| Abstract: | The kinetic network (KN) model discussed previously in the context of monodisperse and bimodal polymer systems is extended to polymers of arbitrary molecular weight distribution. A generalization is proposed for the flow-dependent entanglement loss term in the structure equation, replacing the shear rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} by a new variable \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \Gamma $\end{document} which reduces to\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} for simple shear and is more appropriate for elongational and other flows. New data are obtained on shear stress transients of many kinds, using a recently developed parallel-plate rheometer. These data and others on steady and transient flows of well-characterized polydisperse polymers in shear and in elongation are used to demonstrate that the KN model predictions are valid. Comparisons with predictions for monodisperse polymers having the same as M w polydisperse systems show that transient behavior—especially stress overshoot—is particularly sensitive to details of the molecular weight distribution. Further possible improvements in the theory are suggested, and the relationship of the KN model to other recent network models is discussed. The KN model has greater data fitting capabilities, with fewer parameters, than any other model available at present. |
