Table 3 Kinetic study model fitting parameters.

Pseudo first order

\({q}_{t}= {q}_{e} (1- {e}^{- {K}_{1}t}\))

q_e is the adsorption capacity at equilibrium, k₁ is the pseudo-first-order rate constant

K₁ (min⁻¹)

q_e (mg/g)

R²

Pseudo second order

\({q}_{t}= \frac{{{q}_{e}}^{2} {K}_{2} t}{1+ {q}_{e} {K}_{2} t}\)

k₂ is the pseudo-second-order rate constant

K₂ (g/(mg min))

q_e (mg/g)

R²

Mixed first and second order

\({q}_{t}= {q}_{e}\frac{1- {e}^{- K t}}{1- {f}_{2} {e}^{- K t}}\)

f₂ is the mixed 1 st, 2nd order coefficient, k is the adsorption rate constant

K (min⁻¹)

q_e (mg/g)

f₂ (g/(mg.min))

R²

Avrami model

\({q}_{t}= {q}_{e} \left(1-{\left[{e}^{- {K}_{av}t}\right]}^{{n}_{av}}\right)\)

k_av is the Avrami rate constant and n_av is the model's component

K_av (min⁻¹)

n_av (−)

q_e (mg/g)

R²

Intraparticle diffusion

\({q}_{t}= {K}_{ip} \sqrt{t}+ {C}_{ip}\)

C_ip is intraparticle diffusion constant and k_ip is a measure of diffusion coefficient

k_ip

C_ip

R²