| Abstract: | The relaxation of an entangled polymeric medium in the viscoelastic plateau is investigated theoretically by using the slip-link representation of topological constraints. In addition to the chain retraction process introduced by Daoudi and investigated theoretically by Doi, we show that two processes contribute significantly to the relaxation: The first, “equilibration across slip-links,” is a longitudinal reequilibration between parts of the chain which have been differently extended or compressed, depending on their initial orientation relatively to the strain tensor. The second, “tube relaxation,” is a mean-field representation of the loss of topological constraints on one chain due to the retraction of the others. Closed analytical expressions for the stress accounting for these three processes are derived and compared with previous theories: the relaxation should be much more progressive than previously predicted, and the terminal time for retraction is reduced significantly by tube relaxation. |
