## 3 Results and Discussion  
### Perlite Characterization and Perlite as a Lead Ion Sorbent  
Figure 1 shows the morphological structure of a perlite bead, together with its inner porosity. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Test** & **Flow Rate** & **Influent Conc. ** & **Bead Size** & **Bed Volume** & **Bed Amount** & **Q\({}_{\text{exp}}\)** & **BV** \\
**No. ** & **(L\(\cdot\)h\({}^{-1}\))** & **(mg\(\cdot\)L\({}^{-1}\))** & **(mm)** & **(cm\({}^{3}\))** & **(g)** & **(mg\(\cdot\)g\({}^{-1}\))** & **BV** \\ \hline
1 & 0.3 & 2 & 1–2 & 16 & 2 & 1.10 \(\pm\)  
Perlite is considered a mesoporous material (20-500 A pore diameter), with an average pore radius of 16.535 A, a BET total surface area of 1.664 m\({}^{2}\cdot\)g\({}^{-1}\), a total volume of the pores of 0.008 cm\({}^{3}\)g\({}^{-1}\), and a surface area of 1.010 m\({}^{2}\cdot\)g\({}^{-1}\). Figure 2 shows the breakthrough curves for experiments carried out at a 0.3 L-h\({}^{-1}\) flow-rate, with 2 mg\(\cdot\)L\({}^{-1}\) of lead ion concentration and a variable amount (2-4 g) and bed volume (16-30 cm\({}^{3}\)) of the sorbent. In these tests, as perlite dosage and volume increased, metal removal efficiency was higher, because a more effective diffusion of lead ions throughout the sorbent was obtained, together with breakpoints reached at increasing bed volumes. Overall retention capacities were experimentally determined at 1.1, 1.45, 1.7, and 2.0 mg/g\({}_{\text{sorbent}}\)\({}^{-1}\) and breakpoints were determined at 55, 80, 91, and 100 BV, respectively, for 2, 2.6, 3.2, and 4 g of perlite, as shown in Table 1.  
Figure 1: SEM images of the surface of a perlite bead (**top**) and of the inner perlite structure (**bottom**). From the reported microscopic observations and Brunauer-Emmett-Teller measurements (BET) measurements, metal retention by the sorbent was ascribed to the specific surface area and to the corresponding large sorbent pores exposed to the liquid-phase, allowing for free migration of the hydrated lead ions (4.01 A hydrated radius) to the functional groups of the silico-aluminate matrix. As previously observed [45], lead ions are mostly absorbed/adsorbed by ion exchange (65-70%)--especially with Na\({}^{+}\) ions, but also with Ca\({}^{2+}\) and K\({}^{+}\) ions--at the negative silicate functional groups present on the perlite surface. This is represented by the following reaction:  
\[\text{nPerlite-(C}^{\text{m+}})+\text{Pb}^{2+}\rightarrow\text{(Perlite)}_{ \text{n}}\text{-Pb}^{2+}+\text{n(C}^{\text{m+}}) \tag{2}\]  
Sorption may also be attributed, on a smaller scale, to Van der Waals forces at non-specific, functional groups. Figure 2B shows the kinetic study for lead ion retention on perlite, at different sorbent dosages. Time-dependent breakthrough curves showed a direct linear dependence of t\({}_{0.5}\) vs. g\({}_{\text{sorbent}}\), as demonstrated in Figure 2C. Figure 3A shows the breakthrough curves for experiments carried out at a 0.3 L\(\cdot\)h\({}^{-1}\) flow-rate, with 4 g of perlite and variable lead ion concentration (2-10 mg of Pb\({}^{+2}\) L\({}^{-1}\)). Figure 2: (**A**) Breakthrough curves for lead ion retention at different perlite dosages (2, 2.6, 3.2, and 4 g; 1–2 mm bead size range; 0.3 L\(\cdot\)h\({}^{-1}\) flow-rate; 2 mg of Pb\({}^{+2}\) L\({}^{-1}\); T = 298 K). (**B**) Time-dependent breakthrough curves. (**C**) Correlation of the half exchange time, t\({}_{0.5}\), vs. perlite dosage. In comparing the curves, it was observed that, as the initial metal concentration C\({}_{0}\) increased, an retention capacities also increased, together with anticipation of the breakthrough point (perlite exhaustion).