## 3 Results and Discussion
### Electrokinetic Analysis of Treated Lithotypes
It is likely that such particles readily produce a monolayer on the negatively-charged stone surface (more so in the case of Obernkirchen stone, whose IEP is lower than that of the other two stones), which may prevent further absorption and penetration of the product if the stone porosity and pore size distribution are small enough to result in pore clogging, as seems to be the case for WNC on Apuan marble. Indeed, since the TiO\({}_{2}\) particle size in WNC is larger than the average pore size in Apuan marble (Tables 1 and 2), it is reasonable to assume that this component of the nanocomposite formulation does not penetrate into the pores and remains on the stone surface. Further to that, the hydrophization  
Figure 4: Correlation between dry matter (mg/cm\({}^{2}\)) and \(\Delta\)IEP (Equation (2)) for lithotypes after treatment with WNC/ANC. resulting from the incipient modification of the outer stone surface may counteract further absorption and dry matter deposition. Then, additional contributions to the penetration effectiveness may result from the different degree of condensation (see particle size in Table 2) and, albeit to a lower extent, the different viscosity of the matrix-forming alkylalkoxysilane sols. In order to attempt a quantitative estimation of the extent of surface modification produced by the two coatings, the index of surface modification (ISM) calculated from the isoelectric points of both stones and coatings (Equation (3)) was considered. In accordance with its definition, ISM is a dimensionless parameter that does not depend on the inherent isoelectric points of different coatings, thus making it possible to establish a comparison between them. The validity of this approach was assessed by considering possible correlations of ISM with the reduction of capillary water absorption and surface wettability of treated stones, which are both dependent on the extent of surface hydrophobization. The definition of ISM rests on the assumption that, since films on glass slides make up less heterogeneous surfaces compared to treated stones, their IEP values (IEP\({}_{\text{s}}\)) may be expected to approximate those of the corresponding products more closely than the values measured on treated stones (IEP\({}_{\text{t}}\)). Hence, it was assumed that \(\left|\right.\text{IEP}_{\text{s}}\)-IEP\({}_{\text{t}}\left|\right.>\left|\right.\text{IEP}_{\text{t}}\)-IEP\({}_{\text{t}}\left|\right.\) or, equivalently, \(0<\text{ISM}<1\), with zero indicating no modification with respect to the untreated stone and one representing the virtual limit condition where the treated stone is homogeneously covered by the coating and behaves in the same way as the product film on glass slides. The ISM values of ANC are higher than those of WNC (Table 7), yet while on Apuan marble, the difference is relevant, on Balegem and Obernkirchen stones, it is far less so. Moreover, both products display the lowest ISM values on Balegem stone and higher values on Obernkirchen, whereas in the case of Apuan marble, the trend is different: ANC exhibits a value comparable to that seen on Obernkirchen, while the value for WNC is significantly lower. The differences between the two products can be interpreted in the sense that ANC gives rise to a more homogeneous modification of stone surfaces compared to the other product. However, on Balegem and Obernkirchen stones, the difference is rather small and may well fall within the experimental error. The lowest ISM values found on Balegem may be ascribed to the higher nanoscale roughness of this stone (Table 1), which is likely to produce a less effective surface coverage. In apparent agreement with the ISM data, the results of water absorption (Table 8) and static contact angle (Table 9) measurements show that ANC is more effective than WNC, and particularly so in reducing water absorption, which is likely to be more suitable than the static contact angle to assess the effectiveness of treatments, indicating the penetration and coverage of the outermost layer of pore walls.