Analysis and Stability of Bent–Core Liquid Crystal Fibers

In this paper we analyze a free–boundary model for free–standing fibers made from smectic layers of kinked (bent–core) liquid crystal molecules. In [1] a radial model was proposed to explain how fibers form (assuming radially symmetric configurations) based on the distinctive packing and ferroelectric properties of bent–core molecules. We develop this model further to include smectic energy terms so as to allow for non–circular cross–sections with non–radial configurations and fields. We show that the relative size of the energy’s elasticity constants can be used to determine the stability (instability) of radially symmetric fibers with respect to non–radial perturbations. ∗Research of both authors supported by NSF grants DMS-0456286 and DMS-0604839.