Curvature-induced defect unbinding in toroidal geometries

Area of Science:

• Soft Matter Physics
• Materials Science
• Physical Chemistry

Background:

• Vesicles and toroidal structures are fundamental in various scientific disciplines.
• Understanding orientational order, such as hexatic order, is crucial for describing the properties of these systems.

Purpose of the Study:

• To compute the total energy of hexatic order within a toroidal geometry, including disclination charges.
• To investigate the energetic favorability of defects in toroidal systems under different conditions.

Main Methods:

• Explicit computation of total energy for hexatic order on a torus.
• Application of the one Frank constant approximation for tilt or nematic order on the torus.

Main Results:

• Excess disclination defects are energetically favored in 'fat' tori or vesicles of moderate size, despite no topological necessity.
• The study provides a framework for understanding defect formation in curved, ordered systems.

Conclusions:

• Topological defects can be energetically driven even when not topologically required in toroidal systems.
• Findings have implications for the self-assembly and behavior of soft matter systems, with potential experimental consequences.