## 2 Results and Discussion
### Sorption Properties
#### 2.2.2 Uptake Kinetics  
Uptake kinetics can be controlled by different mechanisms: resistance to diffusion (bulk, film and/or intraparticle, RIDE, resistance to intraparticle diffusion equation) and the proper reaction rate (including the pseudo-first-order rate equation, PFORE, or pseudo-second-order rate equation, PSORE). Figure 3 shows the kinetic profiles (duplicate experiments) for the sorption of Sr(II) using AO-APEI sorbent at pH 6 (equilibrium pH 7.1). The equilibrium is reached within 90-120 min of contact. The kinetic profile is characterized by a first initial section with a steep linear slope: about 50% of total sorption occurs within the first 25 min of contact. The profiles are modeled using the PFORE and the RIDE (solid lines) (the PSORE fit is presented in Figure S7). Table 1 reports the parameters of these models (and the relevant determination coefficients). Best fits were obtained using the PFORE (highest determination coefficients and better approach of equilibrium sorption capacities). The apparent rate coefficient (k\({}_{1}\)) is close to \(3.35\times 10^{-2}\) min\({}^{-1}\). [PERSON] et al. (2009) reported better fits of kinetic profiles with the PSORE in the case of Cu(II) uptake by amidoxime-based sorbents. In their case, the value of k\({}_{1}\) was strongly affected by the mode of synthesis; for the most efficient sorbent, the values were comparable to the values found for AO-APEI. [PERSON] et al. (2009) also commented that PSORE was more efficient than PFORE for the modeling of kinetic curves for Cu(II) and Zn(II) removal using lignocellulosic support functionalized with amidoxime groups.  
Figure 2: Effect of pH on Sr(II) sorption capacity onto APEI and AO-APEI sorbents—(duplicate experiments; sorbent dosage, SD: 0.375 g L\({}^{-1}\); C\({}_{0}\): 29.7 mg Sr L\({}^{-1}\); temperature: 25 \(\pm\) 1 \({}^{\circ}\)C; agitation speed: 140 rpm; contact time: 48 h).  
Though the resistance to the intraparticle diffusion equation (RIDE, or Crank equation) gives little lower determination coefficients, the kinetic profile is relatively well fitted by the model (Figure 3b). The effective diffusion coefficient is in the range of \(6.7\)-\(7\times 10^{-9}\) m\({}^{2}\) min\({}^{-1}\). This is about one order of magnitude lower than the value reported for self-diffusion of Sr(II) in water (i.e., \(4.75\times 10^{-8}\) m\({}^{2}\) min\({}^{-1}\)) [71]. This means that resistance to intraparticle diffusion cannot be neglected in the control of mass transfer of Sr(II) into the sorbent; however, the textural analysis shows that AO-APEI is a porous material (see Section 2.1.2); this can explain the relatively high diffusion coefficient (only seven times lower than free diffusivity). For amidoxime-fibrous sorbent, [PERSON] et al. [62] reported diffusion coefficients close to \(4.5\times 10^{-8}\) m\({}^{2}\) min\({}^{-1}\) for U(VI) binding. For uranium recovery from seawater using amidoxime-based polymeric sorbents, [PERSON] et al. [72] found diffusivity coefficients close to \(1.05\times 10^{-14}\) m\({}^{2}\) min\({}^{-1}\). The formation of uranium tricarbonate anions hindered the diffusion of metal ions into the polymer compared to uranyl-spiked synthetic solutions (around \(6.6\times 10^{-9}\) m\({}^{2}\) min\({}^{-1}\), against \(4.67\times 10^{-9}\) m\({}^{2}\) min\({}^{-1}\) for the self-diffusivity of uranyl ions in water [62]). They showed that the limiting kinetic step was the decomplexation of [UO\({}_{2}\)(CO\({}_{3}\))\({}_{3}\)]\({}^{4-}\).