Spherical nematics with a threefold valence

TL;DR

This paper theoretically investigates the defect arrangements in thin nematic shells, identifying optimal configurations, analyzing thermal fluctuations, and explaining experimental stability of certain defect patterns.

Contribution

It introduces a detailed theoretical model for defect energetics and arrangements in nematic shells, aligning with experimental observations and explaining stability.

Findings

Optimal defect arrangement on a great circle forming an isosceles triangle.

Energy of three-defect configuration is comparable to other defect configurations.

Large energy barriers contribute to the long-term stability of observed defect patterns.

Abstract

We present a theoretical study of the energetics of thin nematic shells with two charge one-half defects and one charge-one defect. We determine the optimal arrangement: the defects are located on a great circle at the vertices of an isosceles triangle with angles of 66 degrees at the charge one-half defects and a distinct angle of 48 degrees, consistent with experimental findings. We also analyse thermal fluctuations around this ground state and estimate the energy as a function of thickness. We find that the energy of the three-defect shell is close to the energy of other known configurations having two charge-one and four charge one-half defects. This finding, together with the large energy barriers separating one configuration from the others, explains their observation in experiments as well as their long-time stability.