Reptation with Configuration-Dependent Constraint Release in the Dynamics of Flexible Polymers

The effect of simultaneous reptation and tube deformation on the dynamic properties of polymers has been examined. We propose the configuration-dependent constraint release (CDCR) mechanism. The decay of the memory of the tube orientation is assumed to be governed by Rouse dynamics, and therefore the rate of tube deformation, or constraint release in our model, varies along the contour of the tube. This is in contrast with the type of model originally proposed by Graessley, where constraint release occurs uniformly along the chain contour. We reformulate Graessley's model in our terminology in order to make comparisons with our CDCR model. We examine two categories of situations. One is binary blends of polymers, with the longer components too dilute to entangle among themselves, where the effects of constraint release can be arbitrarily exaggerated and separated from reptation. The second is monodisperse polymers. For the blends in a constraint release dominant regime, relaxation of orientation in a polymer after a constant step strain occurs much less uniformly along the chain in the CDCR model than in Graessley's model. This difference could be sought experimentally. Overall, for CDCR the effect of constraint release competing with reptation is smaller than in the Graessley model under equivalent circumstances. One manifestation of this is in the prediction of the zero shear rate viscosity variation with molecular weight. CDCR overpredicts the experimental viscosity but goes asymptotically to pure reptation at high molecular weight where Graessley's model un-derpredicts the viscosity and does not go to the pure reptation limit. The self-diffusion coefficient obtained from our model is the same as that of the Graessley model, while the end-to-end vector correlation function is quite different: Our model predicts that the combination of constraint release and reptation processes shifts the characteristic time but does not change the distribution of the relaxation modes of this function, while the Graessley model predicts the change of the mode distribution due to the combination of these processes. This gives another method for the experimental examination of these models.