Strength of the disclination

The elastic energy is proportional to the square of the strength of the disclination and increases... 

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. 

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... 

An important conclusion obtained from Equation (1.33) is that the deformation energy is proportional to the square of the disclination strength to. The equation is derived for a special case but the above conclusion is universal, with only the coefficient being different. It is expected that a to = 2 disclination is likely to divide into two to = 1 disclinations or so, in order to achieve a more stable configuration. 

Figures, (a) Wedgedisclinationof strength-t-l ina capillary the arrangement near the center has a discontinuity and must involve a core, (b) Escape of the disclination in the third dimension the arrangement is continuous with no core [34],...

We have so far assumed Kxx=K22=K =K. Real nematics are of course, elastically anisotropic. From the values of the energies of the disclinations calculated for the case where Ki =K22 K22 it follows that the wedge disclinations are more stable than the twist disclinations if A 22>A =Af i=A 33, and vice versa. Anisimov and Dzyaloshin-skii [38] have shown that lines of half-integral strength may be stable against three-dimensional perturbations if the twist elastic constant (22 i/2(A, j-i-A"3 3). More precisely,... 

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]. 

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... 

Figure 1.20 The liquid crystal director configurations of the disclinations with variety of strengths.

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 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 =. ... 

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