Phase-Separation Perspective on Dynamic Heterogeneities in Glass-Forming Liquids

We study dynamic heterogeneities in a model glass former whose overlap with a reference configuration is constrained to a fixed value. We find that the system phase separates into regions of small and large overlap, indicating that a nonzero surface tension plays an important role in the formation of dynamical heterogeneities. We calculate an appropriate thermodynamic potential and find evidence of a Maxwell construction consistent with a spinodal decomposition of two phases. Our results suggest that even in standard, unconstrained systems dynamic heterogeneities are the expression of an ephemeral phase-separating regime ruled by a finite surface tension.

Figure 1

Fluctuations of the overlap field $\delta q(\mathbf{r},t)=q(\mathbf{r},t)-⟨q(t)⟩$ for a 2D slice of the system. Upper panels: Unconstrained system. Lower panels: Constrained system ($\widehat{Q}=0.25$). Left panels: $t={\tau }_{\alpha }$. Right panels: Large times. $L=16$. Each panel displays four copies of the same system.

Figure 2

$S(k,t)$ at different times for the unconstrained (left) and constrained (right, $\widehat{Q}=0.25$) cases. Left inset: Correlation length $\xi (t)$ as extracted from Eq. (2). Right inset: $S(k,t{)}^{-1}$ vs $k^2$. $T=T_{\mathrm{MC}}$ and $L=16$.

Figure 3

Left: The estimator $A/B$ [see Eq. (2)] vs time, at $T=T_{\mathrm{MC}}$ in the constrained (circles) and unconstrained (triangle) cases. Right: The same at $T=1.55T_{\mathrm{MC}}$. $L=16$.

Figure 4

Energy difference $\Delta E(t)=E(t)-E_0$ vs $t$ at $T=T_{\mathrm{MC}}$ with constrained dynamics, $\widehat{Q}=0.25$. $E_0$ is a parameter of the fit $E(t)=E_0+\gamma t^{-1/3}$. The line is $1/t^{1/3}$, corresponding to the surface tension exponent $\theta =2$.

Figure 5

The derivative $W^{\prime }(\widehat{Q})$ of the thermodynamic potential at different temperatures, ranging from $2.13T_{\mathrm{MC}}$ to $0.89T_{\mathrm{MC}}$. Inset: A cartoon of Maxwell’s construction for the potential and its derivative.