Skip to main content

Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Table 1 Common solid-state reaction mechanisms [44, 45]

From: Thermogravimetric and kinetic analysis to discern synergy during the co-pyrolysis of microalgae and swine manure digestate

Reaction mechanisms Differential form f(α) Integral form g(α)
A2—Nucleation and nuclei growth (Avrami Eq. 1) \( 2(1 - \alpha )[ - \ln (1 - \alpha )]^{1/2} \) \( [ - \ln (1 - \alpha )]^{1/2} \)
A3—Nucleation and nuclei growth (Avrami Eq. 2) \( 3(1 - \alpha )[ - \ln (1 - \alpha )]^{3/2} \) \( [ - \ln (1 - \alpha )]^{1/3} \)
A4—Nucleation and nuclei growth (Avrami Eq. 3) \( 4(1 - \alpha )[ - \ln (1 - \alpha )]^{3/4} \) \( [ - \ln (1 - \alpha )]^{1/4} \)
R2—Phase boundary controlled reaction (contracting area) \( 2(1 - \alpha )^{1/2} \) \( [1 - (1 - \alpha )]^{1/2} \)
R3—Phase boundary controlled reaction (contracting volume) \( 3(1 - \alpha )^{2/3} \) \( [1 - (1 - \alpha )]^{1/3} \)
D1—One-dimensional diffusion \( (1/2)\alpha \) \( \alpha^{2} \)
D2—Two-dimensional diffusion (Valensi equation) \( [ - \ln (1 - \alpha )]^{ - 1} \) \( (1 - \alpha )\ln (1 - \alpha ) + \alpha \)
D3—Three-dimensional diffusion (Jander equation) \( (3/2)[1 - (1 - \alpha )^{1/3} ]^{ - 1} (1 - \alpha )^{2/3} \) \( [1 - (1 - \alpha )^{1/3} ]^{2} \)
D4—Three-dimensional diffusion (Ginstling–Brounshtein equation) \( (3/2)[1 - (1 - \alpha )^{1/3} ]^{ - 1} \) \( [1 - (2/3)\alpha )] - (1 - \alpha )^{2/3} \)
F1—Random nucleation with one nucleus on the individual particle \( 1 - \alpha \) \( - \ln (1 - \alpha ) \)
F2—Random nucleation with two nuclei on the individual particle \( (1 - \alpha )^{2} \) \( 1/(1 - \alpha ) \)
F3—Random nucleation with three nuclei on the individual particle \( (1/2)(1 - \alpha )^{3} \) \( 1/(1 - \alpha )^{2} \)
P1—Mampel power law \( \left( {n \, = \,{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}} \right) \) \( 2\alpha^{1/2} \) \( \alpha^{1/2} \)
P2—Mampel power law \( \left( {n \, = \,{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 3}}\right.\kern-0pt} \!\lower0.7ex\hbox{$3$}}} \right) \) \( 3\alpha^{2/3} \) \( \alpha^{1/3} \)
P3—Mampel power law \( \left( {n \, = \,{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 4}}\right.\kern-0pt} \!\lower0.7ex\hbox{$4$}}} \right) \) \( 4\alpha^{3/4} \) \( \alpha^{1/4} \)