The seminal ideas of de Gennes and Doi and Edwards have provided the theoretical framework for much of the recent effort to model the rheological behavior of entangled polymer melts and solutions. Recent theoretical work has incorporated a number of important additions to the basic Doi-Edwards theory, including an explicit description of chain stretch and additional relaxation mechanisms such as contour length fluctuations (CLF) and convective constraint release (CCR). However, very little quantitative data has been published on the rheological behavior of entangled systems in strong flows. Hence, a comprehensive examination of the theoretical developments has not been possible. The experiments described in this paper use the filament stretching rheometer to obtain transient extensional stress growth data and steady state uniaxial extensional viscosity data for a number of entangled, narrow molecular weight distribution polystyrene solutions in the strain-rate regime characterized by a significant degree of both chain alignment and stretch. These results are then compared with theoretical predictions for a number of the current generation of reptation-based models, including mechanisms for chain stretching, contour length fluctuations, and convective constraint release. These comparisons demonstrate that when the model parameters are properly obtained from linear viscoelastic measurements, the recent model due to Mead, Larson, and Doi (Macromolecules 1998, 31, 7895) provides quantitative predictions for this class of flows for solutions spanning the complete range from very lightly to highly entangled solutions.
We examine the influence of the number of entanglements per chain (Z) on the uniaxial extensional rheology of polymer melts and concentrated solutions. We subject fluids with wide range of Z (13–51) to uniaxial extensional flow at strain rates that also spans a wide range: starting at strain rates that much less than the inverse of the longest measurable relaxation time of the chains to strain rates that are in excess of the order of the inverse of the Rouse time of the chain. The results show that the value of Z critically influences extensional flow at all strain rates examined. The combination of results presented here and those from recent literature clearly establish areas where the agreement between tube theory and experiments is less than satisfactory. These differences are particularly evident at strain rates wherein chain stretching is expected to play a role. There are also differences in the behavior of polystyrene melts and other systems investigated. Taking together exiting data indicate that the universality of the tube model may break down at large strain rates. It is possible that the monomeric friction coefficient depends sensitively on molecular architecture and the surrounding environment. The presence of pendant groups on the monomer background may influence the friction coefficient. Predicting this apriori remains a challenge. Additionally we show that the parameter λmax/Z, where λmax is the ratio of the maximum length of a polymer chain to its equilibrium length, influences the flow behavior to the extent that fluids having equal values of λmax/Z demonstrate similar rheological behavior at all deformation rates when the extensional flow response is suitably scaled. We also compare our results with those obtained on other polymer melts in uniaxial extensional flow reported previously in literature.
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