## 2 Calorimetric Analysis, Aging and Compatibility Studies on Industrial-Grade Fatty Acid Mixture
### Experimental Procedure  
Two measurement devices were used: the differential scanning calorimetry (DSC) technique and thermogravimetric (TD) analysis. The DSC technique is used to validate the basic parameters of the PCMs, namely, their melting temperature (\(T_{mp}\)) and enthalpy variation (\(L\)) during phase change. The melting point temperature is approximated by the onset technique if the PCM is pure, but if mixtures are analyzed, this onset refers only to the beginning of the transition. The latent heat is determined from the integration of the heat flow signal over the transition period [26]. Both these steps were undertaken using the Setaram DSC131 in 120 uL cells. A melting/crystallization cycle is carried out at a heating rate of 2 \({}^{\circ}\)C/min, limiting the cells' inner thermal gradients. The stability of the PCM over thermal cycles is then characterized using the same technique but on a different equipment (Perkin-Elmer Pyris Diamond), reducing the experiment time as it works with higher heating rates (20 \({}^{\circ}\)C/min), thanks to a small crucible (60 uL) and a power compensation system. Both measurements follow a similar temperature scan protocol, involving at least three melting/crystallization cycles around the melting temperature (+/-35 and 30 \({}^{\circ}\)C, respectively, for the parameters' validation and the stability study), each cycle being separated by an isothermal _plateau_ ensuring a complete phase change (5 min for the \begin{table}
\begin{tabular}{c c c} \hline
**Compound** & **Formula** & **Mass Percentage (\%)** \\ \hline Stearic acid & CH3(CH2)16 COOH & 50–55 \\ Palmitic acid & CH3(CH2)14 COOH & 42–50 \\ Myristic acid & CH3(CH2)12 COOH & 0–2 \\ Lauric acid & CH3(CH2)10 COOH & 0–1 \\ Others & & 0–1.5 \\ \hline \end{tabular}
\end{table} 
Table 1: Composition of the industrial grade fatty acid mixture. Setaram DSC131 and 1 min for the Perkin Elmer Pyris Diamond). The first thermal cycle melts the PCM and generates its homogeneous distribution at the bottom of the crucible to optimize its thermal contact with the walls. The second cycle, called the reference cycle, is used to measure the temperature and the change in enthalpy during the phase transition. Finally, the third cycle is used to check the thermo-physical properties measured during the second cycle. That third cycle is then compared to the 38 th and 75 th cycles in the case of the stability study. The cell and sample masses were weighted before and after the DSC measurement using a Mettler Toledo XP26 (uncertainty \(\pm\) 0.002 mg). Additionally, the two calorimeters were calibrated, for temperature and energy, using five standard materials whose properties are referenced in Table 2.  
Measurement uncertainties due to environmental conditions (temperature and humidity variations) and experimental conditions (related to the measuring devices during filling, packaging and weighting of the crucibles in the first instance, and then to the post-processing of the results in the second instance) were estimated via a repeatability study on a standard substance whose melting temperature is closest to our field of study, i.e., Naphthalene. Five strictly identical experiments were performed on each calorimeter to determine the standard deviation (\(\sigma\)) of the \(T_{mp}\) and \(L\) distribution. The uncertainty (\(\delta\)) was then provided by Student's Law (Equation (1)), which is particularly suitable when the number of experiments is small. \[\delta=St_{N-1,\gamma}.\frac{\sigma}{\sqrt{N}} \tag{1}\]  
\(St_{N-1,\gamma}\) is Student's number, which depends on the number of experiments and the level of confidence, \(\gamma\), desired (in our case \(N=5\) and \(\gamma\) = 99%, thus \(St_{4.99\%}=4.604\)). The application of this method to the Setaram DSC131 apparatus leads us to consider an uncertainty of \(\pm\)0.2 \({}^{\circ}\)C on the melting temperature and \(\pm\)4.9% on the latent heat.