Advertisement

The Daoud and Cotton blob model and the interaction of star-shaped polymers

  • Albert Johner
  • Nam-Kyung Lee
Regular Article
  • 64 Downloads

Abstract.

Since it was first proposed in 1982, the Daoud and Cotton (DC) model for star-shaped polymers was intensively used also for self-assembled copolymers and small colloids grafted with long polymers. We try to clarify the position of the DC model and focus on the star partition function which plays a central role in self-assembly and gives access to the star-star interaction. While the predicted star-star interaction agrees with scattering data by Likos et al. (Phys. Rev. Lett. 80, 4450 (1998)), an extensive simulation by Hsu et al. (Macromolecules, 37, 4658 (2004)) does not recover the prediction for the partition function. We try to reconcile this seemingly conflicting results. We discuss star-star interactions, star free energy in \( \theta\) -solvents, mixing of A/B branches in copolymer stars, within or beyond the Daoud and Cotton blob model.

Graphical abstract

Keywords

Soft Matter: Polymers and Polyelectrolytes 

References

  1. 1.
    M. Daoud, J.P. Cotton, J. Phys. (Paris) 43, 531 (1982)CrossRefGoogle Scholar
  2. 2.
    T.A. Witten, P.A. Pincus, Macromolecules 19, 2509 (1986)ADSCrossRefGoogle Scholar
  3. 3.
    C.N. Likos, H. Löwen, M. Watzlawek, B. Abbas, O. Jucknischke, J. Allgaier, D. Richter, Phys. Rev. Lett. 80, 4450 (1998)ADSCrossRefGoogle Scholar
  4. 4.
    M. Benhamou, M. Himmi, H. Kaidi, J. Mol. Liq. 230, 337 (2017)CrossRefGoogle Scholar
  5. 5.
    G. Grest, L. Fetters, J. Huang, D. Richter, Adv. Chem. Phys. 94, 67 (1996)Google Scholar
  6. 6.
    R. Whitfield, A. Anastasaki, N.P. Truong, P. Wilson, K. Kempe, J.A. Burns, T.P. Davis, D.M. Haddleton, Macromolecules 49, 8914 (2016)ADSCrossRefGoogle Scholar
  7. 7.
    X. Lang, W.R. Lenart, J.E.P. Sun, B. Hammouda, M.J.A. Hore, Macromolecules 50, 2145 (2017)ADSCrossRefGoogle Scholar
  8. 8.
    R. Everaers, A.Y. Grosberg, M. Rubinstein, A. Rosa, Soft Matter 13, 1223 (2017)ADSCrossRefGoogle Scholar
  9. 9.
    R. Hu, D.T. Wu, Phys. Rev. E 95, 042502 (2017)ADSCrossRefGoogle Scholar
  10. 10.
    I.O. Lebedeva, E.B. Zhulina, F.A.M. Leermakers, O.V. Borisov, Langmuir 33, 1315 (2017)CrossRefGoogle Scholar
  11. 11.
    M. Wengenmayr, R. Dockhorn, J.U. Sommer, Macromolecules 49, 9215 (2016)ADSCrossRefGoogle Scholar
  12. 12.
    P. Hebbeker, A.A. Steinschulte, S. Schneider, J. Okuda, M. Moeller, F.A. Plamper, S. Schneider, Macromolecules 49, 8748 (2016)ADSCrossRefGoogle Scholar
  13. 13.
    O. Rud, T. Richter, O. Borisov, C. Holm, P. Kosovan, Soft Matter 13, 3264 (2017)ADSCrossRefGoogle Scholar
  14. 14.
    H. Zhang, W. Wang, S. Mallapragada, A. Travesset, D. Vaknin, Nanoscale 9, 164 (2017)CrossRefGoogle Scholar
  15. 15.
    X.W. Gu, X. Ye, D.M. Koshy, S. Vachhani, P. Hosemann, A.P. Alivisatos, Proc. Natl. Acad. Sci. U.S.A. 114, 2836 (2017)ADSCrossRefGoogle Scholar
  16. 16.
    T. Krentz, M.M. Khani, M. Bell, B.C. Benicewicz, J.K. Nelson, S. Zhao, H. Hillborg, L.S. Schadler, J. Appl. Polym. Sci. 134, 44347 (2017)CrossRefGoogle Scholar
  17. 17.
