Viscosity Overshoot in Biaxial Elongational Flow: Coarse-Grained Molecular Dynamics Simulation of Ring-Linear Polymer Mixtures

Viscosity overshoot of entangled polymer melts has been observed under shear flow and uniaxial elongational flow, but has never been observed under biaxial elongational flow. We confirmed the presence of viscosity overshoot under biaxial elongational flows observed in a mixed system of ring and linear polymers expressed by coarse-grained molecular dynamics simulations. The overshoot was found to be more pronounced in weakly entangled melts. Furthermore, the threshold strain rate $\dot{\varepsilon}_{\rm th}$ distinguishing linear and nonlinear behaviors was found to be dependent on the linear chain length as $\dot{\varepsilon}_{\rm th}(N)\sim N^{-1/2}$, which differs from the conventional relationship, $\dot{\varepsilon}_{\rm th}(N) \sim N^{-2}$, expected from the inverse of the Rouse relaxation time. We have concluded that the cooperative interactions between rings and linear chains were enhanced under biaxial elongational flow.