| A tube and reptation model is presented which is capable of generating quantitative predictions of the nonlinear rheological properties of polydisperse linear polymer melts in steady shear flow and transient uniaxial extension. While the basic framework of this model is similar to that of the original Doi-Edwards model, it incorporates several more recently introduced concepts such as “double reptation”, “chain stretching” and “convective constraint release”. By including all of these concepts into a single model, we are able to quantitatively predict the steady shear flow properties of polydisperse linear polymer melts. In addition, it is shown that this resulting model approximately satisfies several well-established empirical laws such as the Cox-Merz rule, Laun's rule and Gleissele's mirror relations. On the other hand, this resulting model is not able to qualitatively predict the rheological properties of a certain polydisperse linear polymer melt under any flow that involves chain stretching. In order to remedy this shortcoming, physics that were missing in the original model must be discovered and introduced. In particular, for a typical commercial resin the molecular weight distribution is quite broad. Therefore, the very long chains in such a resin will be partially surrounded by very short chains that relax very quickly. Because the lifetime of these short chain entanglements may be extremely small relative to the relaxation times of the long chains, it is possible that they will have no effect on the slow stretch relaxation of these long chains. Since these entanglements still have lifetimes long enough to effect the rapid orientational relaxation of the long chains, it becomes necessary to model the stretch and orientation dynamics of the long chains in separate tubes. In effect, these short-lived entanglements appear as solvent with respect to the stretch relaxation of the long chains and therefore the stretch dynamics of the long chains must be modeled in a diluted tube. In addition, when a diluted tube becomes stretched it is necessary to introduce new physical mechanisms of stretch and orientation. |
