Frank anchoring

Disclination lines are energetically disfavored because they produce gradients in the director profile and Frank stresses. So if the sample is left alone, the disclination lines and loops spontaneously shrink in length and annihilate one another (see Fig. 10-22) until no disclinations are left—except for any that are pinned by any impurities in the fluid or by wall irregularities, and those trapped because of incompatibilities in anchoring conditions at surfaces (Chuang et al. 1991 Nagaya et al. 1992). 

The applicability of this sort of growth mechanism depends, however, upon the assumption that we are dealing with a perfect, smooth crystal surface. This is not often the case. Real crystal surfaces generally have imperfections of various kinds and, under certain circumstances, may even be rough on a molecular scale. The most important type of imperfection, from the point of view of crystal growth, is the screw dislocation. As was first pointed out by Frank (1949), a screw dislocation emerging from a crystal face provides a step on the surface to which atoms can be added continuously without causing it to disappear. The step is anchored... 

Fig. 4.12. (a) Temperature dependence of azimuthal Wtp dots) and zenithal Wo (squares) anchoring coefficients for nematic 5CB on rubbed Nylon with Tni being the transition temperature into the isotropic phase (b) A comparison of the ratios of the two anchoring coefficients W jW p (circles) with the ratio of the corresponding Frank elastic constants KijK2 [Q5](solid line) [64]. 

Fig. 1 Field-driven director configurations in (a) a nematic liquid (conventional Fredericks effect) and (b) a nematic elastomer slab floating in liquid between rigid electrodes. They initially have a uniform planar orientation before imposing field E in the direction shown by the arrow. In (a), the director at the surfaces are anchored, and the rotation angle of director has a finite distribution along the field axis, with the maximum at the middle layer of the cell. The recovery force for the director originates from the Frank elasticity. In (b), the director is capable of uniform rotation under electric fields, and the Frank elasticity plays no role in the recovery force...

The simplest dislocation multiplication process is the Frank-Read source, which is illustrated in Figure 11. Imagine that a segment of a dislocation line BC lies on the slip plane, leaving the slip plane at B and C, so that B and C act as anchoring points, or alternately B and C may be impurity particles or dislocation nodes. Under the influence of the applied stress the dislocation segment bows out, expands, and finally breaks loose from the anchoring points to form a dislocation... 

Fig. 11. Operation of a Frank-Read Source. In (a) the dislocation leaves the slip plane at B and C, which act as anchoring points. Under an applied stress the dislocation segment BC expands, finally forming a loop around BC, leaving a dislocation segment between B and C. (e) The dislocation bowed out just before the loop breaks loose from the pinning points from Weertman and Weertman and Read. ...

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