## Materials and Methods
### Testing of Stone Specimens  
#### 2.4.1 Streaming Current Measurements  
Streaming current measurements on untreated/treated lithotypes and glass slides were performed using the SURPASS Electrokinetic analyser (Anton Paar GmbH, Graz, Austria), with a measuring cell covering an area of 25 \(\times\) 5 mm. Then, 10-3 M KCl in ultrapure water (18.2 M\(\Omega\)-cm) was used as the electrolyte. In each measurement, four pressure ramps from 0-400 mbar were applied, and the apparent zeta (\(\zeta\)) potential was calculated from the slope of streaming current vs. pressure, according to the Smoluchowski Equation (1). Here, the apparent \(\zeta\) potential was considered since in tangential electrokinetic measurements performed on a porous substrate, the ionic conductivity within the porous structure and in the stagnant layer (shallows of the outer rough surface lying below the slip plane) contributes to the observed streaming current. While this contribution is difficult to evaluate by streaming potential measurements, it can be accounted for by performing streaming current measurements at different heights of the gap between the measuring cell surfaces [32].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Stone Type** & **WNC** & **ANC** \\ \hline Apuan marble & \textless{}0.01 & 0.5 \(\pm\) 0.2 \\ Balegem & 6 \(\pm\) 3 & 10 \(\pm\) 2 \\ Obernkirchen & 7 \(\pm\) 1 & 20 \(\pm\) 4 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Dry matter per unit area (mg/cm\({}^{2}\)) absorbed by the stone specimens treated with WNC and with ANC (each value is the average from three treated specimens).  
Unfortunately, the adjustable gap cell required for such a measurement is not suited for the analysis of large specimens such as the natural stone samples of the present study. Nevertheless, the apparent \(\zeta\) potential considered hereafter, though not accurate for describing the average surface charge density of such samples, is still a useful parameter to evaluate the extent of modifications induced by the application of a treatment modifying both the outer stone surface and, to some extent, the pore walls. The isoelectric point (IEP), i.e., the pH value at which \(\zeta=0\), was determined by performing a sequence of measurements at slightly different pH values by means of an automatic titrator. Treated lithotypes and glass slides were analysed 1 month after the application of the products in order to allow for the formation of a seemingly stable gel network.  
The shift of the isoelectric point relative to the untreated lithotype (\(\Delta\)IEP) is given in Equation (2):  
\[\Delta\text{IEP}=\frac{\text{IEP}_{\text{t}}-\text{IEP}_{\text{nt}}}{\text{IEP }_{\text{nt}}}, \tag{2}\]  
where \(\text{IEP}_{\text{t}}\) is the isoelectric point of the treated lithotype and \(\text{IEP}_{\text{nt}}\) that of the untreated lithotype.  
Then, in order to explore the possibility of using electrokinetic data for a quantitative estimation of the extent of surface modification produced by the two coatings, the shift of the isoelectric point was normalized according to Equation (3):  
\[\text{ISM}=\frac{\left|\text{IEP}_{\text{t}}-\text{IEP}_{\text{nt}}\right|}{ \left|\text{IEP}_{\text{s}}-\text{IEP}_{\text{nt}}\right|}, \tag{3}\]  
where ISM stands for index of surface modification, an empirical parameter proposed here as a means for evaluating the change in surface properties with respect to the untreated lithotype, and \(\text{IEP}_{\text{s}}\) is the isoelectric point of the coating applied on glass slides.