Abstract.
We study the cylinder to sphere morphological transition of diblock copolymers in aqueous solution with a hydrophobic block and a charged block. We find a metastable undulated cylinder configuration for a range of charge and salt concentrations which, nevertheless, occurs above the threshold where spheres are thermodynamically favorable. By modeling the shape of the cylinder ends, we find that the free-energy barrier for the transition from cylinders to spheres is quite large and that this barrier falls significantly in the limit of high polymer charge and low solution salinity. This suggests that observed undulated cylinder phases are kinetically trapped structures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F.S. Bates, Science 251, 898 (1991).
F.S. Bates, G.H. Fredrickson, Annu. Rev. Phys. Chem. 41, 525 (1990).
G.H. Fredrickson, The Equilibrium Theory of Inhomogeneous Polymers (Oxford University Press, Oxford, 2006).
M.W. Matsen, M. Schick, Phys. Rev. Lett. 72, 2660 (1994).
A.N. Semenov, Sov. Phys. JETP 61, 733 (1985).
G.M. Grason, B.A. DiDonna, R.D. Kamien, Phys. Rev. Lett. 91, 058304 (2003)
J.N. Israelachvili, Intermolecular and Surface Forces (Academic Press, London, 1992).
S. Jain, F.S. Bates, Science 300, 460 (2003).
S. Jain, F.S. Bates, Macromolecules 37, 1511 (2004).
L. Zhang, K. Yu, A. Eisenberg, Science 272, 1777 (1996).
D.E. Discher, A. Eisenberg, Science 297, 697 (2002).
Y. Geng, F. Ahmed, N. Bhasin, D.E. Disher, J. Phys. Chem. B 109, 3772 (2005).
D. Bendejacq, M. Joanicot, V. Ponsinet, Eur. Phys. J. E 17, 83 (2005).
S.E. Burke, A. Eisenberg, Langmuir 17, 6705 (2001).
P.D. Olmsted, S.T. Milner, Phys. Rev. Lett. 72, 936 (1994)
E.B. Zhulina, O.V. Borisov, Macromolecules 29, 2618 (1996)
R.R. Netz, Europhys. Lett. 47, 391 (1999).
A. Jusufi, C.N. Likos, H. Löwen, J. Chem. Phys. 116, 11011 (2002).
K. Kenmotsu, Surfaces with Constant Mean Curvature (American Mathematical Society, Providence, 2003).
I.M. Mladenov, Eur. Phys. J. B 29, 327 (2002).
P. Pincus, Macromolecules 24, 2912 (1991).
S. Alexander, J. Phys. (Paris) 38, 983 (1997)
A.V. Korobko, W. Jesse, S.U. Egelhaaf, A. Lapp, J.R.C. van der Maarel, Phys. Rev. Lett. 93, 177801 (2004).
O.V. Borisov, E.B. Zhulina, Macromolecules 36, 10029 (2003).
T. Tlusty, S.A. Safran, R. Strey, Phys. Rev. Lett. 84, 1244 (2000)
A. Halperin, S. Alexander, Macromolecules 22, 2403 (1989).
E.E. Dormidontova, Macromolecules 32, 7630 (1999).
F.J. Esselink, E.E. Dormidontova, G. Hadziiannou, Macromolecules 31, 4873 (1998).
R. Lund, L. Willner, J. Stellbrink, P. Lindner, D. Richter, Phys. Rev. Lett. 96, 068302 (2006).
E.A.G. Aniansson, S.N. Wall, J. Phys. Chem. 78, 1024 (1974).
E.A.G. Aniansson, S.N. Wall, J. Phys. Chem. 79, 857 (1975).
M.W. Matsen, J. Chem. Phys. 114, 8165 (2001).
H.A. Kramers, Physica 7, 284 (1940).
E.L. Thomas, D.M. Anderson, C.S. Henkee, D. Hoffman, Nature 334, 598 (1988).
M.W. Matsen, F.S. Bates, Macromolecules 29, 7641 (1996).
H. Junnai, Y. Nishikawa, R.J. Spontak, S.D. Smith, D.A. Agard, T. Hashimoto, Phys. Rev. Lett. 84, 518 (2000).
T.T. Nguyen, A. Gopal, K.Y.C. Lee, T.A. Witten, Phys. Rev. E 72, 051930 (2005).
E.g., S.A. Safran, Statistical Thermodynamics of Surfaces, Interfaces, and Membranes (Addison-Wesley, Reading, MA, 1994).
J.B. Fournier, P. Galatola, Europhys. Lett. 39, 225 (1997).
I. Tsafrir, D. Sagi, T. Arzi, M.-A. Guedeau-Boudeville, V. Frette, D. Kandel, J. Stavens, Phys. Rev. Lett. 86, 1138 (2001).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Grason, G.M., Santangelo, C.D. Undulated cylinders of charged diblock copolymers. Eur. Phys. J. E 20, 335–346 (2006). https://doi.org/10.1140/epje/i2006-10025-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epje/i2006-10025-1