Abstract
The self-consistent field theory (SCFT) based upon coarse-grained model is especially suitable for investigating thermodynamic equilibrium morphology and the phase diagram of inhomogeneous polymer systems subjected to phase separation. The advantage of this model is that the details of the chain such as the architecture of the chain and the sequence of blocks can be considered. We present here an overview of SCFT approach and its applications in polymeric systems. In particular, we wish to focus on our group’s achievements in applications of SCFT in such fields: simulation of microphase separation morphologies of multiblock copolymers with a complex molecular architecture, interactions between brush-coated sheets in a polymer matrix, mixtures of flexible polymers and small molecular liquid crystals at the interface, shapes of polymer-chain-anchored fluid vesicles, self-assembled morphologies of block copolymers in dilute solution, and so on. Finally, the further developments as well as the perspective applications of SCFT are discussed.
Similar content being viewed by others
References
Hadjichristidis, N., Pispas, S., Floudas, G., Block Copolymers, Hoboken: John Wiley & Sons, 2003.
Leibler, L., Theory of microphase separation in block copolymers, Macromolecules, 1980, 13: 1602–1617.
Semenov, A. N., Contribution to the theory of microphase layering in block-copolymer melts, Sov. Phys. JEPT, 1985, 61: 733–742.
Milner, S. T., Witten, T. A., Cates, M. E., A parabolic density profile for grafted polymers, Europhys. Lett., 1988, 5: 413–418.
Matsen, M. W., The standard Gaussian model for block copolymer melts, J. Phys: Condens. Matter, 2002, 14: R21–R47.
Matsen, M. W., Schick, M., Stable and unstable phases of a diblock copolymer melt, Phys. Rev. Lett., 1994, 72: 2660–2663.
Feynman, R. P., Hibbs, A. R., Quantum Mechanics and Path Integrals, New York: McGraw-Hill Book Company, 1965.
Edwards, S. F., The statistical mechanics of polymers with excluded volume, Proc. Phys. Soc., 1965, 85: 613–624.
Edwards, S. F., Theory of polymer solutions at intermediate concentration, Proc. Phys. Soc., 1966, 88: 265–280.
Flory, P. J., The configuration of real polymer chains, J. Chem. Phys., 1949, 17: 303–310.
Ryder, L. H., Quantum Field Theory, 2nd ed., Cambridge: Cambridge University Press, 1996.
Fredrickson, G. H., Ganesan, V., Drolet, F., Field-theoretic computer simulation methods for polymers and complex fluids, Macromolecules, 2002, 35: 16–39.
deGennes, P. G., Prost, J., The Physics of Liquid Crystals, Oxford: Clarendon press, 1993.
Shi, A. C., Noolandi, J., Theory of inhomogeneous weakly charged polyelectrolytes, Macromol. Theory Simul., 1999, 8: 214–229.
Helfand, E., Theory of inhomogeneous polymers: Fundamentals of the Gaussian random-walk model, J. Chem. Phys., 1975, 62: 999–1005.
Morse, D. C., Fredrickson, G. H., Semiflexible polymers near Interfaces, Phys. Rev. Lett., 1994, 73: 3235–3238.
Drolet, F., Fredrickson, G. H., Combinatorial screening of complex block copolymer assembly with self-consistent field theory, Phys. Rev. Lett., 1999, 83: 4317–4320.
Holden, G., Legge, N. R., Quirk, R. et al., Thermoplastic Elastomers, 2nd ed., Cincinnati: Hanser/Gardner Publishers, 1996.
Park, M., Harrison, C., Chaikin, P. M. et al., Block copolymer lithography: Periodic arrays of similar to 10(11) holes in 1 square centimeter, Science, 1997, 276: 1401–1404.
Archibald, D. D., Mann, S., Template mineralization of self-assembled anisotropic lipid microstructures, Nature, 1993, 364: 430–433.
Morkved, T. L., Wiltzius, P., Jaeger, H. M. et al., Mesoscopic self-assembly of gold islands and diblock-copolymer films, Appl. Phys. Lett., 1994, 64: 422–424.
Tang, P., Qiu, F., Zhang, H. D. et al., Morphology and phase diagram of complex block copolymers: ABC linear triblock copolymers, Phys. Rev. E, 2004, 69: 031803.
Tang, P., Qiu, F., Zhang, H. D. et al., Morphology and phase diagram of complex block copolymers: ABC star triblock copolymers, J. Phys. Chem. B, 2004, 108: 8434–8438.
Hamley, I. W., The Physics of Block Copolymers, Oxford: Oxford University Press, 1998.
Bates, F. S., Fredrickson, G. H., Block copolymers — Designer soft materials, Physics Today, 1999, 52: 32–38.
Mogi, Y., Kotsuji, H., Kaneko, Y. et al., Tricontinuous morphology of triblock copolymers of the ABC type, Macromolecules, 1992, 25: 5412–5415.
Gido, S. P., Schwark, D. W., Thomas, E. L. et al., Observation of a non-constant mean curvature interface in an ABC triblock copolymer, Macromolecules, 1993, 26: 2636–2640.
