Revealing the Link between Structural Relaxation and Dynamic Heterogeneity in Glass-Forming Liquids

Despite the use of glasses for thousands of years, the nature of the glass transition is still mysterious. On approaching the glass transition, the growth of dynamic heterogeneity has long been thought to play a key role in explaining the abrupt slowdown of structural relaxation. However, it still remains elusive whether there is an underlying link between structural relaxation and dynamic heterogeneity. Here, we unravel the link by introducing a characteristic time scale hiding behind an identical dynamic heterogeneity for various model glass-forming liquids. We find that the time scale corresponds to the kinetic fragility of liquids. Moreover, it leads to scaling collapse of both the structural relaxation time and dynamic heterogeneity for all liquids studied, together with a characteristic temperature associated with the same dynamic heterogeneity. Our findings imply that studying the glass transition from the viewpoint of dynamic heterogeneity is more informative than expected.

Figure 1

(a) Angell plots of structural relaxation time $\tau$ versus scaled reciprocal temperature $T_{\mathrm{ref}}/T$ for systems with different potentials and pressures. $T_{\mathrm{ref}}$ is determined according to $\tau (T_{\mathrm{ref}})={\tau }_g\approx 2.16\times {10}^4$. (b) Correlation between $\tau$ and ${\alpha }_{2,\max }$. Symbols in (a) and (b) have the same meanings.

Figure 2

(a) Maximum non-Gaussian parameter ${\alpha }_{2,\max }$ versus reduced structural relaxation time $\tau /{\tau }^{*}$, with ${\tau }^{*}$ being the characteristic time scale under the iso-${\alpha }_{2,\max }$ condition (${\alpha }_{2,\max }\approx 1.67$ here). The solid lines are fits to ${\alpha }_{2,\max }\sim (\tau /{\tau }^{*}{)}^{\nu }$, with $\nu =0.8$ (black line) and $\nu =0.3$ (red line). (b) Correlation between ${\tau }^{*}$ and kinetic fragility $m$, where $m$ is calculated at $T_g=T_{\mathrm{ref}}$ as set in Fig. 1. The black solid line is a fit to ${\tau }^{*}\sim m^{-\gamma }$, where $\gamma =3.3$. (c) Universal scaling between $\tau$ and ${\tau }_{{\alpha }_{2,\max }}$. The solid lines are fits to $\tau /{\tau }^{*}\sim ({\tau }_{{\alpha }_{2,\max }}/{\tau }^{*}{)}^{\beta }$, where $\beta =1.2$ (black line) and $\beta =1.5$ (red line). (d) ${\alpha }_{2,\max }$ versus scaled reciprocal temperature $T^{*}/T$, with $T^{*}$ being the characteristic temperature. The black and red solid lines are fitting curves consistent with the VFT fitting in Fig. 3 and power-law fittings in Fig. 2 [Eq. (4) can be derived from Eqs. (1) and (5)]: ${\alpha }_{2,\max }=0.093\exp [1.285/(T/T^{*}-0.705)]$ and ${\alpha }_{2,\max }=0.299\exp [0.482/(T/T^{*}-0.705)]$, respectively.

Figure 3

Scaled structural relaxation time $\tau /{\tau }^{*}$ versus scaled reciprocal temperature $T^{*}/T$ for all systems studied. Black solid curve is the VFT fit: $y=0.00337\exp [1.606/(x-0.705)]$, where $x=T/T^{*}$ and $y=\tau /{\tau }^{*}$. Red dashed curve is a fit to the MC form: $y=0.00314(x-0.809{)}^{-3.441}$. Blue dashed-dotted curve indicates the ECG fit: $y=0.373\exp [95.845(x^{-1}-0.917{)}^2]$. Navy dashed-dotted-dotted curve is a fit to the AM form: $y=0.00943\exp [(1.284/x{)}^{5.542}]$. Magenta dotted curve is the MYEGA fit: $y=0.00782\exp [(0.0730/x)\exp (4.052/x)]$. (Inset) $\tau (T)$ for a Hertz system at $P=5\times {10}^{-7}$, whose corresponding scaled data lie in the shadowed region in the main panel. Note that the curve in the inset can be fitted well with all the above five forms before scaling. After scaling, it lies in the region where only VFT works in the main panel.