The European Physical Journal E

, Volume 23, Issue 2, pp 135–144 | Cite as

Finite-stretching corrections to the Milner-Witten-Cates theory for polymer brushes

Article

Abstract.

This paper investigates finite-stretching corrections to the classical Milner-Witten-Cates theory for semi-dilute polymer brushes in a good solvent. The dominant correction to the free energy originates from an entropic repulsion caused by the impenetrability of the grafting surface, which produces a depletion of segments extending a distance μ∝L-1 from the substrate, where L is the classical brush height. The next most important correction is associated with the translational entropy of the chain ends, which creates the well-known tail where a small population of chains extend beyond the classical brush height by a distance ξ∝L-1/3. The validity of these corrections is confirmed by quantitative comparison with numerical self-consistent field theory.

PACS.

68.47.Pe Langmuir-Blodgett films on solids; polymers on surfaces; biological molecules on surfaces 61.41.+e Polymers, elastomers, and plastics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S.T. Milner, Science 251, 905 (1991). CrossRefADSGoogle Scholar
  2. S.F. Edwards, Proc. Phys. Soc. London 85, 613 (1965). MATHCrossRefGoogle Scholar
  3. S.T. Milner, T.A. Witten, M.E. Cates, Macromolecules 21, 2610 (1988). CrossRefADSGoogle Scholar
  4. A.N. Semenov, Sov. Phys. JETP 61, 733 (1985). Google Scholar
  5. S. Alexander, J. Phys. (Paris) 38, 983 (1977). Google Scholar
  6. R. Baranowski, M.D. Whitmore, J. Chem. Phys. 103, 2343 (1995). CrossRefADSGoogle Scholar
  7. R.R. Netz, M. Schick, Macromolecules 31, 5105 (1998). CrossRefADSGoogle Scholar
  8. S.T. Milner, J. Chem. Soc. Faraday Trans. 86, 1349 (1990). CrossRefGoogle Scholar
  9. M.S. Kent, L.T. Lee, B.J. Factor, F. Rondelez, G.S. Smith, J. Chem. Phys. 103, 2320 (1995). CrossRefADSGoogle Scholar
  10. M.P. Pépin, M.D. Whitmore, J. Chem. Phys. 111, 10381 (1999). CrossRefADSGoogle Scholar
  11. C. Seidel, R.R. Netz, Macromolecules 33, 634 (2000). CrossRefADSGoogle Scholar
  12. T. Kreer, S. Metzger, M. Müller, K. Binder, J. Chem. Phys. 120, 4012 (2004). CrossRefADSGoogle Scholar
  13. S.T. Milner, T.A. Witten, Macromolecules 25, 5495 (1992). CrossRefADSGoogle Scholar
  14. T.A. Witten, L. Leibler, P.A. Pincus, Macromolecules 23, 824 (1990). CrossRefADSGoogle Scholar
  15. H. Orland, M. Schick, Macromolecules 29, 713 (1996). CrossRefADSGoogle Scholar
  16. P.G. de Gennes, Macromolecules 13, 1069 (1980). CrossRefADSGoogle Scholar
  17. A.E. Likhtman, A.N. Semenov, Europhys. Lett. 51, 307 (2000). CrossRefADSGoogle Scholar
  18. P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, 1979). Google Scholar
  19. M.W. Matsen, in Soft Matter, Vol. 1: Polymer Melts and Mixtures, edited by G. Gompper, M. Schick (Wiley-VCH, Weinheim, 2006). Google Scholar
  20. M.W. Matsen, J. Chem. Phys. 121, 1938 (2004). CrossRefADSGoogle Scholar
  21. M.W. Matsen, J. Chem. Phys. 117, 2351 (2002). CrossRefADSGoogle Scholar
  22. R.R. Netz, M. Schick, Europhys. Lett. 38, 37 (1997). CrossRefADSGoogle Scholar
  23. M.W. Matsen, J.M. Gardiner, J. Chem. Phys. 118, 3775 (2003). CrossRefADSGoogle Scholar
  24. When comparing our results with those of reference netz1998, be aware that they measure distances in terms of \(\hat{z} \equiv (\pi^2/6)^{1/3} L\) and they characterize the brush by the parameter β≡ (3π4/32)1/3 L2/a2N. Google Scholar
  25. J.U. Kim, B. O'Shaughnessy, Phys. Rev. Lett. 89, 238301 (2002); Macromolecules 39, 413 (2006). CrossRefADSGoogle Scholar
  26. G.E. Yakubov, B. Loppinet, H. Zhang, J. Rühe, R. Sigel, G. Fytas, Phys. Rev. Lett. 92, 115501 (2004). CrossRefADSGoogle Scholar
  27. D. Ausserré, H. Hervet, F. Rondelez, Phys. Rev. Lett. 54, 1948 (1985). CrossRefADSGoogle Scholar
  28. K. Takahashi, Y. Yunoki, J. Phys. Soc. Jpn. 22, 219 (1967); D.C. Morse, G.H. Fredrickson, Phys. Rev. Lett. 73, 3235 (1994). ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ReadingReadingUK

Personalised recommendations