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Table 1

Parameters of fitted kinetic models for the adsorption of MG and RhB on S-Fe NCs

Initial concentration (mmol L⁻¹)	MG			RhB
Initial concentration (mmol L⁻¹)	0.882	1.370	2.055	0.882	1.370	2.055
Pseudo-first-order
k₁ (min⁻¹)	0.11 ± 0.03	0.14 ± 0.03	0.13 ± 0.02	0.05 ± 0.01	0.05 ± 0.01	0.09 ± 0.03
q_e,cal (mmol g⁻¹)	3.16 ± 0.17	3.66 ± 0.18	4.03 ± 0.17	2.20 ± 0.08	2.48 ± 0.12	2.60 ± 0.18
q_e,exp (mmol g⁻¹)	3.52	4.06	4.44	2.26	2.60	3.00
R²	0.902	0.909	0.937	0.972	0.945	0.854
SSE	1.096	1.350	1.162	0.167	0.408	1.126
Pseudo-second-order
k₂ (g (mmol·min)⁻¹)	0.05 ± 0.01	0.05 ± 0.01	0.04 ± 0.01	0.03 ± 0.00	0.02 ± 0.00	0.05 ± 0.02
q_e,cal (mmol g⁻¹)	3.39 ± 0.13	3.93 ± 0.13	4.35 ± 0.11	2.42 ± 0.07	2.74 ± 0.11	2.80 ± 0.15
R²	0.965	0.971	0.983	0.988	0.978	0.934
SSE	0.393	0.427	0.306	0.075	0.180	0.507
Elovich model
α	3.10 ± 0.06	5.78 ± 1.41	4.63 ± 1.52	0.43 ± 0.11	0.44 ± 0.07	1.87 ± 0.37
β	2.04 ± 0.09	1.88 ± 0.09	1.62 ± 0.11	2.25 ± 0.19	1.97 ± 0.11	2.36 ± 0.11
R²	0.994	0.993	0.985	0.980	0.991	0.993
SSE	0.063	0.102	0.272	0.123	0.069	0.053
Double-constant rate equation
A_s	1.30 ± 0.08	1.66 ± 0.11	1.75 ± 0.16	0.57 ± 0.09	0.60 ± 0.06	0.97 ± 0.04
K_s	0.19 ± 0.01	0.17 ± 0.01	0.18 ± 0.02	0.27 ± 0.03	0.28 ± 0.02	0.21 ± 0.01
R²	0.983	0.980	0.965	0.950	0.978	0.995
SSE	0.188	0.296	0.650	0.300	0.160	0.042
Intraparticle diffusion model
k_t1 (mmol (g·min^0.5)⁻¹)	0.35 ± 0.00	0.40 ± 0.02	0.49 ± 0.07	0.25 ± 0.01	0.24 ± 0.01	0.20 ± 0.02
C₁	0.84 ± 0.02	1.12 ± 0.06	1.00 ± 0.0.26	0.17 ± 0.05	0.30 ± 0.03	0.87 ± 0.09
R₁	0.999	0.995	0.940	0.993	0.997	0.964
k_t2 (mmol (g·min^0.5)⁻¹)	0.08 ± 0.00	0.08 ± 0.01	0.09 ± 0.01	0.03 ± 0.01	0.06 ± 0.02	0.09 ± 0.00
C₂	2.36 ± 0.08	2.92 ± 0.11	3.15 ± 0.14	1.87 ± 0.10	1.71 ± 0.20	1.69 ± 0.05
R₂	0.978	0.950	0.942	0.842	0.881	0.995

Initial concentration (mmol L⁻¹)	MG			RhB
Initial concentration (mmol L⁻¹)	0.882	1.370	2.055	0.882	1.370	2.055
Pseudo-first-order
k₁ (min⁻¹)	0.11 ± 0.03	0.14 ± 0.03	0.13 ± 0.02	0.05 ± 0.01	0.05 ± 0.01	0.09 ± 0.03
q_e,cal (mmol g⁻¹)	3.16 ± 0.17	3.66 ± 0.18	4.03 ± 0.17	2.20 ± 0.08	2.48 ± 0.12	2.60 ± 0.18
q_e,exp (mmol g⁻¹)	3.52	4.06	4.44	2.26	2.60	3.00
R²	0.902	0.909	0.937	0.972	0.945	0.854
SSE	1.096	1.350	1.162	0.167	0.408	1.126
Pseudo-second-order
k₂ (g (mmol·min)⁻¹)	0.05 ± 0.01	0.05 ± 0.01	0.04 ± 0.01	0.03 ± 0.00	0.02 ± 0.00	0.05 ± 0.02
q_e,cal (mmol g⁻¹)	3.39 ± 0.13	3.93 ± 0.13	4.35 ± 0.11	2.42 ± 0.07	2.74 ± 0.11	2.80 ± 0.15
R²	0.965	0.971	0.983	0.988	0.978	0.934
SSE	0.393	0.427	0.306	0.075	0.180	0.507
Elovich model
α	3.10 ± 0.06	5.78 ± 1.41	4.63 ± 1.52	0.43 ± 0.11	0.44 ± 0.07	1.87 ± 0.37
β	2.04 ± 0.09	1.88 ± 0.09	1.62 ± 0.11	2.25 ± 0.19	1.97 ± 0.11	2.36 ± 0.11
R²	0.994	0.993	0.985	0.980	0.991	0.993
SSE	0.063	0.102	0.272	0.123	0.069	0.053
Double-constant rate equation
A_s	1.30 ± 0.08	1.66 ± 0.11	1.75 ± 0.16	0.57 ± 0.09	0.60 ± 0.06	0.97 ± 0.04
K_s	0.19 ± 0.01	0.17 ± 0.01	0.18 ± 0.02	0.27 ± 0.03	0.28 ± 0.02	0.21 ± 0.01
R²	0.983	0.980	0.965	0.950	0.978	0.995
SSE	0.188	0.296	0.650	0.300	0.160	0.042
Intraparticle diffusion model
k_t1 (mmol (g·min^0.5)⁻¹)	0.35 ± 0.00	0.40 ± 0.02	0.49 ± 0.07	0.25 ± 0.01	0.24 ± 0.01	0.20 ± 0.02
C₁	0.84 ± 0.02	1.12 ± 0.06	1.00 ± 0.0.26	0.17 ± 0.05	0.30 ± 0.03	0.87 ± 0.09
R₁	0.999	0.995	0.940	0.993	0.997	0.964
k_t2 (mmol (g·min^0.5)⁻¹)	0.08 ± 0.00	0.08 ± 0.01	0.09 ± 0.01	0.03 ± 0.01	0.06 ± 0.02	0.09 ± 0.00
C₂	2.36 ± 0.08	2.92 ± 0.11	3.15 ± 0.14	1.87 ± 0.10	1.71 ± 0.20	1.69 ± 0.05
R₂	0.978	0.950	0.942	0.842	0.881	0.995

⁠, n is the total amount of data points, q_e,cal and q_e,exp (mmol g⁻¹) are the calculated and experimental adsorption capacity, respectively.

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