Concentration fluctuations and reptation dynamics in polymer solutions and melts

The dynamics of linear polymer chains in the entanglement regime is considered theoretically. The following results are obtained. 1.(i) If volume interactions (of polymer links) are absent, the largest conformational relaxation time τmax is not larger than O(M3), where M is the molecular weight of a polymer chain (M → ∝), the inequality τmax ⩽ O(M3) being valid regardless of the particular mechanism of the polymer dynamics.2.(ii) The effect of volume interactions results in a considerable slowing down of the macromolecular motions. This dynamical effect is governed by the parameter α ∝M1 4Mc3 4. In particular, for M > Mc (Mc is the molecular weight per entanglement) the following behavior of the viscosity η of the system is predicted: η ∝ M3(1 + α) for α > 1 and η ∝ exp(const. × α4 3) for α > 1.