## 3 Results
### Sorption Tests
#### 3.2.3 Uptake Kinetics  
Mono-component solutions: Figure 5 compares the kinetic profiles for the sorption of Ni(II), Zn(II) and Hg(II) using G@MChs. A contact time of 60 min is sufficient for reaching the equilibrium. Residual concentrations follow the expected trend in terms of preference: Hg(II) \(>\) Zn(II) \(>\) Ni(II). The initial slopes of the plots of relative concentrations are very close for Hg(II) and Zn(II), and larger than for Ni(II). [PERSON]'s rules also apply to kinetic behavior in terms of comparative reactivity. This is consistent with the current trends (although the study of the pH effect showed that, for Hg(II), the speciation effect occults the impact of HSAB concepts). The equilibrium time is relatively fast; however, taking into account the size of sorbent particles, one would expect the sorption to be faster. Different modes of resistance to mass transfer (including bulk diffusion, film, and intraparticle diffusions) may contribute to the control of uptake kinetics. In addition, the proper reaction rate may play a role in this control. By extrapolation to homogeneous reactions, the kinetic profiles can be modeled using the pseudo-first- and pseudo-second-order rate equations (summarized in Table S1, in addition to the Crank equation that can be used for approaching the resistance to intraparticle diffusion). In the case of heterogeneous systems, the rate coefficients obtained in the fitting of experimental profiles should be considered as apparent rate constants (which implicitly take into account the resistances to diffusion). Table 1 summarizes the fitted parameters for the different models and the three metal ions (together with the statistical criteria; i.e., R\({}^{2}\) and AIC). It is apparent that the kinetic profiles for Ni(II) and Zn(II) are preferentially fitted by the PFORE, while Hg(II) sorption better follows the PSORE. In Figure 5, the solid lines represent the fitting of experimental curves with the PFORE; the fittings with the PSORE and the RIDE are reported in Figures S6 and S7, respectively. The PSORE is frequently associated with chemisorption; however, [PERSON] [52] and [PERSON] et al. [53] pointed out the importance of the appropriate selection of experimental conditions for giving sense to this assertion. [PERSON] et al. [53] commented that the concentration and the sorbent dose must be selected to avoid the strong variation of the concentration of the adsorbate in the solution for correctly attributing the binding mechanism to chemisorption (with best PSORE fitting). Alternatively, the fitting of the kinetic profile with the PSORE only reflects the control of resistance to intraparticle diffusion. The values of the q\({}_{\text{eq,1}}\) (PFORE) are remarkably close to the experimental values of the sorption at equilibrium. The apparent rate coefficients (i.e., k\({}_{1}\)) vary in the range 0.05-0.09 min\({}^{-1}\), according the series: Zn(II) \(>\) Hg(II) \(>\) Ni(II). The application of the Crank equation (RIDE) shows lower quality for fitting the experimental profiles. However, it is possible to approach the order of magnitude of the apparent diffusion coefficients of target metal ions in G@MChs (i.e., \(\sim\)2-5 \(\times\) 10\({}^{-12}\) m\({}^{2}\) min\({}^{-1}\)), which are four order of magnitude lower than their molecular diffusivity in water (i.e., \(\sim\)4-5 \(\times\) 10\({}^{-8}\) m\({}^{2}\) min\({}^{-1}\)). The intraparticle diffusivity coefficients follow the trend: Zn(II) \(>\) Ni(II) \(>\) Hg(II), which is not directly correlated with the ionic size of hydrated species (Hg(II) \(>\) Zn(II) \(>\) Ni(II)). Again, the speciation of metal ions (especially for Hg(II)) may interfere with the effective size of diffusing species. The relative values of the intraparticle diffusion coefficients (compared with molecular diffusivity) mean that the contribution of resistance to intraparticle diffusion cannot be neglected.