Stochastic and pre-averaged non-linear rheology models for entangled telechelic star polymers

We present a simplified stochastic model designed to exemplify the non-linear rheology of entangled supramolecular polymeric materials. We have developed a simplified stochastic model for the rheology of entangled telechelic star polymers. As a toy model for entanglement effects, we use the Rolie-Poly equations [1] that we decorate with finite extensibility. Additionally, we include a stretch-dependent probability of detachment for the stickers. In both linear and non-linear regimes, we explore the parameter space, indicating the parameter values for which qualitative changes in response to the applied flow are predicted. Theory and results in the linear rheology regime are consistent with previous more detailed work of van Ruymbeke and co-workers [2]. Finally, we develop a pre-averaged version of the stochastic equations described above to obtain a set of non-stochastic coupled equations that produces very similar predictions but requires less computing resources. This pre-averaged model is based on two tensors representing the attached and detached chain populations and a scalar quantity that represents the fraction of these populations