Nematic-isotropic phase transitions in liquid crystals are often characterized by islands of one phase surrounded by the other with the phase boundary itself sometimes possessing corners or cusps. In this talk I will introduce a model problem that seeks to describe these transitions and has a mechanism for phase boundary singularity formation. The study is part rigorous, part formal, and part computation. This is joint work with Dmitry Golovaty, Peter Sternberg, and Raghav Venkatraman.