## Materials and Methods
### Sorption Experiments  
The standard solution (1000 mg\(\cdot\)L\({}^{-1}\)) of Pb\({}^{2+}\), Cu\({}^{2+}\), or Zn\({}^{2+}\) was diluted to the target concentration levels by deionized water as experimental working solutions.  
In the sorption kinetic experiments, 2.00 g PPG-nZVI beads were added into 400 mL of Pb\({}^{2+}\), Cu\({}^{2+}\) or Zn\({}^{2+}\) solutions. The supernatant was taken out at different shaking time intervals in order to analyze the concentration of heavy metal. To measure the sorption isotherms of each heavy metal ion by PPG-nZVI beads, 0.25 g PPG-nZVI beads were added to 50 mL of various of concentration (1-80 mg\(\cdot\)L\({}^{-1}\)) with the heavy metal working solution in a series of 50 mL centrifuge tubes. All tubes were shaken in a temperature-controlled shaker (150 r\(\cdot\)min\({}^{-1}\), 25 \({}^{\circ}\)C \(\pm\) 1) for 24 h which was long enough to reach equilibrium as tested by the kinetic study. In kinetic and isotherm study, the solution pH is 5.0.  
To study the influence of initial pH on the removal of Cu\({}^{2+}\), the initial pH of the solutions was adjusted to 3.0, 4.0, 5.0, and 5.5. To examine the effect of ionic strength on sorption, the concentration of Na\({}^{+}\) in 20 mg\(\cdot\)L\({}^{-1}\) Pb\({}^{2+}\), Cu\({}^{2+}\) or Zn\({}^{2+}\) solution was adjusted to 0.00 M, 0.01 M, 0.05 M, 0.10 M with sodium nitrate as background solution. The dosage of PPG-nZVI beads in the solution was 5.00 g\(\cdot\)L\({}^{-1}\). The initial Pb\({}^{2+}\), Cu\({}^{2+}\) or Zn\({}^{2+}\) concentration was 20.0 mg\(\cdot\)L\({}^{-1}\). After reaching equilibrium, the beads were separated from the aqueous phase. The concentration of heavy metal in the supernatant was analyzed by ICP-OES 710.  
The pseudo first order model and the pseudo second order model are used to fit the data of sorption kinetics. The models are presented using the following Equations (1) and (2):  
\[q_{\rm t}=\ q_{\rm e}\left(1-e^{-k_{\rm t}t}\right) \tag{1}\]  
\[q_{\rm t}=\frac{k_{2}q_{\rm e}^{2}t}{1+k_{2}q_{\rm e}t} \tag{2}\]  
where \(q_{\rm t}\) (mg\(\cdot\)g\({}^{-1}\)) and \(q_{\rm e}\) (mg\(\cdot\)g\({}^{-1}\)) are the amounts of the metals adsorbed on per unit of adsorbent at any time \(t\) (h) and equilibrium, respectively; \(k_{1}\) (h\({}^{-1}\)) and \(k_{2}\) (g\(\cdot\)mg\({}^{-1}\cdot\)h\({}^{-1}\)) are the constants of the kinetic model, respectively. The nonlinear forms of Langmuir model and Freundlich model are adopted to fit the sorption data. The models are expressed as Equations (3) and (4):  
\[q_{\rm e}=\ q_{\rm m}K_{\rm L}\frac{C_{\rm e}}{1+K_{\rm L}C_{\rm e}} \tag{3}\]  
\[q_{\rm e}=K_{\rm F}C_{\rm e}^{\rm n} \tag{4}\]  
where \(q_{\rm e}\) (mg\(\cdot\)g\({}^{-1}\)) is the amount of the adsorbate on the surface of the adsorbent at equilibrium; \(C_{\rm e}\) (mg\(\cdot\)L\({}^{-1}\)) is the equilibrium concentration of the adsorbate in solution; \(q_{m}\) (mg\(\cdot\)g\({}^{-1}\)) is the maximum sorption capacity generated from the Langmuir model; \(K_{\rm L}\) (L\(\cdot\)mg\({}^{-1}\)) is a constant for Langmuir model related to the energy of sorption and the affinity of the binding sites; while \(K_{\rm F}\) ((mg\(\cdot\)g\({}^{-1}\)) (L\(\cdot\)mg\({}^{-1}\))\({}^{n}\)) is the Freundlich constants related to sorption capacity; n is the empirical parameter varied with the degree of heterogeneity of adsorbing sites. Data analysis was carried out by Origin 8.0.