Gemma, T., Hatano, A., Dotera, T., Monte Carlo simulations of the morphology of ABC star polymers using the diagonal bond method, Macromolecules, 2002, 35: 3225–3237.
He, X. H., Huang, L., Liang, H. J. et al., Self-assembly of star block copolymers by dynamic density functional theory, J. Chem. Phys., 2002, 116: 10508–10513.
Bohbot-Raviv, Y., Wang, Z. G., Discovering new ordered phases of block copolymers, Phys. Rev. Lett., 2000, 85: 3428–3431.
Takano, A., Wada, S., Sato, S. et al., Observation of cylinder-based microphase-separated structures from ABC star-shaped terpolymers investigated by electron computerized tomography, Macromolecules, 2004, 37: 9941–9946.
Sioula, S., Hadjichristidis, N., Thomas, E. L., Direct evidence for confinement of junctions to lines in an 3 miktoarm star terpolymer microdomain structure, Macromolecules, 1998, 31: 8429–8432.
Doane, J. W., Vaz, N. A., Wu, B. G. et al., Field controlled light scattering from nematic microdroplets, Appl. Phys. Lett., 1986, 48: 269–271.
Ding, J. D., Yang, Y. L., Birefringence patterns of nematic droplets, Jpn. J. Appl. Phys., 1992, 31: 2837–2845.
Drzaic, P. S., Polymer dispersed nematic liquid crystal for large area displays and light valves, J. Appl. Phys., 1986, 60: 2142–2148.
Lin, Z. Q., Zhang, H. D., Yang, Y. L., Phase diagrams of mixtures of flexible polymers and nematic liquid crystals in a field, Phys. Rev. E, 1998, 58: 5867–5872.
Yang, Y. L., Lu, J. M., Zhang, H, D. et al., Phase-equilibria in mixtures of thermotropic small molecular liquid-crystals and flexible polymers, Polym. J., 1994, 26: 880–894.
Zhang, H. D., Li, F. M., Yang, Y. L., Statistical thermodynamics theory of phase equilibria in mixtures of thermotropic liquid-crystals and flexible polymers, Science in China, series B, 1995, 38: 412–421.
Chen, Y., Li, J., Zhang, H. D. et al., Theory of inhomogeneous polymers lattice model for the interface between flexible polymer and small molecular liquid crystal, Mol. Cryst. Liq. Cryst., 1995, 258: 37–50.
Zhu, J. X., Ding, J. D., Lu, J. M. et al., Monte Carlo simulation of the interface between flexible polymers and low molecular liquid crystals, Polymer, 39: 6455-6460.
Wang, J. F., Zhang, H. D., Qiu, F. et al., Self-consistent field theory of mixtures of flexible polymers and small liquid crystalline molecules, Acta Chimica Sinica (in Chinese), 2003, 62: 1180–1185.
Zhang, H. D., Lin, Z. Q., Yan, D. et al., Phase separation in mixtures of thermotropic liquid crystals and flexible polymers, Science in China, Series B, 1997, 40: 128–136.
Giannelis, E. P., Krishnamoorti, R. K., Manias, E., Polymer-silicate nanocomposites: Model systems for confined polymers and polymer brushes, Adv. Polym. Sci., 1999, 138: 107–147 and references therein.
de Gennes, P. G., Scaling Concepts in Polymer Physics, New York: Cornell University Press, 1985.
Aubouy, M., Fredrickson, G. H., Pincus, P. et al., End-tethered chains in polymeric matrices, Macromolecules, 1995, 28: 2979–2981.
Leibler, L., Ajdari, A., Mourran, A. et al., Ordering in Macromolecular Systems (eds. Teramoto, A., Kobayashi, M., Norisuji, T.), Berlin: Springer Verlag, 1994.
Gay, C., Wetting of a polymer brush by a chemically identical polymer melt, Macromolecules, 1997, 30: 5939–5943.
Ferreira, P. G., Ajdari, A., Leibler, L., Scaling law for entropic effects at interfaces between grafted layers and polymer melts, Macromolecules, 1998, 31: 3994–4003.
Wang, R., Qiu, F., Zhang, H. D. et al., Interactions between brush-coated clay sheets in a polymer matrix, Phys. Rev. E, 2003, 118: 9447–9456.
Wang, R., Self-assembly of polymer fluids based on self-consistent field theory, Postdoc Report in Fudan University (in Chinese), 2003.
Seifert, U., Lipowsky, R., Structure and Dynamics of Membranes (eds. Lipowsky, R., Sackmann, E.), Amsterdam: Elsevier Science B.V. 1995.
Tsafrir, I., Sagi, D., Arzi, T. et al., Pearling instabilities of membrane tubes with anchored polymers, Phys. Rev. Lett., 2001, 86: 1138–1141.
Frette, V., Tsafrir, I., Guedeau-Boudeville, M. A. et al., Coiling of cylindrical membrane stacks with anchored polymers, Phys. Rev. Lett., 1999, 83: 2465–2468.
Hiergeist, C., Lipowsky, R., Elastic properties of polymer-decorated membranes, J. Phys. II France, 1996, 6: 1465–1481.
