An Efficient Algorithm for Self-consistent Field Theory Calculations of Complex Self-assembled Structures of Block Copolymer Melts

Jun-Qing Song; Yi-Xin Liu; Hong-Dong Zhang

doi:10.1007/s10118-018-2037-7

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An Efficient Algorithm for Self-consistent Field Theory Calculations of Complex Self-assembled Structures of Block Copolymer Melts

Articles | Updated：2021-02-18

- An Efficient Algorithm for Self-consistent Field Theory Calculations of Complex Self-assembled Structures of Block Copolymer Melts
- An Efficient Algorithm for Self-consistent Field Theory Calculations of Complex Self-assembled Structures of Block Copolymer Melts
- Chinese Journal of Polymer Science 2018年36卷第4期页码：488-496
- Affiliations：
  
  State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
- Author bio：
  
  Yi-Xin Liu, E-mail lyx@fudan.edu.cn
- Funds：
- DOI：10.1007/s10118-018-2037-7
  中图分类号：
- 收稿：2017-07-02，
  
  录用：2017-9-8，
  
  网络首发：2017-12-29，
  
  纸质出版：2018-04-05
- Accepted：
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Jun-Qing Song, Yi-Xin Liu, Hong-Dong Zhang. An Efficient Algorithm for Self-consistent Field Theory Calculations of Complex Self-assembled Structures of Block Copolymer Melts[J]. Chinese Journal of Polymer Science, 2018,36(4):488-496.

Jun-Qing Song, Yi-Xin Liu, Hong-Dong Zhang. An Efficient Algorithm for Self-consistent Field Theory Calculations of Complex Self-assembled Structures of Block Copolymer Melts[J]. Chinese Journal of Polymer Science, 2018, 36(4): 488-496.
Jun-Qing Song, Yi-Xin Liu, Hong-Dong Zhang. An Efficient Algorithm for Self-consistent Field Theory Calculations of Complex Self-assembled Structures of Block Copolymer Melts[J]. Chinese Journal of Polymer Science, 2018,36(4):488-496. DOI： 10.1007/s10118-018-2037-7.

Jun-Qing Song, Yi-Xin Liu, Hong-Dong Zhang. An Efficient Algorithm for Self-consistent Field Theory Calculations of Complex Self-assembled Structures of Block Copolymer Melts[J]. Chinese Journal of Polymer Science, 2018, 36(4): 488-496. DOI： 10.1007/s10118-018-2037-7.

摘要

Abstract

Self-consistent field theory (SCFT)

as a state-of-the-art technique for studying the self-assembly of block copolymers

is attracting continuous efforts to improve its accuracy and efficiency. Here we present a fourth-order exponential time differencing Runge-Kutta algorithm (ETDRK4) to solve the modified diffusion equation (MDE) which is the most time-consuming part of a SCFT calculation. By making a careful comparison with currently most efficient and popular algorithms

we demonstrate that the ETDRK4 algorithm significantly reduces the number of chain contour steps in solving the MDE

resulting in a boost of the overall computation efficiency

while it shares the same spatial accuracy with other algorithms. In addition

to demonstrate the power of our ETDRK4 algorithm

we apply it to compute the phase boundaries of the bicontinuous gyroid phase in the strong segregation regime and to verify the existence of the triple point of the O

phase

the lamellar phase and the cylindrical phase.

关键词

Keywords

references

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