Glass relaxation and hysteresis of the glass transition by molecular dynamics simulations

As out-of-equilibrium materials, glasses continually tend to relax toward the metastable supercooled liquid state. Glass relaxation can result in a nonreversible glass transition upon a cooling/reheating cycle. Here, based on molecular dynamics simulations, we present a methodology combining thermal cycles and inherent configuration analysis to investigate the features of relaxation and glass transition reversibility. By considering three archetypical silicate glasses, viz., silica, sodium silicate, and calcium aluminosilicate, we show that, for all the glasses considered herein, the enthalpy relaxation can be well described by mode-coupling theory. Further, we demonstrate the existence of a decoupling between enthalpy and volume relaxation. Finally, we show that enthalpy relaxation results in a nonreversible glass transition—the degree of nonreversibility being strongly system-specific.

Figure 1

Local ground-state enthalpy $H\left(T\right)$ (i.e., enthalpy of the inherent configuration) as a function of temperature $T$ under select cooling rates for (a) silica (S), (b) sodium silicate (NS), and (c) calcium aluminosilicate (CAS). Note that each panel has a different $y$ axis.

Figure 2

Molar volume as a function of temperature upon select cooling rates for (a) S, (b) NS, and (c) CAS. Note that each panel has a different $y$ axis.

Figure 3

(a) Residual enthalpy $\mathrm{\Delta }H\left(\gamma \right)=H\left(\gamma \right)–H(\gamma =0)$ at 0 K for the S, NS, and CAS glasses as a function of the cooling rate $\gamma$, where $H\left(\gamma =0\right)$ is obtained by fitting $H\left(\gamma \right)$ with a power law $H\left(\gamma \right)=H\left(\gamma =0\right)+{\left(A\gamma \right)}^{1/\delta }$. The solid lines are power-law fits [see Eq. (1)]. (b) Molar volume at 0 K of the three glasses considered herein as a function of the cooling rate. The solid lines are to guide the eye.

Figure 4

Fictive temperature $T_{\mathrm{f}}$ as a function of the cooling rate $\gamma$ for the (a) S, (b) NS, and (c) CAS glasses (calculated from the break in slope of the ground-state enthalpy and molar volume vs temperature curves; see Figs. 1 and 2). The dashed lines are to guide the eye. Note that each panel has a different $y$ axis.

Figure 5

Kissinger plots for the (a) S, (b) NS, and (c) CAS glasses. The lines are Kissinger fits [Eq. (2)], which allow us to estimate an apparent activation energy of enthalpy and volume relaxation (see Table 1).

Figure 6

Local ground-state enthalpy $H\left(T\right)$ (i.e., enthalpy of the inherent configuration) as a function of temperature under select cooling/reheating rates for (a) S, (b) NS, and (c) CAS glasses. The solid (same as Fig. 1) and dashed curves refer to the cooling and heating simulations, respectively. Note that each panel has a different $y$ axis.

Figure 7

Relaxation enthalpy (i.e., difference of ground-state enthalpy upon cooling and reheating) as a function of temperature for (a) S, (b) NS, and (c) CAS glasses. The solid lines are Gaussian fits. The values are vertically shifted for clarity. The cooling/reheating rates are (from top to bottom) 100, 10, 1, and 0.1 K/ps.

Figure 8

(a) Temperature at which the enthalpy relaxation is maximum ($T_{max}$), (b) maximum extent of enthalpy relaxation ($\mathrm{\Delta }{H}_{max}$), and (c) typical range of temperature over which enthalpy relaxation occurs ($\mathrm{\Delta }T$) as a function of the cooling/heating rate for S, NS, and CAS. The lines are to guide the eye.

Figure 9

Schematic showing the typical stretched-exponential enthalpy relaxation of a glass in isothermal conditions. The arrows indicate the extent of relaxation that can be achieved between cooling and subsequent reheating in the case of (black) fast cooling/heating and (red) slow cooling/heating.