Telephone-cord instabilities in thin smectic capillaries

Telephone-cord patterns have been recently observed in smectic liquid-crystal capillaries. We analyze the effects that may induce them. As long as the capillary keeps its linear shape, we show that a nonzero chiral cholesteric pitch favors the Sm-A*-Sm-C* transition. However, neither the cholesteric pitch nor the presence of an intrinsic bending stress is able to give rise to a curved capillary shape. The key ingredient for the telephone-cord instability is spontaneous polarization. The free-energy minimizer of a spontaneously polarized Sm-A* phase is attained on a planar capillary, characterized by a nonzero curvature. More interestingly, in the Sm-C* phase the combined effect of the molecular tilt and the spontaneous polarization pushes towards a helicoidal capillary shape, with nonzero curvature and torsion.