Transport properties of glass-forming liquids suggest that dynamic crossover temperature is as important as the glass transition temperature

Abstract

It is becoming common practice to partition glass-forming liquids into two classes based on the dependence of the shear viscosity η on temperature T. In an Arrhenius plot, ln eta vs 1/T, a strong liquid shows linear behavior whereas a fragile liquid exhibits an upward curvature [super-Arrhenius (SA) behavior], a situation customarily described by using the Vogel–Fulcher–Tammann law. Here we analyze existing data of the transport coefficients of 84 glass-forming liquids. We show the data are consistent, on decreasing temperature, with the onset of a well-defined dynamical crossover eta×, where η× has the same value, eta× ≈ 103 Poise, for all 84 liquids. The crossover temperature, T×, located well above the calorimetric glass transition temperature Tg, marks significant variations in the system thermodynamics, evidenced by the change of the SA-like T dependence above T× to Arrhenius behavior below T×. We also show that below T× the familiar Stokes–Einstein relation D/T ∼ eta-1 breaks down and is replaced by a fractional form D/T ∼ eta-zeta, with zeta ≈ 0.85.