The European Physical Journal E

, Volume 28, Issue 1, pp 89–96 | Cite as

Microphase separation in cross-linked polymer blends

Efficient replica RPA post-processing of simulation data for homopolymer networks
  • A. V. Klopper
  • Carsten Svaneborg
  • Ralf Everaers
Open Access
Regular Article


We investigate the behaviour of randomly cross-linked (co)polymer blends using a combination of replica theory and large-scale molecular dynamics simulations. In particular, we derive the analogue of the random phase approximation for systems with quenched disorder and show how the required correlation functions can be calculated efficiently. By post-processing simulation data for homopolymer networks we are able to describe neutron scattering measurements in heterogeneous systems without resorting to microscopic detail and otherwise unphysical assumptions. We obtain structure function data which illustrate the expected microphase separation and contain system-specific information relating to the intrinsic length scales of our networks.


61.25.H- Macromolecular and polymers solutions; polymer melts 61.43.-j Disordered solids 64.75.+g Solubility, segregation, and mixing; phase separation 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion 


  1. 1.
    P.G. de Gennes, J. Phys. (Paris) Lett. 40, L69 (1979).Google Scholar
  2. 2.
    R.M. Briber, B.J. Bauer, Macromolecules 21, 3296 (1988).Google Scholar
  3. 3.
    B. Ewen, D. Richter, Neutron Spin Echo Investigations on the Segmental Dynamics of Polymers in Melts, Networks and Solutions (Springer, Berlin, Heidelberg, 1997).Google Scholar
  4. 4.
    Y.B. Melnichenko, G.D. Wignall, J. Appl. Phys. 102, 021101 (2007).Google Scholar
  5. 5.
    K. Kremer, G.S. Grest, in Monte Carlo and Molecular Dynamics Simulations in Polymer Science, edited by K. Binder (Oxford University Press, New York, 1995).Google Scholar
  6. 6.
    S. Lay, J.-U. Sommer, A. Blumen, J. Chem. Phys. 113, 11355 (2000).Google Scholar
  7. 7.
    P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca and London, 1979).Google Scholar
  8. 8.
    S. Westermann, V. Urban, W. Pyckhout-Hintzen, D. Richter, E. Straube, Macromolecules 29, 6165 (1996).Google Scholar
  9. 9.
    S. Westermann, W. Pyckhout-Hintzen, D. Richter, E. Straube, S. Egelhaaf, R. May, Macromolecules 34, 2186 (2001).Google Scholar
  10. 10.
    M.G. Brereton, T.A. Vilgis, J. Phys. I 2, 581 (1992).Google Scholar
  11. 11.
    M.G. Brereton, T.A. Vilgis, J. Phys. I 2, 2281 (1992).Google Scholar
  12. 12.
    C. Wald, A. Zippelius, P.M. Goldbart, Europhys. Lett. 70, 843 (2005).Google Scholar
  13. 13.
    C. Wald, P.M. Goldbart, A. Zippelius, J. Chem. Phys. 124, 214905 (2006).Google Scholar
  14. 14.
    C. Svaneborg, G.S. Grest, R. Everaers, Polymer 46, 4283 (2005).Google Scholar
  15. 15.
    C. Svaneborg, G.S. Grest, R. Everaers, Phys. Rev. Lett. 93, 257801 (2004).Google Scholar
  16. 16.
    D.J. Read, M.G. Brereton, T.C.B. McLeish, J. Phys. II 5, 1679 (1995).Google Scholar
  17. 17.
    K. Binder, A.P. Young, Rev. Mod. Phys. 58, 801 (1986).Google Scholar
  18. 18.
    S.F. Edwards, P.W. Anderson, J. Phys. F: Metal Phys. 5, 965 (1975).Google Scholar
  19. 19.
    T. Castellani, A. Cavagna, J. Stat. Mech. (2005) P05012.Google Scholar
  20. 20.
    R. Everaers, S.K. Sukumaran, G.S. Grest, C. Svaneborg, A. Sivasubramanian, K. Kremer, Science 303, 823 (2004).Google Scholar
  21. 21.
    M. Benmouna, T.A. Vilgis, M. Daoud, M. Benhamou, Macromolecules 27, 1172 (1994).Google Scholar
  22. 22.
    S. Stepanow, M. Schulz, J. Chem. Phys. 98, 6558 (1993).Google Scholar
  23. 23.
    E. Jarkova, T.A. Vilgis, Macromol. Theory Simul. 13, 592 (2004).Google Scholar
  24. 24.
    G.S. Grest, K. Kremer, Phys. Rev. A 33, 3628 (1986).Google Scholar
  25. 25.
    K. Kremer, G.S. Grest, J. Chem. Phys. 92, 5057 (1990).Google Scholar
  26. 26.
    S.J. Plimpton, Large-scale Atomic/Molecular Massively Parallel Simulator, Scholar
  27. 27.
    S.K. Sukumaran, G.S. Grest, K. Kremer, R. Everaers, J. Polym. Sci. Part B: Polym. Phys. 43, 917 (2005).Google Scholar
  28. 28.
    R. Auhl, R. Everaers, G.S. Grest, K. Kremer, S.J. Plimpton, J. Chem. Phys. 119, 12718 (2003).Google Scholar

Copyright information

© The Author(s) 2009

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • A. V. Klopper
    • 1
  • Carsten Svaneborg
    • 2
  • Ralf Everaers
    • 3
  1. 1.Max Planck Institute for the Physics of Complex SystemsDresdenGermany
  2. 2.Department of Chemistry and Interdisciplinary Nanoscience Center (iNano)University of AarhusÅrhusDenmark
  3. 3.Laboratoire de Physique, École Normale Supérieure de LyonUniversité de LyonLyon Cedex 07France

Personalised recommendations