The limitation for popular descriptions of alpha-relaxation temperature dependence

TL;DR

This paper critically examines three common models for describing alpha-relaxation times in glass-formers, highlighting their limitations in capturing the transition from Arrhenius to non-Arrhenius behavior.

Contribution

It demonstrates that popular models like Vogel-Fulcher-Tammann and double activation law fail to accurately describe the transition region in alpha-relaxation data.

Findings

Vogel-Fulcher-Tammann and double activation functions are only suitable below T_A.

Transition temperature T* in the frustration-limited domains model differs from T_A.

Models do not outperform each other in derivative analysis of relaxation times.

Abstract

Applicability of three popular functions (Vogel-Fulcher-Tammann, double activation law and frustration-limited domains model) for the description of the temperature dependence of alpha-relaxation time tau_alpha is considered for three typical glass-formers (propylene carbonate, ethanol and picoline). Two first functions have three free parameters. It was found that while they are in satisfactory agreement with the experimental data of tau_alpha(T), they fail in describing the transition from an Arrhenius-like to a non-Arrhenius behaviour. This transition is seen in the derivative analysis of tau_alpha(T). We argue that Vogel-Fulcher-Tammann and double activation functions should be applied and compared only at T < T_A, where T_A is the temperature of transition from an Arrhenius-like to a non-Arrhenius behaviour. It was shown that the four-parametric frustration-limited domains model with imbedded transition from Arrhenius to non-Arrhenius behaviour at T = T* also has no advantage in the derivative analysis, since T* is systematically different from TA in the cases considered.