    V.R. Ahuja, J. van der Gucht, W.J. Briels, J. Chem. Phys. 145, 194903 (2016)ADSCrossRefGoogle Scholar
  18. 18.
    J. Irianto, Y. Xia, C.R. Pfeifer, R.A. Greenberg, D.E. Discher, Biophys. J. 112, 446 (2017)ADSCrossRefGoogle Scholar
  19. 19.
    N. Giamblanco, G. Marletta, A. Graillot, N. Bia, C. Loubat, J.F. Berret, ACS OMEGA 2, 1309 (2017)CrossRefGoogle Scholar
  20. 20.
    H.P. Hsu, W. Nadler, P. Grassberger, Macromolecules 37, 4658 (2004)ADSCrossRefGoogle Scholar
  21. 21.
    J. des Cloizeaux, G. Jannink, Polymers in Solution (Oxford University Press, Oxford, 1990)Google Scholar
  22. 22.
    B. Duplantier, J. Stat. Phys. 54, 581 (1989)ADSCrossRefGoogle Scholar
  23. 23.
    L. Schäfer, C. von Ferber, U. Lehr, B. Duplantier, Nucl. Phys. B 374, 473 (1992)ADSCrossRefGoogle Scholar
  24. 24.
    V. Schulte-Frohlinde, Y. Holovatch, C. von Ferber, A. Blumen, Phys. Lett. A 328, 335 (2004)ADSCrossRefGoogle Scholar
  25. 25.
    N.K. Lee, C. Abrams, J. Chem. Phys. 121, 7484 (2004)ADSCrossRefGoogle Scholar
  26. 26.
    C. von Ferber, A. Jusufi, C.N. Likos, H. Löwen, M. Watzlawek, Eur. Phys. J. E 2, 311 (2000)CrossRefGoogle Scholar
  27. 27.
    A.N. Semenov, J.F. Joanny, A.R. Khokhlov, Macromolecules 28, 1066 (1995)ADSCrossRefGoogle Scholar
  28. 28.
    S.T. Milner, T.A. Witten, M.E. Cates, Macromolecules 21, 2610 (1988)ADSCrossRefGoogle Scholar
  29. 29.
    A. Johner, EPL 96, 46004 (2011)ADSCrossRefGoogle Scholar
  30. 30.
    A.N. Semenov, Sov. Phys. JETP 61, 733 (1985)Google Scholar
  31. 31.
    Y.B. Zhulina, V.A. Pryamitsin, O.V. Borisov, Polym. Sci. U.S.S.R. 31, 205 (1989)CrossRefGoogle Scholar
  32. 32.
    S.T. Milner, T.A. Witten, M.E. Cates, Europhys. Lett. 5, 413 (1988)ADSCrossRefGoogle Scholar
  33. 33.
    R.C. Ball, J.F. Marko, S.T. Milner, T.A. Witten, Macromolecules 24, 693 (1991)ADSCrossRefGoogle Scholar
  34. 34.
    J.F. Joanny, L. Leibler, R. Ball, J. Chem. Phys. 81, 4640 (1984)ADSCrossRefGoogle Scholar
  35. 35.
    C. von Ferber, Y. Holovatch, Phys. Rev. E 56, 6370 (1997)ADSCrossRefGoogle Scholar
  36. 36.
    V. Blavatska, C. von Ferber, Y. Holovatch, Condens. Matter Phys. 15, 33603 (2012)CrossRefGoogle Scholar
  37. 37.
    A. Halperin, J.F. Joanny, J. Phys. II 1, 623 (1991)Google Scholar
  38. 38.
    A. Johner, J.F. Joanny, J. Phys. II 6, 511 (1996)Google Scholar
  39. 39.
    G. Volet, L. Auvray, C. Amiel, J. Phys. Chem. B 113, 13536 (2009)CrossRefGoogle Scholar
  40. 40.
    G.M.E. Pozza, S. Crotty, M. Rawiso, U.S. Schubert, P.J. Lutz, J. Phys. Chem. B 119, 1669 (2015)CrossRefGoogle Scholar
  41. 41.
    C.M. Marques, D. Izzo, T. Charitat, E. Mendes, Eur. Phys. J. B 3, 353 (1998)ADSCrossRefGoogle Scholar
  42. 42.
    L. Auvray, private communication. About at the same time as ref. marques1998 was worked out, Lo\"ıc Auvray circulated a calculation of the structure factor. It is in particular cited in ref. lutz2015Google Scholar
  43. 43.
    A. Johner, H. Benoit, J.F. Joanny, Makromol. Chem. Theory Simul. 4, 45 (1995)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut Charles Sadron CNRSUniversité de StrasbourgStrasbourg Cedex 2France
  2. 2.Department of PhysicsSejong UniversitySeoulSouth Korea

Personalised recommendations