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 |
Bibliographical note
Funding Information:The first author (D. Jeong) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2014R1A6A3A01009812 ). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) ( NRF-2014R1A2A2A01003683 ). The authors are grateful to the reviewers whose valuable suggestions and comments significantly improved the quality of this paper.
Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.
Keywords
- Cahn-Hilliard equation
- Diblock copolymer
- Fourier-spectral method
- Hex-cylinder phase
- Nonlocal
ASJC Scopus subject areas
- General Materials Science
- General Physics and Astronomy