Dislocation effects in smectic-A liquid crystals

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Abstract
A method for calculating stress‐strain fields around edge dislocations in smectic‐A samples is discussed. In large part the method is isomorphic with the formalism for calculating magnetic fields around lines of electric current. The force law between dislocations that follows from the analogy is equivalent to the accepted force law between dislocations in crystals. In addition to rederiving the expression for the strain field surrounding an isolated edge dislocation that was first given by de Gennes, we present the solutions for the stress‐strain fields surrounding dislocations near one or two boundaries and also the strain field surrounding an edge dislocation that is curved to form a circular loop. The stress‐strain fields surrounding other defects with the same symmetries and boundary conditions can be expressed in terms of the above‐mentioned solutions using Green's function techniques. The relative stability of dislocations in samples with different types of boundaries and also the effects of dislocations on the elastic properties of smectic samples are also discussed in some detail. We comment briefly on the relation between the analogy discussed here and an earlier one developed by de Gennes.