Unveiling the effects of molecular topology on the viscoelasticity of entangled polymers under gelation

When polymer molecules are constantly crosslinked during the curing process, the presence of intramolecular loops and tree-like hyperbranched structure make the prediction of viscoelastic properties rather complex due to the change of molecular topology. Based on the effective potential in primitive path fluctuations for the relaxation of star polymers [Milner & McLeish, Macromolecules 1997], we propose a novel strategy, i.e., by defining effective relaxation potentials at the “termini” of each polymer strand in a hierarchical manner, to determine the timely movement of the relaxation “front” [Read et al. Science 2011] between the fully relaxed outer layer and the unrelaxed inner core in an arbitrary molecular architecture. For monodisperse polymer systems with specified molecular structure, this model is shown to capture the stress relaxation quite well when compared to those from analytical theories and experimental data. By implementing a kinetic Monte Carlo method [Rui et al. PRL 2016] to access the topological information of crosslinked polymers, this model allows for the prediction of a change in the exponent of power law relationships for rheological moduli at intermediate frequencies with different conversions, which is consistent with the experimental measurements.