Table 2 Adsorption kinetic and diffusion model constants for MB removal using pure diatomaceous mesoporous biosilica.

Kinetic model	Pseudo-first order				Pseudo-second order				Elovich
Kinetic model	q₁, mg g⁻¹	k₁, min⁻¹	R²	Δq, %	q₂, mg g⁻¹	k₂, g (mg min)⁻¹	R²	Δq, %	α, g (mg min)⁻¹	β, mg g⁻¹	R²	Δq, %
SZCZCH193	19.902	0.002	0.887	52.2	39.671	2.71e⁻⁵	0.894	65.4	0.042	0.051	0.893	64.7
SZCZM1342	9.445	0.991	0.979	26.9	14.787	4.09e⁻⁴	0.964	28.2	0.094	0.178	0.969	29.6
SZCZP1809	8.458	0.987	0.989	24.1	12.283	7.74e⁻⁴	0.973	28.9	0.130	0.237	0.976	32.3

Isotherm	Langmuir				Freundlich				Sips
Isotherm	Q⁰_max, mg g⁻¹	K_L, L mg⁻¹	R²	Δq, %	K_F, (mg g⁻¹) (mg L⁻¹)⁻ⁿ	n	R²	Δq, %	q_m, mg g⁻¹	K_S, [(mg L⁻¹)^−1/n]	n	R²	Δq, %
SZCZCH193	6.85	0.31	0.965	11.9	2.37	0.27	0.953	19.6	8.39	0.16	0.65	0.992	7.2
SZCZM1342	16.18	1.35	0.959	48.9	1.88	1.10	0.965	36.3	19.02	0.26	2.26	0.998	6.5
SZCZP1809	27.09	0.24	0.879	> 100	4.94	0.67	0.820	> 100	15.17	0.75	2.87	0.999	20.9

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