Defects nematic droplets

J. Dzubiella, M. Schmidt, H. Lowen. Microstructure of topological defects in nematic droplets (submitted). 

Texture with two point defects at the poles of a nematic droplet. 

Texture with one point defect at the center of a nematic droplet. 

Polymer-dispersed liquid crystals (PDLC) [7] are materials that consist of microscopic nematic droplets, with typical radii from a few hundred Angstrom to more than a micron, embedded in a polymer matrix (see Fig. 1). These systems are interesting both for technical applications and for an understanding of the behavior of mesophases in a confined environment. PDLC droplets also represent practical realizations of systems exhibiting topological defects of interest in many fields... 

Identification of the nematic mesophase through polarized light microscopy is easier than that of the smectic mesophase, because specific defects take a linear form. The nematic mesophase is characterized by a large number of textures Schilieren texture is one of the most common nematic textures with defect centers with two arms, nematic droplets often occur from the isotropic liquid in the form of drops, string texture consists of a disclination type - line and appears as thin lines, and marble texture consists of several zones with different orientations of the director, inducing different color interferences [5]. 

Twist relaxation of splay and bend is a general phenomenon in materials with small K2. Chiral structures can occur in defective nematic samples even when there is no azimuthal anchoring at all. Twisted brushes observed by Press and Arrott in textures of lens-shaped nematic droplets floating on the water surface are one example [15]. Another well-known illustration of twist relaxation is the periodic pattern of stripes that occur in the geometry of splay Frederiks transition in polymer nematics with a small (less than 0.33) ratio K2/K [16]. A field applied normally to the planar nematic cell causes stripe structures composed mostly of twist rather than the uniform splay response observed in regular materials. 

An especially clear demonstration of twist relaxation is given by tangentially anchored spherical nematic droplets suspended in an isotropic matrix (glycerin). Figure 5.3. The director lines join two point defects—boojums at... 

For a sphere, E = 2-, thus the two point defects at the poles of the nematic droplets in Figure 5.3 illustrate the Poincare theorem it does not matter if the interior structure is twisted or not. 

Cholesteric rodlets and spherulites having parallel layers can be devoid of inner defects, but this does not prevent their growth. However, surface points or surface lines are present. Some -n disclinations, resulting from germ coalescence, are frequent, but disappear by confluence with the isotropic interface, as for nematic droplets. 

Points defects are another class of defects in nematic LCs. They occur in droplets and can be also seen in thin capillaries (Fig. 5). The total energy stored in the elastic field around a point defect grows linearly with the radius, R, of the volume enclosed ... 

Textures correspond to various arrangements of defects. When the isotropic liquid is cooled, the nematic phase may appear at the deisotropization point in the form of separate small, round objects called droplets (Fig. 12). These can show extinction crosses, spiral structures, bipolar arrangements, or some other topology depending on boundary conditions. Theoretical studies based on a simple model confirm the stability of radial or bipolar orientation (Fig. 5) [22]. Considerations based on improved theoretical models yield stable twisted... 

When L/p I, the cholesteric does not differ much from the nematic phase. No wonder therefore that optical observations for weakly twisted cholesterics reveal thick (nonsingular) and thin (singular) line defects —disclinations similar to that in the nematic phase. Moreover, in droplets of the so-called compensated cholesteric mixtures with extremely small Ljp one can observe point defects [6] which, from the topological point of view, are allowed only in a nematic phase. 

The distribution of defects in mesophases is often regular, owing to their fluidity, and this introduces pattern repeats. For instance, square polygonal fields are frequent in smectics and cholesteric liquids. Such repeats occur on different scales - at the level of structural units or even at the molecular level. Several types of amphiphilic mesophase can be considered as made of defects . In many examples the defect enters the architecture of a unit cell in a three-dimensional array and the mesophase forms a crystal of defects [119]. Such a situation is found in certain cubic phases in water-lipid systems [120] and in blue phases [121] (see Chap. XII of Vol. 2 of this Handbook). Several blue phases have been modeled as being cubic centred lattices of disclinations in a cholesteric matrix . Mobius disclinations are assumed to join in groups of 4x4 or 8x8, but in nematics or in large-pitch cholesterics such junctions between thin threads are unstable and correspond to brief steps in recombinations. An isotropic droplet or a Ginsburg decrease to zero of the order parameter probably stabilizes these junctions in blue phases. 

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