Disclinations density

The scaling law in Eq. (10-33) was predicted by Marrucci (1984) by assuming that the disclination density at steady state is set by a balance between the viscous energy density r]Y and the Frank elastic energy density K ja. Since the areal density pa is proportional to Pvh a h/a, this balance is... 

A couple of other important limitations of the theory must be acknowledged. First, as noted earlier, on cessation of flow, some LCPs show a gradual increase in orientation rather than the predicted decrease. This suggests that the tensorial form assumed for ([nh]), namely ([nh]) oc S, might not be completely appropriate. A second limitation of the theory is that (11-30) for the disclination density is not appropriate for small-ampIitude oscillatory... 

Mather, P.T. Pearson, D.S. Larson, R.G. Flow patterns and disclination-density measurements in sheared nematic liquid crystals. II. Tumbling 8CB. Liq. Cryst. 1996, 20, 527-538. 

Quite recently, Chen et al. [71b, 80] have developed the technique of banded texture decoration. These authors showed that in thick samples, when the disclination density is small enough due to prior annealing. 

In order to account for the real 3D structure of cylindrical microdomains, we denote the configurations in Fig. 22a, e and c, g as cylinder-phase defects (cyl-dislocation and +1/2 cyl-disclination), and the configurations in Fig. 22b,f and d,h as matrix defects (m-dislocation and m-disclination). In our systems, cyl-dislocations generally develop during the early stages of film annealing when the overall defect density is high. In well-equilibrated films, cyl-dislocations are less frequent as compared to m-dislocations. 

When disclinations are present, the Frank contribution to G should scale with the average spacing a between disclinations as AT ja. For a high density of disclinations... 

For example. Fig. 10-24 shows the steady-state areal density pA of disclinations ( l/2 s... 

Figure 10.24 Areal density of disclination lines in steady-state shearing of 5CB as a function of shear rate for a gap h of 250 pm. Closed symbols are measurements during increasing shear rate open symbols are for decreasing shear rate. For increasing shear rate, at a critical shear rate of about 10.5 sec i, the density of disclinations jumps from zero to a high value. The critical shear rate corresponds to an Ericksen number Er = (yiA y/k s) of 4100. The inset shows the critical shear rate as a function of the increment in angular...

These different contrast mechanisms can all be used to reveal the scale of liquid crystalline polymer microstructures. In specimens that exhibit a mosaic texture, and in those that contain predominantly planar defects, domain size is easily defined in terms of areas that uniformly show extinction between crossed polars. However, if the defects are predominantly linear, as in specimens that exhibit schlieren textures, such simple characterization of microstructural scale is no longer possible. Here it is more convenient to look at the length of disclination line per unit volume, which is equivalent to the number of lines intersecting unit area, and analogous to the dislocation density as defined for crystalline solids. Good contrast is essential in order to obtain an accurate count. Technologically, microstructural scale is of growing interest because of its relevance to processability, mechanical properties and optical transparency. 

---