## 3 Results and Discussion
### Adsorption Isotherms of Biochar Samples  
The obtained equilibrium data were fitted with two parameter linearized forms of isotherms, including Langmuir (Equation (1)), Freundlich (Equation (2)), Dubinin-Radushkevich (D-R) (Equation (3)), and Temkin (Equation (4)) [43] isotherms. The Langmuir isotherm model assumes monolayer adsorption onto a limited number of active sites, each of which can accept only one adsorbate particle. This model also assumes energetic equivalence between active sites and no interactions between the adsorbate particles [18]. The Freundlich isotherm model is based on a multilayer, reversible, and non-ideal adsorption process, and there is no limit on the number of adsorbates that can be adsorbed [18]. The Freundlich isotherm model defines the heterogeneity of the surface as well as the exponential distribution of the active sites and their energies. The D-R isotherm model is used for expressing the mechanism of adsorption with the distribution of Gaussian energy onto the heterogeneous surface. Unlike the [PERSON] and Freundlich isotherm models, this is a semi-empirical equation in which the adsorption follows the pore-filling mechanism [43]. Finally, the Temkin model considers the interaction between the adsorbent and adsorbate, and assumes that the adsorption heat, as a function of the temperature of all \begin{table}
\begin{tabular}{c c c} \hline \hline
**Wave Number** & **Signal Assignment** & **Reference** \\ \hline
3400 & \(-\)OH stretching (water, hydrogen bonded hydroxyl); N–H & [36] \\
2920–2880 & Aliphatic \(-\)CH\({}_{2}\); asymmetric C–H stretching band; Aliphatic & [36; 37] \\
1617 & N–H bending & [38] \\
1558 & C=C of secondary aromatics amines & [37] \\
1521 & Amide N–H bending & [37] \\
1444–1414 & \(-\)CH\({}_{2}\); \(-\)CO\({}_{3}\)\({}^{2}\); aromatic C=C stretching; in-plane bending & \\  & of carbonyl (-COH); Symmetry C=O stretch & [16; 31; 37; 39] \\
1234 & C–O alcohol or carboxylic acid stretching & [38] \\
1103–1093 & C–O or C–O-C bonds stretching or bending & [40] \\
1034 & Symmetric stretching C–O bonds & [37] \\
873–853 & \(-\)CO\({}_{3}\)\({}^{2-}\); Si–H\({}_{2}\) or metallic oxides & [39; 40] \\
711 & \(-\)CO\({}_{3}\)\({}^{2-}\) & [39] \\
620–616 & FeSO\({}_{4}\) & [39] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Reflectance Fourier transform infrared (FTIR) spectrum signal assignments for study biochar samples BC300, BC450, and BC600. molecules existing in the layer, declines linearly rather than logarithmically due to the surface coverage increase [43]. The model equations are presented below:  
\[\frac{C_{e}}{q_{e}} = \frac{1}{k_{L}q_{m}}+\frac{C_{e}}{q_{m}} \tag{1}\] \[\log q_{e} = \log k_{F}+\frac{1}{n}\log C_{e}\] (2) \[\ln q_{e} = \ln q_{m}-k_{DR}\epsilon^{2}\] (3) \[q_{e} = \frac{RT}{b_{T}}\ Ln\ a_{T}+\frac{RT}{b_{T}}\ Ln\ C_{e} \tag{4}\]  
where \(C_{e}\) is the Cu\({}^{2+}\) concentration at reaction equilibrium (mg L\({}^{-1}\)), \(q_{e}\) is the amount (mg L\({}^{-1}\)) of Cu\({}^{2+}\) adsorbed by the BCs at the equilibrium time, \(q_{m}\) is the maximum adsorption capacity (mg g\({}^{-1}\)), and \(k_{L}\) (L mg\({}^{-1}\)) is the Langmuir constant of equilibrium (calculated from the graph of \(C_{e}\ q_{e}\)\({}^{-1}\) vs. \(C_{e}\)). With [PERSON]'s constant, it is possible to calculate the \(R_{L}\) equilibrium factor, which determines the type of adsorption (Equation (5)). \(K_{F}\) is the Freundlich constant of adsorption coefficient (L g\({}^{-1}\)) and \(n^{-1}\) (L mg\({}^{-1}\)) is a constant that defines the intensity of the adsorption on the surface heterogeneity.