## Materials and Methods
### Preparation of Nanofluids Based on Titanium Dioxide TiO\({}_{2}\)  
Titanium dioxide TiO\({}_{2}\) nanoparticles belong to the group of nanoparticles which are insoluble in base liquids. Due to the large surface area and high surface activity, they also tend to aggregate to form larger agglomerates [32; 39]. Agglomeration of nanoparticles, in addition to the severity of sedimentation, may also reduce the thermal conductivity of nanofluids [68]. Therefore, as in the previous case, it is necessary to use a two-step method to prepare nanofluids based on titanium dioxide TiO\({}_{2}\). In addition, a surfactant (dispersant) is also used to reduce the repulsive forces between the nanoparticles and the base liquid [38; 69; 70]. This facilitates the formation of stable colloids, and also reduces the likelihood of the agglomeration of nanoparticles.  
In the process of producing nanofluids based on titanium dioxide TiO\({}_{2}\) nanoparticles, several different surfactants are used, such as hexadecyl trimethyl ammonium bromide [71], silane coupling agent [72], nonionic surfactants [73], and oleic acid [74]. In the present study, the low molecular weight surfactant Span(r) 20 was used to prepare the nanofluids with a titanium dioxide TiO\({}_{2}\) nanoparticles. This allows the creation of secondary forces (van der Waals forces, electrostatic, hydrogen bonds) between the applied nanoparticles and the dispersant [75]. The polar groups of the dispersant interact with the high-energy surface of the titanium dioxide nanoparticles, while the long hydrocarbon chains are soluble in electro-insulating liquids; this enables the adsorption and accumulation of the dispersant molecules at the oil-nanoparticles interface, which allow for obtaining a stable dispersion of the nanoparticle in base liquids [64; 76]. The base liquids doped with the surfactant were subjected to 3 h of sonication in an ultrasonic bath.  
Figure 3: UV-VIS spectra of dielectric liquids modified by fullerene C\({}_{60}\).  
Figure 2: Comparison of prepared samples of fullerene C\({}_{60}\)-based nanofluids with samples of base liquids; from the left: MO—mineral oil, MO + C\({}_{60}\)—mineral oil doped with fullerene C\({}_{60}\), SE—synthetic ester, SE + C\({}_{60}\)—synthetic ester doped with fullerene C\({}_{60}\), NE—natural ester, NE + C\({}_{60}\)—natural ester doped with fullerene C\({}_{60}\).  
In the next step, titanium dioxide TiO\({}_{2}\) nanoparticles were added to the prepared liquids (electro-insulating oils with surfactant). Bearing in mind that the potential of the applied nanoparticles can be released in a situation where they are evenly spread in the base liquids, the prepared nanofluids were subjected to sonication and homogenization. The sonication process was carried out for 5 h at a constant temperature of 60 \({}^{\circ}\)C. In turn, the homogenization process, similarly as in [77], was carried out for one hour (24 kHz and 400 W). After this time, stable colloidal solutions were obtained. Similarly to the nanofluids based on fullerene C\({}_{60}\), once the sonication process was completed, the prepared samples were allowed to stand for several hours, and degassed to remove air bubbles.  
The concentration of surfactant Span(r) 20 in the base liquids was 5.00 g\(\cdot\)L\({}^{-1}\). Having concentrations of surfactants which are too high may cause deterioration of the properties of the base liquids [75]. The concentration of titanium dioxide nanoparticles was 0.82 g\(\cdot\)L\({}^{-1}\). The selected concentrations correspond to the concentrations used to improve the dielectric properties of insulating electro-liquids [49; 73]. Figure 4 presents a comparison of prepared samples of nanofluids based on surfactant and TiO\({}_{2}\) nanoparticles with samples of base liquids. Similarly to the previous case, there was a noticeable change in the color of the insulating liquids as a result of doping with titanium dioxide nanoparticles.