Stability of a split-core configuration induced by saddle-splay elasticity in a submicron nematic liquid crystal spherical droplet

ABSTRACT

We use Landau–de Gennes theory to investigate the configurations of liquid crystals confined to a submicron spherical droplet subject to weak homeotropic anchoring. The results show that in a one-constant approximation, there are three equilibrium configurations: radial hedgehog, ring disclination and uniform, where the radial hedgehog configuration is a stable state. With increasing elastic anisotropy, which is essentially an increase in the splay elastic constant, the radial hedgehog configuration transforms into a split-core configuration, which is metastable. The split-core configuration becomes the lowest-energy state induced by saddle-splay elasticity within appropriate ranges of the radius and elastic anisotropy.

Graphical abstract

KEYWORDS:

• Landau–de Gennes theory
• weak anchoring
• elastic anisotropy
• saddle-splay elastic constant
• split-core configuration
• stable state

Acknowledgments

We sincerely extend our thanks to the financial support of National Natural Science Foundation of China (11374087), Innovation Method Fund of China (2020IM020600), Research Projects of Undergraduate Education and Teaching Reform of China in Hebei University of Technology (201903006, 201904040), Ministry of Education industry-University Cooperative Education Program of China (202102026001), Education Reform project of Higher Education Association of Hebei Province (GJXH2019-019) and the Key Subject Construction Project of Hebei Province University, China.

Disclosure statement

No potential conflict of interest was reported by the author(s).