Curvature and defects in nematic liquid crystals

ABSTRACT

The use of nematic liquid crystals for directed assembly of particles and for the creation of multistable systems depends on the ability to control the topological defects and the distortions of the director field. These are not only driven by topological constraints and by anchoring energies but also by the curvature field created by the bounding surfaces. This review explores the interaction between defects, topology, inclusions and curvature in nematics. I will introduce the relationship between curvature and the Frank elastic energy in nematics, and then I will give an overview of specific examples that show how this coupling can create unexpected behaviours, such as lock-and-key interactions, anchoring transitions on curved surfaces and memory effects.

GRAPHICAL ABSTRACT

KEYWORDS:

• Nematic liquid crystals (LCs)
• topological defects
• curvature
• soft matter
• self-assembly

Acknowledgements

I would like to thank Lisa Tran for discussing the saddle-splay and Randall Kamien, Kathleen Stebe, Shu Yang, Yimin Luo, Mohamed Gharbi, Oksana Manyuhina, Tommaso Bellini, Marco Buscaglia, Roberto Cerbino, Roberto Osellame, Takeaki Araki and Shane Eaton for discussions, guidance and advice.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the Army Research Office [grant number W911NF-16-1-0288]; NSF Office of the Director, Material Science and Engineering Research (MRSEC) grant to University of Pennsylvania [grant number DMR-1120901].