The uncertainty of glass transition temperature in molecular dynamics simulations and numerical algorithm for its unique determination

Abstract

When the cooling rate $v$ is smaller than a certain material-dependent threshold, the glass transition temperature $T_g$ becomes to a certain degree the "material parameter" being nearly independent on the cooling rate. The common method to determine $T_g$ is to extrapolate viscosity $\nu$ of the liquid state at temperatures not far above the freezing conditions to lower temperatures where liquid freezes and viscosity is hardly measurable. It is generally accepted that the glass transition occurs when viscosity drops by $13\leq n\leq17$ orders of magnitude. The accuracy of $T_g$ depends on the extrapolation quality. We propose here an algorithm for a unique determining of $T_g$. The idea is to unambiguously extrapolate $\nu(T)$ to low temperatures without relying upon a specific model. It can be done using the numerical analytical continuation of $\nu(T)$-function from above $T_g$ where it is measurable, to $T\gtrsim T_g$. For numerical analytical continuation, we use the Pade approximant method.