Vogel–Fulcher–Tammann equation
The Vogel–Fulcher–Tammann equation, also known as Vogel–Fulcher–Tammann–Hesse equation or Vogel–Fulcher equation (abbreviated: VFT equation), is used to describe the viscosity of liquids as a function of temperature, and especially its strongly temperature dependent variation in the supercooled regime, upon approaching the glass transition. In this regime the viscosity of certain liquids can increase by up to 13 orders of magnitude within a relatively narrow temperature interval.
The VFT equation reads as follows:
- [math]\displaystyle{ \eta = \eta_0 \cdot e^{\frac{B}{T - T_\mathrm{VF}}} }[/math]
where [math]\displaystyle{ \eta_0 }[/math] and [math]\displaystyle{ B, }[/math] are empirical material-dependent parameters, and [math]\displaystyle{ T_\mathrm{VF} }[/math] is also an empirical fitting parameter, and typically lies about 50 °C below the glass transition temperature[clarification needed]. These three parameters are normally used as adjustable parameters to fit the VFT equation to experimental data of specific systems.
The VFT equation is named after Hans Vogel, Gordon Scott Fulcher (1884–1971) and Gustav Tammann (1861–1938).
References
- Vogel, Hans (1921). "Das Temperaturabhaengigkeitsgesetz der Viskositaet von Fluessigkeiten" (in de). Physikalische Zeitschrift 22: 645. https://babel.hathitrust.org/cgi/pt?id=mdp.39015020056829&view=1up&seq=723.
- Fulcher, Gordon S. (1925). "Analysis of recent measurements of the viscosity of glasses". Journal of the American Ceramic Society (Wiley) 8 (6): 339–355. doi:10.1111/j.1151-2916.1925.tb16731.x. ISSN 0002-7820.
- Tammann, Gustav; Hesse, W. (1926-10-19). "Die Abhängigkeit der Viscosität von der Temperatur bie unterkühlten Flüssigkeiten" (in de). Zeitschrift für anorganische und allgemeine Chemie (Wiley) 156 (1): 245–257. doi:10.1002/zaac.19261560121. ISSN 0863-1786.
- García Colin-Scherer, Leopoldo; del Castillo, Luis Felipe; Goldstein, Patricia (1989-10-01). "Theoretical basis for the Vogel-Fulcher-Tammann equation". Physical Review B (American Physical Society (APS)) 40 (10): 7040–7044. doi:10.1103/physrevb.40.7040. ISSN 0163-1829. PMID 9991086. Bibcode: 1989PhRvB..40.7040G.
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