Biaxial torus around nematic point defects.

Area of Science:

• Soft Matter Physics
• Liquid Crystal Science
• Continuum Mechanics

Background:

• Nematic liquid crystals exhibit complex ordering described by the Landau-de Gennes theory using a second-order tensor Q.
• Defects in liquid crystals, such as line and point defects, significantly influence material properties.
• Confinement within capillary tubes with homeotropic anchoring introduces boundary effects on liquid crystal ordering.

Purpose of the Study:

• To analyze the biaxial structure of line and point defects in homeotropically anchored nematic liquid crystals confined in capillary tubes.
• To understand the influence of topological charge and confinement on defect core structures.
• To investigate the role of the order parameter and biaxial correlation length in defect morphology.

Main Methods:

• Analytical calculations based on Landau-de Gennes theory.
• Numerical simulations to model defect structures.
• Investigation of defects with topological charges M=1 (line) and M=+/-1 (point).

Main Results:

• The core of a line defect (M=1) is found to be uniaxial along the axial direction.
• Uniaxial ordering at the lateral boundary occurs in two distinct ways, dependent on the axial order parameter's sign.
• Point defects (M=+/-1) show a uniaxial ring surrounded by a biaxial torus, with characteristic lengths depending on cylinder radius and biaxial correlation length.

Conclusions:

• The study elucidates the biaxial and uniaxial structures of line and point defects in confined nematic liquid crystals.
• Defect core structure, particularly for point defects, appears independent of the bulk nematic director field.
• Confinement and anchoring conditions critically dictate the observed defect morphologies and ordering.