Energy-minimizing wavelengths of equilibrium states for diblock copolymers in the hex-cylinder phase
- 주제(키워드) Diblock copolymer , Fourier-spectral method , Hex-cylinder phase , Nonlocal CahneHilliard equation
- 발행기관 한국물리학회
- 발행년도 2015
- 총서유형 Journal
- KCI ID ART002014564
- 본문언어 영어
초록/요약
We investigate the energy-minimizing wavelengths of equilibrium states for diblock copolymers in the hex-cylinder phase. The mathematical model is the CahneHilliard 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.
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