Bistable curvature potential at hyperbolic points of nematic shells

Area of Science:

• Colloid Science
• Liquid Crystals
• Materials Science

Background:

• Nematic shells are colloidal particles with surface-coated nematic liquid crystal molecules.
• These molecules can move freely on the surface while maintaining alignment with the tangent plane.

Purpose of the Study:

• To describe nematic order on a shell using a director field.
• To identify and analyze the fossil component of elastic energy related to surface curvature.

Main Methods:

• Describing nematic order with a unit director field on an orientable surface.
• Minimizing elastic energy as a function of the director field's surface gradient.
• Extracting a curvature-dependent fossil energy component.

Main Results:

• A fossil energy component, dependent only on surface geometry and curvature, was systematically extracted.
• This component creates a curvature potential for molecular torque.
• At hyperbolic points, the curvature-preferred alignment may not align with principal curvatures, resulting in bistable fossil energy.

Conclusions:

• Surface curvature significantly influences molecular alignment and energy states in nematic shells.
• Hyperbolic points are critical sites where curvature-induced bistability arises.
• This understanding is crucial for designing and predicting the behavior of functionalized colloidal systems.