Creep and aging of hard-sphere glasses under constant stress

We investigate the aging behavior of glassy suspensions of nearly hard-sphere colloids submitted to a constant shear stress. For low stresses, below the yield stress, the system is subject to creep motion. As the sample ages, the shear rate exhibits a power-law decrease with time with exponents that depend on the sample age. We use a combination of rheological experiments with time-resolved photon correlation spectroscopy to investigate the time evolution of the sample dynamics under shear on various time and length scales. Long-time light-scattering experiments reveal the occurrence of microscopic rearrangement events that are linked with the macroscopic strain deformation of the sample. Dynamic time sweep experiments indicate that while the internal microscopic dynamics slow down continuously with waiting time, the storage and loss moduli are almost constant after a fast, weak decrease, resembling the behavior of quenched systems with partially frozen-in stresses.

Figure 1

(a) Flow curves of the colloidal suspensions of radius $R=138$ nm at $\varphi =0.6$ (circles), $\varphi =0.62$ (squares), and $\varphi =0.65, R=138$ nm (triangles). The continuous lines are the best fit by an Herschel-Bulkley fluid. (b) Flow curves of the colloidal suspensions of radius $R=300$ nm and $\varphi =0.64$, at constant applied shear rate (diamonds) and extracted from the data presented in Fig. 2 for the young (circles) and aged (squares) samples 100 s after the beginning of the measurements; the full symbols are taken out of equilibrium, and the continuous line corresponds to the Herschel-Bulkley fit of the flow curve measured at constant shear-rates (continuous line).

Figure 2

(a) Normalized deformation $\gamma \sigma /G$ versus time $t$ for $\sigma =0.2$ to 55 Pa for a young ($t_w=300$ s) $\varphi =0.64, R=300$ nm sample. (b) Corresponding shear rates over stress, $\dot{\gamma }/\sigma$, versus time with the dash line indicating the power law $-2/3$. (c) Normalized deformation $\gamma \sigma /G$ versus time $t$ for the same sample and conditions with (a) for an aged sample($t_w={10}^5$ s). (d) $\dot{\gamma }/\sigma$ versus time corresponding to measurements in (c). The dash line indicates power law exponent of $-2/3$ and the solid line, linear decrease. In both (b) and (d) the large squares and circles represent stresses just below and above the yield stress, respectively.

Figure 3

(a) $G^{\prime }$ and $G^{\prime \prime }$ versus time $t$, for a $\varphi =0.6, R=138$ nm suspension with ${\sigma }_1=0.3$ Pa ($G^{\prime } \square , G^{\prime \prime } \circ$) and a ${\sigma }_1=0$ ($G^{\prime } ◊, G^{\prime \prime } ▵$) during superposition experiment at $\omega =2\pi \text{rad}/\mathrm{s}$. (b) $G^{\prime }$ and $G^{\prime \prime }$ versus time $t$, for a $\varphi =0.62, R=138$ nm suspension with ${\sigma }_1=1$ Pa (resp., $\square , \circ$) and a ${\sigma }_1=0$ (resp., $◊, ▵$) during superposition experiment at $\omega =2\pi \text{rad}/\mathrm{s}$. (c) Frequency sweep for a rejuvenated $[G^{\prime }$ ($\circ$), $G^{\prime \prime }$ ($▵$)] and an aged sample $t_w=31000$ s $[G^{\prime }$ ($◊$), $G^{\prime \prime }$ ($\square$)] at $\varphi =0.62, R=138$ nm.

Figure 4

(a) Strain versus time for a $\varphi =0.62, R=138$ nm sample with $\sigma =1$ Pa. (b) Corresponding shear rate (continuous line) versus time, the dotted line shows a $-2/3$ power law.

Figure 5

Dynamic light-scattering experiments during a long creep experiment at $\sigma =1$ Pa (for $\varphi =0.62, R=138$ nm). (a) $g_2\left(\tau \right)-1$ averaged over each subregime, the continuous lines are the best fit by a stretched exponential. (b) $c_I$ versus waiting time $t_w$ for $\tau =1$ s (dark blue), $\tau =10$ s (red), $\tau =105$ s (light green), $\tau =1000$ s (cyan), and $\tau =10887$ s (pink). Vertical black lines separate the three regimes. (c) Relaxation time ${\tau }_f$ versus waiting time, $t_w$.

Figure 6

Correlations in scattered intensity and deformation: (a) $\psi$ [yellow (light gray)] and $c_I$ (dark blue) versus waiting time $t_w$ in regime A for $\tau =273$ s, with ${\gamma }_0=0.03$. (b) $\psi$ [yellow (light gray)] and $c_I$ (dark blue) versus waiting time $t_w$ in regime B for $\tau =1000$ s, with ${\gamma }_0=0.04$. (c) $\psi$ [yellow (light gray)] and $c_I$ (dark blue) versus waiting time $t_w$ in regime C for $\tau =442$ s, with ${\gamma }_0=0.035$. In (a), (b), and (c) we plot $\psi +0.3$ for better visibility. The suspension is at $\varphi =0.62, R=138$ nm.

Figure 7

Stress reversal experiments: (a) Strain versus time for a constant stress of 3 Pa (creep test $\square$) followed by a constant stress 0 Pa (recovery test $\circ$) then a constant stress of $-3$ Pa (reverse creep test $◊$) and finally a constant stress of 0 Pa (recovery test $▵$). (b) Log-log representation of the corresponding shear rates versus time for a PMMA HS glass (particles with $R=138$ nm) at $\varphi =0.65$ in octadecene. The continuous line indicates a power-law exponent $-2/3$.