RELAXATION OF ENTANGLED POLYMERS IN MELTS

In this paper, a theoretical study of the relaxation of entangled polymers in melts is presented, the aim being to reproduce experimental results in a precise manner. The reptation concept introduced by de Gennes is used for this purpose but with strong modifications. Several results are obtained. First, a phenomenological approach is used to confirm the validity of the “double reptation” principle that enables us to deduce the relaxation of a mixture of very long polymers and of moderately long polymers from the relaxation of each species considered separately. This assumption being well verified, the problem reduces to the relaxation of monodisperse polymers. Then, it is shown that the relaxation of such polymers can be deduced from the motions of stress points on the chains. It is assumed that the diffusion constant of a point depends on its position on the chain. Moreover, the fact that sliding motion as well as diffusive motion may simultaneously contribute to reptation is taken into account. Three related models are presented, exactly solved, and discussed. One model gives results in good agreement with experiments (on polybutadiene), and this model, which incorporates diffusion and sliding effects, is especially simple from a mathematical point of view since it belongs to a class of easily tractable models whose study seems promising. © 1990, American Chemical Society. All rights reserved.