Director Deformations, Geometric Frustration, and Modulated Phases in Liquid Crystals

This article analyzes modulated phases in liquid crystals, from the long-established cholesteric and blue to recently discovered twist-bend, splay-bend, splay nematic phases, as well twist-grain-boundary (TGB) helical nanofilament variations on smectic phases. The analysis uses concept of four fundamental modes director deformation: twist, bend, splay, a fourth mode related saddle-splay. Each is coupled specific type molecular order: chirality, polarization perpendicular parallel director, octupolar order. When crystal develops one spontaneous order, ideal local structure becomes nonuniform, with corresponding deformation. In general, frustrated; it cannot fill space. As result, must form complex global phase, which may have combination deformation modes, periodic array defects. Thus, an under geometric frustration provides unified framework understand wide variety