Defects in smectic A phase

The deformations in the smectic A phase liquid crystals are the bending of the smectic layer (accordingly to the splay of the directors) and the dilation or compression of the layers. The energy is thus 

Suppose the edge dislocation is along the y axis and the Burger vector has a thickness of one layer. The smectic layer is in the x-y plane. At equilibrium, the displacement u is expressed by 

It is illustrated that the deformation disappears rapidly in the x-direction and decays slowly in the -direction. The deformation energy is independent of sample dimension. It is concluded that the dissolution of the dislocation doesn t reduce the energy. 

There is a helical structure surrounding the screw dislocation line. The screw dislocation is perpendicular to the smectic layer and the deformation is 

The screw dislocation affects neither the lattice dilation nor the bending of the layer. Thus it isn t associated with an energy penalty. 

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