In this paper, we present a simple and explicit finite difference method for the phase-field model for diblock copolymer melts. A diblock copolymer is a polymer consisting of two types of different monomers bonded covalently to each other to form a single copolymer chain. When the temperature is below the critical temperature, the copolymer melt exhibits microphase separation. The mathematical model is derived from a total free energy functional which contains kinetic, gradient, double well, and long-range nonlocal potentials. The Saul'yev-type scheme based on a linearly stabilized convex splitting method is used for the discretizations. The proposed method is simple and computationally efficient because the scheme is explicit and it does not require any iterative procedures. The proposed scheme not only overcomes the severe time step restriction for the explicit scheme but also works well for the simulations of lamellar and hex-cylinder structures which are characteristic morphologies for diblock copolymer melts after phase separation. Furthermore, the proposed method can be easily applied to the simulations in complex computational domains. We present various numerical tests to demonstrate the performance of the proposed scheme.
Bibliographical noteFunding Information:
C. Lee was supported by the National Research Foundation (NRF), Korea , under project BK21 FOUR. The corresponding author (J.S. Kim) was supported by Korea University Grant . The authors appreciate the reviewers for their insightful comments on the revision of this manuscript.
© 2022 Elsevier B.V.
- Diblock copolymer melts
- Explicit finite difference method
- Saul'yev-type method
ASJC Scopus subject areas
- General Computer Science
- General Chemistry
- General Materials Science
- Mechanics of Materials
- General Physics and Astronomy
- Computational Mathematics