J. Phys. I France 4 (1994) 843-862
The tube diameter in polymer melts, its existence. and its relation to the quantum Hall effectArkady L. Kholodenko1, 2 and Thomas A. Vilgis1
1 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)
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.
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