Kim, Y. W., Sung, W., Membrane curvature induced by polymer adsorption, Phys. Rev. E, 2001, 63: 041910.
Breidenich, M., Netz, R. R., Lipowsky, R. et al., The shape of polymer-decorated membranes, Europhys. Lett., 2000, 49: 431–437.
Breidenich, M., Netz, R. R., Lipowsky, R. et al., Adsorption of polymers anchored to membranes, Eur. Phys. J. E, 2001, 5: 403–414.
Helfrich, W., Elastic properties of lipid bilayers — Theory and possible experiments, Z. Naturforsch, 1973, C 28: 693–703.
Wang, J. F., Guo, K. K., Qiu, F. et al., Predicting shapes of polymer-chain-anchored fluid vesicles, Phys. Rev. E, 2005, 71: 041908.
Ou-Yang, Z. C., Helfrich, W., Instability and deformation of a spherical vesicle by pressure, Phys. Rev. Lett., 1989, 59: 2486–2488.
Guo, K. K., Theoretical studies on the shapes of biological membranes, PhD Thesis in Fudan University (in Chinese), 2005.
Guo, K. K., Qiu, F., Zhang, H. D., Yang, Y. L., Predicting shapes of polymer-chain-anchored fluid vesicles, J. Chem. Phys., 2005, 71: 041908.
Yu, G., Eisenberg, A., Multiple morphologies formed from an amphiphilic ABC triblock copolymer in solution, Macromolecules, 1998, 31: 5546–5549.
He, X. H., Liang, H. J., Huang, L. et al., Complex microstructures of amphiphilic diblock copolymer in dilute solution, J. Phys. Chem. B, 2004, 108: 1731–1735.
Zhu, J. T., Jiang, Y., Liang, H. J. et al., Self-assembly of ABA amphiphilic triblock copolymers into vesicles in dilute solution, J. Phys. Chem. B, 2005, 109: 8619–8625.
Wang, R., Tang, P., Qiu, F. et al., Aggregate morphologies of amphiphilic ABC triblock copolymer in dilute solution using self-consistent field theory, J. Phys. Chem. B, 2005, 109: 17120–17127.
Lambooy, P., Russell, T. P., Kellogg, G. L. et al., Observed frustration in confined block copolymers, Phys. Rev. Lett., 1994, 72: 2899–2902.
Wu, Y. Y., Cheng, G. S., Katsov, K. et al., Composite mesostructures by nano-confinement, Nature Materials, 2004, 3: 816–822.
Yang, Y. Z., Qiu, F., Zhang, H. D. et al., Microphases of asymmetric diblock copolymers in confined thin films, Acta Chimica Sinica (in Chinese), 2004, 62: 1601–1606.
Yang, Y. Z., Block copolymers confined in thin films, Master Degree Thesis in Fudan University (in Chinese), 2006.
Wood, S. M., Wang, Z. G., Nucleation in binary polymer blends: A self-consistent field study, J. Chem. Phys., 2002, 116: 2289–2300.
Wang, J. F., Zhang, H. D., Qiu, F. et al., Nucleation in binary polymer blends: Effects of adding diblock copolymers, J. Chem. Phys., 2003, 118: 8997–9006.
Wang, J. F., Wang, Z. G., Yang, Y. L., Nucleation in binary polymer blends: Effects of foreign mesoscopic spherical particles, J. Chem. Phys., 2004, 121: 1105–1113.
Wang, J. F., Wang, Z. G., Yang, Y. L., Nature of disordered micelles in sphere-forming block copolymer melts, Macromolecules, 2005, 38: 1979–1988.
Xia, J. F., Sun, M. Z., Qiu, F. et al., Microphase ordering mechanisms in linear ABC triblock copolymers: A dynamic density functional study, Macromolecules, 2005, 38: 9324–9332.
Thompson, R. B., Ginzburg, V. V., Masten, M. W. et al., Predicting the mesophases of copolymer-nanoparticle composites, Science, 2001, 292: 2469–2472.
Wang, Q., Taniguchi, T., Fredrickson, G. H., Self-consistent field theory of polyelectrolyte systems, J. Phys. Chem. B, 2004, 108: 6773–6744.
Reister, E., Fredrickson, G. H., Nanoparticles in a diblock co-polymer background: The potential of mean force, Macromolecules, 2004, 37: 4718–4730.
Sides, S. W., Fredrickson, G. H., Parallel algorithm for numerical self-consistent field theory simulations of block copolymer structure, Polymer, 2003, 44: 5859–5866.
Sun, M. Z., Microphase separation and shapes of vesicles based on self-consistent field theory, PhD Thesis in Fudan University (in Chinese), 2006.
Author information
Authors and Affiliations
Corresponding author
Additional information
This review was recommended by Prof. Li Lemin, member of editorial board of Science in China.
Rights and permissions
About this article
Cite this article
Yang, Y., Qiu, F., Tang, P. et al. Applications of self-consistent field theory in polymer systems. SCI CHINA SER B 49, 21–43 (2006). https://doi.org/10.1007/s11426-005-0190-7
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11426-005-0190-7