J. Phys. I France
Volume 4, Numéro 6, June 1994
Page(s) 843 - 862
DOI: 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. 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.

© Les Editions de Physique 1994

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.