## 2 Materials and Methods  
For this study a methyl phenyl siloxane co-polymer, commercially known as Bluesil FLD 550 HT [31] (Bluestar silicones, France), was selected as a representative of the silicone-based oils category. Its main thermos physical properties are summarized in Table 1.  
The experimental procedure was the same as described in previous works [29; 30]; a batch lab-scale dedicated experimental set-up was designed and built for a better understanding of the thermal degradation processes involved in the aging of the oil. A schematic representation is reported in Figure 1.  
The oil samples (300 mL) were inserted into a stainless-steel container (AISI 304) under a nitrogen atmosphere. The temperature was set and controlled by a PID system, and each oil sample was kept under isothermal conditions for a certain time (3 h); then, the main decomposition products were analyzed. The condens  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Therophysical Characteristics** & \\ \hline Composition & Methyl Phenyl siloxane co-polymer \\ Color & colorless \\ Viscosity at 25 \({}^{\circ}\)C, mm\({}^{2}\)/s, approx & 125 \\ Specific gravity at 25 \({}^{\circ}\)C, approx & 1.065 \\ Flash point, \({}^{\circ}\)C, approx & 300 \\ Freezing point, \({}^{\circ}\)C & \(-\)50 \\ Refractive index at 25 \({}^{\circ}\)C, approx & 1.495 \\ Surface tension at 25 \({}^{\circ}\)C, mN/m, approx & 24.5 \\ Vapor pressure at 200 \({}^{\circ}\)C, mbar, approx & \(1.33\times 10^{-2}\) \\ Expansion coefficient between 25 \({}^{\circ}\)C and 100 \({}^{\circ}\)C, approx & \(7.5\times 10^{-4}\) \\ Specific heat between 40 \({}^{\circ}\)C and 200 \({}^{\circ}\)C/gK approx & 1.50 \\ Thermal conductivity, W/mK approx & 0.15 \\ Viscosity, mm\({}^{2}\)/s, approx: & \\ at 100 \({}^{\circ}\)C & 20 \\ at 35 \({}^{\circ}\)C & 84 \\ at 25 \({}^{\circ}\)C & 125 \\ at \(-\)30 \({}^{\circ}\)C & 22,000 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Thermophysical characteristics of Bluesil 550 HT [31].  
Figure 1: Schematic representation of the experimental set-up. In the picture, from the left: nitrogen tank, electrically heated reactor, condensation trap for the condensable products collection, silica trap and the Micro GC with flow controller.  
vapor fraction were collected and analyzed with a gas chromatograph coupled with mass spectrometry instrument, described below. The permanent gas volume fractions were measured by a gas chromatograph. More thermally stressed oil samples (3 h at 475 \({}^{\circ}\)C) were taken as references of \"aged material\" to be compared with fresh (unheated) samples; a different analytical technique, described in the following sections, was used in this study. A kinetics degradation model was developed to describe the oil's behavior in the tested temperature range. To estimate the degradation kinetics rate, some assumptions were necessary; in particular, hydrogen was assumed to be the main product at the investigated temperatures, and its formation was used as an indicator of oil degradation, considering only qualitatively other possible reactions, such as methane production. The back reaction was neglected, given the products were continuously removed by the nitrogen flow. Also, the oil's initial number of moles are considered to be practically unchanged due to their negligible degradation percentage. Considering the batch configuration and a first-order reaction, the Arrhenius constant can be obtained as follows:  
\[C_{t}=\frac{\left(C_{0}*V_{o}-C_{H_{2}}*V_{hs}\right)}{V_{o}} \tag{1}\]  
\[In^{C_{0}}/_{C_{t}}=k*t \tag{2}\]  
\[k=A*e-^{E_{g}/RT} \tag{3}\]  
where  
Co = initial terphenyl concentration [mol/L]  
Vo = oil volume [L]  
Ct = terphenyl concentration [mol/L]  
Vhs = head space volume [L]  
\(C_{\rm H2}\) = Hydrogen concentration [mol/L]  
K = Arrhenius constant  
t = time [min]  
T = temperature [K]  
A = pre-exponential factor  
Ea = activation energy [kJ/mol]  
R = 8.314 [J/mol K]