New insights from transient nonlinear recovery rheology

The transient nonlinear rheology of polymeric materials is of interest for a range of energy and environmental applications including rubber bushings and tires and inks for additive manufacturing. Typical observations include that of the Payne effect, where an overshoot is observed in the dynamic loss modulus during oscillatory shear straining of increasing magnitude. We show this overshoot to be due to an increase in energy dissipated through unrecoverable processes via an iterative recovery rheological protocol. Studying filled polymers and di-block bottlebrush block co-polymers, we show that the dynamic loss modulus can be experimentally decomposed into two components relating to recoverable and unrecoverable processes that may be associated with conformational changes and center of mass motions, respectively. Our experimental observations inspire the construction of a toy model in which the rate of conformation change influences the center of mass motion. In the linear viscoelastic regime, our model resembles the retarded Maxwell or Jeffreys models, but the nonlinear behavior predicts a frequency dependence to the Payne effect. The model also provides insight into the applicability of the Cox-Merz rule that relates the response to small dynamic perturbations to the highly out-of-equilibrium steady-state flow behavior. The model predicts that Cox-Merz is followed unchanged in the terminal regime, where unrecoverable processes account for almost all the energy dissipation, but requires rescaling at higher frequencies, where recoverable and unrecoverable processes dissipate similar amounts of energy. We verify the applicability of the modified rule by comparing it against published data.