Skip to main content
Log in

Theory of microphase separation in charged crosslinked polymer blends with arbitrary charge distribution

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract

In this paper, we are interested in the phase behavior and scattering properties of charged crosslinked polymer blends in solution. The system undergoes a microphase separation, below some critical temperature. To study such a transition, use is made of the standard de Gennes theory based on an analogy with a dielectric medium. This analogy is extended to include the effects of the initial composition fluctuations in order to improve its agreement with experimental data in the small wave vector range. The excluded-volume interactions are explicitly introduced through the blob model. The charge effects on the phase behavior are examined, for any charge distribution of polyions and for any salt concentration. This completes a previous study which was concerned with the situation where only one species is charged. The early kinetics of microphase separation is discussed, and the charges contribution to the growth rate is also evaluated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K. Binder, J. Chem. 79, 6387 (1983).

    ADS  Google Scholar 

  2. M. Benmouna, H. Benoit, Z.A. Akcasu, Macromolecules 20, 1107 (1987).

    Article  ADS  Google Scholar 

  3. R. Roby, J.-F. Joanny, Macromolecules 25, 4612 (1992).

    Article  ADS  Google Scholar 

  4. D. Brosetta, L. Leibler, J.-F. Joanny, Macromolecules 20, 1937 (1987).

    Article  ADS  Google Scholar 

  5. Z.A. Akcasu, Dynamic Light Scattering: The Method and Some Applications, edited by W. Brown (Oxford University Press, Oxford, 1993).

    Google Scholar 

  6. L. Giebel, R. Borsali, E.W. Fisher, G. Meier, Macromolecules 23, 4054 (1990).

    Article  ADS  Google Scholar 

  7. L. Ould Kaddour, C. Strazielle, Polymer 28, 459 (1987).

    Article  Google Scholar 

  8. M.R. Aven, C. Cohen, Macromolecules 23, 476 (1990).

    Article  ADS  Google Scholar 

  9. T. Csiba, G. Jannink, D. Durand, R. Papoular, A. Lapp, L. Auvray, F. Boué, J.-P. Cotton, R. Borsali, J. Phys. (Paris) 1, 381 (1991).

    Google Scholar 

  10. R. Borsali, M. Duval, M. Benmouna, Macromolecules 22, 816 (1989).

    Article  ADS  Google Scholar 

  11. P.J. Daivis, D.N. Pinder, P.T. Callaghan, Macromolecules 24, 170 (1992).

    Article  Google Scholar 

  12. P.-G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, 1979).

    Google Scholar 

  13. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon Press, Oxford, 1989).

    Google Scholar 

  14. C. Itzykson, J.-M. Drouffe, Statistical Field Theory: 1 and 2 (Cambridge University Press, 1989).

  15. R.M. Briber, B.J. Bauer, Macromolecules 21, 3296 (1988).

    Article  ADS  Google Scholar 

  16. P.-G. de Gennes, J. Phys. Lett. 40, 69 (1979).

    Article  Google Scholar 

  17. A. Bettachy, A. Derouiche, M. Benhamou, M. Daoud, J. Phys. II 1, 153 (1991).

    Article  Google Scholar 

  18. A. Derouiche, A. Bettachy, M. Benhamou, M. Daoud, Macromolecules 25, 7188 (1992).

    Article  ADS  Google Scholar 

  19. T.A. Vilgis, M. Benmouna, M. Daoud, M. Benhamou, A. Bettachy, A. Derouiche, Polym. Network Blends 3, 59 (1993).

    Google Scholar 

  20. M. Benmouna, T.A. Vilgis, M. Daoud, M. Benhamou, Macromolecules 27, 1172 (1994).

    Article  ADS  Google Scholar 

  21. M. Benmouna, T.A. Vilgis, M. Benhamou, A. Babaoui, M. Daoud, Macromol. Theory Simul. 3, 557 (1994).

    Article  Google Scholar 

  22. A. Bettachy, A. Derouiche, M. Benhamou, M. Benmouna, T.A. Vilgis, M. Daoud, Macromol. Theory Simul. 4, 67 (1995).

    Article  Google Scholar 

  23. M. Benhamou, J. Chem. Phys. 102, 5854 (1995).

    Article  ADS  Google Scholar 

  24. D.J. Read, M.G. Brereton, T.C.B. McLeish, J. Phys. II 5, 1679 (1995).

    Article  Google Scholar 

  25. A. Bettachy, PhD Thesis, Hassan II-Mohammedia University, 1995.

  26. A. Derouiche, PhD Thesis, Hassan II-Mohammedia University, 1995.

  27. M. Riva, V.G. Benza, J. Phys. II 7, 285 (1997).

    Article  Google Scholar 

  28. M. Benhamou, A. Derouiche, A. Bettachy, J. Chem. Phys. 106, 2513 (1997).

    Article  ADS  Google Scholar 

  29. A. Derouiche, M. Benhamou, A. Bettachy, Eur. Phys. J. E 13, 353 (2005).

    Article  Google Scholar 

  30. M. Benhamou, M. Chahid, Physica A 373, 153 (2007).

    Article  ADS  Google Scholar 

  31. M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Oxford Science Publications, Clarendon Press, 1986).

  32. T.A. Vilgis, M. Benmouna, Macromolecules 24, 4481 (1991).

    Article  ADS  Google Scholar 

  33. The derivation of this formula can be found in ref. [19].

  34. D. Broseta, L. Leibler, J.-F. Joanny, Macromolecules 20, 1935 (1987).

    Article  ADS  Google Scholar 

  35. R.M. Briber, B.J. Bauer, Macromolecules 21, 3296 (1988).

    Article  ADS  Google Scholar 

  36. M. Benhamou, A. Derouiche, A. Bettachy, J. Chem. Phys. 106, 2513 (1997).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Benhamou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boussaid, A., Benhamou, M. & El Fazni, A. Theory of microphase separation in charged crosslinked polymer blends with arbitrary charge distribution. Eur. Phys. J. E 30, 379 (2009). https://doi.org/10.1140/epje/i2009-10536-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2009-10536-1

Keywords

Navigation