A derivation of the Vogel–Fulcher–Tammann relation for supercooled liquids

The non-Arrhenius Vogel–Fulcher–Tamman relation for the viscosity, η, known for about 8 decades, describes simply one of the most characteristic features of supercooled liquids. It may be written η=η0exp[U/k(T−T0)]η=η0expU/kT−T0. Using the Dyre et al. result demonstrating that U is proportional to the shear modulus, G  , and the Interstitialcy Theory of Condensed Matter (ITCM) we derive this relation and obtain T0/Tg=γ/(γ+1)T0/Tg=γ/γ+1 and U=U0/(1+γ)U=U0/1+γ, where U0 is the interstitialcy diffusion energy at the glass temperature. Here, γ is a fragility softening parameter given by γ = βTg(dc /dT)|Tg. β is the shear susceptibility − d ln G /dc, and c is the interstitialcy concentration. γ is also a fragility parameter ranging from 0 for strong materials to 3 or above for fragile ones.