Self-consistent field theory simulations of block copolymer assembly on a sphere

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 75, Issue 3, 2007, Pages

  Chantawansri, Tanya L ^a   Bosse, August W ^b   Hexemer, Alexander ^a,c   Ceniceros, Hector D ^b   García Cervera, Carlos J ^b   Kramer, Edward J ^a,b   Fredrickson, Glenn H ^a,b  

^a University of California   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CYLINDRICAL PHASES; SELF CONSISTENT FIELD THEORY (SCFT); THRESHOLD VALUES;

APPROXIMATION THEORY; COMPUTER SIMULATION; DEFECT STRUCTURES; FREE ENERGY; GROUND STATE;

BLOCK COPOLYMERS;

EID: 33947642483     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.75.031802     Document Type: Article

References (58)

1. J. J. Thomson, Philos. Mag. PHMAA4 0031-8086 7, 237 (1904).
2. B. K. Ganser, S. Li, V. Y. Klishko, J. T. Finch, and W. I. Sundquist, Science SCIEAS 0036-8075 10.1126/science.283.5398.80 283, 80 (1999).
3. C. Varea, J. L. Aragon, and R. A. Barrio, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.4588 60, 4588 (1999).
4. J. Heuser, J. Cell Biol. JCLBA3 0021-9525 10.1083/jcb.108.2.401 108, 401 (1989).
5. T. Kohyama, D. M. Kroll, and G. Gompper, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.061905 68, 061905 (2003).
6. A. R. Bausch, M. J. Bowick, A. Cacciuto, A. D. Dinsmore, M. F. Hsu, D. R. Nelson, M. G. Nikolaides, A. Travesset, and D. A. Weitz, Science SCIEAS 0036-8075 10.1126/science.1081160 299, 1716 (2003).
7. T. Einert, P. Lipowsky, J. Schilling, M. J. Bowick, and A. R. Bausch, Langmuir LANGD5 0743-7463 10.1021/la0517383 21, 12076 (2005).
8. P. Leiderer, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01338394 98, 303 (1995).
9. M. J. Bowick, D. R. Nelson, and A. Travesset, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.8738 62, 8738 (2000).
10. A. Travesset, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.115421 68, 115421 (2003).
11. S. Schneider and G. Gompper, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2004-10464-2 70, 136 (2005).
12. A. Travesset, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.036110 72, 036110 (2005).
13. M. J. Bowick, A. Cacciuto, D. R. Nelson, and A. Travesset, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.185502 89, 185502 (2002).
14. M. Bowick, A. Cacciuto, D. R. Nelson, and A. Travesset, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.249902 89, 249902 (E) (2002).
15. M. J. Bowick, A. Cacciuto, D. R. Nelson, and A. Travesset, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.024115 73, 024115 (2006).
16. D. R. Nelson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.50. 982 50, 982 (1983).
17. J. P. Gaspard, J. F. Sadoc, and R. Mosseri, Proceedings of the Second International Conference on The Structure of Non-Crystalline Materials, Cambridge, 1982 (Taylor and Francis, London, 1982).
18. S. Sachdev and D. R. Nelson, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/17/30/019 17, 5473 (1984).
19. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Oxford Science, New York, 1993).
20. F. C. Frank, Discuss. Faraday Soc. DFSOAW 0014-7664 10.1039/df9582500019 25, 19 (1958).
21. P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, UK, 1995).
22. C. Blanc and M. Kleman, Eur. Phys. J. E EPJSFH 1292-8941 10.1007/s101890170134 4, 241 (2001).
23. R. D. Kamien, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.953 74, 953 (2002).
24. D. R. Nelson, Nano Lett. NALEFD 1530-6984 10.1021/nl0202096 2, 1125 (2002).
25. T. C. Lubensky and J. Prost, J. Phys. II JPAHER 1155-4312 10.1051/jp2:1992133 2, 371 (1992).
26. W. Helfrich, Z. Naturforsch. C ZNFCAP 0341-0471 28, 693 (1973).
