Ultra-long-range dynamic correlations in a microscopic model for aging gels

We use large-scale computer simulations to explore the nonequilibrium aging dynamics in a microscopic model for colloidal gels. We find that gelation resulting from a kinetically arrested phase separation is accompanied by “anomalous” particle dynamics revealed by superdiffusive particle motion and compressed exponential relaxation of time correlation functions. Spatiotemporal analysis of the dynamics reveals intermittent heterogeneities producing spatial correlations over extremely large length scales. Our study is a microscopically resolved model reproducing all features of the spontaneous aging dynamics observed experimentally in soft materials.

Figure 1

Snapshots of the two-dimensional binary Lennard-Jones mixture at large time, $t=2.7\times {10}^4$, following a quench from $T=3.0$ to $T=0.15$ at various densities (a) $\rho =0.3$, (b) $\rho =0.5$, (c) $\rho =0.8$, and (d) $\rho =1.0$.

Figure 2

$\rho =0.5,T=0.15$. (a) Mean-squared displacements, ${\mathrm{\Delta }}^2(t,t_w)$, measured for different ages, $t_w$. A succession of ballistic, subdiffusive caging, superdiffusive cage escape, and long-time near diffusion are observed, with various time dependences indicated via dashed lines. (b) Corresponding self-intermediate scattering function, $F_s(q,t,t_w)$, measured for $q=1$. The dashed lines correspond to fits with compressed exponentials and the corresponding $\beta$ values are indicated.

Figure 3

(a) $F_s(q,t,t_w)$, for different wave vectors $q$, for $t_w={10}^2,T=0.15$, and $\rho =0.5$. The dashed lines correspond to compressed exponential fits with fitting parameters reported in (b) and (c) for both $t_w={10}^2$ (circles) and ${10}^3$ (squares).

Figure 4

For $\rho =0.5$ (left) and 0.8 (right), spatial map of the mobility field, $q(x,y)$, at $t-t_w=482.74$, for $t_w={10}^2$. Black regions represent empty pores. The typical size of the mobile/immobile domains is much larger than both the particle size and the typical pore size, extending over hundreds of particles, as confirmed in Fig. 5.

Figure 5

Spatial correlations of mobility, $G_4(r,t,t_w)$, for different $t-t_w$ (as marked), corresponding to $t_w={10}^2$, at $\rho =0.5$ (a), 0.8 (b), and (c) for different system sizes ($N$), as marked, at $\rho =0.8,t_w=153.19$. (d) Variation of $G_4(r,t,t_w)$ corresponding to (c) with rescaled distances $r/L$.