Disclinations transformations

Hahm J, Sibener SJ (2001) Time-resolved atomic force microscopy imaging studies of asymmetric PS-b-PMMA ultrathin films dislocation and disclination transformations, defect mobility, and evolution of nanoscale morphology. J Chem Phys 114(10) 4730-4740... 

At the late stage of lamella orientation, classical topological defects (dislocations and disclinations) dominate [40, 41] (Fig. 8h and Fig. 9), and their movement and annihilation can be followed in Fig. 8h-i and Fig. 9. The latter presents an example of the apparent topological defect interactions and their transformations. Displayed are two dislocations of PMMA, which have an attractive interaction due to their opposite core sign. Therefore, in the next annealing step the dislocation is shifted... 

Fibers with a radial transverse microstructure can exhibit a crack, which Volk [54] reports will tend to spiral around the fiber axis. The crack is able to transform into a true radial structure along a single filament and vice versa (Figure 7.13). White et al [55] believe that this is due to the annihilation of disclinations, as depicted in Figure 7.14. Yoon et al [56,57] have investigated crack formation in mesophase pitch based carbon fibers. 

Another example is formation of boodjooms at the cell surfaces. Now we are interested not in the linear disclinations responsible for the SchUeren texture but in their nuclei at the solid substrates limiting a liquid crystal cell. The linear discUna-tions of strength s = 1 may annihilate within the bulk due to some reconstruction of the director field induced, for instance, by temperature or a flow of the material. For example, a bulk discUnation of strength s = +1 shown by the solid vertical line in Fig. 8.18b disappears but its nuclei localized at the surfaces transform into new, surface defects. Fig. 8.18c illustrates the situation at one of the two surfaces. The escaped line leaves behind it a boodjoom. We meet such a situation in thick planar cells where the Schlieren textures with four brushes are observed. 

For a disclination with the strength S, as one approaches the center of the disclination, the elastic energy diverges, as shown by Equation (1.124). In reality this will not occur. The liquid crystal will transform either into isotropic phase at the center of the disclination or a different deformation where there is no singularity. Here we only discuss the cases of cylindrical confinements (two-dimensional confinement) where it is possible to obtain analytical solutions. The mechanism of liquid crystal director escape in spherical confinement (three-dimensional confinement) is similar to that of two-dimensional. 

The links between the dimeric units are assumed to broken at the transformation fi om the solid to the mesophase. It is worthwhile noting that the mesophase formed from the isotropic melt appears first as bright bands which resemble those observed in PDFS. Earbom and Hartsbom regarded these bands as rodlike structures and referred to these bands as battonets . On the other hand, these structures can be interpreted as disclination lines From our point of view this question needs further consideration with allowance made for the fact, observed by Earborn and Hartshorn, that battonets can develop from striated bands arising after melting of acircular crystals and for the fact that the mesojdiase is not liquid, but a semi-solid phase. 

Figure 5.8. Continuous transformation of a dischnation k = into a disclination — 5 in real space (director configurations above) and the corresponding transformation of contours in the OP space S /Z2.

The topological classification prohibits transformations of disclinations from one class to another. For example, x n X n + i), and x(n + ) cannot be continuously transformed one into another, despite the apparent similarity in the value of the strength. On the other hand, different lines can be transformed by splitting. For example, according to Table 5.1 and... 

An important property of x dislocations is their ability to split into combinations of A and t disclinations. Of course, these transformations must obey the multiplication rules (5.23). For example, a x line from the class can split into a pair of A and r lines (classes Cx and Q, respectively). An example is shown in Figure 5.11(b), (c) the core splits into a A and r+... 

Figure 5.13(a) shows two entangled disclinations. The question is whether they can be transformed by continuous variations of the directors into an... 

The energy W in equation (3.335) for an axial disclination can be evaluated most easily by transforming to cylindrical coordinates. For 6 given by (3.341) we have, upon using equation (3.337) and the usual chain rule for partial derivatives. 

FIGURE 2.4 Two types of defect formation around a pair of particles. A transient defect structure formed in the early stage becomes unstable and transforms into either, and a new type of (quasi-) stable configuration, in which a single disclination loop is shared by two neighboring particles. 

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