27. A. E. Lobkovsky and T. A. Witten, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.1577 55, 1577 (1997).
28. V. Vitelli and A. M. Turner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.215301 93, 215301 (2004).
29. V. Vitelli and D. R. Nelson, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.051105 70, 051105 (2004).
30. V. Vitelli, Ph.D. thesis, Harvard, 2006 (unpublished).
31. P. Tang, F. Qiu, H. Zhang, and Y. Yang, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.016710 72, 016710 (2005).
32. J. F. Li, J. Fan, H. D. Zhang, F. Qiu, P. Tang, and Y. L. Yang, Eur. Phys. J. E EPJSFH 1292-8941 10.1140/epje/i2006-10035-y 20, 449 (2006).
33. J.-R. Roan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96. 248301 96, 248301 (2006).
34. E. Helfand, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.430517 62, 999 (1975).
35. M. W. Matsen and M. Schick, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.2660 72, 2660 (1994).
36. G. H. Fredrickson, The Equilibrium Theory of Inhomogenous Polymers (Clarendon, Oxford, 2006).
37. M. W. Matsen, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.473778 106, 7781 (1997).
38. M. W. Matsen, Curr. Opin. Colloid Interface Sci. COCSFL 1359-0294 3, 40 (1998).
39. D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications (Society for Industrial and Applied Mathematics, Philadelphia, 1977).
40. J. Adams and P. N. Swarztrauber, computer code SPHEREPACK 3.1 (2003), http://www.scd.ucar.edu/css/software/spherepack
41. K. O. Rasmussen and G. Kalosakas, J. Polym. Sci., Part B: Polym. Phys. JPBPEM 0887-6266 10.1002/polb.10238 40, 1777 (2002).
42. F. S. Bates and G. H. Fredrickson, Annu. Rev. Phys. Chem. ARPLAP 0066-426X 42, 525 (1990).
43. G. H. Fredrickson, V. Ganesan, and F. Drolet, Macromolecules MAMOBX 0024-9297 10.1021/ma011515t 35, 16 (2002).
44. J. J. Sakurai, Modern Quantum Mechanics, Rev. ed. (Addison-Wesley, Reading, MA, 1994).
45. M. Frigo and S. G. Johnson, Proc. IEEE IEEPAD 0018-9219 10.1109/JPROC.2004.840301 93, 216 (2005).
46. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, San Diego, 1995).
47. H. D. Ceniceros and G. H. Fredrickson, Multiscale Model. Simul. MMSUBT 1540-3459 2, 452 (2004).
48. K. Amundson and E. Helfand, Macromolecules MAMOBX 0024-9297 10.1021/ma00058a022 26, 1324 (1993).
49. C. Harrison, Z. Cheng, S. Sethuraman, D. A. Huse, P. M. Chaikin, D. A. Vega, J. M. Sebastian, R. A. Register, and D. H. Adamson, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.011706 66, 011706 (2002).
50. J. P. Boyd, Chebyshev and Fourier Spectral Methods (Dover, Mineola, NY, 2000).
51. P. N. Swarztrauber, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. SJNAEQ 0036-1429 10.1137/0716069 16, 934 (1979).
52. P. N. Swarztrauber, Mon. Weather Rev. MWREAB 0027-0644 10.1175/1520-0493(1993)121<3415:TVHTMF>2.0.CO;2 121, 3415 (1993).
53. B. Machenhauer and R. Daley (unpublished).
54. A. N. Semenov, Sov. Phys. JETP SPHJAR 0038-5646 61, 733 (1985).
55. G. H. Fredrickson, Macromolecules MAMOBX 0024-9297 10.1021/ma00068a043 26, 4351 (1993).
56. Numerical SCFT is difficult at χN 25, because the interfacial scale becomes much narrower than the microdomain period and a large amount of spatial and contour resolution is required [M. W. Matsen, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1374211 114, 10528 (2001)].
57. R. A. Segalman, A. Hexemer, R. C. Hayward, and E. J. Kramer, Macromolecules MAMOBX 0024-9297 10.1021/ma021367m 36, 3272 (2003).
58. M. R. Hammond, S. W. Sides, G. H. Fredrickson, E. J. Kramer, J. Ruokolainen, and S. F. Hahn, Macromolecules MAMOBX 0024-9297 10.1021/ma026001o 36, 8712 (2003).