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Closed-loop phase behaviour in block copolymers


Closed-loop phase diagrams are known in systems with specific intermolecular interactions1,2,3,4. In weakly interacting systems, however, such behaviour has never been observed. Here, diblock copolymers formed from polystyrene covalently linked to poly (n-pentylmethacrylate), P(S-b-nPMA), which have only weak segmental interactions, are shown to exhibit a closed-loop phase behaviour over a narrow range of molecular weight. The endothermic transitions from the disordered to ordered and back to the disordered state, as a function of increasing temperature, are dominantly entropic in origin. The morphology and rheological properties of P(S-b-nPMA) undergo characteristic changes at the transitions. Whereas the disorder-to-order transition temperature increases with decreasing molecular weight, the order-to-disorder transition temperature decreases. At a limiting molecular weight, the closed-loop vanishes and no ordering occurs. These findings provide quantitative insight into an elusive transition in weakly interacting multicomponent systems.

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Figure 1: a, Small-angle X-ray scattering (SAXS) for B-IV P(S-b- n PMA) as a function of the scattering vector ( q ) at various temperatures using increments of 2.5 °C.
Figure 2: a–c, Properties of P(S-b- n PMA) as a function of inverse temperature.
Figure 3
Figure 4: a, Molecular-weight dependence of UODT and LDOT for P(S-b- n PMA).


  1. Malcolm, G.N. & Rowlinson, J.S. The thermodynamic properties of aqueous solutions of polyethylene glycol, polypropylene glycol and dioxane. Trans. Faraday Soc. 53, 921–931 (1957).

    Article  CAS  Google Scholar 

  2. Davies, L.A., Jackson, G. & Rull, L.F. Simulation study of the link between molecular and re-entrant miscibility for a mixture of molecules with directional interactions. Phys. Rev. Lett. 82, 5285–5288 (1999).

    Article  CAS  Google Scholar 

  3. Svoboda, P., Kressler, J., Chiba, T., Inoue, T. & Kammer, H.-W. Light-scattering and TEM analyses of virtual upper critical solution temperature behaviour in PCL/SAN blends. Macromolecules 27, 1154–1159 (1994).

    Article  CAS  Google Scholar 

  4. Abbott, M.M. & Prausnitz, J.M. in Models for Thermodynamic and Phase Equilibria Calculations (ed. Sandler, S. I.) 1–86 (Marcel Dekker, New York, 1994).

    Google Scholar 

  5. Dudowicz, J. & Freed, K.F. Effect of monomer structure and compressibility on the properties of multicomponent polymer blends and solutions: 1. Lattice cluster theory of compressible systems. Macromolecules 24, 5076–5095 (1991).

    Article  CAS  Google Scholar 

  6. Dudowicz, J. & Freed, K.F. Relation of effective interaction parameters for binary blends and diblock copolymers: Lattice cluster theory predictions and comparison with experiment. Macromolecules 26, 213–220 (1993).

    Article  CAS  Google Scholar 

  7. Rosedale, J.H. & Bates, F.S. Rheology of ordered and disordered symmetric poly(ethylenepropylene)-poly(ethylethlene) diblock copolymers. Macromolecules 23, 2329–2338 (1990).

    Article  CAS  Google Scholar 

  8. Bates, F.S., Rosedale, J.H., Bair, H.E. & Russell, T.P. Synthesis and characterization of a model saturated hydrocarbon diblock copolymer. Macromolecules 22, 2257–2564 (1989).

    Article  Google Scholar 

  9. Paul, D.R. & Newman, S. in Polymer Blends 15–115 (Academic, New York, 1978).

    Google Scholar 

  10. Sanchez, I.C. in Polymer Compatibility and Incompatibility (ed. Solc, K.) 59–76 (MMI, New York, 1982).

    Google Scholar 

  11. Koningsveld, R., Stockmayer, W.H. & Nies, E. in Polymer Phase Diagrams 16–65 (Oxford Univ. Press, Oxford, 2001).

    Google Scholar 

  12. Bates, F.S. & Fredrickson, G.H. Block copolymer thermodynamics: theory and experiment. Annu. Rev. Phys. Chem. 41, 525–557 (1990).

