A Strong Segregation Theory for Ring Block Copolymers

doi:10.6023/A17050235

Abstract

Due to the ring structure with no free ends, the traditional strong-segregation theory for linear chains is not adequate for ring block copolymers. We developed the strong-segregation theory for ring block copolymers (SST-ring), by modifying both the entropic free energy term and the interfacial energy term. The ring block copolymer can only form two types of conformations, i.e., the loops on one side of an interface and the bridges connecting two interfaces. For the entropic energy originating from the stretching of the chain conformation under strong-segregation limit, we employ the strategy for calculating the entropic energy of looping and bridging chains connecting interfaces. Since the mixing of components is unavoidable for the ring triblock copolymers to adapt to the classical morphologies, we start from the propagating function of the self-consistent field theory, and deduce the formula of the interfacial energy between two two-component domains under the strong-segregation limit. The formula is reminiscent to the interfacial energy between two single-component domains, except that the Flory-Huggins parameter χ_AB between two components on each side of the interface is replaced by an effective parameter, χ_eff, which is a function of the composite fractions and the Flory-Huggins parameters between each components. The application of SST-ring to ring diblock copolymers is successful to describe the decreased characteristic length and the lifted order-disorder transition point, compared with the corresponding linear diblock copolymers with the same segment number N. We find that the critical χ_AB^N value of the ordered-disordered transition is 1.59 times that of the linear diblock polymers, and the characteristic lengths of the ring diblock copolymers are always 0.63 times of those of linear diblock copolymers. This agrees qualitatively with the predictions of the self-consistent theory, with slight quantitative difference originating from the strong-segregation limit assumption. For the SST-ring calculations for ring triblock copolymers in two-dimensions, corresponding to the film with the thickness much smaller than the radius of gyration of the polymer, we consider two types of micro phase structures:the classical morphologies (lamellae and cylinders) with multi-component domains, and the tiling-brick structures ([6,6,6] and[8,8,4], where the numbers denote the side numbers of the bricks) consisting of the single-component domains. SST-ring predicts that the ternary diagram consists of both types of the micro phase structures. When the Flory-Huggins parameters between any two components are equal, the phase diagram has a three-fold rotational symmetry to the center of the regular triangle, and three mirror symmetric axis crossing three vertices of the triangle, respectively. Our SST-ring theory is easy to be applied to different morphologies of ring block copolymers.

Key words: strong segregation theory, strong segregation limit, ring block copolymers, phase diagram, interfacial energy

Cite this article

Liu Ming, Yang Yingzi, Qiu Feng. A Strong Segregation Theory for Ring Block Copolymers[J]. Acta Chim. Sinica, 2017, 75(9): 884-892.

