## 2 Materials and Methods
### Experimental and Theoretical Validations
#### 2.5.2 Thermodynamic Modeling of the Solid-Liquid Equilibrium  
Most models aiming at modeling the solid-liquid equilibrium of organic compounds' binary systems are either limited to the depiction of simple eutectic systems or rely on experimental data to fit unknown parameters. A model was implemented using Matlab Software (MathWorks, Natick, MA, USA) for this study. It is a combination of the models described in Reference [18] accounting for the polymorphic behavior of fatty acids and in Reference [19] introducing means of modeling the effect of the peritectic transition on the liquidus line. When a pure component is cooled/heated, different solid-solid transitions may occur. Most models tend to neglect those transitions because of their weak enthalpy value. However, fatty acids show a strongly polymorphic behavior. This polymorphic behavior is highly influenced by the cooling/heating rate and the nature of the liquid mixture made of both components. The polymorphism of even saturated fatty acids was studied in Reference [20]. The authors showed that two main parameters can influence the materials behavior and the resulting properties: The polarity in solution of the multicomponent mixture and the crystal growth kinetics. It is therefore primordial to consider, for the material properties, the ones that match the experimental conditions. As the DSC analyses in Reference [15] and our experiment with the IRT method were performed at a 1 \({}^{\circ}\)C/min rate, a slow crystal growth rate is assumed. Additionally, as PA and SA both consist in long carbon chains with only one polar group at the end, the blend of both is considered to be weakly polar [21]. The polymorphic transitions temperatures and enthalpies considered for this study are given in Table 2. They were extracted from Reference [20] considering the assumptions previously stated. As most models rely on the assumption that both pure components are not miscible in the solid phase, the peritectic transition represents a major challenge in the modeling of solid-liquid equilibrium of complex organic mixtures. Therefore, the results may differ significantly depending on this assumption. To overcome this issue, the peritectic compound can be seen as a completely new compound obtained through a reaction of both pure components for a specific stoichiometry. This stoichiometry cannot be known prior to the establishment of the phase diagram. However, given the phase diagram plotted by the authors in Reference [15], a 0.4-0.6 molar ratio can be assumed for this binary system. Only one additional parameter is required to model the liquidus line with this assumption. This parameter is the equilibrium constant of the involved chemical reaction. It assumes that an actual reaction occurs, which is not the case for this system. The peritectic compound is merely a crystal composed of both pure components in a fixed stoichiometric. Therefore, the value computed for this parameter can be considered as an adjustable parameter rather than a meaningful physical value for this reaction. Its purpose is here to allow the best fit between the model and experimental data.