Threads, Nuclei and Disclinations

In order to do this, consider a disclination line viewed from the end and mark the tangents to the director field in the plane perpendicular to the line (see Fig. 9.8a). The schematic corresponds to what is easily observed in thin layers, without special treatment of the substrate, when molecules are confined to the plane of the layer. The resulting texture is called a Schlieren texture. The strength or rank of the line S is defined as the total rotation Q of the director along a closed path around the line, divided by 2tt (i.e., Q = 27tS ). It is attributed a sign -f or — depending on whether the director rotation occurs 

The equilibrium condition obtained by minimising the total energy is just = 0.  

Solutions have the form 9 r) = ra(f) r), in good agreement with optical observations. 

With the notation of Fig. 9.8, we have V0 = S/r, where r is the distance from the line. The distortion energy per unit length of line, also called the line tension, can be written in polar coordinates 

R is of the order of the sample dimensions and fc is the radius of the disclination core, i.e., the distance of molecular order over which Hooke-type elasticity is no longer valid. We must add the disclination core energy to (9.9). This is difficult to calculate exactly, but it does not exceed the energy of the disordered nematic [ k T — Tc)], where is the nematic to isotropic transition temperature. 

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