Using Molecular Models and Recovery Rheology to Predict the Stress Response of Polymer Networks

Polymer networks can exhibit a wide variety of viscoelastic behavior by changing its crosslinking density. However, even prior to full network formation, varying the crosslinking reaction extent can produce very different stress responses. For example, at low crosslinking extent, only small clusters exist, and fluid-like behavior dominates. At higher crosslinking extent below a materials gel point, large clusters can exhibit elastic behavior, allowing the system to be solid-like at short time scales. However, it is unclear what molecular processes create these macroscopically observable stress responses.

Recent work from the Rogers group has demonstrated that by decomposing the loss modulus into recoverable and unrecoverable contributions, a continuous transition from recoverable, namely solid-like, to unrecoverable, namely fluid-like, behavior can be observed for yield stress fluids¹. Inspired by this, they also examined the dynamic response of gelling systems with a similar decomposition. Again, they observed a continuous transition, except now from fluid-like to solid-like behavior.

To bring molecular context to this behavior, we present a first-principles model to describe the dominant molecular resistances. By assuming an affine deformation and network growth following the critical percolation model, we model the dynamic response of pre-percolated telechelic networks. Our model predicts three distinct regimes in the stress relaxation of nearly percolated gels, notably predicting the onset of solid-like behavior on short time scales prior to the gel point. With increasing extent of crosslinking, our model predicts a continuous transition from primarily unrecoverable to recoverable behavior, which is consistent with observations from the Rodger’s group. Additionally, the model maintains classical gelation predictions, such as a divergence in the flow viscosity.

Our model gives insight into the molecular basis of polymer network stress response, as well as demonstrates the applicability of recovery rheology for describing the evolving viscoelastic behavior in polymer gels and networks.