An Efficient Algorithm for Self-consistent Field Theory Calculations of Complex Self-assembled Structures of Block Copolymer Melts
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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.
KeywordsBlock 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).
- 2.de Gennes, P. G. "Scaling concepts in polymer physics", Cornell University Press, Ithaca 1969.Google Scholar
- 5.Fredrickson, G. H. "The equilibrium theory of inhomogeneous polymers", Oxford University Press, New York 2006.Google Scholar
- 14.Semenov, A. N. Contribution to the theory of microphase layering in block-copolymer melts. Zh. Eksp. Teor. Fiz. 1985, 88(4), 1242–1256.Google Scholar
- 21.Stasiak, P.; Matsen, M. W. Efficiency of pseudo-spectral algorithms with Anderson mixing for the SCFT of periodic block-copolymer phases. Eur. Phys. J. E 2011, 34(10), DOI: 10.1140/epje/i2011-11110-0Google Scholar
- 22.Liu, Y. X.; Zhang, H. D. Exponential time differencing methods with Chebyshev collocation for polymers confined by interacting surfaces. J. Chem. Phys. 2014, 140(22), DOI: 10.1063/1.4881516Google Scholar
- 25.Krogstad, S. "Topics in numerical Lie group integration", Ph.D. thesis, The University of Bergen, 2003.Google Scholar
- 33.Tyler, C. A.; Morse, D. C. Orthorhombic Fddd network in triblock and diblock copolymer melts. Phys. Rev. Lett. 2005, 94(20), DOI: 10.1103/PhysRevLett.94.208302Google Scholar
- 34.Press, W. H., Teukolsky, S. A. Vetterling, W. T. and Flannery, B. P., "Numerical recipes 3rd edition: The art of scientific computing", Cambridge University Press, New York 2007.Google Scholar