## 3 Results
### Adsorption Kinetics  
The rate and the characteristics of the adsorption of target analytes onto EgLiCl-mGO were investigated via pseudo-first-order and pseudo-second-order models. The samples of heavy metals (50 mL, 20 mg L\({}^{-1}\)) were prepared and EgLiCl-mGO (1.0 \(\times\) 10\({}^{-2}\) g L\({}^{-1}\)) was added. The adsorption of ions was followed up at different time points, ranging from 1 to 60 min at room temperature.  
The pseudo-first-order kinetic modeling is provided in the following equation:  
\[\ln(q_{e}-q_{t})=\ln q_{\text{max}}-k_{1}t \tag{9}\]  
\(q_{t}\) (mg g\({}^{-1}\)) and \(k_{1}\) (min\({}^{-1}\)) are the amounts of adsorbed ions onto EgLiCl-mGO at several times and the pseudo-first-order kinetic, respectively [42; 43; 44; 45]. Figure S7 shows the plot.  
The pseudo-second-order kinetic is plotted according to Equation (10).  
\[\frac{t}{q_{t}}=\frac{1}{k_{2}\times q_{cal}^{2}}+\frac{1}{q_{cal}}\times t \tag{10}\]  
where \(q_{t}\) (mg g\({}^{-1}\)) and \(k_{2}\) (g mg\({}^{-1}\) min\({}^{-1}\)) are the amount of adsorbed analyte onto the surface of solid adsorbent at various times and the rate constant of the pseudo-second-order kinetic, respectively [42; 43]. Figure S8 shows the plot.  
Figures S7 and S8 are presented in the Electronic Supplementary Materials (ESMs). The R\({}^{2}\) of the pseudo-first-order model was in the scope of 0.99 for both ions so the adsorption rate-controlling step was performed by occupying empty adsorption sites of EgLiCl-mGO by Pb(II) and Cd(II) (Table 7) [44; 45; 46].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Pb(II)**} & \multicolumn{2}{c}{**Cd(II)**} \\ \cline{2-5}  & **Parameters** & **R\({}^{2}\)** & **Parameters** & **R\({}^{2}\)** \\ \hline \multirow{2}{*}{[PERSON]} & \(q_{0}=75.18\) & 0.99 & \(q_{0}=50\) & \\  & \(K_{L}=2.83\) & & \(K_{L}=1.45\) & \\ \multirow{2}{*}{[PERSON]} & \(n=4.52\) & & \(n=2.48\) & \\  & \(K_{f}=45.36\) & & \(K_{f}=24.77\) & 0.99 \\ \multirow{2}{*}{[PERSON]} & \(B=233.31\) & & \(B=178.38\) & \\  & \(A_{T}=100.48\) & & \(A_{T}=7.02\) & 0.93 \\ \multirow{2}{*}{[PERSON]} & \(q_{m}=1.51\) & & \(q_{m}=25.1\) & \\  & \(K_{E}=727.18\) & & \(K_{E}=2.76\) & \\ \multirow{2}{*}{[PERSON]} & \(n=-4.52\) & & \(n=-2.4\) & \\  & \(K_{H}=31.6\times 106\) & & \(K_{H}=2.9\times 103\) & 0.97 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Adsorption isotherms for Pb(II) and Cd(II) onto EgLiCl-mGO.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Analy** & **Model** & **Parameters** & **Values** & **R\({}^{2}\)** \\ \hline \multirow{3}{*}{Pb(II)} & Pseudo first order & \(k_{1}\) (min\({}^{-1}\)) & 0.03 & \\  & & \(q_{e}\) (mg g\({}^{-1}\)) & 95.40 & \\ \multirow{3}{*}{Pb(II)} & Pseudo second order & \(k_{2}\) (g mg\({}^{-1}\) min\({}^{-1}\)) & \(4.04\times 10^{-4}\) & \\  & & \(q_{e}\) (mg g\({}^{-1}\)) & 111.11 & 0.95 \\ \hline \multirow{3}{*}{Cd(II)} & Pseudo first order & \(k_{1}\) (min\({}^{-1}\)) & 0.023 & \\  & & \(q_{e}\) (mg g\({}^{-1}\)) & 67.46 & \\ \multirow{3}{*}{Pb(II)} & Pseudo second order & \(k_{2}\) (g mg\({}^{-1}\) min\({}^{-1}\)) & \(1.7\times 10^{-3}\) & \\  & & \(q_{e}\) (mg g\({}^{-1}\)) & 88.49 & \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of kinetic models for Pb(II) and Cd(II) adsorption onto EgLiCl-mGO.