## 3 Results and Discussion
### Optical Absorption Spectra
This means that PVP increased the concentration by up to one order of magnitude with respect to pure water. It is also remarkable that for CTAB the concentration increase with laser fluence was far weaker than for PVP and pure water. We speculate that CTAB is only effective in preventing agglomeration up to a certain concentration (i.e., there is a saturation of the stabilizing effect), and for this reason the agglomeration becomes dominant beyond 1 \(\times\) 10\({}^{11}\)-3 \(\times\) 10\({}^{11}\) particles/cm\({}^{3}\), preventing further increases of the concentration even if the ablation rate is raised. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Medium** & **Fluence (J/cm\({}^{2}\))** & **Diameter (nm)** & \
\begin{tabular}{c} **Standard** \\ **Deviation (nm)** \\ \end{tabular} &
\begin{tabular}{c} **Concentration** \\ **(Particles/cm\({}^{3}\))** \\ \end{tabular} \\ \hline \multirow{3}{*}{H\({}_{2}\)O} & 10.2 & \(40\pm 5\) & 14.8 & 2.3 \(\times\) 10\({}^{10}\) \\  & 19.1 & \(40\pm 5\) & 15.9 & 7.5 \(\times\) 10\({}^{10}\) \\  & 25.5 & \(40\pm 5\) & 16.5 & 2.2 \(\times\) 10\({}^{11}\) \\ \hline \multirow{3}{*}{H\({}_{2}\)O + CTAB} & 10.2 & \(34\pm 3\) & 14.5 & 8.6 \(\times\) 10\({}^{10}\) \\  & 19.1 & \(34\pm 3\) & 16.3 & 2.2 \(\times\) 10\({}^{11}\) \\  & 25.5 & \(34\pm 3\) & 16.8 & 2.3 \(\times\) 10\({}^{11}\) \\ \hline \multirow{3}{*}{H\({}_{2}\)O + PVP} & 10.2 & \(21\pm 2\) & 15.9 & 2.4 \(\times\) 10\({}^{11}\) \\  & 19.1 & \(21\pm 2\) & 16.5 & 1.0 \(\times\) 10\({}^{12}\) \\ \cline{1-1}  & 25.5 & \(21\pm 2\) & 18.5 & 1.4 \(\times\) 10\({}^{12}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Diameter \(\pm\) standard deviation, and concentration of Ag NPs obtained from the analysis of the TEM images and the fit of the optical spectra. Figure 4: (**a**) Diameter and standard deviation, shown as error bars, and (**b**) Concentration of Ag NPs by laser ablation at 800 nm as a function of solvent solution and laser fluence. On the other hand, we did not observe any effect of laser fluence on the NP size, which might indicate that the final size is determined by the dynamics of agglomeration and growth in the solution rather than by the ablation rate. Other authors [41] have obtained similar results using nanosecond laser pulses, reporting only a slight increase in Ag NP size as a function of laser fluence, from 8 to 13 nm for 40 and 70 mJ/pulse. In any case, this small growth within a broad size distribution is not enough to appreciably shift the position of the LSPR, as is shown in the present optical measurements and calculations. If we compare the present results with those reported by [PERSON] et al. [16] for pure water, the obtained size and size distribution is quite similar, about 40 nm for the mean diameter and 16 nm for the standard deviation. In any case, the concentration of the obtained colloids is more remarkable. The ablation conditions of [PERSON] et al. [16] were 30 min at 10 Hz (1.8 \(\times\) 10\({}^{4}\) laser pulses), which implies a colloidal solution with quite a low concentration, as can be noticed in their TEM images and also in the low absorbance that they report. With our experimental conditions, 10 min at 1 kHz (6 \(\times\) 10\({}^{5}\) laser pulses), we obtained a much higher concentration, and consequently, some agglomeration is unavoidable. In the present case, the use of stabilizers is--if not mandatory--at least highly recommended, and provides a great advantage with respect to the use of pure water. The effect of the surfactant for the ageing of the colloidal solution is depicted in Figure 5 for CTAB (the results for PVP are very similar). The use of CTAB [43] and PVP [17] has already been investigated in some previous works, but using nanosecond PLA instead of femtosecond PLA. We have observed some differences in the samples obtained in CTAB with respect to the ones obtained by [PERSON] et al. [39]. In that work, the LSPR exhibited a red-shift of around 30 nm with respect to pure water, which they explain as an effect of the formation of larger particles.