## 3 Results and Discussions
### Metal Ion Extraction Performance in the Homologous Series of JNPs  
The metal ion extraction and recovery performance in the homologous series of JNPs, with the varying Janus lobe size was investigated for Cr(IV) and Cu(II). One way to indirectly prove the presence of bPEI on the P(3-TSPM) lobe is by increasing its surface area and observing the effect on the metal ion extraction capacity. In the homologous series of JNP-bPEI 2 mL, 3 mL, 4 mL, by increasing the TSPM/TESPN lobe size while the PS lobe remains unchanged, the surface area of the bPEI covered TSPM/TESPN lobe also increases, thus the extraction capacity of the JNPs should also increase. To quantitatively assess this, due to the fact that in the extraction/recovery experiments we have used the same mass of particles, see Table S2, we must be careful to consider the mass of a single particle also increases with an increase in the TSPM/TESPN lobe, which means that fewer nanoparticles will be present in a given mass of JNPs used for extraction. A normalization procedure was devised to account for this effect. Since the average volumes of the individual lobes \(V_{\text{PS}}\), \(V_{\text{TSPM}}\) and their average densities \(\rho_{\text{PS}}=1.03\) g/mL, \(\rho_{\text{TSPM}/\text{TESPN}}=1.07\) g/mL are known, the average mass of a single particle can be calculated according to the following equation:  
\[m_{\text{JNP}}=V_{\text{PS}}\times\rho_{\text{PS}}+V_{\text{TSPM}/\text{TESPN}} \times\rho_{\text{TSPM}/\text{TESPN}} \tag{3}\]  
From this, the approximate number of JNPs in a given dry mass of particles \(m_{\text{w}}\) can be calculated using the following equation:  
\[N_{\text{JNP}}=\frac{m_{\text{w}}}{m_{\text{JNP}}} \tag{4}\]  
To make the trends of \(q_{\text{e}}\) and \(q_{\text{r}}\) of the homologous series visible, the \(m_{\text{w}}\) values were normalized for an arbitrary particle number of \(10^{12}\) and by plugging in the obtained values in Equations (1) and (2) the normalized metal ion extraction \(q_{\text{Ne}}\) and recovery \(q_{\text{Nr}}\) efficiencies are obtained. The un-normalized and normalized values with Cr(VI) and Cu(II) are depicted in Figure S11 and Figure S12. Normalized values indicate a significant increase in the extraction and recovery capacities with increasing TSPM/TESPN lobe size in the  
Figure 4: Graph showing the metal ion extraction capacity \(q_{\text{e}}\) (solid bars) and the metal ion recovery capacity \(q_{\text{r}}\) (dotted bars). Error bars represent \(\pm\) 1 \(\sigma\). homologous series JNP-bPEI 2 mL, 3 mL and 4 mL. The extraction and recovery capacities of the tested homologous series are listed in Table S2. In comparison, [PERSON] et al. [16] reported \(q_{\text{e}}\)\(\approx\) 32 mg/g for both Cu(II) and Cr(VI) for their PEI-PS nanoparticles. This is a factor of 5.3 and 2.1 higher than the values found during this study for Cu(II) and Cr(VI), respectively. One possible explanation could be the smaller size of PEI-PS as compared to JNP-bPEI, which results in a higher surface area. Furthermore, PEI-PS is completely covered in bPEI, while only half of JNP-bPEI is covered. It is instructive to compare the maximum ion uptake obtained for the JNP-bPEI (where the bPEI is a multidentate ligand brush or corona), with the maximum ion load of other micro- and nanoparticles carrying other types of ligands, immobilized in different ways, capable of forming chemical or physical bonds with the metal ion. Among these, most noteworthy are ion imprinted polymer (IIP) micro- and nanoparticles (with ligands immobilized in the bulk of the polymer, capable of chemical bonding with the metal ion), core-shell micro- and nanoparticles whereas the shell is constituted of IIPs, micro- and nanoparticles carrying surface ligands, micro- and nanoparticles carrying anionic functional groups such as ion-exchangers, or agro-based biomasses (capable of interacting with metal ions via physical bonds), etc.