Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T19:20:13.596Z Has data issue: false hasContentIssue false
  • English
  • Français

Discovery of New Metastable Patterns in Diblock Copolymers

Published online by Cambridge University Press:  03 June 2015

Kai Jiang ,
Chu Wang ,
Yunqing Huang  and
Pingwen Zhang
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
*
Email:chu.wang.pku@gmail.com
Email:huangyq@xtu.edu.cn
Corresponding author.Email:pzhang@pku.edu.cn
Email:jiangkai@pku.edu.cn
Get access

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.

Keywords

65M7076A15Metastable patternsdiblock copolymersself-consistent field theory (SCFT)space group theoryinitial values
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 2 , August 2013 , pp. 443 - 460
Copyright
Copyright © Global Science Press Limited 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Park, C., Yoon, J., and Thomas, E.L.Enabling nanotechnology with self assembled block copolymer patterns. Polymer, 44(22):6725–6760, 2003.Google Scholar
[2]Lodge, T.P.Block copolymers: past successes and future challenges. Macromolecular Chemistry and Physics, 204(2):265–273, 2003.Google Scholar
[3]Matsen, M.W.The standard Gaussian model for block copolymer melts. Journal of Physics: Condensed Matter, 14:R21–R47, 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):7667–7670, 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):533–562, 1998.Google 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):367–450, 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):301–316, 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):4225–4228, 1995.CrossRefGoogle ScholarPubMed
[11]Matsen, M.W. and Schick, M.Stable and unstable phases of a diblock copolymer melt. Physical Review Letters, 72(16):2660–2663, 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):4317–4320, 1999.Google 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):1777–1783, 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):2449–2451, 2006.Google 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, 2:452–474, 2004.Google 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, 229:7796–7805,2010.Google 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):1602–1617, 1980.Google 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):4063–4075, 1994.Google 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):383–406, 2005.Google Scholar
[24]Ranjan, A. and Morse, D.C.Landau theory of the orthorhombic Fddd phase. Physical Review E, 74(1):11803, 2006.Google Scholar
[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.Google 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):72–84, 2009.CrossRefGoogle Scholar