## 3 Results and Discussion
### Optical Properties  
The optical behaviour of nanodispersions is a key parameter to take into account for the proposed solar energy application. Therefore, this paragraph briefly summarizes the results of the comparative optical characterization of S- and P-GnP-based nanofluids, studied at both low- and high-intensity irradiation regimes. More details of these investigations can be found in Reference [21]. First, it is interesting to underline that some spectral differences exist among samples due to the different nanoadditive types. The shape of the UV plasmonic peak and of its tail appears different for the two dispersions, consistent with the dissimilar functionalization [21]. Both nanoadditives, even at the considered low concentrations, remarkably reduce the transmittance in relation to water in the whole investigated range, but P-GnP samples show a generalized higher extinction coefficient than S-GnP samples, resulting in a better solar absorber. As for the effect of concentration, it is worth mentioning that increasing the mass loading of nanoadditives causes the extinction coefficient to grow, although this trend is not exactly proportional to the mass ratios. The knowledge of the extinction coefficient \(\mu(\lambda)\) allows us to estimate the sunlight extinction fraction (\(EF\)), corresponding to the fraction of the incident sunlight \(I(\lambda)\)[57] that is absorbed by the liquid through a propagation path of length, \(x\), according to the following equation [58; 59]:  
\[EF(x)=1-\frac{\int_{\lambda_{min}}^{\lambda_{MAX}}I(\lambda)\cdot e^{-\mu( \lambda)x}d\lambda}{\int_{\lambda_{min}}^{\lambda_{MAX}}I(\lambda)d\lambda}, \tag{1}\]  
where \(\lambda_{MAX}\) and \(\lambda_{min}\) and are the maximum and minimum wavelength, 300 and 2500 nm, respectively. Sunlight results completely extinguished (\(EF=1\)) within the first 5 mm of the sample in case of the P-GnP nanofluid, while it takes about 25 mm for that of the S-GnP. As a term of comparison, pure water shows an EF value lower than 0.4 after a propagation path as long as 50 mm. Non-linear optical properties of nanofluids are also of interest, considering that the energy densities achievable in our experiments are compatible with solar concentration systems, allowing to evaluate possible further applications of these nanofluids in solar vapor generation and solar desalination. Therefore, the sample transmittance at high light input intensities was measured. Due to the characteristics of the setup, the experiments were possible only on the 0.005 wt% concentration. In fact, the samples featuring the highest investigated nanoadditive loading (0.05 wt%) turned out to prevent any transmission of the input laser beam in the 10-mm long optical cell. Figure 5 reports the results concerning the non-linear behavior of the two different kinds of nanofluids, for three considered wavelengths. The P-GnP samples often result in a considerably lower non-linear transmittance if compared with the corresponding S-GnP nanofluids, according to the comparison between linear extinction coefficients. The more pronounced non-linearity is always at 355 nm and the less pronounced is at 532 nm, with the 1064 nm showing an intermediate behavior. Interestingly, the relative wavelengths trend does not reflect the relative values of linear extinction coefficient, deserving further investigations. At higher input energies (not shown in Figure 5) the 1064 nm curves change the concavity, resulting in a non-monotonic behavior. This effect could be explained by a damage occurring in the nanostructures, as already hypothesized in other studies for different carbon derivatives [60].