Relaxation kinetics in fragile glass-forming liquids: a dispersive kinetics view of Vogel–Tammann–Fulcher behaviour in o-terphenyl

In plots of viscosity against reciprocal temperature, the cross-over temperature, T-B, denotes an important change in the glass relaxation kinetics. Falling between the glass transition temperature (T-g) and melting temperature (T-m) of a fragile glass forming liquid, T-B characterises the point of divergence between the slower, primary alpha-relaxation behaviour (that is largely associated with the translational mobility within heterogeneous/caged domains inside the glass) and the faster, secondary beta-relaxation (corresponding to constrained, higher-energy molecular rotation) in the pre-vitrified liquid. In this work, it is proposed that the Vogel-Tammann-Fulcher (VTF) equation describes relaxation processes that are aligned with the concept of dispersive kinetics, meaning they are underpinned by a distribution of activation energies rather than a single energy barrier, as in the case of Arrhenian kinetics. The Avrami-Erofe'ev equation, a type of dispersive kinetics model, is applied to the canonical o-terphenyl system to help rationalize the increase in the activation energy observed on cooling at temperatures staying above T-B that reflect various degrees of dynamical arrest in the fragile glass-former. Moreover, the dimensionless constant, D, in the VTF equation is correlated to the rate of change in the activation energy with temperature. Lastly, T-B is determined to have both kinetic and thermodynamic foundations.