(227ae) A Constitutive Model for Monodisperse and Polydisperse Entangled Polymers Incorporating Binary Entanglement Pair Dynamics and a Configuration Dependent Friction Coefficient

We present a new model (MBP: Mead-Banerjee-Park) which introduces the concept of a conformation dependent friction coefficient (CDFC) based on the relative orientation of a test Kuhn bond to the surrounding matrix Kuhn bonds and entanglement dynamics (ED) of discrete entanglement pairs into the MLD “toy” model [Mead et al., J. Rheol. 59, 335-363 (2015)]. The model for monodisperse system was successfully validated against experimental data in transient and steady extensional and shear flows. It simultaneously predicts the monotonic thinning of the extensional flow curve of monodisperse PS melts [Bach et al., Macromolecules 36, 5174-5179 (2003)] and extension hardening of monodisperse PS solutions [Bhattacharjee et al., Macromolecules 35, 10131-10148 (2002)]. The results also show that the rheological properties in nonlinear extensional flows of PS melts are sensitive to CDFC but not to convective constraint release (CCR) while those for shear flows are influenced more by CCR. The model can be extended to polydisperse systems by incorporating the “diluted stretch tube” theory [Mishler and Mead, J. Non-Newton Fluid. 197, 61-79 (2013)]. This concept underlines the presence of characteristic time (stretch and orientation relaxation time) spectra for a system with a broad molecular weight distribution (MWD) and leads to a modified entanglement microstructure, i.e. reduction in the number of viable ‘stretch entanglements’ for a given MWD component. The transient and steady extensional flows of polydisperse PS melts with broad MWD are predicted by the polydisperse MBP model and compared with the corresponding experimental data.