(116g) A 'semi-Toy' Molecular Constitutive Model for Entangled Polydisperse Linear and/or Star Flexible Polymers with Contour Length Fluctuations

The polydisperse Mead-Park (MP) 'toy' molecular constitutive models [Mead et al (2018) J. Rheol. 62:121-135] have been derived and quantitatively evaluated with experimental data in fast, transient extensional and shear flows. Although the MP model performs reasonably well in nonlinear flows, it fails to quantitatively capture linear viscoelastic flows principally because it does not explicitly include contour length fluctuations (CLFs) in its derivation. We rectify this serious deficiency by deriving the new “semi-toy” polydisperse model which approximately captures the time dependent physics of CLFs by only partially suppressing the tube coordinate dependence of the tube orientation survival equation. The new polydisperse “semi-toy” molecular model is a mathematically tractable model that includes entanglement dynamics, contour length fluctuations, constraint release Rouse (CRR), configuration dependent friction coefficient (CDFC), reptation, double reptation constraint release, CCR as well as conventional and partially diluted and disentangled tube-chain stretching¹. Since CLFs are appropriately accounted for, the new 'semi-toy' model can also simulate quantitatively polydisperse systems of linear and/or star polymers in arbitrary slow or fast flows. The polydisperse semi-toy model is evaluated by simulating interrupted shear experiments that are known to be sensitive to the dynamics of the underlying entanglement microstructure [Dealy and Tsang (1981) J Applied Poly Sci 26:1149-1158; (1981) JNNFM (1981) 9:203-222]. The polydisperse semi-toy model does a credible job of capturing the complex dynamics of the transient peak stress overshoot phenomenon observed in this experiment. Consistent with previous experimental studies, we find that the characteristic time scale for re-entanglement is more than an order of magnitude larger than the shear stress relaxation time [Roy and Roland (2013) Macromolecules 46: 9403-9408].