, for historical reasons, smectic A, smectic B,...) hâve 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 hâve 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 molécules. Thèse molécules can stack up in columns which are themselves organized in a two-dimensional array. There is no positional corrélation between molécules in one column and molécules in the other columns.
Liquid crystals hâve been very useful in the study of phase transitions,1 physics of defects,2 rheology, plasticity, and pattern formation in nonlinear physics. This last topic includes studies of convection4 and Frederiks transitions in nematics,5 frustration in cholesterics,6 Saffman-Taylor fingering,7 and moving interfaces separating a liquid crystalline phase from another phase of the same material. This article reviews some récent experiments on the growth of liquid crystal phases that focus on front morphology. One finds that interfaces can be planar, curved, "cellular" (i.e., periodic), or even chaotic and nonstationary, depending on growth velocity and other control parameters. Two expérimental techniques hâve been used to study the dynamics of interfaces. In the first, one works at a température that is constant and below the solidification point (free growth). The nucleation and growth of germs are observed via optical microscopy. Hère, the control parameter is the undercooling. In the second technique, the sample is placed in a température gradient, in a so-called "directional solidification" apparatus. The sample straddles the space between two ovens held at différent températures and is pushed at constant velocit
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