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Discovery of New Metastable Patterns in Diblock Copolymers

Published online by Cambridge University Press:  03 June 2015

Kai Jiang*
Affiliation:
LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, P.R. China
Chu Wang*
Affiliation:
LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China
Yunqing Huang*
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, P.R. China
Pingwen Zhang*
Affiliation:
LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China
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Abstract

The ordered patterns formed by microphase-separated block copolymer systems demonstrate periodic symmetry, and all periodic structures belong to one of 230 space groups. Based on this fact, a strategy of estimating the initial values of self-consistent field theory to discover ordered patterns of block copolymers is developed. In particular, the initial period of the computational box is estimated by the Landau-Brazovskii model as well. By planting the strategy into the whole-space discrete method, several new metastable patterns are discovered in diblock copolymers.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2013

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References

[1]Park, C., Yoon, J., and Thomas, E.L.Enabling nanotechnology with self assembled block copolymer patterns. Polymer, 44(22):67256760, 2003.CrossRefGoogle Scholar
[2]Lodge, T.P.Block copolymers: past successes and future challenges. Macromolecular Chemistry and Physics, 204(2):265273, 2003.CrossRefGoogle Scholar
[3]Matsen, M.W.The standard Gaussian model for block copolymer melts. Journal of Physics: Condensed Matter, 14:R21R47, 2002.Google Scholar
[4]Kim, M.I., Wakada, T., Akasaka, S., Nishitsuji, S., Saijo, K., Hasegawa, H., Ito, K., and Takenaka, M.Stability of the Fddd phase in diblock copolymer melts. Macromolecules, 41(20):76677670, 2008.CrossRefGoogle Scholar
[5]Cheng, S.Z.D. and Keller, A.The role of metastable states in polymer phase transitions: Concepts, principles, and experimental observations. Annual Review of Materials Science, 28(1):533562, 1998.CrossRefGoogle Scholar
[6]E, W., Engquist, B., Li, X., Ren, W., and Vanden-Eijnden, E.Heterogeneous multiscale methods: a review. Communications in Computational Physics, 2(3):367450, 2007.Google Scholar
[7]Abukhdeir, N.M. and Rey, A.D.Simulation of spherulite growth using a comprehensive approach to modeling the first-order isotropic/smectic-A mesophase transition. Communications in Computational Physics, 7(2):301316, 2010.Google Scholar
[8]Cheng, X., Lin, L., E, W., Zhang, P., and Shi, A.C.Nucleation of ordered phases in block copolymers. Physical Review Letters, 104(14):148301, 2010.CrossRefGoogle ScholarPubMed
[9]Grason, G.M., DiDonna, B.A., and Kamien, R.D.Geometric theory of diblock copolymer phases. Physical Review Letters, 91(5):58304, 2003.CrossRefGoogle ScholarPubMed
[10]Matsen, M.W.Stabilizing new morphologies by blending homopolymer with block copolymer. Physical Review Letters, 74(21):42254228, 1995.CrossRefGoogle ScholarPubMed
[11]Matsen, M.W. and Schick, M.Stable and unstable phases of a diblock copolymer melt. Physical Review Letters, 72(16):26602663, 1994.CrossRefGoogle ScholarPubMed
[12]Drolet, F. and Fredrickson, G.H.Combinatorial screening of complex block copolymer assembly with self-consistent field theory. Physical Review Letters, 83(21):43174320, 1999.CrossRefGoogle Scholar
[13]Guo, Z., Zhang, G., Qiu, F., Zhang, H., Yang, Y., and Shi, A.C.Discovering ordered phases of block copolymers: New results from a generic Fourier-space approach. Physical Review Letters, 101(2):28301, 2008.CrossRefGoogle ScholarPubMed
[14]Rasmussen, K.Ø. and Kalosakas, G.Improved numerical algorithm for exploring block copolymer mesophases. Journal of Polymer Science Part B: Polymer Physics, 40(16):17771783, 2002.CrossRefGoogle Scholar
[15]Cochran, E.W., Garcia-Cervera, C.J., and Fredrickson, G.H.Stability of the gyroid phase in diblock copolymers at strong segregation. Macromolecules, 39(7):24492451, 2006.CrossRefGoogle Scholar
[16]Thompson, R.B., Rasmussen, K.Ø., and Lookman, T.Improved convergence in block copolymer self-consistent field theory by Anderson mixing. The Journal of Chemical Physics, 120:31, 2004.CrossRefGoogle ScholarPubMed
[17]Ceniceros, H.D. and Fredrickson, G.H.Numerical solution of polymer self-consistent field theory. Multiscale Modeling and Simulation, 2:452474, 2004.CrossRefGoogle Scholar
[18]Stasiaka, P. and Matsen, M.W.Efficiency of pseudo-spectral algorithms with Anderson mixing for the SCFT of periodic block-copolymer phases. The European Physical Journal E, 34:110, 2011.CrossRefGoogle Scholar
[19]Jiang, K., Huang, Y., and Zhang, P.Spectral method for exploring patterns of diblock copolymers. Journal of Computational Physics, 229:77967805,2010.CrossRefGoogle Scholar
[20]Fredrickson, G.H.The equilibrium theory of inhomogeneous polymers. Oxford University Press, USA, 2006.Google Scholar
[21]Leibler, L.Theory of microphase separation in block copolymers. Macromolecules, 13(6):16021617, 1980.CrossRefGoogle Scholar
[22]Hajduk, D.A., Harper, P.E., Gruner, S.M., Honeker, C.C., Kim, G., Thomas, E.L., and Fetters, L.J.The gyroid: a new equilibrium morphology in weakly segregated diblock copolymers. Macromolecules, 27(15):40634075, 1994.CrossRefGoogle Scholar
[23]Erukhimovich, I.Y.Weak segregation theory and non-conventional morphologies in the ternary ABC triblock copolymers. The European Physical Journal E, 18(4):383406, 2005.CrossRefGoogle ScholarPubMed
[24]Ranjan, A. and Morse, D.C.Landau theory of the orthorhombic Fddd phase. Physical Review E, 74(1):11803, 2006.CrossRefGoogle ScholarPubMed
[25]Henry, N.F.M. and Lonsdale, K.International tables for X-ray crystallography. Kynoch Press, 1952.Google Scholar
[26]Fredrickson, G.H. and Helfand, E.Fluctuation effects in the theory of microphase separation in block copolymers. The Journal of Chemical Physics, 87:697, 1987.CrossRefGoogle Scholar
[27]Abreu, E., Douglas, J., Furtado, F. and Pereira, F.Operator splitting for three-Phase flow in heterogeneous porous media. Communications in Computational Physics, 6(1):7284, 2009.CrossRefGoogle Scholar
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Discovery of New Metastable Patterns in Diblock Copolymers
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