The Doi−Edwards (DE) theory for the rheological properties of entangled polymer melts and solutions successfully predicts the response to large step-shear strains but fails to predict other nonlinear shear properties, such as the steady-state viscosity or the relaxation of stress after cessation of steady shearing. Many of these failures remain even in the extension of the theory by Marrucci and Grizzuti (Gazz. Chim. Ital. 1988, 118, 179) to allow deformation-induced “tube stretch”. Here, we find that a much more successful theory can be obtained by also accounting for “convective constraint release”, i.e., the loss of entanglement constraints caused by the retraction of surrounding chains in their tubes. (Marrucci, G. J. Non-Newtonian Fluid Mech. 1996, 62, 279 and Ianniruberto, G.; Marrucci, G. J. Non-Newtonian Fluid Mech. 1996, 65, 241). , In the molecular model developed here, convective constraint release can both shorten the reptation tube and allow reorientation of interior tube segments. The revised model predicts many of the features of steady and transient shearing flows. These include a region of nearly constant steady-state shear stress at shear rates between the inverse zero-shear reptation time and the inverse Rouse time, similar to that seen in the experiments of Bercea et al. (Macromolecules 1993, 26, 7095) and also predicted by Marrucci and Ianniruberto (Macromol. Symp. 1997, 117, 233). The predictions of transient stresses after startup and cessation of shear are also in good agreement with experiments, as are predictions of nonmonotonicity in the extinction angle after stepup or stepdown in shear rate.

Numerical and analytical methods are developed to invert the double reptation mixing rule to determine the molecular weight distribution (MWD). An analytic method involving Mellin transforms is developed for the case of a single exponential monodisperse relaxation function. A general analytic solution for the MWD is generated for a step-function monodisperse relaxation function. Numerical methods are developed for more general multiple time constant monodisperse relaxation functions. Both analytical and numerical methods are simple, robust, and capable of appropriately handling error-infected experimental data. The power-law relaxation modulus associated with broad MWD commercial polymer is analytically inverted to generate the corresponding molecular weight distribution. MWDs calculated from rheological data for polybutadiene and polypropylene are in close agreement with the corresponding GPC data and are very sensitive to small amounts of high molecular weight material present. The fundamental origins of this sensitivity lie in the intrinsically nonlinear nature of the dependence of rheological properties on molecular weight. The quality of the results suggest that the ‘‘double reptation’’ mixing rule captures an essential feature of the physics of entangled polydisperse polymeric systems.

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