VogelFulcher

VogelFulcher refers to the Vogel-Fulcher-Tammann (VFT) relation, an empirical formula used to describe how the dynamics of glass-forming liquids slow dramatically as temperature decreases toward the glass transition. It is commonly applied to describe the temperature dependence of viscosity η(T) and structural relaxation time τ(T).

The most common form is τ(T) = τ0 exp[ D T0 / (T − T0) ], with τ0 a pre-exponential time, T0 the Vogel temperature (typically below the glass transition temperature Tg), and D a strength or fragility parameter. A similar expression is used for viscosity, η(T) = η0 exp[ D T0 / (T − T0) ]. As T approaches T0 from above, the equation predicts a divergence of τ or η, though the physical interpretation of this divergence remains debated. T0 is not directly observable and is determined from fits to experimental data; it is often well below Tg or even negative depending on the liquid.

Origins and usage: the relation is named after Jan Vogel (1921) and Floris Fulcher (1925) and was later associated with G. Tammann, hence Vogel-Fulcher-Tammann. It is widely used in glass science and polymer physics to fit viscosity or relaxation data of many supercooled liquids and to characterize fragility, a measure of how rapidly dynamics change with temperature.

Limitations: while useful as an empirical model, the VFT form is not universal. Some systems exhibit deviations, and the predicted finite-temperature divergence may not reflect microscopic mechanisms. Other models, such as the Williams-Landel-Ferry equation, are sometimes preferred near Tg.