On the difference between weakly and strongly entangled linear polymers

The paper proposes an explanation of the second critical point in viscoelastic behaviour of linear polymers, position of which, according to Ferry (1980), is empirically estimated as M* approximate to (4.6 - 12)M-e, where M-e is the length of the macromolecule between adjacent entanglements'. Thepaperbegins with an introduction to the dynamics of a single macromolecule in the entangled system. Diffusive and reptation mechanisms of relaxation of macromolecules are considered and compared, which allows one to introduce the division between weakly and strongly entangled systems and to calculate the dynamic transition point as M* - 10M(e). Three types of linear polymer systems ought to be considered, according to the ratio of the length of the macromolecule M to M-e: M < 2M(e) - non-entangled system, 2M(e) < M < 10M(e) - weakly entangled systems and M > 10M(e) - strongly entangled systems. Reptation motion of macromolecules can be noticeable only in the strongly entangled systems. It is shown for these systems that contribution of reptation relaxation in low-frequency linear viscoelasticy can be neglected, while one has to take reptation relaxation into account to obtain the correct dependence of effects of the second order on the length of the macromolecule. (C) 2004 Elsevier B.V. All rights reserved.