Self-assembling Behavior of Symmetric Coil-semiflexible-coil Triblock Copolymers†

doi:10.7503/cjcu20140330

Abstract

Abstract:

The self-assembly of symmetric coil-semiflexible-coil triblock copolymers in 2D space was investigated using self-consistent field theory(SCFT). The semiflexible block and the coil block of the copolymers were described as wormlike chain model, and Gaussian chain model, respectively. A highly accurate and efficient operator splitting pseudospectral algorithm combined with SPHEREPACK software package was employed to solve modified diffusion equations for the propagators of wormlike chains. The anisotropic interactions favoring the parallel alignment between semiflexible segments was described by Maier-Saupe orientational interactions $μN$ , and the enthalpic interactions between coil and semiflexible segments were described by isotro-pic Flory-Huggins interactions $χN$ . By increasing $χN$ and volume fraction of the coil blocks, a phase diagram including isotropic, nematic, smectic-C, tetragonal cylinders, oblique pucks, broken lamella pucks and rice-shaped phase for symmetric coil-semiflexible-coil triblock copolymers was built. At relatively low coil fractions and strong interactions, semctic-C phases were readily formed because the strong chain-stretching energy, which came from the highly ordered orientation of semiflexible blocks, dominates the system free energy. In the meanwhile, the stretch from two coil sides to the bridged semiflexble block results in a higher chain-stretching energy. Therefore, more smectic-C phases formed than that in biblock copolymers. The tetragonal cylinders exhibiting weak segregation were obtained in the region of coil fractions from 0.5 to 0.6. With the increase of coil fractions and orientational interactions, hexagonal packed pucks were found. In the rhombus and rectangle liquid crystal domain, the coil-semiflexible block junctions were observed at opposite sides, therefore a cross-link conformation of the semiflexible blocks was produced. More interestingly, the semiflexible chain folds twice along the short side of the rectangle liquid crystal domain of the oblique pucks at coil fraction 0.6 and broken lamella pucks at coil fraction 0.7. Chain folding behavior increases the interfaces between coils and semiflexible blocks allowing for the coils with larger fractions to gain conformational entropy. When the coil fraction is 0.8, chain folding behavior decreases and the semiflexible blocks orient along the long side of the rectangle liquid crystal domain, forming rice-shaped phase. These simulation results are of paramount importance in rationalizing chain folding phenomena and understanding the nucleation mechanism of liquid crystals.

Key words: Symmetric coil-semiflexible-coil triblock copolymer, Self-consistent field theory(SCFT), Wormlike chain model, Self-assembly, Chain folding, Nucleation mechanism of liquid crystal

CLC Number:

O631.1⁺3

TrendMD:

YANG Guang, WANG Chuanming, TANG Ping, GU Songyuan. Self-assembling Behavior of Symmetric Coil-semiflexible-coil Triblock Copolymers^†[J]. Chem. J. Chinese Universities, 2014, 35(8): 1799.

Figures/Tables 9

Fig.1 Phase diagram of symmetric coil-semiflexible-coil triblock copolymers from 2D calculations

Fig.2 Smectic-C phase f=0.4, χN=19, μN=76(A), profiles of density φA(l) and φB(l) and averaged orientation order parameter S(l) with the axis l along the lamellar normal n(B) and the schematic model of the smectic-C phase(C) (A) The red and green colors represent the coil and semiflexible blocks, respectively.

Fig.3 Free energy per chain Ftotal consists of AB interfacial energy FAB, Maier-Saupe orientational interaction FM-S and polymer stretching entropy Fel for smectic-C phase in the case of f=0.4, χN=19 and μN=76

Fig.4 Domain spacing Lb of smectic-C phase as a function of χN(f=0.4, μ/χ=4)(A), averaged orientation order parameter S and titling angle Θ in the middle of semiflexible B block domain as a function of χN(B) and free energy per chain Ftotal consists of AB interfacial energy FAB, Maier-Saupe orientational interaction FM-S and polymer stretching entropy Fel as a function of χN(C)

Fig.5 Orientational parameters of semctic-C phase as a function of f with χN=17(a) and χN=25(b) vs. averaged orientation order parameter S(A) and titling angle Θ in the middle of semiflexible B block domain(B)

Fig.6 Tetragonal cylinders of f=0.5, χN=11(A), the middle segment distributions φ(r,s=0.5)(B) and the density distributions of A-B junctions φ(r,s=0.25) and φ(r,s=0.75) of tetragonal cylinders(C) and the schematic model of the tetragonal cylinders(D) The red and green colors represent the coil and semiflexible blocks, respectively.

Fig.7 Oblique pucks of f=0.6, χN=15(A), schematic model of puck phase corresponding to the rod domain(B) and middle segment distributions φ(r,s=0.5) of puck phase(C) (A) The red and green colors represent the coil and semiflexible blocks, respectively.

Fig.8 Broken lamella pucks of f=0.7, χN=21 The red and green colors represent the coil and semiflexible blocks, respectively.

Fig.9 Rice-shaped phase of f=0.8, χN=29(A) and middle segment distributions φ(r,s=0.5) of rice-shaped phase(B) The red and green colors represent the coil and semiflexible blocks, respectively.

