Elasticity, Facilitation, and Dynamic Heterogeneity in Glass-Forming Liquids

We study the role of elasticity-induced facilitation on the dynamics of glass-forming liquids by a coarse-grained two-dimensional model in which local relaxation events, taking place by thermal activation, can trigger new relaxations by long-range elastically mediated interactions. By simulations and an analytical theory, we show that the model reproduces the main salient facts associated with dynamic heterogeneity and offers a mechanism to explain the emergence of dynamical correlations at the glass transition. We also discuss how it can be generalized and combined with current theories.

Figure 1

(a) The average persistence function $⟨P(t)⟩$ for $T=0.100$, 0.060, 0.040, 0.030, 0.025, 0.020, 0.018, 0.015, and 0.013 (from left to right). (b) The relaxation time ${\tau }_{\alpha }$ for the models with (circle) and without (square) elastic interaction. ${\tau }_{\alpha }$ is defined by $⟨P({\tau }_{\alpha })⟩=1/2$. The dashed straight line defines an (average) activation energy barrier $\mathrm{\Delta }E({\overline{\sigma }}^{\mathrm{act}})$.

Figure 2

Snapshots for local persistence $p_i({\tau }_{\alpha })$ when $P({\tau }_{\alpha })\approx 1/2$ for $T=0.040$ (a) and $T=0.013$ (b), respectively. The system size is $L=128$. Red and blue sites correspond to mobile [$p_i({\tau }_{\alpha })=0$] and immobile [$p_i({\tau }_{\alpha })=1$] sites, respectively.

Figure 3

(a) Time and temperature evolution of ${\chi }_4(t)$ for $T=0.100$, 0.060, 0.040, 0.030, 0.025, 0.020, 0.018, 0.015, and 0.013 (from left to right). (b) The peak value of ${\chi }_4$ as a function of ${\tau }_{\alpha }$ for the models with (circle) and without (square) elastic interactions.

Figure 4

Probability distribution function of the local stress $P(\sigma )$. The dashed curve indicates the solution of the mean-field (MF) theory at $T\to 0$. The vertical arrows indicate the location of ${\overline{\sigma }}^{\mathrm{act}}$ and $-{\overline{\sigma }}^{\mathrm{act}}$ extracted from $\mathrm{\Delta }E({\overline{\sigma }}^{\mathrm{act}})$ with the activation energy barrier in Fig. 1. Recall that ${\sigma }_c=1$.