Importance of chain tumbling and finite extension on the start-up and relaxation behavior of transient networks

Associative polymer networks are ubiquitous in tissue and biomedical engineering. However, the particular molecular attributes that contribute to the macroscopic behavior like shear thinning, self-healing, and yield stress are less well known. Here we incorporate chemical kinetics in the the Smoluchowski Equation capable of modeling the full network chain end-to-end distance distribution while tracking the fraction of looped, bridged, and dangling chains in the gel. In steady shear, we see the development of non-monotonic flow instabilities when the rate of chain association and dissociation are slower than the rate of chain relaxation. These instabilities arise due to a combination of chain finite extensibility and tumbling. During start-up of steady shear, the combination of these two phenomena also results in stress overshoots followed by multiple damped oscillations toward steady-state. The timescale of chain relaxation after the cessation of shear is dominated by the chain kinetics of association and dissociation as a function of the fraction of dangling chains present at any time post-shear.