Export EndNote|Reference Manager|ProCite|BibTeX|RefWorks

share this article

References

[1] Bates, F. S.; Fredrickson, G. H. Annu. Rev. Phys. Chem. 1990, 41, 525.
[2] Bates, F. S.; Fredrickson, G. H. Phys. Today 1999, 52, 32.
[3] Hamley, I. W. Angew. Chem., Int. Ed. 2003, 42, 1692.
[4] Park, C.; Yoon, J.; Thomas, E. L. Polymer 2003, 44, 6725.
[5] Hashimoto, T.; Nagatoshi, K.; Todo, A.; Hasegawa, H.; Kawai, H. Macromolecules 1974, 7, 364.
[6] Hashimoto, T.; Todo, A.; Itoi, H.; Kawai, H. Macromolecules 1977, 10, 377.
[7] Todo, A.; Uno, H.; Miyoshi, K.; Hashimoto, T.; Kawai, H. Polym. Eng. Sci. 1977, 17, 587.
[8] Hashimoto, T.; Shibayama, M.; Kawai, H. Macromolecules 1980, 13, 1237.
[9] Hashimoto, T.; Fujimura, M.; Kawai, H. Macromolecules 1980, 13, 1660.
[10] Fujimura, M.; Hashimoto, H.; Kurahashi, K.; Hashimoto, T.; Kawai, H. Macromolecules 1981, 14, 1196.
[11] Finnemore, A.; Scherer, M.; Langford, R.; Mahajan, S.; Ludwigs, S.; Meldrum, F. C.; Steiner, U. Adv. Mater. 2009, 21, 3928.
[12] Hajduk, D.; Harper, P.; Gruner, S.; Honeker, C.; Kim, G.; Thomas, E.; Fetters, L. Macromolecules 1994, 27, 4063.
[13] Bailey, T.; Pham, H.; Bates, F. Macromolecules 2001, 34, 6994.
[14] Matsushita, Y.; Hayashida, K.; Dotera, T.; Takano, A. J. Phys. Condens. Matter 2011, 23, 284111.
[15] Huang, L.; Huang, T.; Bai, Y.; Zhou, Y. Acta Chim. Sinica 2016, 74, 990 (in Chinese). (黄磊, 黄通, 白永平, 周永丰, 化学学报, 2016, 74, 990.)
[16] Huang, F.; Xu, P.; Lü, Y.; Lin, S. Chin. J. Org. Chem. 2016, 36, 2220 (in Chinese). (黄锋, 徐鹏翔, 吕翌晟, 林绍梁, 有机化学, 2016, 36, 2220.)
[17] Wu, Y.; Tao, Y.; Cai, K.; Liu, S.; Zhang, Y.; Chi, Z.; Xu, J.; Wei, Y. Chin. J. Chem. 2015, 33, 1338.
[18] Wang, T.; Wang, H.; Xing, L.; Zhang, W.; Gao, C. Chin. J. Chem. 2015, 33, 207.
[19] Leibler, L. Macromolecules 1980, 13, 1602.
[20] Volker, A.; Simon, P. F. W. Block Copolymers I, Springer, Berlin, Heidelberg, 2005, pp. 125～212.
[21] Semenov, A. J. Exp. Theor. Phys. 1985, 61, 733.
[22] Milner, S. Macromolecules 1994, 27, 2333.
[23] Olmsted, P.; Milner, S. Macromolecules 1998, 31, 4011.
[24] Milner, S. T.; Witten, T. A.; Cates, M. E. Europhys. Lett. 1988, 5, 413.
[25] Klymko, T.; Subbotin, A.; ten Brinke, G. Macromolecules 2007, 40, 2863.
[26] Subbotin, A.; Klymko, T.; ten Brinke, G. Macromolecules 2007, 40, 2915.
[27] Klymko, T.; Subbotin, A.; ten Brinke, G. J. Chem. Phys. 2008, 129, 114902.
[28] Klymko, T.; Markov, V.; Subbotin, A.; ten Brinke, G. Soft Matter 2009, 5, 98.
[29] Matsen, M. W.; Schick, M. Phys. Rev. Lett. 1994, 72, 2660.
[30] Tyler, C.; Qin, J.; Bates, F. S.; Morse, D. Macromolecules 2007, 40, 4654.
[31] Zhang, G.; Qiu, F.; Zhang, H.; Yang, Y.; Shi, A. Macromolecules 2010, 43, 2981.
[32] Markov, V.; Subbotin, A.; ten Brinke, G. Phys. Rev. E 2011, 84, 041807.
[33] Zhang, G.; Fan, Z.; Yang, Y.; Qiu, F. J. Chem. Phys. 2011, 135, 174902.
[34] Kim, J. U.; Yang, Y. B.; Lee, W. B. Macromolecules 2012, 45, 3263.
[35] Xie, N.; Li, W.; Qiu, F.; Shi, A. ACS Macro Lett. 2014, 3, 906.
[36] Kikuchi, M.; Binder, K. J. Chem. Phys. 1994, 101, 3367.
[37] Groot, R.; Madden, T.; Tildesley, D. J. Chem. Phys. 1999, 110, 9739.
[38] Marko, J. F. Macromolecules 1993, 26, 1442.
[39] Grosberg, A. Y. Phys. Rev. Lett. 2000, 85, 3858.
[40] Moore, N. T.; Lua, R. C.; Grosberg, A. Y. Proc. Natl. Acad. Sci. U. S. A. 2004, 101, 13431.
[41] Suzuki, J.; Takano, A.; Matsushita, A. J. Chem. Phys. 2015, 142, 044904.
[42] Yang, Y.; Qiu, F.; Zhang, H.; Yang, Y. Acta Chim. Sinica 2004, 62, 1601 (in Chinese). (杨颖梓, 邱枫, 张红东, 杨玉良, 化学学报, 2004, 62, 1601.)
[43] Ma, X.; Cheng, C.; Yang, Y.; Qiu, F. Soft Matter 2014, 10, 6005.
[44] Zhulina, Y.; Semenov, A. Polym. Sci. U. S. S. R. 1989, 31, 196.
[45] Zhulina, E. B.; Halperin, A. Macromolecules 1992, 25, 5730.
[46] Edwards, S. F. Proc. Phys. Soc. 1965, 85, 613.
[47] Grason, G. M. Phys. Rep. 2006, 433, 1.
[48] Matsen, M. W. J. Phys.: Condens. Matter 2002, 14, R21.
[49] Thomas, E. L.; Kinning, D. J.; Alward, D. B.; Henkee, C. S. Macromolecules 1987, 20, 2934.
[50] Ashcroft, N. W.; Mermin, N. D. Solid State Physics, Harcourt College, Fort Worth, 1976.

环型嵌段高分子的强分凝理论方法