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 ${\tau }_{\mathrm{R}}\sim N^2{\tau }_{\alpha }$. After application of shear $\text{gdot}$, transient stress growth ${\sigma }_{xy}(t)\mathrm{/}\text{gdot}$ first obeys the linear growth ${\int }_0^{t}d{t}^{\mathrm{\prime }}G(t^{\mathrm{\prime }})$ 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 $\text{gdot}$ larger than ${\tau }_{\mathrm{R}}^{-1}$. 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 $\text{gdot}$ in the shear-thinning regime.