Relation between Thermodynamics and Kinetics of Glass-Forming Liquids

Vitrification of a supercooled liquid is often characterized by the hypothetical kinetic instability point, the Vogel-Fulcher temperature $T_0$, and the thermodynamic one, the Kauzmann temperature $T_K$. The widely believed relation $T_0\cong T_K$ is regarded as the supporting evidence of a direct connection between the thermodynamics and kinetics of glass-forming liquids. Here we demonstrate that $T_K/T_0$ systematically increases from unity with a decrease in the fragility, contrary to the common belief. This systematic deviation may be explained by a synergistic effect between the weaker cooperativity and the stronger tendency of short-range ordering in stronger glass formers.

Figure 1

Correlation between $T_K/T_0$ and the fragility index $D$ for materials listed in Table . The horizontal dotted line is a line of $T_K/T_0=1$. Note that (i) the deviation of $T_K$ from $T_0$ is considerable, which is sometimes more than 100 K for strong liquids, and (ii) it systematically increases with an increase in $D$ for various types of glass formers. Thus, we believe that the observed systematic increase in $T_K/T_0$ with $D$ is far beyond errors and meaningful, despite the fact that the extrapolations of $T_K$ and $T_0$ inevitably contain large ambiguity especially for strong liquids.

Figure 2

Temperature dependence of $C_P$ (top) and $\sigma$ (bottom). Short-range bond ordering results in the deviation of $T_K$ from $T_0$ toward the high-temperature side and the extra contribution to the $C_P$ jump at $T_g$, $\delta C_P$. The latter may explain unusually large $\delta C_P(T_g)$ for alcohols and metallic glass formers [2].