### 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 |
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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 |

### Keywords

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

### ASJC Scopus subject areas

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

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## Cite this

*Current Applied Physics*,

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