## 3 Results and Discussion
### Adsorption Kinetics  
Figure 4 reports that at the initial Hg(II) concentration of 1000 ppb, 100% breakthrough (BT) was not achievable for all of the studied sorbents after 60 min treatments. Low %BT values (<30%) for C@ Fe\({}_{3}\)O\({}_{4}\) and uncoated Fe\({}_{3}\)O\({}_{4}\) were obtained even after 60 min treatments. On the other hand, 90% BT (q\({}_{\rm{e}}\) = 90.03 mg g\({}^{-1}\)) for 500 Cys-C@ Fe\({}_{3}\)O\({}_{4}\) were obtained after treatments for 45 min and above, while about 40%BT (q\({}_{\rm{e}}\) = 42.0 mg g\({}^{-1}\)) was achieved after 5 min. At BT time of 60 min, the %BT follows the order of 500 Cys-C@Fe\({}_{3}\)O\({}_{4}\)\(>\) 1000 Cys-C@Fe\({}_{3}\)O\({}_{4}\)\(>\) 250 Cys-C@ Fe\({}_{3}\)O\({}_{4}\)\(>\) C@ Fe\({}_{3}\)O\({}_{4}\)\(>\) uncoated Fe\({}_{3}\)O\({}_{4}\), being consistent with the specific surface area, surface functional groups, and adsorption capacity relationship previously discussed. Notably, times to reach 10%BT, 50%BT, and 90%BT of the prepared magnetic sorbents, interpolated from Figure 4, are reported in Table S1. After 60 min of 500 Cys-C@ Fe\({}_{3}\)O\({}_{4}\) treatments, 50%BT and 90%BT were achievable, respectively, at pH = 2 and pH \(\geq\) 6 (Figure S2 and Table S2).  
Kinetic results for Hg(II) adsorption, measured using 0.01 mg L\({}^{-1}\) sorbent suspended in 1000 ppb Hg(II) aqueous solution at pH 6, are illustrated in Figure 5a. For all samples, high Hg adsorption rate was observed during the first 10 min and reached an equilibrium after 20 min. The greater adsorption efficiency of C@Fe\({}_{3}\)O\({}_{4}\) relative to uncoated magnetite is likely due to the presence of surface hydroxyl groups, and its higher surface area. For Cys-C@Fe\({}_{3}\)O\({}_{4}\) samples, which exhibit lower surface area than C@Fe\({}_{3}\)O\({}_{4}\), the relatively high adsorption capacity is related to the metal-chelating ability of the -NH\({}_{2}\) and -SH functional groups in the appended L-cysteine. Notably, the highest Hg uptake was 90 mg.g\({}^{-1}\) by 500 Cys-C@Fe\({}_{3}\)O\({}_{4}\). Further increases in cysteine content (1000 Cys-C@Fe\({}_{3}\)O\({}_{4}\)) resulted in lower Hg(II) removal efficiency, likely due to the deposition of bulk cysteine on the carbon shell (XRD result, Figure 3a) that could inhibit effective adsorption by internal pores. Mercury removal experiments were further conducted for longer periods (60 min) to ensure adsorption saturation. To study the adsorption mechanism, 500 Cys-C@Fe\({}_{3}\)O\({}_{4}\), which exhibits the highest level of Hg(II) uptake, was selected as representative of Cys-C@Fe\({}_{3}\)O\({}_{4}\), along with uncoated Fe\({}_{3}\)O\({}_{4}\) and C@Fe\({}_{3}\)O\({}_{4}\) for comparison. Pseudo-second-order kinetic models (Figure 5b) were then applied to probe the mechanism [33; 54]. The correlation coefficients for the pseudo-second-order kinetic model are very close to 1, and the calculated equilibrium adsorption capacities (\(q_{\rm{e,cal}}\)) derived from this model are also much closer to the experimentally determined adsorption capacities (\(q_{\rm{e,exp}}\)) than that derived using the pseudo first  
Figure 4: Hg(II) treatment time dependence of % Breakthrough (BT) at initial Hg(II) concentration of 1000 ppb and sorbent loading of 0.01 g L\({}^{-1}\). High reproducibility of the measurements is indicated by small standard deviations from five identical batch experiments.  
order kinetic model. These results also support the assumption that sorption should occur through chemical adsorption rather than mass transport [55].