## 3 Results and Discussions
Alkoxy radicals (RO-) and hydroxyl radicals (-OH) generated during XLPE thermal deterioration react with alkyl radicals (R-) or hydrogen radicals (H-) to produce ROR or ROH [27]. As a result, C-O-C and -OH peaks appeared in the FT-IR analysis. It was necessary to convert the results obtained through the above FTIR analysis into quantitative values for deterioration. First, C=O and C-O-C functional groups, whose absorbance peaks increased with deterioration, were selected. These peaks were quantified by the following equations [28]:  
\[CI-1=\frac{Area\ under\ band\ 1500\ \sim\ 1850\ \mathrm{cm}^{-1}}{Area\ under\ band\ 1425\ \sim\ 1500\ \mathrm{cm}^{-1}} \tag{4}\]\[CI-2=\frac{Area\;under\;band\;1500\;\sim\;1850\;\mathrm{cm}^{-1}}{Area\;under\;band \;2500\;\sim\;3000\;\mathrm{cm}^{-1}} \tag{5}\]  
where _CI_ represents the carbonyl index and was calculated in two ways. The carbonyl peak area was calculated as the ratio of the methylene functional group peak area to the C-H stretching vibration peak area. In general, the carbonyl index is calculated using the ratio of the peak absorbance to the functional group [29; 30]. However, in this study, as mentioned in the FT-IR results, the peak absorbance inversion occurred due to the deterioration of the C=O separation. This made it difficult to calculate the carbonyl index from the peak absorbance; therefore, it was calculated as an area ratio. Figure 8 shows the carbonyl index-1 and -2 obtained by calculation, and _CI-1_ and _CI-2_ showed similar trends. There were almost no changes in _CI_ at 100 and 120 \({}^{\circ}\)C. However, the _CI_ of XLPE exposed to 140 and 160 \({}^{\circ}\)C increased with exposure time, and the value changed more rapidly as the temperature increased. _CI_ indicates an increase in the oxygen ratio in the XLPE material, which consisted of only carbon and hydrogen. An increase in the oxygen ratio can lead to polarity in the non-polar XLPE insulator (the main cause of a decrease in insulating performance). The DSC thermograms of XLPE are shown in Figures S1 (heating) and S2 (cooling), respectively, and the melting point (_Tm_) and crystallization temperature (_Tc_) trends are shown in Figure 9. The _Tm_ and _Tc_ of the unaged XLPE were 104.71 \({}^{\circ}\)C and 94.74 \({}^{\circ}\)C, respectively, and there was little change in the _Tm_ and _Tc_ when the temperature was 100 and 120 \({}^{\circ}\)C. However, when exposed to temperatures of 140 and 160 \({}^{\circ}\)C, _Tm_ and _Tc_ moved to a low temperature after 18 days. Additionally, the _Tm_ and _Tc_ peak intensities decreased. To quantify this DSC result, the degree of crystallinity was calculated using the following equation:  
\[x_{DSC}(\%)=\frac{\Delta H_{m}}{\Delta H_{o}}\times 100\% \tag{6}\]  
where \(x_{DSC}\) (%) is the degree of crystallinity calculated through DSC, \(\Delta H_{m}\) is the fusion enthalpy, and \(\Delta H_{o}\) is the theoretical melting enthalpy for the complete crystallinity PE, \(\Delta H_{o}\) = 287.3 J g\({}^{-1}\)[31]. Figure 8: Carbonyl index of different XLPE depending on aging time and temperature: (**a**) carbonyl index-1 and (**b**) carbonyl index-2. The lamellar thickness was calculated using the Thompson-Gibbs equation [32,33]:  
\[L=\frac{2\sigma_{e}T_{m}^{0}}{\left(T_{m}^{0}-T_{m}\right)\Delta H_{m}} \tag{7}\]  
where \(L\) is the lamellar thickness (nm), \(\sigma_{e}\) is the free surface energy, \(T_{m}^{0}\) is the equilibrium melting temperature, \(T_{m}^{0}=141.45\)\({}^{\circ}\)C, \(Tm\) is the melting point, and \(\Delta H_{m}\) is the fusion enthalpy. The \(x_{DSC}\) and \(L\) values are shown in Figure 10, and the XLPE properties due to degradation obtained through DSC are presented in Figure 4:0 In the case of unheated XLPE, the \(x_{DSC}\) was confirmed to be 30.01%. There was only a slight increase compared to the initial value (no significant change) when the temperature was 100 and 120 \({}^{\circ}\)C. However, in the case of XLPE exposed to 140 and 160 \({}^{\circ}\)C, \(x_{DSC}\) reduction proceeded rapidly.