Molecular mobility in driven monomeric and polymeric glasses

We show that in monomeric supercooled liquids and glasses that are plastically flowing at a constant shear stress $\sigma$ while being deformed with strain rate $\dot{\epsilon }$, the microscopic structural relaxation time ${\tau }_{\mathrm{str}}$ is given by the universal relation $\sigma /G_{\infty }\dot{\epsilon }$ with $G_{\infty }$ a modulus. This equality holds for all rheological regimes from temperatures above the glass transition all the way to the athermal limit, and arises from the competing effects of elastic loading and viscous dissipation. In macromolecular (polymeric) glasses, however, the stress decouples from this relaxation time and ${\tau }_{\mathrm{str}}$ is in fact further reduced even though $\sigma$ rises during glassy strain hardening. We develop expressions to capture both effects and thus provide a framework for analyzing mobility measurements in glassy materials.

Figure 1

(a) True stress vs true strain during deformation at constant true strain rates ${10}^{-3}$ (red), ${10}^{-4}$ (green), ${10}^{-5}$ (cyan), ${10}^{-6}$ (magenta), and temperature $T=0.3<T_g$. (b) Structural relaxation time vs true strain.

Figure 2

Main panel: post-yield relaxation times ${\tau }_{\text{pl}}$ vs $({\sigma }_z-{\sigma }_x)/G_{\infty }{\dot{\epsilon }}_z$, where $G_{\infty }=17$ was measured in the fluid state. Data for eight temperatures $T=0.0$ (black), $T=0.1$ (green), $T=0.2$ (red), $T=0.3$ (blue), $T=0.4$ (cyan), $T=0.5$ (magenta), $T=0.6$ (orange), and $T=0.7$ (brown) are shown. Upper inset: same data but plotted against $1/{\dot{\epsilon }}_z$ only. Lower inset: data collapse when time is measured in units of the longest relaxation time.

Figure 3

(a) True stress vs true strain during deformation of polymer glasses at constant true strain rates ${10}^{-3}$ (red), ${10}^{-4}$ (green), ${10}^{-5}$ (cyan), ${10}^{-6}$ (magenta), and temperature $T=0.2$. (b) Relaxation time ${\tau }_{\mathrm{str}}$ vs true strain. Solid lines show the functions ${\tau }_{\mathrm{str}}={\tau }_0{\left[{\sigma }_0/({\sigma }_z-{\sigma }_x)\right]}^n$ with $n=0.5$.

Figure 4

Main panel: post-yield relaxation times in polymer glasses, where $G_{\infty }=11$ and the values of $n=0.8,0.6,0.5,0.5,0.2,0.05$ at temperatures $T=0,0.1,0.2,0.3,0.4,0.5$, respectively. Colors as in Fig. 2. Upper inset: same data but plotted against $1/{\dot{\epsilon }}_z$ only. Lower inset: data collapse when time is measured in units of the longest relaxation time.

Figure 5

KWW exponent $\beta$ during steady-state flow of (a) the binary LJ mixture and (b) the polymer glass. Colors reflect temperatures $T=0.0$ (black), 0.1 (green), 0.2 (red), 0.3 (blue), 0.4 (cyan), 0.5 (magenta), and 0.6 (orange).