## 1 Introduction  
Energy consumption is a real challenge nowadays, particularly in the building sector, representing a significant part of it [1]. That is why many studies have been interested in and are still interested in finding ways and solutions to save energy and reduce greenhouse gas emissions. In fact, solar energy is one of these solutions, but the problem of intermittency is imposed. In this regard, storing and using renewable energy become an urgent need in order to reduce energy consumption and then to improve indoor thermal comfort [1; 2; 3]. The heat storage is the key technology to streamline energy consumption and improve energy efficiency by reducing the gap between energy available and demand in buildings. There are different types of heat storage as sensitive, latent, thermochemical or chemical [1]. Therefore, phase change materials (PCM) have been advanced as one of the potential solutions to meet some of these expectations. Indeed, cementitious materials incorporating PCM, improve the thermal comfort of building, by increasing its inertia, thus avoiding sudden changes in the indoor temperature [4; 5; 6; 7; 8; 9; 10]. In the current market, there is a range of commercialized encapsulated phase change materials (solid-liquid) developed by leading companies such as BASF, Climator, Cristopia, Dupont de Nemours, Rubitherm, and Winco Technologies. All these technologies use encapsulated paraffin (micronal) as solid liquid phase change materials (SL-PCM). However, three significant drawbacks arise when utilizing SL-PCM. Firstly, the flammability of paraffin must be noticed. The associated risk is particularly unconvinient with fire safety requirements within buildings [11]. Secondly, because of a transition to a liquid state, such PCM require encapsulation to prevent against the leakage risk within the building material. The technologies for containment involve encapsulations, which can be intricate, costly, and energy-intensive. Thirdly, the presence of PCM in the cement matrix can cause sustainability problems such as the drop in their mechanical performance [2; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16] and the appearance of cracking [1; 3; 14; 17]. When PCM is added to the mix, it influences the mechanical and even thermal properties such as the thermal conductivity of concrete [16]. The decrease of compressive strength seems to be more pronounced than that of tensile strength [18]. The volume instability of these SL-PCM generated durability problems (cracking, etc.) constraining their use in the building sector despite their energy efficiency. To address these challenges, solid solid phase change material (SS-PCM) with crystalline to amorphous conversion while remaining at a solid state, have been developed [19; 20; 21; 22; 23]. Among these researchers, [PERSON] et al. [23] has been developing several SS-PCM including the innovative PUX1520 used in this work. This SS-MCP exhibits interesting and relevant physical and thermal properties (89 J.g\({}^{-1}\) at 22 \({}^{\circ}\)C). for applications in the building sector. The solid liquid phase change of SL-PCM consists in endothermic melting during the heat charging phase and exothermic crystallization during the heat discharging phase. Solid solid phase change of SS-PCM undergoes a microstructural phase change from crystalline to amorphous while remaining at a solid state. This is referred to as the charging process. Conversely, when the temperature decreases, the SS-PCM releases heat as it crystallizes again, undergoing the discharging process (reversible conversion). The SS-PCM, more stable than SL-PCM, should be more suitable for building applications (masonry coating, bricks, roof coating, covering panels, etc.). The innovative poly (ether urethane) based SS-PCM PUX1520 has interesting physical and thermal properties that are relevant for building applications [23; 24]. Its integration in plaster has been the subject of preliminary studies [23], which have highlighted the interest and advantages of this technology SS-PCM compared with SL-MCP.