Strength of a disclination

Liquid crystals may have line defects called disclinations. The name comes from discontinuity and inclination. The director rotates about a line normal to the disclination. The strength of a disclination, S, is defined by... 

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... 

The integer n is called the Prank index of the disclination. It is worth noting that in some articles, for example Bouligand [22] or Chandrasekhar [38], the order or strength of a disclination has been defined by s =. ... 

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... 

Figure 2. Director field in the neighborhood of the core of a disclination line of strength S Wedge discli-nations (after Frank [33]).

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... 

The growth of the LC phase occurs when reaction time is in the range from 202 s to 392 s for this sample. As a result, the total view area becomes an anisotropic LC phase, and the sum of the strength of all disclinations in the sample tends to be zero. The typical schlieren texture is formed at this moment [17]. 

It is not difficult to visualise the director configuration for some of these axial disclinations. If m, which is called the strength of the disclination, is positive, then the director rotates counter-clockwise in traversing a counter-clockwise path around the disclinatiom If m is negative, the director rotates clockwise in traversing this same... 

Disclinations are defects existing in liquid crystals involving a localized rearrangement of the molecular director. The strength of the disclination expresses the angular reorientation of the local directors occurring about the centre of the disclination. 

Figure 3.20 Examples of flux lines which are tangential to the orientation of the director n around an axial line disclination located perpendicular to the page and passing through the point indicated by a black dot. Various cases of Rrank index n are given together with the associated solution B provided by equation (3.341). The strength of such disclinations is often defined by s = f. The bold lines represent the singular radial lines obtained from equation (3.347). The constant 0o has been set to zero except for the examples of Prank index n = 2.

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...

The local translational and orientational order of atoms or molecules in a sample may be destroyed by singular points, lines or walls. The discontinuities associated with the translational order are the dislocations while the defects associated with the orientational order are the disclinations. Another kind of defect, dispirations, are related to the singularities of the chiral symmetry of a medium. The dislocations were observed long after the research on them began. The dislocations in crystals have been extensively studied because of the requirement in industry for high strength materials. On the contrary, the first disclination in liquid crystals was observed as early as when the liquid crystal was discovered in 1888, but the theoretical treatment on disclinations was quite a recent endeavor. 

Figure 1.21(a), and rotate the two opposite slips of the cut A1 and A2 by 7T. 7r is a symmetry element. Insert a new sample piece of liquid crystals and arrange their director to fit the directors on the A1 and A2 slips, as shown Figure 1.21(b). The liquid crystals then relax themselves to the configuration shown in Figure 1.21(c). A disclination with the strength of —1/2... 

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