Directing the self-assembly of block copolymers into a metastable complex network phase via a deep and rapid quench

Physical Review Letters

Volumn 111, Issue 26, 2013, Pages

  Müller, Marcus ^a   Sun, De Wen ^a  

^a Institut Theoretische Physik   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COARSE GRAINED MODELS; FREE-ENERGY LANDSCAPE; MOLECULAR ARCHITECTURE; MOLECULAR CONFORMATION; PARTICLE-BASED SIMULATION; PERIODIC MINIMAL SURFACES; SELF-ASSEMBLING BLOCK COPOLYMERS; SPONTANEOUS FORMATION;

BLENDING; BLOCK COPOLYMERS; COMPUTER SIMULATION; FREE ENERGY;

SELF ASSEMBLY;

EID: 84891708705     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.111.267801     Document Type: Article

References (47)

1. M. W. Matsen and F. S. Bates, Macromolecules 29, 1091 (1996). MAMOBX 0024-9297 10.1021/ma951138i
2. F. Drolet and G. H. Fredrickson, Phys. Rev. Lett. 83, 4317 (1999). PRLTAO 0031-9007 10.1103/PhysRevLett.83.4317
3. Y. Bohbot-Raviv and Z.-G. Wang, Phys. Rev. Lett. 85, 3428 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.85.3428
4. Z. J. Guo, G. J. Zhang, F. Qiu, H. D. Zhang, Y. L. Yang, and A. C. Shi, Phys. Rev. Lett. 101, 028301 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101. 028301
5. C.-Z. Zhang and Z.-G. Wang, Phys. Rev. E 73, 031804 (2006). PLEEE8 1539-3755 10.1103/PhysRevE.73.031804
6. A. J. Meuler, M. A. Hillmyer, and F. S. Bates, Macromolecules 42, 7221 (2009). MAMOBX 0024-9297 10.1021/ma9009593
7. H. Sai, K. W. Tan, K. Hur, E. Asenath-Smith, R. Hovden, Y. Jiang, M. Riccio, D. A. Muller, V. Elser, L. A. Estroff, S. M. Gruner, and U. Wiesner, Science 341, 530 (2013). SCIEAS 0036-8075 10.1126/science.1238159
8. T. A. Shefelbine, M. E. Vigild, M. W. Matsen, D. A. Hajduk, M. A. Hillmyer, E. L. Cussler, and F. S. Bates, J. Am. Chem. Soc. 121, 8457 (1999). JACSAT 0002-7863 10.1021/ja991442h (Pubitemid 29453380)
9. B. K. Cho, A. Jain, S. M. Gruner, and U. Wiesner, Science 305, 1598 (2004). SCIEAS 0036-8075 10.1126/science.1100872 (Pubitemid 39296350)
10. A. M. Urbas, M. Maldovan, P. DeRege, and E. L. Thomas, Adv. Mater. 14, 1850 (2002). ADVMEW 0935-9648 10.1002/adma.200290018
11. K. Hur, Y. Francescato, V. Giannini, S. A. Maier, R. G. Hennig, and U. Wiesner, Angew. Chem., Int. Ed. Engl. 50, 11985 (2011). ACIEAY 0570-0833 10.1002/anie.201104888
12. R. Mezzenga, W. B. Lee, and G. H. Fredrickson, Trends Food Sci. Technol. 17, 220 (2006). TFTEEH 0924-2244 10.1016/j.tifs.2005.11.009
13. M. W. Matsen, Phys. Rev. Lett. 99, 148304 (2007); PRLTAO 0031-9007 10.1103/PhysRevLett.99.148304 M. W. Matsen, Phys. Rev. Lett. 74, 4225 (1995). PRLTAO 0031-9007 10.1103/PhysRevLett.74.4225
14. T. Dotera, Phys. Rev. Lett. 89, 205502 (2002). PRLTAO 0031-9007 10.1103/PhysRevLett.89.205502
15. F. J. Martinez-Veracoechea and F. A. Escobedo, Macromolecules 42, 1775; MAMOBX 0024-9297 10.1021/ma802427a F. J. Martinez-Veracoechea and F. A. Escobedo Macromolecules 42, 9058 (2009). MAMOBX 0024-9297 10.1021/ma901591r
16. B. Rathke, H. Baumgartl, and R. Strey, AIP Conf. Proc. 534, 414 (2000).
17. U. Heuert, M. Krumova, G. Hempel, M. Schiewek, and A. Blume, Rev. Sci. Instrum. 81, 105102 (2010). RSINAK 0034-6748 10.1063/1.3481164
18. F. S. Bates and P. Wiltzius, J. Chem. Phys. 91, 3258 (1989). JCPSA6 0021-9606 10.1063/1.456901
19. J. Kojima, M. Takenaka, Y. Nakayama, and T. Hashimoto, Macromolecules 32, 1809 (1999). MAMOBX 0024-9297 10.1021/ma980799n
20. M. Takenaka, H. Takeno, T. Hashimoto, and M. Nagao, J. Chem. Phys. 124, 104904 (2006). JCPSA6 0021-9606 10.1063/1.2149861
21. M. Müller and J. J. de Pablo, Annu. Rev. Mater. Sci. 43, 1 (2013). ARMSCX 0084-6600 10.1146/annurev-matsci-071312-121618
22. The metastability of the hexagonally perforated phase along the MFEP from the lamellar to gyroid morphology has been observed in X. Cheng, L. Lin, W. E, P. Zhang, and A. C. Shi, Phys. Rev. Lett. 104, 148301 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.104.148301
