Shear-stress fluctuations and relaxation in polymer glasses

We investigate by means of molecular dynamics simulation a coarse-grained polymer glass model focusing on (quasi-static and dynamical) shear-stress fluctuations as a function of temperature T and sampling time $\Delta t$. The linear response is characterized using (ensemble-averaged) expectation values of the contributions (time-averaged for each shear plane) to the stress-fluctuation relation $\mu_{sf}$ for the shear modulus and the shear-stress relaxation modulus $G(t)$. Using 100 independent configurations we pay attention to the respective standard deviations. While the ensemble-averaged modulus $\mu_{sf}(T)$ decreases continuously with increasing T for all $\Delta t$ sampled, its standard deviation $\delta \mu_{sf}(T)$ is non-monotonous with a striking peak at the glass transition. The question of whether the shear modulus is continuous or has a jump-singularity at the glass transition is thus ill-posed. Confirming the effective time-translational invariance of our systems, the $\Delta t$-dependence of $\mu_{sf}$ and related quantities can be understood using a weighted integral over $G(t)$. This implies that the shear viscosity $\eta(T)$ may be readily obtained from the $1/\Delta t$-decay of $\mu_{sf}$ above the glass transition.