Table 1.

Adsorption isotherm parameters and statistical analysis for the adsorption of MB onto WNS.

Isotherm model	Linear equation	Parameters	Values
Langmuir	$\frac{1}{{\mathrm{q}}_{\mathrm{e}}}=\frac{1}{{\mathrm{q}}_{\mathrm{m}}\times \mathrm{b}}\times \frac{1}{{\mathrm{C}}_{\mathrm{e}}}+\frac{1}{{\mathrm{q}}_{\mathrm{m}}}$ Where b refers to Langmuir adsorption constant	b (L/mg) qm (mg/g) R2 p-value MSE SST SD	0.054 36.631 0.961 0.003 0.000 0.014 0.094
Freundlich	$\log {\mathrm{q}}_{\mathrm{e}}=\log \mathrm{K}+\frac{1}{\mathrm{n}}\log {\mathrm{C}}_{\mathrm{e}}$ Where K refers to Freundlich constant	K (L/mg)1/n n (g/L) R2 p-value MSE SST SD	2.762 1.560 0.941 0.006 0.003 0.197 0.277
D-R	$\ln {\mathrm{q}}_{\mathrm{e}}=\ln {\mathrm{q}}_{\mathrm{DR}}-{\mathrm{\beta }\mathrm{\epsilon }}^2$ Where qDR is D-R isotherm saturation capacity and β is D-R isotherm constant which gives mean free energy (E) per molecule of adsorbate when it is transferred from the bulk solution to the surface of the solid and given by Eq. (1). ε is a temperature dependent parameter and related as $\mathrm{\epsilon }=\mathrm{RT}\ln (1+\frac{1}{{\mathrm{C}}_{\mathrm{e}}})$	β (mol2J2) E (kJ/mol) R2 p-value MSE SST	5 × 10−9 10.00 0.947 0.005 0.018 1.045