## 4 Conclusions  
The analysis of optical and electrochemical measurements carried out with three nanoporous alumina structures (NPASs) with different average pore size, porosity, and symmetric/asymmetric structure (NPAS-Sf: 12 nm, 12%, symmetric; NPAS-Ph: 90 nm, 12%, symmetric; NPAS-And: 10 nm, 23% side (A) and 100 nm 30% size (B), asymmetric) allowed us to establish the effect of sample geometry on characteristic parameters such as the refraction index, extinction coefficient, ion transport number, and permselectivity, as well as interfacial effects, which are of interest in different nanostructure applications.  
In particular, the refraction index seems to depend on sample porosity in the whole range of wavelengths studied (250-1700 nm), but smaller pore size might control the extinction coefficient in the near infrared region.  
With respect to electrochemical characterization using NaCl solutions, pore size clearly controls both diffusive ionic (Cl\({}^{-}\) and Na\({}^{+}\)) transport through the NPASs and interfacial effects. Consequently, sample NPAS-Sf presents higher anionic permselectivity (Na\({}^{+}\) exclusion) due to its higher positive effective fixed charge and solution concentration-polarization effect. It also exhibits higher electrical resistance ascribed to its lower solution content due to its small pore size. These results prove that the optical and diffusive transport functional properties of NPASs can be controlled by tuning their porosity or pore size, respectively, which might be of significant interest for technological applications of these nanoporous structures.  
The following are available online at [[http://www.mdpi.com/2076-3417/10/14/4864/s1](http://www.mdpi.com/2076-3417/10/14/4864/s1)]([http://www.mdpi.com/2076-3417/10/14/4864/s1](http://www.mdpi.com/2076-3417/10/14/4864/s1)), Figure S1: Scheme of spectroscopy ellipsometry measurement for a homogeneous sample, Figure S2: Scheme of a) electrochemical test-cell and b) solid sample/electrolyte electrical distribution and interfacial effects, Figure S3: Analysis of the pore radii distribution for the studied samples, Figure S4: Time evolution of triatiated water activity in donor and receiver solutions for NPAS-Sf and NPAS-And.  
[PERSON] and [PERSON] designed and coordinated the experiments; [PERSON] and [PERSON] synthesized experimental NPAS and performed electron microscopy characterization of the samples; membrane potential and electrochemical impedance spectroscopy measurements and data analysis were performed by [PERSON]; [PERSON] carried out spectroscopic ellipsometry measurements; all authors have read and agreed to the published version of the manuscript. All authors have read and agreed to the published version of the manuscript.  
This work has been supported by MINECO and ISCIII under Research Projects No. MAT2016-76824-C3-3-R and FISS-19-DTS19/00088, respectively.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & **Rs/s (\(\Omega\))** & **Cs/s (F)** \\ \hline NPAS-Sf & 8840 & 9.4\(\times\) 10\({}^{-12}\) \\ NPAS-Ph & 7400 & 8.3\(\times\) 10\({}^{-12}\) \\ NPAS-And & 7800 & 7.9\(\times\) 10\({}^{-12}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Values determined for the electrical resistance and capacitance of the three 0.002 M NaCl solution/sample (s/s) systems.  
**Acknowledgments:** Scientific support from the SCT's of the University of Oviedo (Nanoporous Membranes Laboratory and Electronic Microscopy units) and the SCBI (Supercomputer and Bioinformatics Service) of Malaga University are acknowledged.  
**Conflicts of Interest:** The authors declare no conflict of interest.