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:
where is activation energy of viscosity, is temperature, is the molar gas constant and is approximately a constant.
The viscous flow in amorphous materials is characterised by a deviation from the Arrhenius-type behaviour: changes from a high value at low temperatures (in the glassy state) to a low value at high temperatures (in the liquid state). Depending on this change, amorphous materials are classified as either
*strong when: or
The fragility of amorphous materials is numerically characterized by the Doremus’ fragility ratio:
and strong material have whereas fragile materials have
The viscosity of amorphous materials is quite exactly described by a two-exponential equation:
with constants and related to thermodynamic parameters of joining bonds of an amorphous material.
Not very far from the
glass transition temperature, , 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, , then the two-exponential equation simplifies to an Arrhenius type equation:
where is the
enthalpy of formationof broken bonds (termed configurons) and is the enthalpyof their motion.
When the temperature is less than the glass transition temperature, , 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, , the two-exponential equation also simplifies to an Arrhenius type equation:
When the temperature is higher than the glass transition temperature, , 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.
* [http://science.nasa.gov/headlines/y2003/16oct_viscosity.htm Undercooled fluids]
* [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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