Ideal Glass States Are Not Purely Vibrational: Insight from Randomly Pinned Glasses

We use computer simulations to probe the thermodynamic and dynamic properties of a glass former that undergoes an ideal glass transition because of the presence of randomly pinned particles. We find that even deep in the equilibrium glass state, the system relaxes to some extent because of the presence of localized excitations that allow the system to access different inherent structures, thus giving rise to a nontrivial contribution to the entropy. By calculating with high accuracy the vibrational part of the entropy, we show that also in the equilibrium glass state thermodynamics and dynamics give a coherent picture, and that glasses should not be seen as a disordered solid in which the particles undergo just vibrational motion but instead as a system with a highly nonlinear internal dynamics.

Figure 1

(a) Time dependence of the mean squared displacement $\mathrm{\Delta }(t)$ for different concentrations of pinned particles, $c$, at $T=0.45$ for $N=1200$. The horizontal dashed line is the height of the plateau for $c=0.2$. (b) The dynamic overlap function $Q(t)$ at $T=0.45$ for $N=1200$ and concentrations $c$ at which the system is in the equilibrium glass state. The horizontal dashed arrows are the static overlap functions $Q^{(\mathrm{static})}$ evaluated from the parallel tempering simulations. The inset shows the state points for the presented $Q(t)$ in the phase diagram from Ref. [18].

Figure 2

The mean-squared displacement ${\mathrm{\Delta }}_{\alpha }$ at $T=0.45$ for $N=1200$ used for the Frenkel-Ladd thermodynamic integration. The horizontal dashed line is the plateau height for $c=0.2$ shown in Fig. 1. The solid line corresponds to the behavior of the Einstein solid, ${\mathrm{\Delta }}_{\alpha }=3/(2\alpha )$.

Figure 3

(a) $c$ dependence of the total entropy $s_{\mathrm{tot}}$, as well as different estimates of the vibrational entropy. (b) $c$ dependence of $s_{\mathrm{tot}}-s_{\mathrm{vib}}$. The open and filled symbols are for $N=300$ and $N=1200$, respectively. The horizontal arrows locate $T_K(c)$, where the skewness of the overlap distribution becomes zero [18].

Figure 4

(a)–(c): $e_{\mathrm{IS}}(t)$ at $T=0.45$ and $c=0.2$ for $N=300$ samples with (a) $10^4$ and (b) $10^8$ MC time steps, and with (c) $2\times {10}^9$ PT time step. Different lines correspond to different samples. (d)–(f): Superposition of the corresponding snapshots (sample 1) of the IS configurations with (d) $10^4$ and (e) $10^8$ MC time steps, and with (f) $2\times {10}^9$ PT time step. Pinned particles are shown in red (reduced in size to 0.5), and nonpinned A and B particles are shown in gray and blue, respectively.