First-Order Phase Transition in a Model Glass Former: Coupling of Local Structure and Dynamics

Recently, numerical evidence for a dynamical first-order phase transition in trajectory space [L. O. Hedges et al., Science 323, 1309 (2009)] has been found. In a model glass former in which clusters of 11 particles form upon cooling, we find that the transition has both dynamical and structural character. It occurs between an active phase with a high fraction of mobile and low fraction of cluster particles, and an inactive phase with few mobile but many cluster particles. The transition can be driven both dynamically and structurally with a chemical potential, showing that local order forms a mechanism for dynamical arrest.

Figure 1

(a) Structural relaxation time ${\tau }_{\alpha }$ vs inverse temperature $1/T$. Open circles are numerical data. The solid line is the Vogel-Fulcher-Tammann (VFT) fit, the dashed line is the Elmatad-Chandler-Garrahan (ECG) fit holding for $T<T_0$. (b) Mean population $⟨n{⟩}_0$ of $11A$ clusters (see the inset picture). The filled circle shows the largest population ($\simeq 0.33$) of $11A$ clusters we have reached in the simulations. Using a power law extrapolation (line) implies a fictive temperature $T\simeq 0.35$.

Figure 2

Left column: $s$ ensemble (a) Probability distributions $p(c)$ for the density of mobile particles $c$ for two trajectory lengths. The nonconcave shape indicates a phase transition in trajectory space as becomes obvious from the bimodal distribution (b) at the field $s^{*}$ that maximizes the fluctuations $⟨c^2{⟩}_s-⟨c{⟩}_s^2$. (c) Average fractions of mobile particles (solid lines) and $11A$ cluster population (dashed lines) vs the biasing field $s$. Right column: (d)–(f) as left column but for the $\mu$ ensemble. Throughout, bright (red) and dark (blue) lines refer to $K=100$ and $K=200$, respectively, with an additional data set $K=20$ in (d).

Figure 3

Radial distribution functions for (a) the large $A$ particles and (b) the small $B$ particles for both the unbiased ensemble ($\mu =0$, solid line) and in the inactive phase ($\mu =0.014>{\mu }^{*}$, dashed line). (c) The intermediate scattering function (ISF) for the $A$ particles. (d) Slow decay of the ISF for the melting runs (black line). Also shown are the ISFs for equilibrated systems at $T=0.6$ and the lower temperature $T=0.5$. (e) Time evolution of mobile (solid line) and cluster particle (dashed line) populations, where $t=0$ corresponds to the interface.

Figure 4

Logarithm of the joint probability $p(n,c)$ shown for (a) the unbiased ensemble and at coexistence in (b) the dynamical $s$ ensemble ($s=s^{*}$) and (c) the structural $\mu$ ensemble ($\mu ={\mu }^{*}$) for trajectory length $K=200$ (all plots show the same data reweighted differently). The phase diagram in the $s\mathrm{\text{−}}\mu$ plane is sketched in the upper corner.