Viscous flow in amorphous materials (e.g. in glasses and melts) ^{[1]}^{[2]}^{[3]} is a thermally activated process:
where Q is the activation energy of viscosity, T is temperature, R is the molar gas constant and A is approximately a constant.
The viscous flow in amorphous materials is characterised by a deviation from the Arrheniustype behaviour: Q changes from a high value Q_{H} at low temperatures (in the glassy state) to a low value Q_{L} at high temperatures (in the liquid state). Depending on this change, amorphous materials are classified as either
The fragility of amorphous materials is numerically characterized by the Doremus' fragility ratio:
R_{D} = Q_{H} / Q_{L}
and strong material have R_{D} < 2; whereas fragile materials have R_{D} ≥ 2
The viscosity of amorphous materials is quite exactly described by a twoexponential equation:
with constants A_{1}, A_{1}, B, C, and D related to thermodynamic parameters of joining bonds of an amorphous material.
Not very far from the glass transition temperature (T_{g} this equation can be approximated by a VogelTammannFulcher (VTF) equation or stretched exponenttype equation.^{[4]}
If the temperature is significantly lower than the glass transition temperature (T < T_{g}), then the twoexponential equation simplifies to an Arrhenius type equation:
with:
Q_{H} = H_{d} + H_{m}
where H_{d} is the enthalpy of formation of broken bonds (termed configurons) and H_{m} is the enthalpy of their motion.
When the temperature is less than the glass transition temperature, T < T_{g}, the activation energy of viscosity is high because the amorphous materials are in the glassy state and most of their joining bonds are intact.
If the temperature is highly above the glass transition temperature, T > T_{g}, the twoexponential equation also simplifies to an Arrhenius type equation:
with:
Q_{L} = H_{m}
When the temperature is higher than the glass transition temperature (T < T_{g}), the activation energy of viscosity is low because amorphous materials are melt and have most of their joining bonds broken which facilitates flow.
An example of glass viscosity is given in Calculation of glass properties, in which the viscosity is around 10^{12} Pa·s at 400 °C.
