## 3 Results and Discussion
### Competitive Adsorption of Four Metal Ions  
The results of the competitive adsorption of four metal ions by the GO/P(AA-co-AM) hydrogels under eight different competitive adsorption principles were investigated, as shown in Figure 9. To determine the strength of the competitive ability of the hydrogel adsorption for different metal ions, the affinity between metal ions and the GO/P(AA-co-AM) hydrogels was shown by the competitive partition coefficient \(K_{d}\) and the selection coefficient \(\alpha\). The equations used to determine the competitive partition coefficient \(K_{d}\) and the selection coefficient \(\alpha\) are expressed as follows:  
\[K_{d}=\left(Q_{i}/C_{01}+Q_{2}/C_{02}+\cdots+Q_{j}/C_{0j}\right) \tag{7}\]  
\[\alpha=K_{d}(T)/K_{d}(I) \tag{8}\]  
where \(K_{d}\) is the competitive partition coefficient, \(Q_{i}\) is the amount of component I adsorbed (mg:g\({}^{-1}\)), \(C_{0i}\) is the initial concentration of competing metal ions (mg:L\({}^{-1}\)), and \(\alpha\) is the selectivity coefficient. \(K_{d}\) (T) and \(K_{d}\) (I) are the \(K_{d}\) for strongly and weakly adsorbed ions, respectively. The equation provides the sum of the partition coefficients, \(K_{d}\), for all different adsorbents within the same system as 1. On this basis, the larger the value of \(K_{d}\), the more competitive the adsorbent is for the active site of the adsorbent within this system relative to other adsorbents, and the stronger the affinity of this adsorbent with the adsorbent than \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**adsorbent**} & \multicolumn{5}{c}{\(Q_{m}\)/mg.g\({}^{-1}\)} & \multirow{2}{*}{**Report**} \\ \cline{2-2} \cline{4-6}  & **Cu\({}^{2+}\)** & & **Pb\({}^{2+}\)** & **Zn\({}^{2+}\)** & **Cd\({}^{2+}\)** \\ \hline GO/P(AA-AM) & 787.4 & 990.09 & 763.36 & 729.93 & \\ P(AA-AM) & 185.73 & 587.99 & 208.42 & 402.86 & [30] \\ P(AA/AM) & 69.81 & - & - & - & [31] \\ P(AA/MMA) & 153.8 & 216.1 & - & - & [32] \\ ATP/P(AA/AM) & 156.3 & 84.03 & - & - & [33] \\ FA/P(AA/AM) & - & 103.8 & - & - & [34] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Maximum adsorption of heavy metal ions on the GO/P(AA-AM) hydrogels in comparison with other literature. Figure 8: (**a**) [PERSON] isotherm model and (**b**) Freundlich isotherm model of GO/P(AA-co-AM) adsorption of Cu(II), Pb(II), Zn(II), and Cd(II) ions (pH = 4, T = 25 \({}^{\circ}\)C, \(t\) = 60 min). other adsorbents. For the selection coefficient \(\alpha\), when the value of \(\alpha\) is larger, it means that for two different metal ions in the same adsorption system, the adsorbent is more selective for the strong adsorbent ions. The results of the competitive adsorption of the GO/P(AA-co-AM) hydrogels for the adsorption of four metal ions for eight different competitive adsorption principles are shown in Figure 9. The partition coefficients \(K_{d}\) and the selection coefficients \(\alpha\) for competitive adsorption are shown in Table 3. It can be seen from the figure that when the four metal ions are no longer present in the solution alone, the adsorption of the GO/P(AA-co-AM) hydrogel for all four metal ions decreases to varying degrees, and it can be seen that the most significant decrease in the adsorption of the hydrogel for the four metal ions is for Pb. Moreover, in the presence of other metal ions, the adsorption of the hydrogels for Pb decreases by about 50% compared with the adsorption of Pb by the hydrogel alone. The adsorption capacity of Pb decreased by about 50% from 950.4 mg\(\cdot\)g\({}^{-1}\) to about 480 mg\(\cdot\)g\({}^{-1}\). As shown in Table 3, the competitive nature of the Cu, Pb, and Cd metal ions is relatively similar, and the selection coefficients, \(\alpha\), for the three metal ions are all around 1 for the four different competitive adsorption principles. When the four metal ions are in the same system, the partition coefficients for the Cu, Pb, and Cd metal ions can be Cu \(>\) Cd \(>\) Pb.