## 1 Introduction  
The building sector is critical in the effort to move towards carbon neutrality in France. In 2019, it was responsible for 20% of greenhouse gas emissions and accounted for 46% of all energy consumption. This consumption level grew continuously between 1990 and 2001, the year when it reached its peak. In 2018, 82% of CO\({}_{2}\) emissions in the residential sector were generated by the heating of buildings [1]. In the current context of energy transition and the fight against global warming, the building sector is indeed a priority with great potential for improvement. Major renovations are necessary to reduce the energy and environmental impact of built structures and comply with the requirements for an energy transition. It has thus become necessary to design tools and materials to enhance not only energy performance but also the building environment and life cycle, while preserving the health and well-being of its occupants. This study is focused on the energy storage in a coating, by using phase change materials (PCMs) to reduce energy consumption in buildings. These PCMs are materials that can transition between solid and liquid phases, reversibly, and exchange energy with their environment. They melt when reaching the corresponding melting temperature, in absorbing heat and releasing it later once the temperature has dropped and then solidifying. These materials have a high latent energy per unit volume. If this amount of energy is high, the heat storage/releaseproperties will be more attractive. PCM stores more energy than a conventional building material, such as brick, with an equal mass. Thus, latent heat and sensible heat together constitute the total amount of energy the PCM can store. Several types of PCM exist, including hydrated salts, paraffin, fatty acids, and eutects of organic and non-organic compounds. [PERSON] [2] established a classification (Figure 1) of a large number of PCMs potentially used for energy storage, grouped into four families: paraffin, organic, inorganic, and eutectic. This author also detailed the main selection criteria for these materials (Table 1). However, PCMs must satisfy several technical requirements, such as chemical stability and toxicity [3; 4], to ensure safe use. Figure 1: _Cont._  
Figure 1: **(a)** Thermal properties of paraffin PCM; **(b)** thermal properties of organic PCM; **(c)** thermal properties of eutectic mixture; **(d)** thermal properties of inorganic PCM [2]. As detailed in Figure 1, the range of PCMs is quite wide, featuring various thermophysical properties and paving the way for many possible uses. Hence, energy storage technologies, thanks to the use of phase change materials (PCMs), are used in many fields. [PERSON] et al. [5] described the primary uses for these types of materials. Nasa [6] introduced certain paraffin-based PCMs (dodecane, hexadecane) in energy storage modules that served to control the temperature of the rover batteries used on Mars, by means of damping extreme temperature variations. [PERSON] et al. [7] also dealt with the application of PCMs (paraffin, salt, milk fat) for thermal control, but especially for cooling electronic packaging to keep the temperature below a safety limit (60 \({}^{\circ}\)C). [PERSON] et al. [8] used a PCM combined with graphene to reduce overheating in electric batteries; in this case, adding graphene improved the thermal conductivity of the PCM in order to enhance the thermal exchanges. Other authors, e.g., [PERSON] et al. [9], used an inorganic salt-based PCM and combined it with a conventional material, namely carbon fiber, to increase thermal conductivity and evaluate the thermal storage properties. It is also possible to produce solar energy storage with PCMs, which constitutes one of the main advantages of this type of material. In the literature, [PERSON] et al.