Chinese Journal of Polymer Science

, Volume 36, Issue 4, pp 488–496 | Cite as

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


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 O70 phase, the lamellar phase and the cylindrical phase.


Block copolymer Self-consistent field theory Algorithm Pseudo-spectral Phase structure 


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This work was financially supported by the China Scholarship Council (No. 201406105018), the National Natural Science Foundation of China (No. 21004013) and the National Basic Research Program of China (No. 2011CB605701).


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Copyright information

© Chinese Chemical Society, Institute of Chemistry, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular ScienceFudan UniversityShanghaiChina

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