## 3 Results and Discussion
### Characterization of Permeate  
The permeate concentration was evaluated by a UV-VIS quantitative spectroscopic analysis. Figure 4 shows the concentrations of Reactive Black 5 in the permeates after different adsorption cycles. The reported data show that the C1, C2, C3, and C4 columns exceeded a concentration of 3.5 mg/L of Reactive Black 5 in the permeate after 38, 9, 6, and 1 cycles, respectively. This concentration coincided with the limit beyond which the permeate was no longer visually colorless. Column C5 is not shown in the graph because it returned a colored permeate in the first cycle, with a concentration of 7 mg/L, demonstrating the ineffectiveness of adsorption. The amounts of dye in the permeate and retentate dye were calculated and are reported in Table 4.  
The removal of dye was almost total until the achievement of chromatic change, after which the substance not adsorbed considerably increased. The adsorption capacity (\(q_{e}\), Equation (4)) was calculated as the ratio between the amount of permeate dye until  
\begin{table}
\begin{tabular}{c c c c c c}  
the color change and the amount of MWCNTs used in the column, using the following equation:  
\[q_{e}=\frac{m_{permate}}{m_{MWCNTs}}=\frac{\left(C_{i}-C_{f}\right)\times V}{m_{ MWCNTs}} \tag{4}\]  
where \(C_{i}\) is the concentration of mother liquor (mg/L), \(C_{f}\)is the final concentration of permeate (mg/L), and \(V\) is the volume of treated solution (L). Figure 5 reports the adsorption capacity as a function of number of values. The obtained exploitation values from the ratio (R) between retained substance until color change (mgRet) and the amount of MWCNTs (gMWCNTs) used in the column were calculated (Table 4). The column C1 ensured a better use of MWCNTs. The efficiency of removal of columns (RE) for each cycle is plotted in Figure 6. It was obtained using Equation (5):  
\[RE\ (\%)=\frac{C_{i}-C_{f}}{C_{i}}\times 100 \tag{5}\]  
where \(C_{i}\) and \(C_{f}\) are the initial and final concentrations, respectively. Figure 5: Adsorption capacity as a function of number of cycles. The data obtained allow us to say that during the adsorption process, two factors intervened simultaneously: the quantity of nanotubes used and the contact times. By increasing the thickness of the nanotubes inside the column, the solution found a greater resistance to its descent, which also led to an increase in contact times. Both the greater quantity of nanotubes and the longer contact times create the conditions for a greater adsorption of the column. For example, for the C1 column, which had a greater quantity of nanotubes and longer contact times, the result was greater adsorption. The adsorption was due to the great van der Waals forces between the dye and the carbon nanotubes. Permeate values were further investigated by means of total carbon (TOC), inorganic carbon (IC), and total organic carbon (TOC) analysis. In particular, the initial solution of the RB5 dye and the permeates of the columns at different numbers of cycles were subjected to analysis. Table 5 reports the values related to this analysis. Two important results can be noted. The first is that all of the adsorbent columns reported an excess of inorganic carbon (IC) compared to that obtained in the mother liquor of RB5. It also stabilized at low values after an initial high peak in the first filtration step. This result is probably related to a leaching effect of the MWCNTs. Initially, the TOC was partially decreased compared to the mother liquor of RB5. Then it increased as the permeate was close to the color-change state. The TOC variation, for permeate and mother liquor, was to assume a degradation of dye molecule inside MWCNT layer, where a chromophore group was adsorbed at least, as demonstrated by UV-VIS, while part of organic carbon (OC) could remain in the permeate passing through the MWCNT layer.