Strength of disclination in nematics

The sign of m depends on whether n and the closed contour (i.e., the Burger s circle) have the same direction. 

Assume the nematic liquid crystals to be a homogeneous planar structure, i.e., the directors lie in the x-y plane, making an angle 4 with respect to the x axis. For simplicity, we further suppose that all the three elastic constants are equal, i.e., Ku = K22 = K33 = K. Thus the energy density 

If the disclination line is a wedged one and is along the z axis, then the solution of Equation (1.30c) is 

Substitute the solution back into Equation (1.28). The energy per unit length of an isolated disclination in a cylindrical sample of a diameter R is 

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. 

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