Hairpin turn dislocations in two-dimensional smectic phases of long semiflexible polymers

We elucidate hairpin turn dislocations in two-dimensional smectic phases of long semi-flexible polymers. We discuss hairpin shapes, sizes, and free energies. We find that hairpin dislocation core may be, under some circumstances, substantially bigger than the smectic period size. Such hairpin dislocations are accompanied by large voids that are stable equilibrium structures with sizes determined by a competition of the polymer bending elasticity and smectic bulk elasticity. The large size of hairpin voids is associated with a low hairpin energy, much smaller than anticipated before. The actual hairpin shape, size, and energy are all qualitatively sensitive to the detailed nature of smectics. We document this by considering hairpin dislocations in lyotropic smectics (systems stabilized by repulsion between polymers, with a positive osmotic pressure) and in thermotropic smectics (systems stable even at zero osmotic pressure, with a preferred distance between semiflexible molecules). We discuss in detail hairpin dislocations in lyotropic sterically stabilized Smectics as well as in DNA-cationic lipid complexes. We elucidate the extinction of hairpin dislocations by annihilations with polymer end points. In lyotropic smectics, rates of these processes are shown to be limited by sluggish reptation of semiflexible molecules, as well as by substantial energy barriers.