Shear-stress fluctuations and relaxation in polymer glasses.

We investigate by means of molecular dynamics simulation a coarse-grained polymer glass model focusing on (quasistatic and dynamical) shear-stress fluctuations as a function of temperature T and sampling time Δt. The linear response is characterized using (ensemble-averaged) expectation values of the contributions (time averaged for each shear plane) to the stress-fluctuation relation µ_{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 µ_{sf}(T) decreases continuously with increasing T for all Δt sampled, its standard deviation δµ_{sf}(T) is nonmonotonic 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 Δt dependence of µ_{sf} and related quantities can be understood using a weighted integral over G(t).

Shear Modulus and Shear-Stress Fluctuations in Polymer Glasses.

Using molecular dynamics simulation of a standard coarse-grained polymer glass model, we investigate by means of the stress-fluctuation formalism the shear modulus µ as a function of temperature T and sampling time Δt. While the ensemble-averaged modulus µ(T) is found to decrease continuously for all Δt sampled, its standard deviation δµ(T) is nonmonotonic, with a striking peak at the glass transition. Confirming the effective time-translational invariance of our systems, µ(Δt) can be understood using a weighted integral over the shear-stress relaxation modulus G(t). While the crossover of µ(T) gets sharper with an increasing Δt, the peak of δµ(T) becomes more singular. It is thus elusive to predict the modulus of a single configuration at the glass transition.

Numerical determination of shear stress relaxation modulus of polymer glasses.

Focusing on simulated polymer glasses well below the glass transition, we confirm the validity and the efficiency of the recently proposed simple-average expression [Formula: see text] for the computational determination of the shear stress relaxation modulus G(t). Here, [Formula: see text] characterizes the affine shear transformation of the system at t = 0 and h(t) the mean-square displacement of the instantaneous shear stress as a function of time t. This relation is seen to be particulary useful for systems with quenched or sluggish transient shear stresses which necessarily arise below the glass transition. The commonly accepted relation [Formula: see text] using the shear stress auto-correlation function c(t) becomes incorrect in this limit.

Shear-stress fluctuations in self-assembled transient elastic networks.

Focusing on shear-stress fluctuations, we investigate numerically a simple generic model for self-assembled transient networks formed by repulsive beads reversibly bridged by ideal springs. With Δt being the sampling time and t_{☆}(f)∼1/f the Maxwell relaxation time (set by the spring recombination frequency f), the dimensionless parameter Δx=Δt/t_{☆}(f) is systematically scanned from the liquid limit (Δx≫1) to the solid limit (Δx≪1) where the network topology is quenched and an ensemble average over m-independent configurations is required. Generalizing previous work on permanent networks, it is shown that the shear-stress relaxation modulus G(t) may be efficiently determined for all Δx using the simple-average expression G(t)=µ_{A}-h(t) with µ_{A}=G(0) characterizing the canonical-affine shear transformation of the system at t=0 and h(t) the (rescaled) mean-square displacement of the instantaneous shear stress as a function of time t. This relation is compared to the standard expression G(t)=c[over ̃](t) using the (rescaled) shear-stress autocorrelation function c[over ̃](t). Lower bounds for the m configurations required by both relations are given.