Twisted-grain-boundary (TGB) phases: nanostructured liquid-crystal analogue of Abrikosov vortex lattices

Abstract

Twisted-grain-boundary (TGB) phases shown by some liquid-crystalline materials have properties common to those of both smectic and cholesteric phases. Following analogy between liquid crystals and super conductors proposed by de Gennes [Solid State Commun., 10, 753 (1972)], Renn and Lubensky [Phys. Rev. A, 38, 2132 (1988)] theoretically predicted a chiral analog of the smectic A (SmA*) phase, which is now known as TGBA phase. The TGBA phase was experimentally observed for the first time by Goodby et al. [Nature, 337, 449 (1989)] in the chiral homologous series of ferroelectric liquid-crystal material R- and S-1-methylheptyl 4′-[(4′′-n-alkoxyphenyl)propionoyloxy]-biphenyl-4-carboxylates (nP1M7), with n = 13,14,15. Since then, more than a hundred pure and mixed systems showing TGBA phase have been found. Later, Renn derived a mean-field phase diagram based on the chiral Chen-Lubensky model, and predicted two more TGB phases, namely TGBC and TGBC*. These two phases have also been experimentally observed in many systems, and in a few, the phase diagram is similar to that predicted by Renn. Unlike the TGBA phase, several theoretical models have been proposed for TGBC and TGBC* phases, and it remains to be ascertained whether all the types of proposed TGBC/TGBC* structures experimentally exist. A review of the theoretically predicted and experimentally observed TGB phases is given in the present article. Some recently observed novel optical textures of the TGB phases are also reported.