Microscopic View of Accelerated Dynamics in Deformed Polymer Glasses

A molecular level analysis of segmental trajectories obtained from molecular dynamics simulations is used to obtain the full relaxation time spectrum in aging polymer glasses subject to three different deformation protocols. As in experiments, dynamics can be accelerated by several orders of magnitude, and a narrowing of the distribution of relaxation times during creep is directly observed. Additionally, the acceleration factor describing the transformation of the relaxation time distributions is computed and found to obey a universal dependence on the strain, independent of age and deformation protocol.

Figure 1

Distributions of first hop times $t_1$ (a)–(c) and persistence times $\tau$ (d)–(f) in an aging polymer glass subject to deformation for three waiting times $t_w=750$ (black), 7500 (red or gray), and 75 000 (green or light gray). Panels (a) and (d) correspond to a step stress with amplitude $\sigma =0.4$ (dashed) and 0.5 (dotted). Solid dots show $p(\tau )$ for $t<{\tau }_{\alpha }$ (see text) and $t_w=75000$. Panels (b) and (e) refer to deformation at imposed strain rate $\dot{ϵ}=8.9\times {10}^{-7}$ (dashed) and $8.9\times {10}^{-6}$ (dotted), while panels (c) and (f) show the effect of a step strain with amplitude $ϵ=0.02$ (dashed) and 0.04 (dotted). For comparison, the corresponding distributions in an undeformed, aging glass are also shown in every panel (solid lines). Straight lines indicate power law with the given slopes. Insets show the mechanical response to (a) $\sigma =0.4$ (solid) and 0.5 (dashed), (b) $\dot{ϵ}=8.9\times {10}^{-7}$, and (c) $ϵ=0.04$ for the three wait times.

Figure 2

Strain rate versus hop rate for $\sigma =0.5$ (○), 0.4 (□), 0.3 (△), 0.2 (◇) and $t_w=750$ (black), 7500 (red or gray), and 75 000 (green or light gray). Solid symbols show data for chains of length 100.

Figure 3

(a) Cumulative probability distribution of the first relaxation event for the undeformed glass (solid line) and under deformation with a step stress $\sigma =0.4$ (○), a step strain $ϵ=0.01$ (▵), and a constant strain rate $\dot{ϵ}=8.5\times {10}^{-7}$ (□) for $t_w=75000$. (b) Acceleration ratio $t_1^u/t_1^d$ as a function of global strain $ϵ$ for three different deformation protocols. Stress step: $\sigma =0.3$ (○), 0.4 (□), 0.5 (△); constant strain rate: $\dot{ϵ}=8.9\times {10}^{-6}$ (◇), $8.9\times {10}^{-7}$ (▽); strain step (◁). For each: $t_w=75000$ (black), 22 500 (red or gray). Solid symbols show data for chains of length 100.