Abstract.
Using a scaling approach we consider a 2D comb copolymer brush under bending deformations. We show that the rectilinear brush is locally stable and can be characterized by a persistence length λ increasing with the molecular weight of grafting side chains as λ ∼ M3. A bending instability due to redistribution of the side chains appears in the non-linear regime where bending is strong. Arguments are presented that the brush conformations consist of alternating rectilinear and bent sections corresponding to the different free-energy minima.
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T. Birshtein, O. Borisov, E. Zhulina, A. Khokhlov, T. Yurasova, Polymer Sci. USSR 29, 1293 (1987).
G. Fredrickson, Macromolecules 26, 2825 (1993).
A. Subbotin, M. Saariaho, O. Ikkala, G. ten Brinke, Macromolecules 33, 3447 (2000).
R. Stepanyan, A. Subbotin, G. ten Brinke, Macromolecules 35, 5640 (2002).
L. Feuz, F.A.M. Leermakers, M. Textor, O. Borisov, Macromolecules 38, 8891 (2005).
M. Wintermantel, M. Gerle, K. Fischer, M. Schmidt, I. Wataoka, H. Urakawa, K. Kajiwara, Y. Tsukahara, Macromolecules 29, 978 (1996).
S. Sheiko, M. Möller, Chem. Rev. 101, 4099 (2001).
S. Lecommandoux, F. Chécot, R. Borsali, M. Schappacher, A. Deffieux, A. Brlet, J.P. Cotton, Macromolecules 35, 8878 (2002).
T. Stephan, S. Muth, M. Schmidt, Macromolecules 35, 9857 (2002).
Y. Rouault, O.V. Borisov, Macromolecules 29, 2605 (1996).
M. Saariaho, O. Ikkala, I. Szleifer, I. Erukhimovich, G. ten Brinke, J. Chem. Phys. 107, 3267 (1997).
M. Saariaho, I. Szleifer, O. Ikkala, G. ten Brinke, Macromol. Theory Simul. 7, 211 (1998).
R. Connolly, G. Bellesia, E.G. Timoshenko, Y.A. Kuznetsov, S. Elli, F. Ganazzoli, Macromolecules 38, 5288 (2005).
J. de Jong, G. ten Brinke, Macromol. Theory Simul. 13, 318 (2004).
P.G. Khalatur, A.R. Khokhlov, S.A. Prokhorova, S.S. Sheiko, M. Möller, P. Reineker, D.G. Shirvanyanz, N. Starovoitova, Eur. Phys. J. E 1, 99 (2000).
I. Potemkin, Eur. Phys. J. E 12, 207 (2003).
I. Potemkin, A. Khokhlov, S. Prokhorova, S. Sheiko, M. Möller, K. Beers, K. Matyjaszewski, Macromolecules 37, 3918 (2004).
M.O. Gallyamov, B. Tartsch, A.R. Khokhlov, S.S. Sheiko, H.G. Börner, K. Matyjaszewski, M. Möller, Macromol. Rapid Commun. 25, 1703 (2004).
J. de Jong, A. Subbotin, G. ten Brinke, Macromolecules 38, 6718 (2005).
M. Daoud, J. Cotton, J. Phys. (Paris) 43, 531 (1982).
T.M. Birshtein, E.B. Zhulina, Macromol. Theory Simul. 6, 1169 (1997).
A.N. Semenov, Sov. Phys. JETP 61, 733 (1985).
S.T. Milner, T.A. Witten, M.E. Cates, Macromolecules 21, 2610 (1988).
E.B. Zhulina, O.V. Borisov, V.A. Priamitsin, J. Colloid Interface Sci. 137, 495 (1989).
A.E. Likhtman, A.N. Semenov, Macromolecules 27, 3103 (1994).
R.S. Ball, J.F. Marco, S.T. Milner, T.A. Witten, Macromolecules 24, 693 (1991).
H. Li, T.A. Witten, Macromolecules 27, 449 (1994).
F.D. Gakhov, Boundary Value Problems (in Russian, Nauka, Moscow, 1977).
A.D. Polyanin, A.V. Manzhirov, Handbook of Integral Equations (CRC Press, Boca Raton, 1998).
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Subbotin, A., de Jong, J. & ten Brinke, G. Spontaneous bending of 2D molecular bottle-brush. Eur. Phys. J. E 20, 99–108 (2006). https://doi.org/10.1140/epje/i2005-10122-7
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DOI: https://doi.org/10.1140/epje/i2005-10122-7