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Defect unbinding on a toroidal nematic shell.

Dalija Jesenek1, Samo Kralj, Riccardo Rosso

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This summary is machine-generated.

Topological defects in 2D nematic liquid crystals on toroidal shells are studied. Defects and anti-defects assemble on inner and outer circles, with critical conditions estimated using an electrostatic analogy.

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Area of Science:

  • Soft Matter Physics
  • Liquid Crystal Science
  • Topological Defects

Background:

  • Nematic liquid crystals exhibit textures with topological defects (TDs).
  • Toroidal shells present unique topological constraints for defect formation.
  • The total topological charge of TDs on a torus is zero.

Purpose of the Study:

  • Investigate the behavior and distribution of topological defects in 2D nematic liquid crystal textures on a toroidal shell.
  • Determine the influence of toroidal geometry and extrinsic free energy on defect unbinding and assembly.

Main Methods:

  • Utilized a mesoscopic Landau-de Gennes approach.
  • Employed a 2D nematic order tensor (Q).
  • Analyzed defect behavior based on coupling with the torus's Weingarten tensor.

Main Results:

  • Fat tori demonstrate the unbinding of topological defects.
  • In the absence of extrinsic free energy, defects and anti-defects localize at the innermost and outermost circles, respectively.
  • An electrostatic analogy was used to estimate the critical condition for TD onset.
  • The presence of extrinsic free energy repels defects from these regions.

Conclusions:

  • The geometry of the toroidal shell significantly influences the arrangement of topological defects in nematic liquid crystals.
  • Extrinsic free energy provides a mechanism to control defect localization on toroidal surfaces.