Double-well elastic theory for twist-bend nematic phases

Area of Science:

• Materials Science
• Condensed Matter Physics
• Soft Matter Physics

Background:

• Twist-bend nematic liquid crystals (TBNLCs) possess a unique ground state characterized by a heliconical molecular arrangement.
• This structure involves uniform precession of the nematic director around an axis at a fixed angle.
• Both left-handed and right-handed helical senses are permissible in the ground state.

Purpose of the Study:

• To develop a quadratic elastic theory for single helical nematic phases.
• To model the twist-bend nematic phase by combining opposite helicities.
• To investigate the interfacial properties between states of opposite helicities.

Main Methods:

• Formulation of a quadratic elastic theory for helical nematic phases.
• Introduction of an additional director field to describe the helix axis.
• Combination of elastic energies for opposite helical variants to model the TBNLC phase.

Main Results:

• The proposed theory utilizes the same elastic constants as classical nematic theory, all requiring positive values.
• An extra director field is introduced to describe the helix axis, which is redundant in ordinary nematics.
• The combination of opposite helicities results in a non-convex energy landscape for TBNLCs.
• Minimal energy states with opposite helicities can form interfaces on developable surfaces, including cones.

Conclusions:

• The developed elastic theory accurately describes single helical nematic phases.
• The theory provides a framework for understanding the complex energy landscape of twist-bend nematics.
• The study reveals novel interfacial geometries, such as cones, formed by oppositely-handed helical states.