| Issue |
J. Phys. I France
Volume 4, Number 6, June 1994
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|---|---|---|
| Page(s) | 843 - 862 | |
| DOI | https://doi.org/10.1051/jp1:1994232 | |
J. Phys. I France 4 (1994) 843-862
The tube diameter in polymer melts, its existence. and its relation to the quantum Hall effect
Arkady L. Kholodenko1, 2 and Thomas A. Vilgis11 Max-Planck-Institut für Polymerforschung, P.O. Box 3148, D-55021 Mainz, Germany
2 375 H. L. Hunter Laboratories, Clemson University, Clemson, SC 29634-1905, U.S.A.
(Received 20 August 1993, revised 23 February 1994, accepted 2 March 1994)
Abstract
The self consistent single tube model which plays the major role in the
reptation theory of de Gennes, Doi and Edwards is reanalyzed with help
of the discovered analogy with quantum Hall effect (QHE). We study the
existence and the stability of a given tube caused by its interactions
with other tubes. The interaction is of a topological nature due to the
effects of entanglements. The formalism developed allows us to explain
the observed crossover from the reptation to the Rouse regime in terms
of melting transition of a quasi-lattice of de Gennes tubes. Some of
the major results of the existing packing and scaling theories relating
the monomer density to the tube radius are obtained as limiting cases
of a more general theory. The results of our calculations are supported
by the most recent Monte Carlo simulations.
© Les Editions de Physique 1994