Viscosity of Amorphous Materials - Viscosity of Amorphous Materials

Viscosity of Amorphous Materials

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

where Q is activation energy, T is temperature, R is the molar gas constant and A is approximately a constant.

The viscous flow in amorphous materials is characterized by a deviation from the Arrhenius-type behavior: 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 ≥ Q_L.

The fragility of amorphous materials is numerically characterized by the Doremus’ fragility ratio:

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 two-exponential equation:

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-Fulcher-Tammann (VFT) 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:

with:

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:

with:

When the temperature is higher than the glass transition temperature, T > T_g, the activation energy of viscosity is low because amorphous materials are melted and have most of their joining bonds broken, which facilitates flow.