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.

Keywords:

• TGB phases
• Chirality
• Smectic slabs
• Phase diagram
• Optical texture
• Goldstone modes
• Soft modes

Acknowledgements

The author takes pleasure to thank many of the research workers who promptly sent their articles, especially on original optical textures. Thanks are due to Prof. R. Dabrowski for providing binary mixture of 7OCB and 5∗CBB for the dielectric study, and to Prof. W. Kuczynski for several discussions on TGB phases. Thanks are also due to the University Grants Commission and Department of Science and Technology, New Delhi, for funding most of the experimental work of the author done on the above topic. The author is grateful to Prof. S. L. Srivastava for his valuable comments and suggestions on the work.

Notes

¹Readers should bear in mind that in the case of N∗ phase, director continuously rotates while moving along helix axis , whereas in TGBA phase, is constant throughout the length of the smectic slab/block and it changes by discrete angle Δχ only after jumping from one slab to the other.

² Here it is important to emphasize that in early years SmA∗ and TGBA phases were considered to be synonyms but now it is well settled that SmA∗ phase represents the orthogonal SmA phase formed by the chiral molecules of ferroelectric liquid crystal materials (_∗ represents simply the chirality of molecules and not the twisting of the slabs). In TGBA phase SmA slabs are rotated from one slab to the next as discussed for figure 1.