# Quantifying the Effect of Catalysts on the Lifetime of Transformer Oil
## 4 Results
### Changes in the IR Region of the Electromagnetic Spectrum
Nevertheless, three oil samples were analyzed for each level of thermal aging in this study; this procedure proved to be sufficient and exhibited the desired trends in absorbance at 3650 cm\({}^{-1}\), as shown in Figure 6.  
Figure 6: Evaluation of the FT-IR absorbance at 3650 cm\({}^{-1}\) for oil samples aged at constant temperatures for various aging times (**a**) without (C\(-\)) and (**b**) with catalysts (C+). As previously described, in the case of UV-Vis spectroscopy, experimentally observed trends were mathematically fitted, but in this case, it was more advantageous to use a simple quadratic function for this purpose. As shown in Figure 6a,b, the resulting R\({}^{2}\) values range from 0.989 to 0.994, which is sufficient for the indirect derivation of the endpoint criterion (see detailed discussion related to testing the significance of R\({}^{2}\) using values of the two-tailed test criterion, e.g., in [38]), as well as for quantifying the remaining lifetime of the tested oil using FT-IR. The same times were used to achieve the tan \(\delta\) criterion as those previously used in the case of UV-Vis spectroscopy. This procedure is outlined in Figure 7, and a summary of the fitting and calculated parameters for FT-IR is provided in Table 2. As can be observed from Table 2, the degree of reduction in the oil lifetime quantified by FT-IR is in the range 35 \(\pm\) 0.5% for each aging temperature used. From these results, it can be concluded with a high degree of certainty that the rate of reduction in the low-temperature antioxidant concentration is temperature independent within the studied temperature range. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Temperature** **(\({}^{\circ}\)C)**} & **Catalysts** & \multicolumn{2}{c}{**Fitting Parameters (\(y\) = \(ax^{2}\) + \(bx\))**} & **Endpoint** & **Time to** & **Reduction** \\  & **(Yes/No)** & \(a\) & \(b\) & **R\({}^{2}\)** & **Criterion** & **Criterion** & **in Lifetime** \\  & & & & **(a.u.)** & **(Hours)** & **(\%)** \\ \hline \multirow{2}{*}{110} & No & \(-8.71\times 10^{-8}\) & \(-1.25\times 10^{-5}\) & 0.989 & \multirow{2}{*}{0.763} & 2197 & \multirow{2}{*}{34.5} \\  & Yes & \(-2.14\times 10^{-8}\) & \(-1.98\times 10^{-5}\) & 0.990 & & & 1439 & \\ \hline \multirow{2}{*}{120} & No & \(-3.84\times 10^{-8}\) & \(-2.06\times 10^{-5}\) & 0.990 & \multirow{2}{*}{0.735} & 1177 & \multirow{2}{*}{35.3} \\  & Yes & \(-9.18\times 10^{-8}\) & \(-2.55\times 10^{-5}\) & 0.993 & & & 761 & \\ \hline \multirow{2}{*}{130} & No & \(-3.01\times 10^{-7}\) & \(-1.27\times 10^{-5}\) & 0.994 & \multirow{2}{*}{0.713} & 556 & \multirow{2}{*}{35.3} \\  & Yes & \(3.94\times 10^{-7}\) & \(-1.41\times 10^{-4}\) & 0.994 & & & 360 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: FT-IR—summary of the fitting and calculated parameters of the mineral oil aged with (C+) and without (C\(-\)) catalysts. Figure 7: Aging temperature of 130 \({}^{\circ}\)—an example of the indirect derivation of the endpoint criteria for FT-IR absorbance at 3650 cm\({}^{-1}\).