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.
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References
S.T. Milner, Science 251, 905 (1991).
S.F. Edwards, Proc. Phys. Soc. London 85, 613 (1965).
S.T. Milner, T.A. Witten, M.E. Cates, Macromolecules 21, 2610 (1988).
A.N. Semenov, Sov. Phys. JETP 61, 733 (1985).
S. Alexander, J. Phys. (Paris) 38, 983 (1977).
R. Baranowski, M.D. Whitmore, J. Chem. Phys. 103, 2343 (1995).
R.R. Netz, M. Schick, Macromolecules 31, 5105 (1998).
S.T. Milner, J. Chem. Soc. Faraday Trans. 86, 1349 (1990).
M.S. Kent, L.T. Lee, B.J. Factor, F. Rondelez, G.S. Smith, J. Chem. Phys. 103, 2320 (1995).
M.P. Pépin, M.D. Whitmore, J. Chem. Phys. 111, 10381 (1999).
C. Seidel, R.R. Netz, Macromolecules 33, 634 (2000).
T. Kreer, S. Metzger, M. Müller, K. Binder, J. Chem. Phys. 120, 4012 (2004).
S.T. Milner, T.A. Witten, Macromolecules 25, 5495 (1992).
T.A. Witten, L. Leibler, P.A. Pincus, Macromolecules 23, 824 (1990).
H. Orland, M. Schick, Macromolecules 29, 713 (1996).
P.G. de Gennes, Macromolecules 13, 1069 (1980).
A.E. Likhtman, A.N. Semenov, Europhys. Lett. 51, 307 (2000).
P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, 1979).
M.W. Matsen, in Soft Matter, Vol. 1: Polymer Melts and Mixtures, edited by G. Gompper, M. Schick (Wiley-VCH, Weinheim, 2006).
M.W. Matsen, J. Chem. Phys. 121, 1938 (2004).
M.W. Matsen, J. Chem. Phys. 117, 2351 (2002).
R.R. Netz, M. Schick, Europhys. Lett. 38, 37 (1997).
M.W. Matsen, J.M. Gardiner, J. Chem. Phys. 118, 3775 (2003).
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.
J.U. Kim, B. O'Shaughnessy, Phys. Rev. Lett. 89, 238301 (2002); Macromolecules 39, 413 (2006).
G.E. Yakubov, B. Loppinet, H. Zhang, J. Rühe, R. Sigel, G. Fytas, Phys. Rev. Lett. 92, 115501 (2004).
D. Ausserré, H. Hervet, F. Rondelez, Phys. Rev. Lett. 54, 1948 (1985).
K. Takahashi, Y. Yunoki, J. Phys. Soc. Jpn. 22, 219 (1967); D.C. Morse, G.H. Fredrickson, Phys. Rev. Lett. 73, 3235 (1994).
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Kim, J., Matsen, M. Finite-stretching corrections to the Milner-Witten-Cates theory for polymer brushes. Eur. Phys. J. E 23, 135–144 (2007). https://doi.org/10.1140/epje/i2007-10188-1
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DOI: https://doi.org/10.1140/epje/i2007-10188-1