(468h) Predictions for Non-Linear Flows of Polydisperse Blends Based on a Differential-Constitutive Analogue of the Double Reptation Model

The flows of industrially relevant polymeric materials are notoriously difficult to model due in part to the broad distribution of molecular weights. While double reptation theory provides a simple and useful description of polydisperse blends in the linear flow regime, at present there is no comparable model in the non-linear flow regime. A true tube-based model is possible in the bi-disperse limit [1], but unfortunately this model is computationally intractable for spatially resolved flows. For studies of spatially resolved flows, multimode constitutive models have greater practical value. Multimode models describe a blend’s overall rheology as the superposition of responses from a set of simple constitutive models, fit to experimental data. However, the multimode approach can be unreliable: for example, a model fit to simple shear flow data can yield poor predictions for extensional flows.

As an improvement to existing multimode models of polymer blends, we have developed a differential constitutive analogue to double reptation theory. Double reptation theory can be viewed as a temporary network model; entanglements are approximated as mutual, binary, topological constraints between chains, and the stress at an entanglement relaxes when one of the two chains reptates through the constraint [2]. In a differential constitutive framework, we apply the micromechanical model of double reptation to all stress relaxation mechanisms so that entanglements can also relax their stress by chain retraction and convective constraint release. The resulting multimode constitutive model is consistent with classical double reptation in the linear flow regime, but also incorporates the non-linear stress relaxation couplings for strong flow conditions. For well-entangled bi-disperse blends, our multimode model yields predictions that are qualitatively consistent with the more detailed (but computationally challenging) tube-based theory. We believe that the differential constitutive analogue to double reptation theory offers a compelling balance between reliability and practical utility for predicting flow behavior in industrially relevant polymer blends.

[1] D. J. Read, K. Jagannathan, S. K. Sukumaran, and D. Auhl, Journal of Rheology 56, 823 (2012)

[2] J. des Cloizeaux, Europhysics Letters, 5 (5), pp 437 – 442 (1998)