## Materials and Methods
### Modeling
#### Dynamic Runs Modeling  
The dynamic parameters were obtained by evaluation of the resulting S-shaped breakthrough curves. First of all, the length of the Mass Transfer Zone (MTZ), \(L_{z}\)--i.e., the zone of the packed column where the active anion exchange is supposed to happen under dynamic conditions (according to Michaels mathematical approach, m [55])--was estimated. Therefore, \(L_{z}\) can be computed from the following expression:  
\[L_{z}=L_{b}\ \frac{V_{t}-V_{b}}{FV_{t}-(1-F)\ V_{b}} \tag{6}\]  
where \(L_{b}\) is the bed length, \(V_{b}\) is the breakthrough volume, \(V_{t}\) is the volume of the eluting solution at the bed exhaustion and \(F\) is the symmetry index of the breakthrough curve, defined as:  
\[F\ =\ \frac{\int_{V_{b}}^{V_{t}}(C_{0}-C)dV}{C_{0}(V_{t}-V_{b})} \tag{7}\]  
Here, \(C_{0}\) and \(C\) are the initial and the actual concentrations of the ion entering the SMZ micelle, respectively. The integral at the numerator can be estimated from the breakthrough plot through the evaluation of the area delimited by the abscissa axis, the horizontal line denoting the value of the original ion concentration, the vertical line having equation \(V=V_{b}\) and the S-shaped curve. Given the uncertainty in evaluating the real values of \(V_{b}\) and \(V_{t}\), the breakthrough and exhaustion volumes have been estimated, according to a consolidate practice, at 0.05 \(C_{0}\) and 0.95 \(C_{0}\).  
The X-anion exchange capacity (X-AEC)--i.e., the exchange capacity of each sample under dynamic conditions (\(C_{t}\))--was estimated in a similar way as described above, according to the following equation:  
\[C_{t}=\frac{\int_{0}^{V_{t}}(C_{0}-C)dV}{m} \tag{8}\]  
where \(m\) is the mass of the exchanger. The Working Exchange Capacity (WEC or \(C_{w}\))--that is, the profitable ion exchange capacity under the assumption that the maximum allowable concentration of the ingoing ion in the effluent is that reached at the breakthrough point--was estimated according to the following equation:  
\[C_{w}=\frac{\int_{0}^{V_{b}}(C_{0}-C)dV}{m} \tag{9}\]  
Knowing \(C_{t}\), \(C_{w}\) and the total anion exchange capacity (AEC), the dynamic selectivity (S), defined as the ratio between the X-AEC and the total AEC, which appraises the tuff preference in dynamic conditions for the ingoing anion, and the efficiency (E), namely the ratio between WEC and total AEC, can be easily calculated:  
\[S=\frac{C_{t}}{AEC} \tag{10}\]  
\[E=\frac{C_{w}}{AEC} \tag{11}\]  
The breakthrough curves were also modeled by the Thomas equation [56], which is applicable to processes whose reaction kinetics are reversible and obey a second-order law and whose thermodynamics follow the Langmuir isotherm. The Thomas equation calculates the maximum solid phase concentration of the solute on the exchanger and the exchange rate constant for a continuous exchange process. The equation can be conveniently linearized as follows:  
\[ln\left(\frac{C_{0}}{C(t)}-1\right)=\frac{k_{T}q_{0}m}{Q}-\frac{k_{T}C_{0}}{Q }V(t) \tag{12}\]where \(k_{T}\) (L mg\({}^{-1}\) min\({}^{-1}\)) is the Thomas rate constant, \(q_{0}\) (mg g\({}^{-1}\)) is the equilibrium amount of As ions per gram of the exchanger (that coincides with the X-AEC of the exchanger), \(Q\) is the eluent flow rate (L min\({}^{-1}\)), _V(t)_ is the effluent volume (L) and m is the amount of exchanger in the column (g).