## Materials and Methods
### Preparation of Nanofluids Based on Fullerene C\({}_{60}\)  
As is known from the literature, one of the main difficulties associated with the preparation of stable electro-insulating nanofluids is the fact that nanoparticles are hard-soluble compounds, or insoluble in base liquids [(33; 61)]. It is difficult to obtain a stable dispersion of nanoparticles in electro-insulating liquids. Therefore, in most cases, a two-step method is used to create nanoliquids [(32; 38)]. In the first stage of this method, the nanofiller is prepared in the form of a dry powder (through the use of chemical or physical methods). Then, in the second stage, the prepared nanofiller is dispersed in the base fluid (e.g., by using mechanical mixing, either ultrasonic or homogenization).  
The preparation of stable nanofluids based on mineral oil or esters and fullerene C\({}_{60}\) was carried out in accordance with the procedures presented in [(62; 63)]. The addition of fullerene C\({}_{60}\) to the base liquid results in the sedimentation and agglomeration of molecules [(32)]. This, in turn, may cause a reduction or deterioration of selected properties of nanofluids. In order to prevent these phenomena, it is necessary to use mechanical methods to obtain the true solutions [(38)]. Therefore, electro-insulating liquids after the addition of fullerene C\({}_{60}\) were mechanically mixed (for 72 h) and then, as shown by [PERSON] et al. [(47)], were placed in an ultrasonic bath. The sonication process was carried out for 5 h at a constant temperature of 60 \({}^{\circ}\)C [(63; 64)]. After the sonication process, the prepared samples were allowed to stand for several hours and degassed to remove air bubbles.  
The concentration of fullerene C\({}_{60}\) in the base liquids was 0.1 g\(\cdot\)L\({}^{-1}\), which corresponds to the concentrations used to improve the dielectric properties of electro-insulating liquids [(65; 66)]. Figure 2 presents a comparison of prepared samples based on fullerene C\({}_{60}\) with samples of base liquids. As can be seen, there is a noticeable change in the color of the electro-insulating liquids as a result of doping with fullerene C\({}_{60}\). Mineral oil and natural ester doped with fullerene C\({}_{60}\) are characterized by a yellow-brown color, while the synthetic ester is characterized by a violet color. The yellow-brown color is most probably associated with the effect of unsaturated bonding of liquid with fullerene C\({}_{60}\), as indicated by the presence of a peak at 433 nm in the UV/VIS spectrum of the analyzed samples (Figure 3). As reported in [(67)], a peak in the range of 430-450 nm indicates the addition of 1.2 double bonds to the fullerene cage. UV/VIS spectra were taken on a Jasco V-530 apparatus (Jasco Corporation, Tokyo, Japan). As a reference, pure electro-insulating liquids were used.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Electro-Insulating Liquid** & \multicolumn{2}{c}{**Level of Moisture**} & \multicolumn{2}{c}{**Acid Number**} & \multicolumn{2}{c}{**Surface Tension**} \\ \cline{2-5}  & **WCO [ppm]** & **RS\({}_{\text{30}}\)\({}^{\circ}\)C** & **[mgKOH/goil]** & **[mN/m]** \\ \hline Mineral Oil & 2 & 2.8\% & \textless{}0.01 & 49.0 \\ Synthetic Ester & 45 & 2.2\% & \textless{}0.03 & - \\ Natural Ester & 34 & 3.3\% & 0.02 & 25.0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Moisture levels and acid numbers of the electro-insulating liquids used.  
Figure 1: Chemical structure of surfactant Span® 20.