Energy-minimizing wavelengths of equilibrium states for diblock copolymers in the hex-cylinder phase
- Authors
- Jeong, Darae; Lee, Seunggyu; Choi, Yongho; Kim, Junseok
- Issue Date
- 7월-2015
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- Diblock copolymer; Fourier-spectral method; Hex-cylinder phase; Nonlocal Cahn-Hilliard equation
- Citation
- CURRENT APPLIED PHYSICS, v.15, no.7, pp.799 - 804
- Indexed
- SCIE
SCOPUS
KCI
- Journal Title
- CURRENT APPLIED PHYSICS
- Volume
- 15
- Number
- 7
- Start Page
- 799
- End Page
- 804
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/93164
- DOI
- 10.1016/j.cap.2015.04.033
- ISSN
- 1567-1739
- 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 root 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. (C) 2015 Elsevier B.V. All rights reserved.
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