## 3 Results and Discussion
### Electrokinetic Analysis of Treated Lithotypes
The difference between the two products is relevant in the case of Apuan marble and increasingly smaller for Balegem and Obernkirchen stones. Similarly, the difference between the products in the static contact angle with water of treated vs. untreated lithotypes (\(\Delta\theta\)) is only evident in the case of Apuan marble, where ANC imparts to the surface a higher hydrophobic character with respect to WNC, while it is totally negligible for the other two stones. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Stone Type**} & \multicolumn{2}{c}{**ISM**} \\ \cline{2-3}  & **WNC** & **ANC** \\ \hline Apuan marble & 0.71 \(\pm\) 0.08 & 0.91 \(\pm\) 0.01 \\ \hline Balegem & 0.62 \(\pm\) 0.09 & 0.68 \(\pm\) 0.07 \\ \hline Obernkirchen & 0.83 \(\pm\) 0.03 & 0.86 \(\pm\) 0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Index of surface modification (ISM) for the lithotypes treated with WNC or ANC. A correlation between ISM values for each coating-stone system and the corresponding IC\({}_{\rm rel}\) values can be made by inspection of Figure 5. In fact, for each lithotype, the lowest IC\({}_{\rm rel}\) value was obtained for the specimen treated with ANC, the formulation showing the highest ISM value. In particular, the large difference between the products in terms of IC\({}_{\rm rel}\) observed on Apuan marble corresponds to a comparatively large difference in terms of ISM. Consistent with the observations about IC\({}_{\rm rel}\), the trend of \(\Delta\theta\) values for each lithotype also corresponds rather well to that observed for ISM (Figure 6). In particular, for Apuan marble, the large difference in \(\Delta\theta\) between WNC and ANC reflects an equally large difference in ISM, while the limited to negligible variation observed for Balegem and Obernkirchen corresponds to a similarly small variation in \(\Delta\theta\). Finally, it can be observed that, on Apuan marble, both coatings produced an increase in static  
Figure 5: Correlation between the index of surface modification (ISM, Equation (3)) and IC\({}_{\rm rel}\) (see Section 2.4.2) for lithotypes after treatment with WNC/ANC. contact angle that was smaller than that observed on Balegem and Obernkirchen. This deviation may be tentatively ascribed to the much lower porosity of marble, leading to a rather effective coverage of the outer stone surface (and thus high ISM value), but a less effective hydrophobic modification for corresponding low surface energy coating material due to the lower surface roughness of stone and the resulting lower contribution to the measured contact angle by the Cassie-Baxter state [44; 45]. Thus, the empirical ISM parameter, which was anticipated to reflect the extent of surface modification, showed indeed a correlation with the reduction of water absorption and surface wettability of treated stones. In particular, on Balegem and Obernkirchen stones, where the two coatings provided similar results in terms of ISM, similar values of IC\({}_{\rm rel}\) and \(\Delta\theta\) were also observed, while their different interactions with water observed on Apuan marble were also accompanied by a greater difference in ISM. In this latter case, ANC was seen to produce a greater reduction in capillary water absorption and a greater increase in static contact angle as compared to the other product. Such a difference reflects, though not exclusively, those seen in the interaction of the products with the stone surface and in their penetration effectiveness, which were discussed earlier with reference to the respective amounts of absorbed dry matter. In particular, the low porosity and low pore diameter of marble, alongside the cationic surface charge (higher IEP with respect to ANC) and larger sized particles in the WNC formulation, result in poorer penetration of this product and are likely responsible for the less homogeneous stone surface modification and less effective hydrophobization achieved.