Energy-minimizing wavelengths of equilibrium states for diblock copolymers in the hex-cylinder phase

Darae Jeong, Seunggyu Lee, Yongho Choi, Junseok Kim

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We investigate the energy-minimizing wavelengths of equilibrium states for diblock copolymers in the hex-cylinder phase. The mathematical model is the Cahn-Hilliard equation with long-range interactions. The numerical scheme is based on a linearly gradient stable method and the resulting discrete system of equations is solved by a Fourier-spectral method. We solve the equations in non-square domains because the periodic unit is not a square. We choose the computational domains as rectangles of aspect ratio 3 (height/width). We run the computation until the system reaches a numerical equilibrium state. We repeat these calculations in domains of gradually increasing size and then find the wavelength that minimizes the domain-size-scaled total energy. We investigate the effect of the parameters on the energy-minimizing wavelength. We also propose a formula for a non-square domain that is close to a square domain and has an exact periodicity.

Original languageEnglish
Pages (from-to)799-804
Number of pages6
JournalCurrent Applied Physics
Volume15
Issue number7
DOIs
Publication statusPublished - 2015 Apr 25

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Block copolymers
copolymers
Wavelength
wavelengths
energy
Aspect ratio
Mathematical models
rectangles
spectral methods
aspect ratio
periodic variations
mathematical models
gradients
interactions

Keywords

  • Cahn-Hilliard equation
  • Diblock copolymer
  • Fourier-spectral method
  • Hex-cylinder phase
  • Nonlocal

ASJC Scopus subject areas

  • Materials Science(all)
  • Physics and Astronomy(all)

Cite this

Energy-minimizing wavelengths of equilibrium states for diblock copolymers in the hex-cylinder phase. / Jeong, Darae; Lee, Seunggyu; Choi, Yongho; Kim, Junseok.

In: Current Applied Physics, Vol. 15, No. 7, 25.04.2015, p. 799-804.

Research output: Contribution to journalArticle

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