Abstract.
In de Gennes-Doi-Edwards theory for entangled polymeric melts, a length scale r0 is introduced, giving the equilibrium mesh size of the physical network of chains. Each polymer molecule is then represented as a random walk, with a step size r0 (a “subchain”, made up of n0 Kuhn segments) dictated by the existence of entanglements. Progressing from this simple picture, an issue that has been constantly overlooked so far, despite its potential relevance, is that of finite-size effects at the de Gennes-Doi-Edwards characteristic length scale. Actually, since a subchain in a melt is a “small”, nonmacroscopic system, fluctuations of both its length and its number of Kuhn segments are certainly nonnegligible. An ad hoc theoretical treatment from nonstandard (nano) statistical mechanics and thermodynamics seems then required, to find the anticipated equilibrium statistical distributions of the subchain population. In this contribution, we carefully discuss this topic. Some predictions from the nonstandard fluctuation-inclusive approach on the statistics of subchains are here obtained, and compared with existing simulations, even down to the atomistic level.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P.G. de Gennes, J. Chem. Phys. 55, 572 (1971).
M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Clarendon, New York, 1986).
S. Shanbhag, R.G. Larson, Macromolecules 39, 2413 (2006).
K. Foteinoupoulou, N.C. Karayiannis, V.G. Mavrantzas, M. Kroger, Macromolecules 39, 4207 (2006).
C. Tzoumanekas, D.N. Theodorou, Macromolecules 39, 4592 (2006).
L.J. Fetters, D.J. Lohse, S.T. Milner, W.W. Graessley, Macromolecules 32, 6847 (1999).
L.D. Landau, E.M. Lifshitz, Statistical Physics (Pergamon, Oxford, 1988).
T.L. Hill, Statistical Mechanics (McGraw-Hill, New York, 1956).
F. Greco, Macromolecules 37, 10079 (2004).
D. Ferri, F. Greco, Macromolecules 39, 5931 (2006).
T.L. Hill, Thermodynamics of Small Systems (Benjamin, New York, 1964).
T.L. Hill, Nano Lett. 1, 111 (2001).
G. Glatting, R.G. Winkler, P. Reineker, Macromolecules 26, 6085 (1993).
J.D. Schieber, J. Chem. Phys. 118, 5162 (2003).
S.F. Edwards, Proc. Phys. Soc. (London) 92, 9 (1967).
P.G. de Gennes, J. Phys. (Paris) 36, 1199 (1975).
P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell, Ithaca, 1979).
S.F. Edwards, K.E. Evans, J. Chem. Soc. Faraday Trans. 77, 1913 (1981).
E. Helfand, D.S. Pearson, J. Chem. Phys. 79, 2054 (1983).
S. Shanbhag, M. Kroger, Macromolecules 40, 2897 (2007).
Y. Masubuchi, J.I. Takimoto, K. Koyama, G. Ianniruberto, G. Marrucci, F. Greco, J. Chem. Phys. 115, 4387 (2001).
J.T. Padding, W.J. Briels, J. Chem. Phys. 117, 925 (2002).
R. Everaers, S.K. Sukumaran, G.S. Grest, C. Svaneborg, A. Sivasubramanian, K. Kremer, Science 303, 823 (2004).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Greco, F. Equilibrium statistical distributions for subchains in an entangled polymer melt. Eur. Phys. J. E 25, 175–180 (2008). https://doi.org/10.1140/epje/i2007-10278-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epje/i2007-10278-0