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Temperature-dependent orientational ordering on a spherical surface modeled with a lattice spin model.

Alan M Luo1, Stefan Wenk1, Patrick Ilg2

  • 1ETH Zürich, Department of Materials, Polymer Physics, CH-8093 Zürich, Switzerland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 13, 2014
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Summary
This summary is machine-generated.

Orientational ordering on spherical surfaces is studied. The ground state with four +1/2 defects is stable, showing a smooth transition to ordered phases and subdiffusive defect motion.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Understanding orientational ordering is crucial in various physical systems.
  • Spherical surfaces present unique challenges for ordering due to curvature.
  • Defects are inherent in ordered systems on curved manifolds.

Purpose of the Study:

  • To investigate orientational ordering of rods on a spherical surface.
  • To analyze the role and stability of defects in spherical systems.
  • To compare ordering and elastic properties on spherical versus planar surfaces.

Main Methods:

  • Monte Carlo simulations.
  • Brownian dynamics simulations.
  • Analysis of director fluctuations and defect core displacements.

Main Results:

  • A stable ground state with four +1/2 point defects was identified across a wide temperature range.
  • A smooth transition from disordered to ordered phases was observed upon decreasing temperature.
  • Subdiffusive behavior of defect cores was found, with estimated diffusion constants.

Conclusions:

  • The presence of defects is unavoidable for perfect nematic ordering on a sphere.
  • The Frank elastic constant on a sphere can be estimated from director fluctuations.
  • Defect dynamics on spherical surfaces exhibit unique characteristics, including subdiffusion.