Telephone-cord instabilities in thin smectic capillaries

TL;DR

This paper investigates the mechanisms behind telephone-cord patterns in smectic liquid crystal capillaries, highlighting the role of spontaneous polarization in inducing curved and helicoidal shapes.

Contribution

It identifies spontaneous polarization as the key factor causing telephone-cord instabilities, expanding understanding of shape transitions in smectic liquid crystal capillaries.

Findings

Spontaneous polarization induces nonzero curvature in smectic capillaries.

Chiral cholesteric pitch influences phase transitions but not shape.

Helicoidal shapes arise from combined molecular tilt and polarization effects.

Abstract

Telephone-cord patterns have been recently observed in smectic liquid crystal capillaries. In this paper we analyse 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 SmA*-SmC* transition. However, neither the cholesteric pitch nor the presence of an intrinsic bending stress are 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 SmA* is attained on a planar capillary, characterized by a nonzero curvature. More interestingly, in the SmC* phase the combined effect of the molecular tilt and the spontaneous polarization pushes towards a helicoidal capillary shape, with nonzero curvature and torsion.