Local Plastic Response and Slow Heterogeneous Dynamics of Supercooled Liquids

We demonstrate, via numerical simulations, that the relaxation dynamics of supercooled liquids correlates well with a plastic length scale measuring a particle’s response to impulsive localized perturbations and weakly to measures of local elasticity. We find that the particle averaged plastic length scale vanishes linearly in temperature and controls the super-Arrhenius temperature dependence of the relaxation time. Furthermore, we show that the plastic length scale of individual particles correlates with their typical displacement at the relaxation time. In contrast, the local elastic response only correlates with the dynamics on the vibrational timescale.

Figure 1

(a) Time dependence of the average displacement of a particle in response to a force acting on the time window identified by the shaded region. The dashed lines mark the asymptotic displacement values $L(T,f)$. The filled red stars mark the $\mathrm{\Delta }x({\tau }_{\mathrm{CR}})$ for $T\ge 0.5$. (b) The asymptotic displacement grows linearly in temperature below the onset temperature marked by the vertical dashed line, $L\propto (T-T_0)$. (c) A plot of $A(f)=L(T,f)/(T-T_0)$ reveals that, below the onset temperature, the asymptotic displacement grows linearly in $f$ for large enough forces.

Figure 2

The cage-relative relaxation time grows exponentially with the reciprocal plastic length $1/\xi (T)=(1-f/f_0)(1-T/T_0)/L(T,f)$. Data refer to $\rho =1.2$.

Figure 3

Time dependence of Spearman’s rank correlation coefficient $S$ between the CR mean-square displacement of the particles at time $t$ and (1) their CR mean-square displacement at $t={\tau }_{\beta }$, (2) their participation fraction $p$, (3) their mean-square displacement evaluated in the harmonic approximation, and (4) their plastic length scale $\xi$. The blue dashed line represents the average CR mean-square displacement.