Defect Pattern Formation, Stripe Instabilities, and Geometric Memory at the Nematic-Smectic A Liquid Crystal Phase Transition

We examine a surprising morphological sequence of defects and distortions in a hybrid-aligned liquid crystal film on a water substrate, connecting boojum defect networks in the nematic phase to self-organized focal conic domain arrays in the smectic phase upon cooling through the phase transition. Just prior to the phase transition, director field stripe distortions arise in the nematic phase with stripe orientations dictated by the pre-existing boojums. Upon the transition into the smectic A phase, the stripes break up into rows of elliptic-hyperbolic focal conic domains aligned along the stripe direction. We present a theoretical and numerical investigation of the appearance of nematic stripe distortions as driven by the increasing cost of bend distortions upon approaching the phase transition. We also demonstrate the geometrical connection between these stripe distortions and the focal conic domain rows that follow during cooling. This connection shows how memory of the original boojum network persists in the self-organized patterning of smectic focal conic domains.