The European Physical Journal E

, Volume 20, Issue 1, pp 99–108 | Cite as

Spontaneous bending of 2D molecular bottle-brush

  • A. Subbotin
  • J. de Jong
  • G. ten Brinke
Regular Article


Using a scaling approach we consider a 2D comb copolymer brush under bending deformations. We show that the rectilinear brush is locally stable and can be characterized by a persistence length λ increasing with the molecular weight of grafting side chains as λ ∼ M3. A bending instability due to redistribution of the side chains appears in the non-linear regime where bending is strong. Arguments are presented that the brush conformations consist of alternating rectilinear and bent sections corresponding to the different free-energy minima.


82.35.Jk Copolymers, phase transitions, structure 89.75.Fb Structures and organization in complex systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    T. Birshtein, O. Borisov, E. Zhulina, A. Khokhlov, T. Yurasova, Polymer Sci. USSR 29, 1293 (1987).CrossRefGoogle Scholar
  2. 2.
    G. Fredrickson, Macromolecules 26, 2825 (1993).CrossRefGoogle Scholar
  3. 3.
    A. Subbotin, M. Saariaho, O. Ikkala, G. ten Brinke, Macromolecules 33, 3447 (2000).CrossRefGoogle Scholar
  4. 4.
    R. Stepanyan, A. Subbotin, G. ten Brinke, Macromolecules 35, 5640 (2002).CrossRefGoogle Scholar
  5. 5.
    L. Feuz, F.A.M. Leermakers, M. Textor, O. Borisov, Macromolecules 38, 8891 (2005).CrossRefGoogle Scholar
  6. 6.
    M. Wintermantel, M. Gerle, K. Fischer, M. Schmidt, I. Wataoka, H. Urakawa, K. Kajiwara, Y. Tsukahara, Macromolecules 29, 978 (1996).CrossRefGoogle Scholar
  7. 7.
    S. Sheiko, M. Möller, Chem. Rev. 101, 4099 (2001).CrossRefGoogle Scholar
  8. 8.
    S. Lecommandoux, F. Chécot, R. Borsali, M. Schappacher, A. Deffieux, A. Brlet, J.P. Cotton, Macromolecules 35, 8878 (2002).CrossRefGoogle Scholar
  9. 9.
    T. Stephan, S. Muth, M. Schmidt, Macromolecules 35, 9857 (2002).CrossRefGoogle Scholar
  10. 10.
    Y. Rouault, O.V. Borisov, Macromolecules 29, 2605 (1996).CrossRefGoogle Scholar
  11. 11.
    M. Saariaho, O. Ikkala, I. Szleifer, I. Erukhimovich, G. ten Brinke, J. Chem. Phys. 107, 3267 (1997).CrossRefADSGoogle Scholar
  12. 12.
    M. Saariaho, I. Szleifer, O. Ikkala, G. ten Brinke, Macromol. Theory Simul. 7, 211 (1998).Google Scholar
  13. 13.
    R. Connolly, G. Bellesia, E.G. Timoshenko, Y.A. Kuznetsov, S. Elli, F. Ganazzoli, Macromolecules 38, 5288 (2005).CrossRefGoogle Scholar
  14. 14.
    J. de Jong, G. ten Brinke, Macromol. Theory Simul. 13, 318 (2004).CrossRefGoogle Scholar
  15. 15.
    P.G. Khalatur, A.R. Khokhlov, S.A. Prokhorova, S.S. Sheiko, M. Möller, P. Reineker, D.G. Shirvanyanz, N. Starovoitova, Eur. Phys. J. E 1, 99 (2000).CrossRefGoogle Scholar
  16. 16.
    I. Potemkin, Eur. Phys. J. E 12, 207 (2003).CrossRefGoogle Scholar
  17. 17.
    I. Potemkin, A. Khokhlov, S. Prokhorova, S. Sheiko, M. Möller, K. Beers, K. Matyjaszewski, Macromolecules 37, 3918 (2004).CrossRefGoogle Scholar
  18. 18.
    M.O. Gallyamov, B. Tartsch, A.R. Khokhlov, S.S. Sheiko, H.G. Börner, K. Matyjaszewski, M. Möller, Macromol. Rapid Commun. 25, 1703 (2004).CrossRefGoogle Scholar
  19. 19.
    J. de Jong, A. Subbotin, G. ten Brinke, Macromolecules 38, 6718 (2005). CrossRefGoogle Scholar
  20. 20.
    M. Daoud, J. Cotton, J. Phys. (Paris) 43, 531 (1982).ADSGoogle Scholar
  21. 21.
    T.M. Birshtein, E.B. Zhulina, Macromol. Theory Simul. 6, 1169 (1997).CrossRefGoogle Scholar
  22. 22.
    A.N. Semenov, Sov. Phys. JETP 61, 733 (1985).Google Scholar
  23. 23.
    S.T. Milner, T.A. Witten, M.E. Cates, Macromolecules 21, 2610 (1988).CrossRefGoogle Scholar
  24. 24.
    E.B. Zhulina, O.V. Borisov, V.A. Priamitsin, J. Colloid Interface Sci. 137, 495 (1989).CrossRefGoogle Scholar
  25. 25.
    A.E. Likhtman, A.N. Semenov, Macromolecules 27, 3103 (1994).CrossRefGoogle Scholar
  26. 26.
    R.S. Ball, J.F. Marco, S.T. Milner, T.A. Witten, Macromolecules 24, 693 (1991).CrossRefGoogle Scholar
  27. 27.
    H. Li, T.A. Witten, Macromolecules 27, 449 (1994).CrossRefGoogle Scholar
  28. 28.
    F.D. Gakhov, Boundary Value Problems (in Russian, Nauka, Moscow, 1977).Google Scholar
  29. 29.
    A.D. Polyanin, A.V. Manzhirov, Handbook of Integral Equations (CRC Press, Boca Raton, 1998).Google Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2006

Authors and Affiliations

  1. 1.Institute of Petrochemical SynthesisRussian Academy of SciencesMoscowRussia
  2. 2.Laboratory of Polymer Chemistry and Materials Science CentreUniversity of GroningenGroningenThe Netherlands

Personalised recommendations