    Article  CAS  Google Scholar 

  13. Hashimoto, T. in Thermoplastic Elastomers (eds Legge, N. R., Holden, G. & Schroeder, H. E.) 349–383 (Hanser, New York, 1987).

    Google Scholar 

  14. Sanchez, I.C. & Lacombe, R.H. Statistical thermodynamics of polymer solutions. Macromolecules 11, 1145–1156 (1978).

    Article  CAS  Google Scholar 

  15. Dudowicz, J. & Freed, K.F. Explanation for the unusual phase behaviour of polstyrene-b-poly(n-alkyl methacrylate) diblock copolymers: Specific interactions. Macromolecules 33, 5292–5299 (2000).

    Article  CAS  Google Scholar 

  16. Hino, T. & Prausnitz, J.M. Lower and upper critical ordering temperatures in compressible diblock copolymer melts from a perturbed hard-sphere-chain equation of state. Macromolecules 31, 2636–2648 (1998).

    Article  CAS  Google Scholar 

  17. Russell, T.P., Karis, T.E., Gallot, Y. & Mayes, A.M. A lower critical ordering transition in a diblock copolymer melt. Nature 368, 729–731 (1994).

    Article  CAS  Google Scholar 

  18. Pollard, M., Russell, T.P., Ruzette, A.V.G., Mayes, A.M. & Gallot, Y. The effect of hydrostatic pressure on the lower critical ordering transition in diblock copolymers. Macromolecules 31, 6493–6498 (1998).

    Article  CAS  Google Scholar 

  19. Ruzette, A.V.G. et al. Phase behaviour of diblock copolymers between styrene and n-alkyl methacrylates. Macromolecules 31, 8509–8516 (1998).

    Article  CAS  Google Scholar 

  20. Ruzette, A.V.G. & Mayes, A.M. A simple free energy model for weakly interacting polymer blends. Macromolecules 34, 1894–1907 (2001).

    Article  CAS  Google Scholar 

  21. Ruzette, A.V.G., Banerjee, P., Mayes, A.M. & Russell, T.P. A simple model for baroplastic behaviour in block copolymer melts. J. Chem. Phys. 114, 8205–8209 (2001).

    Article  CAS  Google Scholar 

  22. Lee, C.H., Saito, H., Goizueta, G. & Inoue, T. An immiscibility loop in isotactic/partially hydrogenated oligo(styrene-co-indene) blend. Macromolecules 29, 4274–4277 (1996).

    Article  CAS  Google Scholar 

  23. Leibler, L. Theory of microphase separation in block copolymers. Macromolecules 13, 1602–1617 (1980).

    Article  CAS  Google Scholar 

  24. Sakamoto, N. & Hashimoto, T. Ordering dynamics of a symmetric polystyrene-block-polyisoprene; 2. Real-space analysis on the formation of lamellar microdomain. Macromolecules 31, 3815–3823 (1990).

    Article  Google Scholar 

  25. Winey, K.I., Gobran, D.A., Xu, Z., Fetters, L.J. & Thomas. E.L. Compositional dependence of the order-disorder transition in diblock copolymers. Macromolecules 27, 2392–2397 (1994).

    Article  CAS  Google Scholar 

  26. Ramachandrarao, V.S., Gupta R.R., Russell T.P. & Watkins J.J. Enhancement of diblock copolymer ordering kinetics by supercritical carbon dioxide annealing. Macromolecules 34, 7923–7925 (2001).

    Article  CAS  Google Scholar 

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This work was supported by Teralevel Nanodevice (TND) projects (supported by the Korean Ministry of Science and Technology (MOST), the Applied Rheology Center governed by the Korean Organization of Science and Engineering Foundation (KOSEF)), and by the Department of Energy, the Office of Basic Energy Science and The National Science Foundation-supported Materials Research Science and Engineering Center, at the University of Massachusetts. Small-angle X-ray scattering measurements were performed at the Pohang Light Source, Korea, and were supported by MOST and POSCO.

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Correspondence to Jin Kon Kim or Thomas P. Russell.

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Yeol Ryu, D., Jeong, U., Kon Kim, J. et al. Closed-loop phase behaviour in block copolymers. Nature Mater 1, 114–117 (2002).

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