Vogel-Fulcher-Tammann equation

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The Vogel-Fulcher-Tammann equation , also Vogel-Fulcher-Tammann-Hesse equation or Vogel-Fulcher equation (short: VF equation ), is used in the manufacture and shaping of glass products to calculate the viscosity behavior above the transformation temperature used. A precise description of the viscosity is particularly relevant for organic glasses such as polymers , as it is a measure of the glass transition temperature at which the viscosity increases sharply.

The VF equation describes the increase in the viscosity of supercooled liquids, a calculation rule is contained in DIN ISO 7884-1 (viscosity and viscometric fixed points):

With

  • temperature-independent material parameters and
  • the bird temperature , which is approx. 50 ° C below the glass temperature.

The VF equation is equivalent to the Williams-Landel-Ferry equation , or WLF equation for short, with which it is linked via the time-temperature superposition principle:

(Note that this has a different meaning and value than in the VF equation.)

In this representation is

  • the decadic logarithm
  • the shift factor to the reference temperature
  • the relaxation time of - relaxation , which typically occurs at the glass transition.
  • and are constants which for many polymeric glass formers lie in the range of and if the glass transition temperature is chosen as the reference temperature.

The equivalence with the WLF equation results from

and

The Vogel-Fulcher-Tammann equation was named after H. Vogel, Gordon Scott Fulcher (1884-1971) and Gustav Tammann (1861-1938).

literature

  • H. Vogel: “The law of temperature dependence of the viscosity of fluids”. Physical Journal, Vol. 22, 1921, p. 645.
  • Gordon S. Fulcher (1925): "Analysis of recent measurements of the viscosity of glasses", Journal of the American Ceramic Society 8 pp. 339-355.
  • Gustav Tammann , W. Hesse (1926): "The dependence of the viscosity on the temperature in supercooled liquids", magazine for inorganic and general chemistry 156 pp. 245-257.
  • LS Garca-Coln, LF del Castillo, and Patricia Goldstein (1989): Theoretical basis for the Vogel-Fulcher-Tammann equation . Phys. Rev. B 40, 7040.