## 2 Experimental Design
### Analytical Procedure and Quality Control  
There are various atomic spectrometry techniques, which include Flame Atomic Adsorption (AA), Graphite Furnace AA, and Inductively Coupled Plasma Mass Spectrometry (ICP-MS). In particular, the Inductively Coupled Plasma--Atomic Emission Spectroscopy (ICP-AES) technique permits the complete atomization of the elements in a sample. This feature minimizes the potential for chemical interferences. It is considered as a true multi-element technique with exceptional sample throughput, and with a very wide range of analytical signal intensity [47]. Therefore, the HMIs are analyzed in their aqueous phase by ICP-AES technology (Optima 7300 DV, Part No. N0770796, Serial No. 077C8071802, Firmware Version 1.0.1.0079; Perkin Elmer Inc.; Waltham, MA, USA); with corresponding WinLab32 Software (Version 4.0.0.0305). The analyte primary wavelengths of each HMI element targeted were selected as 327.393 for Cu, 238.204 for Fe, 231.604 for Ni, 220.353 for Pb, and 206.200 for Zn, respectively; on the basis that these wavelengths have the strongest emission and provide the best quantifiable detection limits (QDL). Analysis is conducted with a plasma setting in radial view (to concentrations of greater than 1 mg/L), with QDLs of 0.05 mg/mL for Cu, Fe, Ni, and Zn, and 0.10 mg/mL for Pb. The spectrometer settings involve auto sampling of 45 s normal time at a rate of 1.5 mL/min, and a processing setting of 3 to 5 points per peak with 2 point spectral corrections. The calibration curve is generated 'through zero' by applying a stock blank and a multi-element Quality Control Standard 4 with 1, 10, 50, 90, and 100 mg/L concentrations (as per Standard Methods Part 3000) [46]. In comparison to the 'linear calculated intercept' calibration method, only a 0.15 mg/L (or 0.66%) maximum discrepancy is observed among all average concentration values, demonstrating an accurate overall calibration. In addition, the median 50 mg/L calibration standard is applied as a check parameter, with the intent to ensure a higher accuracy of all experimental measurements. Triplicate readings and their mean concentrations in calibration units are generated in mg/L by the corresponding WinLab32 Software. The sorbed amount of HMI is calculated from the difference between the starting concentration and its concentration in the 0.45 \(\upmu\)m filtered samples' supernatant. During every ICP-AES analytical session, several quality control methods are applied, and evaluated by three check parameters to assess the calibration quality [48]. Firstly, the percent relative standard deviation (%RSD) reports an average of 0.433%, which is well within the <3% limit recommended. The triplicate concentration of the median standard has an average value of 49.26 mg/L, and is within 5% of the known value. Finally, the correlation coefficient of each HMI analyte primary wavelength reports an average of 0.999977, which is very close to unity. Therefore, the data is relatively accurate, highly reproducible, and the experimental replicates are reliable based on the calibration relationship established. The multi-component stock is created by diluting the respective HMI nitrate salts of three 1-L stock solutions, acidified to a pH of 2.0 \(\pm\) 0.1, and then re-combined. These 3 stocks (denoted as X, Y, Z) are diluted by one 50% step to be within the 0-100 mg/L calibration range, analyzing each separately and combined (denoted as M). The consistency in stock preparation is demonstrated in Table 2. The average diluted concentrations of the X, Y, and Z influent stocks for Cu\({}^{2+}\), Fe\({}^{3+}\), Ni\({}^{2+}\), Pb\({}^{2+}\), and Zn\({}^{2+}\) are 70.15, 39.25, 61.18, 216.02, and 66.54 mg/L, respectively. The diluted concentration of the M influent stock for Cu\({}^{2+}\), Fe\({}^{3+}\), Ni\({}^{2+}\), Pb\({}^{2+}\), and Zn\({}^{2+}\) are 70.22, 39.21, 60.48, 213.22, and 65.98 mg/L, respectively. A maximum difference of 2.80 mg/L, equivalent to 1.3%, is detected for the Pb\({}^{2+}\) stock.