Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing

被引:130
作者
Matsen, M. W. [1 ]
机构
[1] Univ Reading, Dept Math, Reading RG6 6AX, Berks, England
基金
英国工程与自然科学研究理事会;
关键词
MICROPHASE SEPARATION; ORDERED PHASES; SPHERICAL MICELLES; DIBLOCK COPOLYMERS; FDDD PHASE; STABILITY; CONVERGENCE;
D O I
10.1140/epje/i2009-10534-3
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
We study the numerical efficiency of solving the self-consistent field theory (SCFT) for periodic block-copolymer morphologies by combining the spectral method with Anderson mixing. Using AB diblock-copolymer melts as an example, we demonstrate that this approach can be orders of magnitude faster than competing methods, permitting precise calculations with relatively little computational cost. Moreover, our results raise significant doubts that the gyroid ( G) phase extends to infinite chi N. With the increased precision, we are also able to resolve subtle free-energy differences, allowing us to investigate the layer stacking in the perforated-lamellar (PL) phase and the lattice arrangement of the close-packed spherical (S-cp) phase. Furthermore, our study sheds light on the existence of the newly discovered Fddd (O-70) morphology, showing that conformational asymmetry has a significant effect on its stability.
引用
收藏
页码:361 / 369
页数:9
相关论文
共 40 条
[1]   FLUCTUATIONS, CONFORMATIONAL ASYMMETRY AND BLOCK-COPOLYMER PHASE-BEHAVIOR [J].
BATES, FS ;
SCHULZ, MF ;
KHANDPUR, AK ;
FORSTER, S ;
ROSEDALE, JH ;
ALMDAL, K ;
MORTENSEN, K .
FARADAY DISCUSSIONS, 1994, 98 :7-18
[2]   Numerical solution of polymer self-consistent field theory [J].
Ceniceros, HD ;
Fredrickson, GH .
MULTISCALE MODELING & SIMULATION, 2004, 2 (03) :452-474
[3]  
Cochran E.W., COMMUNICATION
[4]   Stability of the gyroid phase in diblock copolymers at strong segregation [J].
Cochran, EW ;
Garcia-Cervera, CJ ;
Fredrickson, GH .
MACROMOLECULES, 2006, 39 (07) :2449-2451
[5]   A comparative study on methods for convergence acceleration of iterative vector sequences [J].
Eyert, V .
JOURNAL OF COMPUTATIONAL PHYSICS, 1996, 124 (02) :271-285
[6]  
Fredrickson G., 2006, The Equilibrium Theory of Inhomogeneous Polymers
[7]   FLUCTUATION EFFECTS IN THE THEORY OF MICROPHASE SEPARATION IN BLOCK COPOLYMERS [J].
FREDRICKSON, GH ;
HELFAND, E .
JOURNAL OF CHEMICAL PHYSICS, 1987, 87 (01) :697-705
[8]   Renormalization of the one-loop theory of fluctuations in polymer blends and diblock copolymer melts [J].
Grzywacz, Piotr ;
Qin, Jian ;
Morse, David C. .
PHYSICAL REVIEW E, 2007, 76 (06)
[9]   Discovering ordered phases of block copolymers: New results from a generic Fourier-space approach [J].
Guo, Zuojun ;
Zhang, Guojie ;
Qiu, Feng ;
Zhang, Hongdong ;
Yang, Yuliang ;
Shi, An-Chang .
PHYSICAL REVIEW LETTERS, 2008, 101 (02)
[10]   Stability of the perforated layer (PL) phase in diblock copolymer melts [J].
Hajduk, DA ;
Takenouchi, H ;
Hillmyer, MA ;
Bates, FS ;
Vigild, ME ;
Almdal, K .
MACROMOLECULES, 1997, 30 (13) :3788-3795