Activation energy values for different solid-state thermal degradation mechanisms based on Coats–Redfern method17.
Region | Reaction model | g(α) | 10 °C min−1 | 20 °C min−1 | 30 °C min−1 | 40 °C min−1 | Average E-values | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
E, kJ mol−1 | R 2 | E, kJ mol−1 | R 2 | E, kJ mol−1 | R 2 | E, kJ mol−1 | R 2 | E, kJ mol−1 | R 2 | |||
I | A2 | [−ln(1 − α)]1/2 | 37.35 | 0.99 | 37.46 | 0.99 | 40.15 | 0.99 | 39.28 | 0.99 | 38.56 | 0.99 |
A3 | [−ln(1 − α)]1/3 | 21.76 | 0.98 | 21.76 | 0.99 | 23.52 | 0.99 | 22.91 | 0.99 | 22.49 | 0.99 | |
A4 | [−ln(1 − α)]1/4 | 13.96 | 0.98 | 13.91 | 0.99 | 15.20 | 0.99 | 14.72 | 0.99 | 14.45 | 0.98 | |
F0 | α | 73.09 | 0.98 | 73.49 | 0.98 | 78.30 | 0.98 | 76.83 | 0.99 | 75.43 | 0.98 | |
F1 | −ln(1 − α) | 84.15 | 0.99 | 84.56 | 0.99 | 90.04 | 0.99 | 88.38 | 0.99 | 86.78 | 0.99 | |
F2 | [1 − 1/(1 − α)]/−1 | 96.56 | 1.00 | 96.96 | 1.00 | 103.19 | 1.00 | 101.32 | 1.00 | 99.51 | 1.00 | |
F3 | [1 − 1/(1 − α)2]/−2 | 110.27 | 1.00 | 110.67 | 1.00 | 117.72 | 1.00 | 115.62 | 1.00 | 113.57 | 1.00 | |
F4 | [1 − 1/(1 − α)3]/−3 | 125.22 | 1.00 | 125.61 | 1.00 | 133.56 | 1.00 | 131.22 | 1.00 | 128.90 | 1.00 | |
F5 | [1 − 1/(1 − α)4]/−4 | 141.30 | 0.99 | 141.68 | 0.99 | 150.60 | 0.99 | 148.00 | 0.99 | 145.39 | 0.99 | |
F5.5 | [1 − 1/(1 − α)4.5]/−4.5 | 149.73 | 0.99 | 150.10 | 0.99 | 159.53 | 0.99 | 156.79 | 0.99 | 154.04 | 0.99 | |
D1 | α 2 | 155.61 | 0.98 | 156.62 | 0.99 | 166.35 | 0.99 | 163.49 | 0.99 | 160.52 | 0.99 | |
D2 | (1 − α)ln(1 − α) + α | 162.56 | 0.99 | 163.57 | 0.99 | 173.71 | 0.99 | 170.74 | 0.99 | 167.65 | 0.99 | |
D3 | [1 − (1 − α)1/3]2 | 170.08 | 0.99 | 171.09 | 0.99 | 181.68 | 0.99 | 178.58 | 0.99 | 175.36 | 0.99 | |
D4 | [1 − (2/3)α] − (1 − α)2/3 | 165.07 | 0.99 | 166.07 | 0.99 | 176.36 | 0.99 | 173.36 | 0.99 | 170.21 | 0.99 | |
R2 | 1 − (1 − α)1/2 | 78.45 | 0.99 | 78.86 | 0.99 | 84.00 | 0.99 | 82.43 | 0.99 | 80.94 | 0.99 | |
R3 | 1 − (1 − α)1/3 | 80.32 | 0.99 | 80.72 | 0.99 | 85.97 | 0.99 | 84.38 | 0.99 | 82.85 | 0.99 | |
II | A2 | [−ln(1 − α)]1/2 | 8.76 | 0.91 | 8.98 | 0.96 | 8.90 | 0.97 | 8.00 | 0.95 | 8.66 | 0.95 |
A3 | [−ln(1 − α)]1/3 | 2.37 | 0.61 | 2.43 | 0.79 | 2.35 | 0.84 | 1.70 | 0.67 | 2.21 | 0.73 | |
A4 | [−ln(1 − α)]1/4 | — | — | — | — | — | — | — | — | — | — | |
F0 | α | 12.82 | 0.89 | 13.20 | 0.94 | 13.15 | 0.96 | 12.07 | 0.94 | 12.81 | 0.93 | |
F1 | −ln(1 − α) | 27.93 | 0.96 | 28.61 | 0.98 | 28.56 | 0.99 | 26.89 | 0.98 | 28.00 | 0.98 | |
F2 | [1 − 1/(1 − α)]/−1 | 48.64 | 0.98 | 49.70 | 0.99 | 49.64 | 1.00 | 47.18 | 0.99 | 48.79 | 0.99 | |
F3 | [1 − 1/(1 − α)2]/−2 | 74.47 | 0.99 | 75.99 | 1.00 | 75.91 | 1.00 | 72.46 | 1.00 | 74.71 | 1.00 | |
F4 | [1 − 1/(1 − α)3]/−3 | 104.22 | 0.99 | 106.27 | 1.00 | 106.19 | 1.00 | 101.59 | 1.00 | 104.57 | 1.00 | |
F5 | [1 − 1/(1 − α)4]/−4 | 136.62 | 0.99 | 139.24 | 1.00 | 139.14 | 1.00 | 133.31 | 1.00 | 137.08 | 1.00 | |
F5.5 | [1 − 1/(1 − α)4.5]/−4.5 | 153.46 | 1.00 | 156.39 | 1.00 | 156.28 | 1.00 | 149.80 | 1.00 | 153.98 | 1.00 | |
D1 | α 2 | 36.07 | 0.94 | 37.07 | 0.97 | 43.18 | 0.95 | 35.02 | 0.97 | 37.83 | 0.96 | |
D2 | (1 − α)ln(1 − α) + α | 44.41 | 0.96 | 45.58 | 0.98 | 52.11 | 0.96 | 43.22 | 0.98 | 46.33 | 0.97 | |
D3 | [1 − (1 − α)1/3]2 | 54.97 | 0.97 | 56.35 | 0.99 | 63.24 | 0.97 | 53.58 | 0.99 | 57.04 | 0.98 | |
D4 | [1 − (2/3)α] − (1 − α)2/3 | 47.90 | 0.96 | 49.14 | 0.98 | 55.79 | 0.97 | 46.64 | 0.98 | 49.87 | 0.97 | |
R2 | 1 − (1 − α)1/2 | 19.69 | 0.94 | 20.21 | 0.97 | 23.54 | 0.95 | 18.80 | 0.97 | 20.56 | 0.96 | |
R3 | 1 − (1 − α)1/3 | 22.28 | 0.95 | 22.85 | 0.98 | 26.27 | 0.96 | 21.34 | 0.98 | 23.19 | 0.97 |