VogelFulchertype

Vogel-Fulcher type refers to a family of empirical models used to describe how the structural relaxation time or viscosity of a liquid grows as temperature decreases toward the glass transition. The most widely used form is the Vogel-Fulcher-Tammann (VFT) equation: tau(T) = tau0 exp[ D T0 / (T − T0) ], where T is temperature, T0 is the Vogel temperature, D is the fragility parameter, and tau0 is a microscopic time scale. This form predicts a rapid, non-Arrhenius increase in relaxation time as T approaches T0 from above, with a divergence at T = T0, although in practice fits are applied over limited temperature ranges above Tg.

Originating in the 1920s and 1930s, the VFT type model is named after Johannes D. Vogel, G. Fulcher, and G. Tammann, who independently studied how viscosity or relaxation times depend on temperature in liquids. It became a standard tool for describing the dramatic slowdown observed in supercooled liquids and polymeric systems as they approach the glass transition.

Parameters and interpretation play a central role in the utility of VFT-type fits. The fragility parameter D gauges how rapidly dynamics change: large D corresponds to “strong” liquids with more Arrhenius-like behavior, while small D indicates “fragile” liquids with steeper deviations from Arrhenius behavior. T0 is the characteristic temperature where the model predicts a divergence, typically well below the experimentally accessible range, and Tg is the practical glass transition temperature defined by a chosen relaxation time or viscosity criterion.

Limitations of the Vogel-Fulcher type include its empirical nature, potential parameter correlations, and dependence on the chosen temperature range. Alternatives such as the Williams-Landel-Ferry (WLF) model or other microscopic approaches are often preferred in different temperature regimes. Nonetheless, VFT-type relations remain widely used for analyzing glass-forming liquids and polymers.