Transformations Between Different Self-Organized Defect Arrays at the Nematic-Smectic A Phase Transition

We model transformations in self-organized liquid crystal defect arrays in hybrid-aligned thin films at the nematic-smectic A phase transition. The smectic A phase forms a packing of focal conic domains, while the nematic phase features a square lattice of boojum surface-defects at larger spacing. Heating from smectic A to nematic transforms the focal conic domain packing into a dense array of boojums, which we study through Landau-de Gennes numerical modeling and a connection to graph theory. The reverse transformation upon cooling proceeds through a very different morphological sequence, beginning with a stripe instability which we examine analytically and numerically. The focal conic domain packings that emerge retain a geometric memory of the nematic boojum configuration.