. 2020 Feb 6;12(2):357. doi: 10.3390/polym12020357

Table 1.

Algebraic expressions of g(α) and f(α) for the kinetic mechanisms of the Coats–Redfern (CR) model used [15].

Mechanism	g(α)	f(α)
A₂, Random nucleation and growth, Avrami Erofe’ve Equation	$\sqrt{(- \ln (1 - α)}$ )	$2 (1 - α) \sqrt{(- \ln (1 - α)})$
A₃, Random nucleation and growth, Avrami Erofe’ve Equation	$\sqrt[3]{(- \ln (1 - α))}$	$3 (1 - α) {(- \ln (1 - α))}^{\frac{2}{3}}$
A₄, Random nucleation and growth, Avrami Erofe’ve Equation	$\sqrt[4]{(- \ln (1 - α))}$	$4 (1 - α) {(- \ln (1 - α))}^{\frac{3}{4}}$
R₁, Unidimensional contraction	$α$	$1$
R₂, Cylindrical phase boundary	$\sqrt{(1 - \ln (1 - α)}$ )	$2 \sqrt{(1 - α)}$
R₃, Spherical phase boundary	$\sqrt[3]{(1 - \ln (1 - α))}$	$3 {(1 - α)}^{\frac{2}{3}}$
D₁, One-dimensional diffusion	$α^{2}$	$\frac{1}{2} α^{- 1}$
D₂, Two-dimensional diffusion (Valensi Equation)	$(1 - α) \ln (1 - α) + α$	${(- \ln (1 - α))}^{- 1}$
D₃, Three-dimensional diffusion (Jander Equation)	${(1 - \sqrt[3]{(1 - α)})}^{2}$	$\frac{3}{2} {(1 - {(1 - α)}^{\frac{1}{3}})}^{- 1} {(1 - α)}^{\frac{2}{3}}$
D₄, Three-dimensional diffusion (Ginstling–Brounshtein Equation)	$(1 - (\frac{2}{3}) α) - {(1 - α)}^{\frac{2}{3}}$	$\frac{3}{2} {(1 - {(1 - α)}^{\frac{1}{3}})}^{- 1}$
F₁, First order (random nucleation with one nucleus on the individual particle)	$- \ln (1 - α)$	$1 - α$
F₂, Second-order (random nucleation with two nuclei on the individual particle)	${(1 - α)}^{- 1}$	${(1 - α)}^{2}$
F₃, Third-order (random nucleation with three nuclei on the individual particle)	${(1 - α)}^{- 2}$	$\frac{1}{2} {(1 - α)}^{3}$