Defects in the columnar liquid crystal

The symmetry elements in the hexagonal structure composed of liquid-like columns are shown in fig. 6.4.1. The director n is parallel to the column axis a (or equivalently a or a ) is the lattice vector of the two-dimensional hexagonal lattice L, and 6 are two-fold axes of symmetry 3 is a three-fold axis and g a six-fold axis. Any point on or , is a centre of symmetry. Any planes normal to n and the planes ( 7 ) and (Lg, 0 are planes of symmetry. Defects in such a structure have been investigated in detail by Bouligand and by Kleman and Oswald.  

The Burgers vector b of a dislocation in the columnar structure is normal to the columnar axis n. In general 

In this case, the dislocation line L is along n, the z axis. Let the Burgers vector be along y. Minimization of the free energy (6.3.1) gives 

These are exactly like the equations for edge dislocations in crystals. The solutions are 

The dislocation line is now normal to n. Let it be along the x axis, so that the only component of the displacement that needs to be considered is u. Minimization of the free energy yields 

---