Table 1 Different reaction models used in the solid-state kinetics (Vyazovkin et al. 2011; Khawam and Flanagan 2006; Milićević et al. 2017; Vyazovkin et al. 2014)
# | Reaction model | f(α) | g(α) |
|---|---|---|---|
Nucleation models | |||
1 | Power law (P2) | 2α1/2 | α1/2 |
2 | Power law (P3) | 3α2/3 | α1/3 |
3 | Power law (P4) | 4α3/4 | α1/4 |
4 | Avrami-Erofeyev (A2) | 2(1−α)[−ln(1−α)]1/2 | [−ln(1−α)]1/2 |
5 | Avrami-Erofeyev (A3) | 3(1−α)[ −ln(1−α)]2/3 | [−ln(1−α)]1/3 |
6 | Avrami-Erofeyev (A4) | 4(1−α)[ −ln(1−α)]3/4 | [−ln(1−α)]1/4 |
7 | Modified Prout-Tompkins (B1) | α(1−α) | ln[α/(1−α)] |
Geometrical contraction models | |||
8 | Contracting area (R2) | 2(1−α)1/2 | 1− (1−α)1/2 |
9 | Contracting volume (R3) | 3(1−α)2/3 | 1− (1−α)1/3 |
Diffusion models | |||
10 | One-dimensional diffusion (D1) | 1/(2α) | α2 |
11 | Two-dimensional diffusion (D2) | − [1/ln(1−α)] | ((1−α)ln(1−α))+α |
12 | Three-dimensional diffusion (D3) | [3(1−α)2/3]/[2(1− (1−α)1/3)] | (1−(1−α)1/3)2 |
13 | Ginstling-Brounshtein (D4) | 3/[2(1−(1−α)−1/3−1)] | 1− (2/3)α−(1−α)2/3 |
Reaction-order models | |||
14 | Zero-order (F0/R1) | 1 | α |
15 | First-order (F1) | (1−α) | −ln(1−α) |
16 | Second-order (F2) | (1−α)2 | [1/(1−α)] −1 |
17 | Third-order (F3) | (1−α)3 | (1/2)[(1−α)−2−1] |