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Glasses and amorphous materials

The viscosity η (Pa·s) of a soda-lime glass is described by the VFT equation log₁₀η = A + B/(T − T₀) with A = −2.5, B = 4300 K and T₀ = 520 K. Which is closest to the temperature at which the viscosity reaches 10¹² Pa·s (a guide to the annealing point, close to the glass transition temperature)?

  1. AAbout 817 K
  2. BAbout 878 K
  3. CAbout 297 K
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Answer: A. About 817 K

Setting log₁₀η = 12 gives T − T₀ = B/(12 − A) = 4300/14.5 ≈ 297 K, so T ≈ 520 + 297 = 817 K (about 543 °C). The VFT equation has the viscosity rise steeply, as if diverging, on approaching T₀, and it can express a stronger temperature dependence than the Arrhenius form. About 878 K is the value obtained by ignoring A and taking B/12, and about 297 K is the value obtained by forgetting to add T₀. In glass processing, articles are formed at the working point, where the viscosity is about 10³ Pa·s, held near the annealing point of about 10¹² Pa·s, and then cooled slowly to below the strain point (about 3×10¹³ Pa·s) to remove residual stress. Knowing how viscosity changes with temperature is the basis for setting forming and annealing conditions.

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