Liquid crystals are materials that have both crystalline order and fluidic properties. In this thesis, I study liquid crystal systems from both halves of this duality: studying first the crystalline order present in the bent-core alpha phase; then viewing liquid crystals as a platform to realize ideal 2D fluids.

Though helices are the most iconic realization of chirality in soft-matter systems, and are a common structural motif in chiral liquid crystals, they have never been observed in smectic liquid crystals composed of achiral molecules. Even though macroscopic chirality can emerge spontaneously in these systems, that chirality has curiously never manifested as a helical structure. In the first half of this thesis, I will discuss the discovery of the bent-core alpha phase: the first unequivocal evidence for helical order in achiral bent-core smectics.

The ‘liquid’ half of liquid crystal systems is because the molecules can translate quasi-freely, resulting in a fluidic disorder. In the latter half of this thesis, I study this fluidic disorder, both in realizations of simple fluids, where the metrology applications of liquid crystal nanofilms are explored, and in realizations of complex topological fluids, where the applicability of the XY model to quenched freely-suspended nanofilms is discussed.