## 3 Results and Discussion
### Sorption Properties
#### 3.2.4. Sorption Selectivity  
The selectivity of the sorbent is a key parameter in the design of new sorbents. To evaluate the preference of the sorbents for the target metals (i.e., Ce(III) and, more generally, REEs), the sorption properties of MC-UR and MC-UR/S were tested using equimolar multicomponent solutions, including Ca(II), Mg(II) (among the alkali-earth elements), Zn(II), Al(III), and Fe(III), as heavy metal ions (including trivalent cations), and Nd(III) as a competitor REE. Figure S14 shows the \(\log_{10}\) plot of the distribution coefficient vs. the equilibrium pH for the two functionalized sorbents. Firstly, we can observe that the distribution ratio is a little higher for the sulfonated sorbent. The bi-functionalization allows for the increase in the selectivity for the REEs (herein, Nd(III) and Ce(III)), especially at the highest pH values (at pH\({}_{\text{eq}}\): 3.7-4.4). In Figure 5, the selectivity coefficients \(\text{SC}_{\text{Ce/metal}}\) are compared for the different competitor metals for the two functionalized sorbents, while Figure S15 visualizes the plots for \(\text{SC}_{\text{Nd/metal}}\). The improvement in the selectivity by sulfonation is due to the proper effect of the sulfonate groups and the impact of the bi-functionality. The two REEs have comparable SC values, and neither of the two sorbents can be used to directly separate the two metals. The improvement in the selective separation by sulfonation (especially at the highest pH values) is less marked in the case of Fe(III). The selectivity coefficients for MC-UR are less influenced by the pH than those for MC-UR/S. Based on the \(\text{SC}_{\text{Ce/metal}}\) and \(\text{SC}_{\text{Nd/metal}}\), the preferential sorption follows the trends below:  
For MC-UR: Ce(III) \(>\) Nd(III) \(>\) Fe(III) \(>\) Al(III) \(>\) Zn(II) \(>\) Mg(II) \(>\) Ca(II)  
For MC-UR/S: Ce(III) \(>\) Nd(III) \(>\) Fe(III) \(>\) Zn(II) \(>\) Mg(II) \(>\) Al(III) \(>\) Ca(II). The sorption capacities are plotted vs. the Shannon ionic radius in Figure S16 at different pH values for both the MC-UR and MC-UR/S sorbents. Irregular (parabolic) trends appear in the acidic solutions. At pH 4.21-5.19 for MC-UR and at pH 3.89-4.75 for MC-UR/S, the sorption capacities linearly increase with the radius of the trivalent metal cations, while the opposite trend is observed for the divalent cations. Surprisingly, in the case of MC-UR/S at pH 3.21, all the sorption capacities follow a linear increasing trend with the Shannon ionic radius (without the breaking difference between the trivalent and divalent cations). Figure S17 explores another type of correlation plotting for the divalent and trivalent cations, the sorption capacities vs. the ionic index (i.e., \(Z^{2}/\tau\), where \(Z\) is the ionic charge of the metal ion and \(\tau\) is its ionic radius). The data were collected from the two sets of pH series, identified in Figure S12 (as linear trends). The two groups of metal ions show relatively good correlations with both MC-UR and MC-UR/S. The same test was performed by plotting the sorption capacities vs. the covalent index (i.e., \(X_{\text{m}}{}^{2}\) * \(\tau\), where \(X_{\text{m}}\) is the Pauling electronegativity, not shown). Herein, it was not possible to identify a clear correlation between the parameters. Apparently, the binding of the metal ions mainly involves ionic interactions rather than covalent bonds. It is noteworthy that cerium sulfate was used for the study of sorption using multicomponent solutions. The control of the pH with HCl and the co-existence of competitor metals, as chloride salts, contribute to maintain at least a fraction of the cerium as cerium chloride cations (i.e., CeCl\({}^{2+}\)) in complement to Ce(SO\({}_{4}\))\({}_{2}\)\({}^{-}\). The residual concentration of Ce(III) is close to 0.4 mmol Ce L\({}^{-1}\), with a sorption capacity close to 0.67 mmol Ce g\({}^{-1}\).