Slow dynamics and stress relaxation in a liquid as an elastic medium

We propose a framework to discuss the transition from exponential relaxation in a liquid to the regime of slow dynamics. For the purposes of stress relaxation, we show that a liquid can be treated as an elastic medium. We discuss that, on lowering the temperature, the feed-forward interaction mechanism between local relaxation events becomes operative and results in slow relaxation.

Figure 1

Orowan’s illustration of a concordant local rearrangement. Solid and dashed lines around the shaded atoms correspond to initial and final positions of a rearrangement, respectively. Arrows show the direction of external stress.

Figure 2

(Color online) Illustration of the feed-forward interaction mechanism between local relaxation events. This mechanism operates within the sphere of radius $r=d$. Shaded and open circles represent local relaxing regions inside and outside, respectively, of the interaction sphere.

Figure 3

Solid lines are solutions of Eq. (7), and dashed lines are fits to SER. From left to right, $\alpha =0.3$, 1.2, and 2.2. SER parameters $(\beta ,\tau )$ are (0.94, 1.12), (0.78, 1.62), and (0.66, 2.51) in the same order.