Table 1.

The models and statistical parameters used in this study 42,43.

Type of equation	Nonlinear form	Parameters
Isotherm models
Langmuir	$q_e=\frac{{Q_{m}K}_L{C}_e}{{1+K}_L{C}_e}$	Ce = adsorbate equilibrium concentration (mg/L) qe = adsorption capacity at equilibrium (mg/g) Qm = monolayer coverage capacity (mg/g) KL = Langmuir isotherm constant (L/mg)
Freundlich	$q_e=K_f{C}_e^{1/n}$	Kf = Freundlich isotherm constant(mg1−(1/n) L1/n g−1) n = adsorption intensity
Sips	${\mathrm{q}}_{\mathrm{e}}=\frac{{\mathrm{q}}_{{\mathrm{m}}_{\mathrm{s}}}{\mathrm{K}}_{\mathrm{s}}{\mathrm{C}}_{\mathrm{e}}^{{\mathrm{m}}_{\mathrm{s}}}}{1+{\mathrm{K}}_{\mathrm{s}}{\mathrm{C}}_{\mathrm{e}}^{{\mathrm{m}}_{\mathrm{s}}}}$	${\mathrm{q}}_{{\mathrm{m}}_{\mathrm{s}}}$= Sips maximum adsorption capacity (mg/g) KS = Sips equilibrium constant ${(\mathrm{L}/\mathrm{mg})}^{{\mathrm{m}}_{\mathrm{s}}}$ mS = Sips model exponent
Hill	${\mathrm{q}}_{\mathrm{e}}=\frac{{\mathrm{qHC}}_{\mathrm{e}}^{\mathit{nH}}}{{\mathrm{K}}_{\mathrm{D}}+{\mathrm{C}}_{\mathrm{e}}^{\mathit{nH}}}$	qH = Maximum uptake saturation (mg/L) ${\mathrm{C}}_{\mathrm{e}}^{\mathit{nH}}$, ${\mathrm{K}}_{\mathrm{D}}$= Hill constants
Redlich-Peterson	${\mathrm{q}}_{\mathrm{e}}=\frac{{\mathrm{K}}_{\mathrm{RP}}{\mathrm{C}}_{\mathrm{e}}}{1+{\mathrm{a}}_{\mathrm{RP}}{\mathrm{C}}_{\mathrm{e}}^{\mathrm{g}}}$	KRP = Redlich-Peterson isotherm constant(L/g) aRP = Redlich-Peterson model constant(mg/L)-g g = Redlich-Peterson model exponent
Khan	${\mathrm{q}}_{\mathrm{e}}=\frac{{\mathrm{q}}_{\mathrm{s}}{b}_k}{{(1+{\mathrm{b}}_{\mathrm{k}}{C}_e)}^{\mathit{ak}}}$	bK = is the Khan model constant aK = Khan model exponent
Kinetic models
Pseudo first-order	$\frac{{\mathrm{dq}}_t}{d_t}=k_1(q_e-q_t)$	qe = adsorption capacity at equilibrium (mg/g) qt = adsorption capacity at any time (mg/g) $k_1$= Rate constant min−1
Pseudo second-order	$\frac{{\mathrm{dq}}_t}{d_t}=k_2{(q_e-q_t)}^2$	$k_2$= Rate constant (g/(mg min))
Intraparticle diffusion kinetic	$q_t=K_t\times t^{0.5}+C_t$	$K_t$= Rate constant (mg/(g min))
Statistical parameter
Coefficient of determination (R2)	$R^2=1-\frac{{\sum }_{i=1}^n{(y_{\mathit{ip}}-y_i)}^2}{{\sum }_{i=1}^n{(y_{\mathit{ip}}-\overline{y})}^2}$	$y_{\mathit{ip}}$=The predicted value by the model yi = The observed value $\overline{y}$ =Mean of observed value $n_p$=The number of variables in the model
Adjusted R-square (R2adj)	$R_{\mathit{adj}}^2=1-(\frac{n-1}{1-\left(n_p,+,1\right)})(1-R^2)$
Sum of squares error (SSE)	$SSE={\sum }_{i=1}^n{(y_{\mathit{ip}}-y_i)}^2$