Viscosity of amorphous materials

Viscous flow in amorphous materials (e.g. in glasses and melts) is a thermally activated process:

$\eta = A \cdot e^{Q/RT}$

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 Arrhenius-type 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

• Strong when: $Q_H - Q_L < Q_L$ or
• Fragile when: $Q_H - Q_L \ge Q_L$

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

Common log of viscosity vs temperature

The viscosity of amorphous materials is quite exactly described by a two-exponential equation:

$\eta = A_1 \cdot T \cdot [1 + A_2 \cdot e^{B/RT}] \cdot [1 + C \cdot e^{D/RT}]$

with constants A₁, A₂, 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 Vogel-Tammann-Fulcher (VTF) equation or stretched exponent-type equation.

If the temperature is significantly lower than the glass transition temperature (T < T_g), then the two-exponential equation simplifies to an Arrhenius type equation:

$\eta = A_LT \cdot e^{Q_H/RT}$

with:

$Q_H = H_d + H_m$

where H_d is the enthalpy of formation of broken bonds (termed configuron s) 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 two-exponential equation also simplifies to an Arrhenius type equation:

$\eta = A_HT\cdot e^{Q_L/RT}$

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 10¹² Pa·s at 400 °C.

See also

• Viscoelasticity
• Glass transition

External links

• Undercooled fluids
• Glass: Liquid or Solid -- Science vs. an Urban Legend