In membranes with nematic liquid-crystalline order, there is a geometric coupling between the nematic director and the shape: nonuniformity in the director induces curvature, and curvature provides an effective potential acting on the director. For a closed vesicle, there must be a total topological charge of +2, which normally occurs as four defects of charge +1/2 each. Previous research has suggested that these four defects will form a regular tetrahedron, leading to a tetrahedral shape of the vesicle, which may be useful in designing colloidal particles for photonic applications. Here, we use three approaches to investigate the behavior of a nematic vesicle: particle-based simulation, spherical harmonic expansion, and finite-element modeling. When liquid crystal has a purely 2D intrinsic interaction, we find that the perfect tetrahedral shape is stable over a wide range of parameters. However, when it has a 3D intrinsic and extrinsic interaction, the perfect tetrahedral shape is never stable; the vesicle is a distorted tetrahedron for small Frank constant and a highly elongated rectangle for larger Frank constant. These results show the difficulty in designing tetrahedral structures for photonic crystals.
Royal Society of Chemistry (RSC)
Nguyen, T.-S., Geng, J., Selinger, R., & Selinger, J. (2013). Nematic order on a deformable vesicle: theory and simulation. Soft Matter. https://doi.org/10.1039/c3sm50489a
Nguyen, Thanh-Son, Jun Geng, Robin Selinger, and Jonathan Selinger. 2013. “Nematic Order on a Deformable Vesicle: Theory and Simulation”. Soft Matter. https://doi.org/10.1039/c3sm50489a.
Nguyen, T.-S., J. Geng, R. Selinger, and J. Selinger. Nematic Order on a Deformable Vesicle: Theory and Simulation. Soft Matter, 2013, doi:10.1039/c3sm50489a.