Probing heterogeneous dynamics from spatial density correlation in glass-forming liquids

We numerically investigate the connection between spatial density correlation and dynamical heterogeneity in glass-forming liquids. We demonstrate that the cluster size defined by the spatial aggregation of densely packed particles (DPPs) can better capture the difference between the dynamics of the Lennard-Jones glass model and the Weeks-Chandler-Andersen truncation model than the commonly used pair correlation functions. More interestingly, we compare the mobility of DPPs and loosely packed particles, and we find that high local density correlates well with slow dynamics in systems with relatively hard repulsive interactions but links to mobile ones in the system with soft repulsive interactions at one relaxation time scale. Our results show clear evidence that the above model dependence behavior stems from the hopping motion of DPPs at the end of the caging stage due to the compressive nature of soft repulsive spheres, which activates the dynamics of DPPs in the $\alpha$ relaxation stage.

Figure 1

$T$ dependence of the number averaged cluster size of DPPs $〈N_c〉$ at $\rho =1.2$ (a) and $\rho =1.9$ (b) for LJ (black squares) and WCA (red circles) systems, and for Wahn (c) and Harm (d) systems. $〈N_c〉$ is obtained by averaging over 1000 configurations in each run, and the error bars are evaluated from eight independent runs.

Figure 2

The correlation between local density and mobility for $A$ particles. The left column shows the mobility of LPPs (scatters in the left of each histogram) and the mobility of DPPs (scatters in the right of each histogram) during time interval ${\tau }_{\alpha }$. The color of each spot represents the degree of probability, and the color bar is shown in (d). Black dashed lines show the average value of the mobility of all the particles. Numbers at the top-left (top-right) of each histogram indicate the values of $P_L$ ($P_D$) (see the text). The right column shows the time dependence of $P_L$ (black squares) and $P_D$ (red circles) values. All results are obtained over 200 isoconfigurational runs for 32 different initial configurations.

Figure 3

The self-part of DPP overlap $q^d\left(t\right)$ (the black solid line) and that of LPP overlap $q^l\left(t\right)$ (the cyan dashed line) for several temperatures in LJ (a), WCA (b), Wahn (c), and Harm (d) systems. Results are for all types of particles. The arrow in (b) roughly marks the end of caging stage $[\text{log}(t/{\tau }_{\alpha })=-2.2]$ for Harm system at $T=5.5$, which falls in between the crossovers for the two species of particles in the system.

Figure 4

Cage correlation functions for DPPs $C_{\text{Cage}}^d\left(t\right)$ (the black solid line), LPPs $C_{\text{Cage}}^l\left(t\right)$ (the cyan dashed line), and all particles $C_{\text{Cage}}^{\mathrm{all}}\left(t\right)$ (the blue dash-dotted line) for several temperatures in LJ (a), WCA (b), Wahn (c), and Harm (d) systems. Results are for all types of particles.

Figure 5

Trajectories of selected DPPs (green) and LPPs (red) for Wahn (a) and Harm (b) systems. Particles that belong to DPPs (or LPPs) in the initial configuration and in the middle of caging stage (we choose $t=10$ for Wahn and $t={10}^3$ for Harm), but escape to LPPs (or DPPs) at the end of caging stage (we choose $t=70$ for Wahn and $t=2\times {10}^5$ for Harm) are selected to track their trajectories until the end of caging. The zoom-in in (b) illustrates the hopping motion.