. 2022 Jul 13;14(14):2855. doi: 10.3390/polym14142855

Table 2.

Nonlinear equations of equilibrium isotherms.

Equilibrium Isotherm	Equation	Constants Significance ¹
Freundlich	$Q_{e} = K_{F} \cdot C_{e}^{1 / n}$	K_F is Freundlich constant, (mg/g)(L/mg)^1/n n is Freundlich constant, dimensionless
Temkin	$Q_{e} = \frac{R \cdot T}{b} \cdot \ln (K_{T} \cdot C_{e})$	R is gas constant, R = 8.314 J/(mol K) T is temperature, K K_T is Temkin constant, L/mg b is Temkin constant, J/mg
Hill	$Q_{e} = \frac{Q_{H} \cdot C_{e}^{n_{H}}}{K_{D} + C_{e}^{n_{H}}}$	Q_H is Hill maximum uptake, mg/g K_D is Hill constant, L/mg n_H is the cooperativity coefficient of the binding interaction, dimensionless
Redlich–Peterson	$Q_{e} = \frac{Q_{R} \cdot C_{e}}{1 + a_{R} \cdot C_{e}^{b_{R}}}$	K_R is Redlich–Peterson constant, L/g a_R is Redlich–Peterson constant, L/mg b_R is Redlich–Peterson exponent, dimensionless
Sips	$Q_{e} = \frac{Q_{S} \cdot {(K_{S} \cdot C_{e})}^{B_{S}}}{1 + {(K_{S} \cdot C_{e})}^{B_{S}}}$	Q_S is Sips maximum uptake, mg/g K_S is Sips constant, L/mg B_S is Sips exponent, dimensionless
Toth	$Q_{e} = \frac{Q_{T} \cdot C_{e}}{{(a_{T} + C_{e})}^{1 / n_{T}}}$	Q_T is Toth maximum uptake, mg/g a_T is Toth constant, L/mg n_T is Toth constant, dimensionless

¹ In all the equations, Q_e is the adsorbate concentration on the solid phase at equilibrium, mg/g and C_e is the adsorbate concentration on the fluid phase at equilibrium, mg/L.