Disclinations of strength

Fig. 3.5.6. (a) Director escape at the centre of a disclination of strength s = 1 in a thin capillary the wall alignment is homeotropic and changes by 90° from wall to axis. (Williams, Pieranski and Cladis< >.) (ft) Projection of the structure on a plane normal to the capillary axis. Nails signify that the director is tilted with respect to the plane of the paper. Solutions with positive and negative tilts are... 

Fig. 3 b shows the director escape at the center of a disclination of strength 5= 1 in a thin capillary of radius R. The arrangement is continuous with no singular line. The deformation involves splay and bend, but no... 

Fig. h. Schematic diagram of moleci lar traj ctories associated with disclinations of strength - 1/2 or - 1. 

They proposed a pure radial splay model to describe the molecular arrangement aro d the lines of strength S = + 1. In investigations Mackley et al. made on a copolyester prepared from Ho mol % poly(ethylene terephthalate) and 60 mol % p-acetoxybenzoic acid, a number of integer disclinations were also observed. However, according to Viney and Windle who carried out some optical observations of Refects in the same copolyester, if disclinations of strength - 1/2 are not. seen below 3H0°C, they are more numerous than those of strength"1 above this temperature. These observations are at variance with results reported by Mackley et al. but seem to corroborate well with optical observations in polyester I (n = 5) made by Kleman et al.. One of the clearest conclusions of their study is obtained from the predominance of s = 1/2 lines ... 

Figure 10.4 Illustration of disclinations of strength 1 ((a) and (b)) and ((c)). The lines indicate the director field orientation.

The strength of a disclination is defined as follows. We traverse the disclination line along the closed contour counterclockwise as shown in sketch (b) and count the angle A( ) the director acquires as a result of the traverse. It is evident that after the full turn A( ) = mn where m = 0,1,2... and, by convention, the strength s = ml2. In fact, we deal with a solution of the Laplace equation, see the next paragraph. Let us count A( ) from the horizontal axis in Fig. 8.14. Then, upon the traverse in the counter-clockwise direction, for disclinations of strength s = 1/2 and s = 1, the... 

POM observation that a Schliren texture with disclinations of strength of 1/2 appeared in that region. Therefore, the mesophase above 70 wt% of E7 corresponds to the nematic state. Figure 6 shows the phase diagram of the (PS[4BC/DM]/ E7) composite in the case of n=40. This diagram is very similar to that for the composite with n=12. A miscible smectic state was also confirmed in the region below 70 wt% of E7. It has been also confirmed that LCP and LC are phase-separated in the case of n=120. 

Figure 6.24 Schematic illustration of disclinations of strengths 1 and 1/2 in liquid crystals with the local directors indicated by the lines. Each type of disclination has a central singularity. Drawn after Donald and Windle (1992, p. 179).

The energy of a disclination at one of the cusp points must also be added to Fsurf [107]. This can be estimated by treating the disclination as an axial disclination of strength s = 1 (see Fig. 3.20 on p.ll4), which is limited to a half-space, since we are examining a disclination at a surface. The integration in 0 in the energy equation (3.352) therefore only takes place over the interval 0 < 0 < tt with Frank index n = 2. The relevant energy per unit area around the disclination is then... 

Fig. 1.19 Sign and strength of nematic disclinations. These ate categorised in terms of their sign (+ or —) and strength (the number of times the local director makes a rotation of 2n in a circuit around the discUnation). When nematic phases are viewed between crossed polars, disclinations of strength 1 appear as Maltese crosses with four btushes - and disclinations of strength h have a two-brush pattern. Although higher orders are possible, the usutil director fields of nematic phases contain only the four types of disclination drawn here...

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