References 38

[1]	Olsen B. D., Segalman R. A., Mater. Sci. Eng. R-Rep., 2008, 62(2), 37—66
[2]	Tao Y. F., Ma B. W., Segalman R. A., Macromolecules, 2008, 41(19), 7152—7159
[3]	Segalman R. A., McCulloch B., Kirmayer S., Urban J. J., Macromolecules, 2009, 42(23), 9205—9216
[4]	Darling S. B., Energ. Environ. Sci., 2009, 2(12), 1266—1273
[5]	Sary N., Rubatat L., Brochon C., Hadziioannou G., Mezzenga R., Macromol. Symp., 2008, 268, 28—32
[6]	Shoji Y., Ishige R., Higashihara T., Watanabe J., Ueda M., Macromolecules, 2010, 43(2), 805—810
[7]	Sary N., Rubatat L., Brochon C., Hadziioannou G., Ruokolainen J., Mezzenga R., Macromolecules, 2007, 40(19), 6990—6997
[8]	Ho C. C., Lee Y. H., Dai C. A., Segalman R. A., Su W. F., Macromolecules, 2009, 42(12), 4208—4219
[9]	Pryamitsyn V., Ganesan V., J. Chem. Phys., 2004, 120(12), 5824—5838
[10]	Chen X. L., Jenekhe S. A., Macromolecules, 2000, 33(13), 4610—4612
[11]	De Cuendias A., Ibarboure E., Lecommandoux S., Cloutet E., Cramail H., J. Polym. Sci., Part A: Polym. Chem., 2008, 46(13), 4602—4616
[12]	Mori Y., Lim L. S., Bates F. S., Macromolecules, 2003, 36(26), 9879—9888
[13]	Ishige R., Ishii T., Tokita M., Koga M., Kang S., Watanabe J., Macromolecules, 2011, 44(12), 4586—4588
[14]	Koga M., Ishige R., Sato K., Ishii T., Kang S., Sakajiri K., Watanabe J., Tokita M., Macromolecules, 2012, 45(23), 9383—9390
[15]	Sato K., Koga M., Kang S., Sakajiri K., Watanabe J., Tokita M., Macromol. Chem. Phys., 2013, 214(10), 1089—1093
[16]	Koga M., Sato K., Kang S., Sakajiri K., Watanabe J., Tokita M., Macromol. Chem. Phys., 2013, 214(20), 2295—2300
[17]	Fredrickson G.H., The Equilibrium Theory of Inhomogenous Polymers, Clarendon Press, Oxford, 2005, 202—276
[18]	Fredrickson G. H., Ganesan V., Drolet F. Macromolecules, 2002, 35(1), 16—39
[19]	Shi A. C., Eds.: Hamley I.W., Developments in Block Copolymer Science and Technology, John Wiley & Sons Ltd.,New York, 2004, Chapter 8
[20]	Wang Y. Q., Tang P., Yang Y. L., Acta Chimica Sinica, 2011, 69(1), 89—94
	(王月强, 唐萍, 杨玉良. 化学学报, 2011, 69(1), 89—94)
[21]	Kratky O., Porod G., Recl. Trav. Chim. Pays-Bas, 1949, 68, 1106—1122
[22]	Saito N., Takahashi K., Yunoki Y., J. Phys. Soc. Jpn., 1967, 22, 219
[23]	Song W., Tang P., Qiu F., Yang Y. L., Shi A. C., Soft Matter, 2011, 7(3), 929—938
[24]	Duchs D., Sullivan D. E., J. Phys.: Condens. Matter, 2002, 14(46), 12189—12202
[25]	Onsager L., Ann. N. Y., Acad. Sci., 1949, 51(4), 627—659
[26]	Song W., Tang P., Zhang H., Yang Y.L., Shi A. C., Macromolecules, 2009, 42(16), 6300—6309
[27]	Gao J., Song W., Tang P., Yang Y., Soft Matter, 2011, 7(11), 5208—5216
[28]	Fredrickson G.H., The Equilibrium Theory of Inhomogenous Polymers, Clarendon Press, Oxford, 2005, 127
[29]	Jiang Y., Zhang W. Y., Chen J. Z. Y., Phys. Rev. E, 2011, 84(4), 041803-1—041803-10
[30]	Gao J., Tang P., Yang Y.L., Soft Matter, 2013, 9(1), 69—81
[31]	Jiang Y., Chen J. Z. Y., Phys. Rev. Lett., 2013, 110(13), 138305-1—138305-5
[32]	Chen J. Z., Zhang C. X., Sun Z. Y., An L. J., Tong Z., J. Chem. Phys., 2007, 127(2), 024105-1—024105-5
[33]	Chen J. Z., Sun Z. Y., Zhang C. X., An L. J., Tong Z., J. Chem. Phys., 2008, 128(7), 074904-1—074904-6
[34]	Shah M., Ganesan V., J. Chem. Phys., 2009, 130(5), 054904-1—054904-12
[35]	De Gennes P.G., The Physics of the Liquid Crystals, Oxford University Press, New York, 1974, 66—70
[36]	Man X., Andelman D., Orland H., Macromolecules, 2010, 43(17), 7261—7268
[37]	Adams J.C., Swarztrauber P. N., SPHEREPACK 3.2: A Model Development Facility, 2003,
[38]	Matsen M. W., Thompson R. B., J. Chem. Phys., 1999, 111(15), 7139—7146
	(Ed.: D, Z)