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Related Experiment Videos

Boundary conditions for equilibrating incommensurate periodic patterns.

Hiroto Ogawa1, Nariya Uchida

  • 1Department of Physics, Tohoku University, Sendai 980-8578, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
PubMed
Summary

This study introduces a numerical scheme to prevent artifacts in simulations of periodic patterns. The method improves the accuracy of finding equilibrium domain morphologies, especially for complex systems.

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Area of Science:

  • Computational materials science
  • Polymer physics

Background:

  • Simulating periodic patterns can lead to artifacts when intrinsic length scales do not match system size.
  • Ginzburg-Landau-type free energy models are used to study domain morphologies in materials.

Purpose of the Study:

  • To introduce a novel numerical scheme to avoid artifacts in simulations of periodic patterns.
  • To improve the accuracy of finding equilibrium domain morphologies from Ginzburg-Landau-type free energy.

Main Methods:

  • A simple numerical scheme is proposed where boundary values are determined by local equilibrium conditions.
  • The scheme is applied to finding equilibrium domain morphologies.

Main Results:

  • The proposed scheme effectively avoids artifacts caused by incommensurability.

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  • It is particularly advantageous for equilibrating patterns with multiple characteristic lengths.
  • Demonstrated success using a block copolymer blend model exhibiting lamellar-lamellar coexistence.

    • Conclusions:

    • The new numerical scheme offers a robust solution for simulating periodic patterns accurately.
    • It enhances the prediction of equilibrium domain morphologies in complex systems like block copolymers.