Determination of tube theory parameters using a simple grid model as an example

Likhtman, Alexei E. and Talib, Mohamad S. and Vorselaars, Bart and Ramirez, Jorge (2013) Determination of tube theory parameters using a simple grid model as an example. Macromolecules, 46 (3). pp. 1187-1200. ISSN 0024-9297

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Abstract

Although the tube theory is successful in describing entangled polymers qualitatively, a more quantitative description requires precise and consistent definitions of its parameters. Here we investigate the simplest model of entangled polymers, namely a single Rouse chain in a cubic lattice of line obstacles, and illustrate the typical problems and uncertainties of the tube theory. In particular we show that in general one needs three entanglement related parameters, but only two combinations of them are relevant for the long-time dynamics. Conversely, the plateau modulus can not be determined from these two parameters and requires a more detailed model of entanglements with explicit entanglement forces, such as the slip-springs model. It is shown that for the grid model the Rouse time within the tube is larger than the Rouse time of the free chain, in contrast to what the standard tube theory assumes.

Keywords:Macromolecules, Reptation, viscoelasticity
Subjects:F Physical Sciences > F170 Physical Chemistry
F Physical Sciences > F162 Polymer Chemistry
F Physical Sciences > F320 Chemical Physics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:18226
Deposited On:05 Aug 2015 12:20

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