Kinetic parameters for the adsorption of malachite green (MG) onto 3-MPA@PMNPs at different initial concentrations of MG^a.

C o (mg L−1)	q e (exp.) (mg g−1)	Pseudo-first-order kinetic model		Pseudo-second-order kinetic model			Elovich kinetic model			Intraparticle diffusion/Weber and Morris kinetic model qt = kipdt0.5			Liquid film diffusion kinetic model ln(1 − F) = −kfdt
		K 1 (min−1)	R 2	K 2 (min−1)	h (mg g−1 min−1)	R 2	α (mg g−1 min−1)	β (g mg−1)	R 2	K ipd (mg g−1 min−0.5)	I	R 2	K fd (g mg−1)	I	R 2
25	2.47	−0.0018	0.19	0.38	0.49	0.99	0.49	0.46	0.91	1.10	0.52	0.76	−0.025	−1.57	0.09
50	4.91	−0.0025	0.41	0.19	0.98	0.99	0.98	0.84	0.95	2.19	1.31	0.79	−0.021	−1.13	0.16
100	9.69	−0.0029	0.46	0.10	1.93	0.99	1.93	1.53	0.90	4.33	3.56	0.68	−0.033	−1.14	0.14
200	18.36	−0.0012	0.10	0.05	3.66	0.99	3.66	2.22	0.74	8.18	10.52	0.45	−0.139	−2.17	0.0003
300	27.22	−0.0021	0.65	0.03	5.44	0.99	5.44	3.30	0.79	12.16	14.62	0.52	−0.123	−1.80	0.031
500	44.89	−0.0024	0.82	0.02	8.96	0.99	8.96	6.31	0.85	20.03	19.56	0.61	−0.051	−1.52	0.048
800	62.57	−0.0028	0.96	0.01	12.5	0.99	12.5	9.78	0.97	27.95	17.17	0.83	−0.035	−0.94	0.111
1000	81.29	−0.0031	0.79	0.01	16.24	0.99	16.2	12.45	0.93	36.31	25.02	0.75	−0.029	−0.75	0.342

^a q _e (exp.): experimental q_e (mg g⁻¹); q_e (cal.): calculated q_e (mg g⁻¹); I: intercept; C_o: initial concentration of the pollutant (mg L⁻¹); h: initial adsorption rate constant (mg g⁻¹ min⁻¹); k₁ & k₂: equilibrium rate constants for pseudo-first and pseudo-second order kinetic models (min⁻¹); R²: regression coefficient; α = adsorption rate constant; β = desorption rate constant; K_fd = film diffusion rate constant (g mg⁻¹); k_ipd = intraparticle diffusion rate constant (mg g⁻¹ min^−0.5).