Dynamics and Rheology of a Supercooled Polymer Melt in Shear Flow

Using molecular dynamics simulations, we study dynamics of a model polymer melt composed of short chains with bead number N=10 in supercooled states. In quiescent conditions, the stress relaxation function $G(t)$ is calculated, which exhibits a stretched exponential relaxation on the time scale of the $\alpha$ relaxation time $\tau_\alpha$ and ultimately follows the Rouse dynamics characterized by the time $\tau_{\rm R} \sim N^2 \tau_\alpha$. After application of shear $\gdot$, transient stress growth $\sigma_{xy}(t)/\gdot$ first obeys the linear growth $\int_0^t dt'G(t')$ for strain less than 0.1 but saturates into a non-Newtonian viscosity for larger strain. In steady states, shear-thinning and elongation of chains into ellipsoidal shapes take place for shear $\gdot$ larger than $\tau_{\rm R}^{-1}$. In such strong shear, we find that the chains undergo random tumbling motion taking stretched and compact shapes alternatively. We examine the validity of the stress-optical relation between the anisotropic parts of the stress tensor and the dielectric tensor, which are violated in transient states due to the presence of a large glassy component of the stress. We furthermore introduce time-correlation functions in shear to calculate the shear-dependent relaxation times, $\tau_\alpha (T,\gdot)$ and $\tau_{\rm R} (T,\gdot)$, which decrease nonlinearly as functions of $\gdot$ in the shear-thinning regime.