# Viscosity of amorphous materials

Viscous flow in amorphous materials (e.g. in glasses and melts) [cite journal|author=R.H.Doremus|year=2002|month=
title=Viscosity of silica|journal=J. Appl. Phys.|volume=92|issue=12 |pages=7619–7629|issn=0021-8979
doi=10.1063/1.1515132
] [cite journal|author=M.I. Ojovan and W.E. Lee|year=2004 |title=Viscosity of network liquids within Doremus approach |journal=J. Appl. Phys.|volume=95|issue=7|pages=3803–3810 |issn=0021-8979 |doi=10.1063/1.1647260 |unused_data=|month] [cite journal|author=M.I. Ojovan, K.P. Travis and R.J. Hand|year=2000|moth= |title=Thermodynamic parameters of bonds in glassy materials from viscosity-temperature relationships|journal=J. Phys.: Condensed matter|volume=19|issue=41 |pages=415107|issn=0953-8984|doi=10.1088/0953-8984/19/41/415107] is a thermally activated process:

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

where $Q$ is 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 $R_D ge 2$

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

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

with constants $A_1 , A_2 , B, C$ 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 a Kohlrausch-type stretched-exponential law.

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:

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

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 two-exponential equation also simplifies to an Arrhenius type equation:

$eta = A_HTcdot e^\left\{Q_L/RT\right\}$

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.

ee also

*Vitrification
*Glass physics

References

* [http://dwb.unl.edu/Teacher/NSF/C01/C01Links/www.ualberta.ca/~bderksen/florin.html Glass: Liquid or Solid -- Science vs. an Urban Legend]

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