### 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 language | English |
---|---|

Pages (from-to) | 799-804 |

Number of pages | 6 |

Journal | Current Applied Physics |

Volume | 15 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2015 Apr 25 |

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### 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

*Current Applied Physics*,

*15*(7), 799-804. https://doi.org/10.1016/j.cap.2015.04.033

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

Research output: Contribution to journal › Article

*Current Applied Physics*, vol. 15, no. 7, pp. 799-804. https://doi.org/10.1016/j.cap.2015.04.033

}

TY - JOUR

T1 - Energy-minimizing wavelengths of equilibrium states for diblock copolymers in the hex-cylinder phase

AU - Jeong, Darae

AU - Lee, Seunggyu

AU - Choi, Yongho

AU - Kim, Junseok

PY - 2015/4/25

Y1 - 2015/4/25

N2 - 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.

AB - 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.

KW - Cahn-Hilliard equation

KW - Diblock copolymer

KW - Fourier-spectral method

KW - Hex-cylinder phase

KW - Nonlocal

UR - http://www.scopus.com/inward/record.url?scp=84928943554&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84928943554&partnerID=8YFLogxK

U2 - 10.1016/j.cap.2015.04.033

DO - 10.1016/j.cap.2015.04.033

M3 - Article

AN - SCOPUS:84928943554

VL - 15

SP - 799

EP - 804

JO - Current Applied Physics

JF - Current Applied Physics

SN - 1567-1739

IS - 7

ER -