Pyrolysis kinetic study of cathode material derived from spent lithium ion batteries (LIBs): Comparison of different models

Figures & data

Figure 1. TG and DTG profiles of cathode at different heating rates

Figure 2. Linear fitting curves under different conversions for model-free methods

Table 1. Kinetic parameters derived from the model-free methods

	FWO		Friedman		KAS		Starink		Tang		Bosewell
α	Eα (kJ/mol)	R	Eα (kJ/mol)	R	Eα (kJ/mol)	R	Eα (kJ/mol)	R	Eα (kJ/mol)	R	Eα (kJ/mol)	R
0.001	12.032	0.9930	3.326	0.9051	4.215	0.9619	4.549	0.9665	4.653	0.9677	8.436	0.9874
0.002	15.582	0.9957	7.214	0.9791	7.255	0.9867	7.615	0.9876	7.725	0.9879	11.824	0.9935
0.003	18.280	0.9983	10.052	0.9943	9.558	0.9968	9.936	0.9969	10.053	0.9969	14.394	0.9978
0.004	19.554	0.9992	11.344	0.9977	10.475	0.9991	10.869	0.9991	10.990	0.9991	15.522	0.9991
0.005	20.772	0.9999	12.546	0.9999	11.297	0.9999	11.710	0.9999	11.836	0.9999	16.574	1.0000
0.006	21.630	0.9997	13.336	0.9985	11.705	0.9955	12.137	0.9960	12.269	0.9961	17.230	0.9988
0.007	22.411	0.9999	14.052	0.9996	12.120	0.9980	12.568	0.9982	12.704	0.9983	17.848	0.9996
0.008	23.111	0.9983	14.702	0.9962	12.544	0.9969	13.004	0.9970	13.145	0.9970	18.429	0.9979
0.009	24.433	0.9960	16.004	0.9909	13.637	0.9901	14.108	0.9906	14.251	0.9908	19.670	0.9943
0.01	26.640	0.9946	18.233	0.9883	15.658	0.9864	16.140	0.9871	16.286	0.9873	21.842	0.9921
0.011	29.365	0.9958	20.994	0.9917	18.200	0.9906	18.693	0.9910	18.841	0.9912	24.545	0.9941
0.012	31.592	0.9998	23.179	0.9993	20.090	0.9983	20.600	0.9985	20.752	0.9985	26.662	0.9994
0.013	36.702	0.9988	28.442	0.9974	25.146	0.9957	25.664	0.9959	25.817	0.9960	31.878	0.9978
0.014	43.187	0.9960	35.145	0.9928	31.641	0.9899	32.167	0.9903	32.320	0.9904	38.537	0.9938
Average	24.664	—	16.326	—	14.539	—	14.983	—	15.117	—	20.242	—

Figure 3. Comparison of kinetic parameters derived from model-free methods

Table 2. Expressions of f(α) and g(α) for reaction mechanisms

Reaction models
Nucleation models	Symbols	f(α)	g(α)
Power law	P1	4α^3/4	α^1/4
Power law	P2	3α^2/3	α^1/3
Power law	P3	2α^1/2	α^1/2
Power law	P4	2/3α^−1/2	α^3/2
Avrami-Erofeev	A2	2(1-α)[-ln(1-α)]^1/2	[-ln(1-α)]^1/2
Avrami-Erofeev	A3	3(1-a)[-ln(1-α)]^2/3	[-ln(1-α)]^1/3
Avrami-Erofeev	A4	4(1-α)[-ln(1-α)]^3/4	[-ln(1-α)]^1/4
Diffusion models
One-dimensional diffusion	D1	1/2α	α^2
Two-dimensional diffusion	D2	[-ln(1-α)]^−1	(1-α)ln(1-α)+ α
Three-dimensional diffusion (Jander equation)	D3	3(1-α)^2/3/2[1-(1-α)^1/3]	[1-(1-α)^1/3]^2
Four-dimensional diffusion (Ginstling-Brounshetein)	D4	3/2[(1-α)^−1/3-1]	1–2α/3-(1-α)^2/3
Reaction order models
First-order	F1	1-α	-ln(1-α)
Second-order	F2	(1-α)^2	1/(1-α)-1
Third-order	F3	(1-α)^3	[1/(1-α)^2–1]/2
Geometrical contraction models
Prout-Tompkins	R1	1	α
Contracting area	R2	2(1-α)^1/2	1-(1-α)^1/2
Contracting volume	R3	3(1-α)^2/3	1-(1-α)^1/3

Figure 4. Reaction mechanism determined using CR and master-plots method