23. T. P. Lodge, Macromol. Chem. Phys. 204, 265 (2003). MCHPES 1022-1352 10.1002/macp.200290073
24. L. Maragliano and E. Vanden-Eijnden, Chem. Phys. Lett. 446, 182 (2007). CHPLBC 0009-2614 10.1016/j.cplett.2007.08.017 (Pubitemid 47381528)
25. M. Venturoli, E. Vanden-Eijnden, and G. Ciccotti, J. Math. Chem. 45, 188 (2009). JMCHEG 0259-9791 10.1007/s10910-008-9376-5
26. M. Müller, Y. G. Smirnova, G. Marelli, M. Fuhrmans, and A. C. Shi, Phys. Rev. Lett. 108, 228103 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108. 228103
27. W. Zhang, T. J. Li, and P. W. Zhang, Commun. Math. Sci. 10, 1105 (2012). 1539-6746 10.4310/CMS.2012.v10.n4.a4
28. K. C. Daoulas, M. Müller, J. J. de Pablo, P. F. Nealey, and G. D. Smith, Soft Matter 2, 573 (2006). SMOABF 1744-683X 10.1039/b602610a (Pubitemid 43938473)
29. M. Müller, J. Stat. Phys. 145, 967 (2011). JSTPBS 0022-4715 10.1007/s10955-011-0302-z
30. M. W. Matsen, J. Phys. Condens. Matter 14, R21 (2002). JCOMEL 0953-8984 10.1088/0953-8984/14/2/201 (Pubitemid 34133730)
31. J. J. Watkins, G. D. Brown, V. S. Ramachandra Rao, M. A. Pollard, and T. P. Russell, Macromolecules 32, 7737 (1999). MAMOBX 0024-9297 10.1021/ma9906377 (Pubitemid 30509417)
32. D. L. Tomasko, H. B. Li, D. H. Liu, X. M. Han, M. J. Wingert, L. J. Lee, and K. W. Koelling, Ind. Eng. Chem. Res. 42, 6431 (2003). IECRED 0888-5885 10.1021/ie030199z
33. E. Yoshida and A. Mineyama, Colloid Polym. Sci. 290, 183 (2012). CPMSB6 0303-402X 10.1007/s00396-011-2536-3
34. L. Y. Shi, Z. H. Shen, and X. H. Fan, Macromolecules 44, 2900 (2011). MAMOBX 0024-9297 10.1021/ma1023704
35. M. Müller, L. G. MacDowell, P. Müller-Buschbaum, O. Wunnike, and M. Stamm, J. Chem. Phys. 115, 9960 (2001). JCPSA6 0021-9606 10.1063/1.1413985 (Pubitemid 33147351)
36. M. Müller, L. G. MacDowell, P. Virnau, and K. Binder, J. Chem. Phys. 117, 5480 (2002). JCPSA6 0021-9606 10.1063/1.1497636
37. E. W. Edwards, M. P. Stoykovich, M. Müller, H. H. Solak, J. J. de Pablo, and P. F. Nealey, J. Polym. Sci. B 43, 3444 (2005). JPLPAY 0887-6266 10.1002/polb.20643 (Pubitemid 43080541)
38. A. H. Schoen, NASA Technical Note No. TN D-5541, 1970 [http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19700020472-1970020472. pdf].
39. P. J. F. Gandy, S. Bardhan, A. L. Mackay, and J. Klinowski, Chem. Phys. Lett. 336, 187 (2001). CHPLBC 0009-2614 10.1016/S0009-2614(00)01418-4 (Pubitemid 33628088)
40. G. E. Schröder-Turk, A. Fogden, and S. T. Hyde, Eur. Phys. J. B 59, 115 (2007). EPJBFY 1434-6028 10.1140/epjb/e2007-00272-6 (Pubitemid 47536704)
41. M. Müller and K. C. Daoulas, Phys. Rev. Lett. 107, 227801 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.107.227801
42. W. E, W. Ren, and E. Vanden-Eijnden, J. Chem. Phys. 126, 164103 (2007). JCPSA6 0021-9606 10.1063/1.2720838 (Pubitemid 46691181)
43. I. G. Kevrekidis, C. W. Gear, and G. Hummer, AIChE J. 50, 1346 (2004). AICEAC 0001-1541 10.1002/aic.10106 (Pubitemid 38856761)
44. The distance of morphologies at s and s ′ is proportional to ∫ d r {( A s- A s ′) 2 + ( B s- B s ′) 2} and we discretized the path into 24 morphologies. The simulations exceeded 10 6 MC steps, and the accuracy of the free energy per chain is on the order of 0.5 k B T.
45. The saddle point between this I-WP and the bcc morphology is affected by the single unit cell. In a larger system the transition would proceed via nucleation.
46. Alternatively, this defining condition for the MFEP with conserved order parameter can be derived by considering the transformation from the particle coordinates to the collective densities; cf. L. Maragliano, A. Fischer, E. Vanden-Eijnden, and G. Ciccotti, J. Chem. Phys. 125, 024106 (2006). JCPSA6 0021-9606 10.1063/1.2212942 (Pubitemid 44088333)
47. G. H. Fredrickson, J. Chem. Phys. 117, 6810 (2002). JCPSA6 0021-9606 10.1063/1.1505025 (Pubitemid 35327233)