Glass Science, Polymer Rheology & Optical Fiber Drawing
Vogel-Fulcher-Tammann Glass Viscosity & Fragility Formula
Calculate Supercooled Glass Melt Log10 Viscosity A + B/(T - T0), Glass Transition Temperature Tg at 10^12 Pa*s, Angell Kinetic Fragility Index m = B*Tg / (Tg - T0)^2, and Dynamic Melt Viscosity (Pa*s).
Control optical-fiber drawing and bottle forming across 10 orders of viscosity magnitude with VFT!
Silicate glasses, metallic glasses, and amorphous polymers violate simple Arrhenius viscosity scaling because cooperative molecular rearrangement freezes rapidly toward the Kauzmann/Vogel temperature T_0! Glass technologists control furnace fining (10^1–10^2 Pa*s), gob forming (10^3–10^6 Pa*s), Littleton softening (~10^6.6 Pa*s), and annealing/glass transition T_g (defined where viscosity hits 10^12 Pa*s!) via the Vogel-Fulcher-Tammann (VFT) equation: Log10(eta_Pa_s) = A_VFT + B_VFT / (T_K - T_0)! Solving Log10(eta) = 12 gives Glass Transition Temperature T_g = T_0 + B_VFT / (12 - A_VFT), while C.A. Angell’s Kinetic Fragility Index m_frag = (B_VFT * T_g) / ((T_g - T_0)^2) classifies "strong" network formers like pure silica (m ~ 20) vs "fragile" molecular melts (m > 80)!
Verify on a Soda-Lime-Silicate Glass Melt—HighTemp_Asymptote A_VFT = -3.0 (B2), VFT_Activation_Parameter B_VFT = 4,500 K (B3), Vogel_Divergence_Temp T_0 = 500 K (B4), and Gob_Working_Temp T_K = 950 K (B5): Log10 Viscosity is -3.0 + 4,500 / (950 - 500) = -3 + 10 = 7.0000 (E2); Glass Transition Temperature T_g at 10^12 Pa*s is 500 + 4,500 / (12 - (-3)) = 800.00 K (526.85 C in E3); Angell Fragility Index m is (4,500 * 800) / (300^2) = 40.00 (E4); and Dynamic Melt Viscosity is 10^7 = 10,000,000.00 Pa*s (E5)!
| VFT Glass Rheology Metric (A=-3.0, B=4,500 K, T0=500 K, T=950 K) | Formula | Verified Output |
|---|---|---|
| Log10 Melt Viscosity (Pa*s) | A_VFT + B_VFT / (Temp_K - T_0) | 7.0000 (2.0000 @ 1,400 K Fining) |
| Glass Transition Temp Tg (K) | T_0 + B_VFT / (12 - A_VFT) | 800.00 K |
| Angell Kinetic Fragility m | (B_VFT * T_g) / ((T_g - T_0)^2) | 40.00 (Intermediate Silicate) |
| Dynamic Melt Viscosity (Pa*s) | 10 ^ Log10_Melt_Viscosity | 10,000,000 Pa*s (100 @ 1,400 K) |
VFT Glass Transition Temperature Tg & Angell Fragility Formula
Validate A_VFT < 12, B_VFT > 0, T_0 >= 0, and Operating_Temp T_K > T_0 (with Log10(eta) <= 13)!
=LET(a_vf, B2, b_vf, B3, t_zr, B4, tp_k, B5, IF(OR(a_vf >= 12, b_vf <= 0, t_zr < 0, tp_k <= t_zr, (a_vf + b_vf / (tp_k - t_zr)) > 13), "Invalid VFT Melt Regime", LET(t_gl, t_zr + b_vf / (12 - a_vf), ROUND((b_vf * t_gl) / ((t_gl - t_zr) ^ 2), 2))))1,400 K Tank-Furnace Fining Viscosity Check
Raise Furnace_Temp B5 from 950 K to 1,400 K: Log10 Viscosity E2 drops 5 orders of magnitude to -3 + 4,500 / 900 = 2.0000, lowering Dynamic Viscosity E5 to a bubble-fining 100.00 Pa*s!
=IF(ISTEXT(E2), E2, ROUND(10 ^ E2, 2))Try the example
Use the original values or change them to test your understanding.