## 3 Results and Discussion
### DOM and HM Bonding Capability and Its Characteristics
#### 3.3.3 DOM-HM Binding Order  
Through two-dimensional correlation analysis of the FTIR spectra of different DOM derived from biochar/biochar + HA at different HM contents demonstrated the vibrational modes of the strongly correlated characteristic peaks and the dynamic order of structural adjustments, as shown in Figure 7A,B. The synchrotron plots for BC-DOM and BC + H-DOM during Mn and Cu titrations exhibited three and four autocorrelation peaks, respectively. The peaks common to both were situated at 1582/1586 cm\({}^{-1}\), 1386 cm\({}^{-1}\), and 1106 cm\({}^{-1}\), and these peaks are related to the asymmetric stretching vibration of COO\({}^{-}\), the bending (or deformation) vibration mode of -OH, and the stretching vibrations of the C-O bond in polysaccharides [61; 62; 63]. Notably, BC + H-DOM showed an additional peak in the range of 800-874 cm\({}^{-1}\), suggesting that the addition of HA affected the deformation of the aromatic C-H bond and thus increased the activity of DOM [47]. \begin{table}
\begin{tabular}{c c c c c} \hline  & & **Log K\({}_{\mathbf{M}}\)** & **R\({}^{\mathbf{2}}\)** & \(\mathbf{f}\) \\ \hline Mn & BC-C1 & 2.01 & 0.88 & 0.61 \\  & BC-C2 & 2.56 & 0.93 & 1.31 \\  & BC-C3 & 3.21 & 0.89 & 2.79 \\  & BC + H-C1 & 3.36 & 0.92 & 8.23 \\  & BC + H-C2 & 3.68 & 0.99 & 5.42 \\  & BC + H-C3 & 3.56 & 0.98 & 1.07 \\ \hline Cu & BC-C1 & 1.25 & 0.94 & 0.39 \\  & BC-C2 & 0.87 & 0.84 & 0.48 \\  & BC-C3 & 1.30 & 0.97 & 0.54 \\  & BC + H-C1 & 0.71 & 0.82 & 0.69 \\  & BC + H-C2 & 0.73 & 0.82 & 0.54 \\  & BC + H-C3 & 0.86 & 0.83 & 0.67 \\ \hline \end{tabular}
\end{table} 
Table 2: Binding parameters between Mn, Cu and BC-DOM and BC + H-DOM components calculated by Stern–Volmer model. Figure 7: _Cont._In the asynchronous plots of Mn, two negative correlation peaks (1582/1106 cm\({}^{-1}\) and 1386/1106 cm\({}^{-1}\)) and one positive correlation peak (1582/1386 cm\({}^{-1}\)) were identified. According to [PERSON]'s rule [64], the sequence of functional group binding to Mn in BC-DOM is 1106 cm\({}^{-1}\), 1582 cm\({}^{-1}\), and 1386 cm\({}^{-1}\). However, after the addition of HA, an additional peak emerged at 801 cm\({}^{-1}\), altering the peak sequence of the functional group of Mn bound to BC + H-DOM to 1582 cm\({}^{-1}\), 1386 cm\({}^{-1}\), 1106 cm\({}^{-1}\), and 801 cm\({}^{-1}\). Therefore, the binding order of BC-DOM with Mn is polysaccharides' C-O bonds-carboxyl groups-phenolic hydroxyl groups. After the addition of HA, the C-H stretching vibration in the aromatic compound altered the binding sequence of Mn to BC + H-DOM. Consequently, the functional groups of Mn bound to BC + H-DOM are, in order, carboxylate, phenolic hydroxyl, polysaccharide C-O bond, and the C-H bond in the aromatic compound. In the asynchronous plots of Cu, BC-DOM exhibited three negatively correlated peaks at 1586/1386 cm\({}^{-1}\), 1586/1106 cm\({}^{-1}\), and 1386/1106 cm\({}^{-1}\). According to the principles of spectral interpretation, the sequence of peaks representing the functional groups of Cu bound to BC-DOM is 1106 cm\({}^{-1}\), 1386 cm\({}^{-1}\), and 1586 cm\({}^{-1}\). However, after the addition of HA, the original three negative correlation peaks transformed into positive correlation peaks, and new negative correlation peaks emerged at 1586/874 cm\({}^{-1}\), 1386/874 cm\({}^{-1}\), and 1106/874 cm\({}^{-1}\). Consequently, the sequence of peaks associated with the functional groups bound to Cu in BC + H-DOM shifted to 874 cm\({}^{-1}\), followed by 1586 cm\({}^{-1}\), 1386 cm\({}^{-1}\), and finally 1106 cm\({}^{-1}\). Specifically, in BC-DOM, the functional groups bound to Cu followed the order of C-O bond, phenolic hydroxyl group, and carboxyl group within polysaccharides. In contrast, for BC + H-DOM, the order of functional groups bound to Cu was C-H bond, carboxyl group, phenolic hydroxyl group, and lastly, the C-O bond in polysaccharides. The results indicated that carboxyl, hydroxyl, and polysaccharide-CO were the primary functional groups present in the humic-like substances within BC-DOM.