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 = η 0 exp U / k T − T 0 . 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 T 0 / T g = γ / γ + 1 and U = U 0 / 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.