## 3 Results and Discussion
### Electrochemical Characterization  
Molecular/ion transport across nanoporous structures is the basis of drug delivery, chemical sensors, and nanofluidic applications, with the nanostructure/solute ratio being a critical point for  
Figure 4: Wavelength dependence of (**a**) refraction index and (**b**) extinction coefficient values for samples: NPAS-Sf (black dense line), NPAS-Ph (red dashed line), NPAS-And surface A (blue dashed-dotted line), and NPAS-And surface B (green dashed-dotted-dotted line). For comparison reasons the refraction index of pure Al\({}_{2}\)O\({}_{3}\) is indicated in (**a**) as a grey dense line. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & **\textless{}n\textgreater{}** & **\textless{}n\textgreater{}** & **\textless{}n\textgreater{}** \\ \hline  & (250–1700) nm & (250–00) nm & (800–1700) nm \\ NPAS-Sf & 1.54 \(\pm\) 0.06 & 1.55 \(\pm\) 0.04 & 1.53 \(\pm\) 0.06 \\ NPAS-Ph & 1.52 \(\pm\) 0.02 & 1.52 \(\pm\) 0.02 & 1.53 \(\pm\) 0.02 \\ NPAS-And (A) & 1.14 \(\pm\) 0.09 & 1.24 \(\pm\) 0.02 & 1.08 \(\pm\) 0.09 \\ NPAS-And (B) & 1.05\(\pm\) 0.05 & 1.11 \(\pm\) 0.02 & 1.06 \(\pm\) 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average values of the refraction index determined for the studied samples for the whole range of wavelength as well as for visible and near infrared optical regions. mass transport control [52; 53; 54]. However, in the case of ions or charged molecules transport, electrical interactions with the nanoporous structures can also play a relevant role, favoring the reduction/increase of co-ions/counter-ions, that is, ions/particles with a similar/opposite sign than that of the nanostructure fixed charge [20; 28; 55]. Effective fixed charge concentrations (\(\mathrm{X_{ef}}\)) and other characteristic diffusive transport parameters such as ion diffusion coefficients (\(\mathrm{D_{i}}\)) and transport numbers (\(\mathrm{t_{i}}\)), which represent the fraction of the total current associated to the movement of an ion (\(\mathrm{t_{i}}=\mathrm{I_{i}/I_{T}}\)), are usually determined by concentration potential (\(\mathrm{\Delta E}\)) experiments, measuring the electrical potential difference (\(\mathrm{\Delta E}\)) at both sides of the nanostructure when it is separating two solutions of the same electrolyte but different concentrations (\(\mathrm{c_{f}}\) and \(\mathrm{c_{v}}\)). The analysis of \(\mathrm{\Delta\Phi}\) values (\(\mathrm{\Delta\Phi}=\mathrm{\Delta E}-\mathrm{\Delta\Phi_{\mathrm{elec}}}\), as was previously indicated in the Section 2.4) was carried out assuming that \(\mathrm{\Delta\Phi}\) consists of the addition of several terms [56; 57]: (i) the electrical potential difference associated to the different mobility/transport number of solution ions into the nanopores (diffusion potential) and (ii) the interfacial potential at each solution/sample surface (Donnan potential), which is strongly dependent on sample fixed charge and could provoke almost the total exclusion of the ions with the same sign as the fixed charge when \(\mathrm{X_{ef}}\) is much higher than the external solution concentration (Donnan exclusion). The following expression relates \(\mathrm{\Delta\Phi}\) values and characteristic transport parameters [40]:  
\[\mathrm{\Delta\Phi}=-\frac{\mathrm{RT}}{w\mathrm{zF}}\left[U\ln\frac{\sqrt{4y_ {v}^{2}+1}\;+wU}{\sqrt{4y_{f}^{2}+1}\;+wU}-\ln\frac{cf}{cv}\frac{\sqrt{4y_{v} ^{2}+1}\;+w}{\sqrt{4y_{f}^{2}+1}\;+w}\right] \tag{4}\]  
where \(\mathrm{w}=(+1)\)/(\(-1\)) depends on the sample electrical character (positive/negative fixed charge), while the parameters \(\mathrm{U}\) and \(\mathrm{y_{i}}\) are related to the ions transport numbers, the effective fixed charge concentration, and the electrolyte concentration [40]. Data analysis was performed according to that already reported [26; 58]  
Figure 5 shows the variation of \(\mathrm{\Delta\Phi}\) values with NaCl concentration ratio (\(\mathrm{c_{v}/c_{c}=c_{v}/0.01}\)) for the three analyzed NPASs, and differences depending on the sample can be observed.