Dislocation and impurity effects in smectic-A liquid crystals

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Abstract
The effects of dislocations and impurities on the macroscopic elastic properties of smectic‐A liquid crystals are discussed. The first conclusion is that smectics behave like linear elastic media only so long as the stresses are smaller than some critical value that is analogous to the critical velocity of a superfluid. Below the critical stress, smectics can store elastic energy without flowing and consequently without any dissipative processes in analogy with the fact that, below a critical velocity, superfluids store kinetic energy without any dissipation. For most practical samples the critical smectic stress is that value for which pinned dislocation will grow unstable; however, for ideal samples, initially free of dislocations, the critical value is determined by the condition of unstable growth of thermally generated dislocation loops. In the linear elastic region both dislocations and impurities modify the macroscopic elastic properties such that the effective elastic constant is smaller than the value for an ideal sample. This is a sort of diaelasticity and can be discussed in the same way as diamagnetism. Impurities are shown to act as sources of stress fields analogous to the way magnetic dipoles and magnetic monopoles are sources of magnetic fields. The result is to predict long‐range elastic interactions between impurities in smectic systems. Since biological systems like chloroplasts and retinal rods have lamellarlike structures that are similar to the smectic structure, there is the possibility that long‐range elastic interactions may play some role in biological function.