# Influence of Water Addition on the Latent Heat Degradation of Sodium Acetate Trihydrate
## 3 Aging Study of Sodium Acetate Trihydrate
### Study of the Raw Material (SAT60%)
This led to the assumption that the probability of a SAT's molecule to be separated (into water and anhydrous sodium acetate) was constant. This is characteristic of an exponential decrease fit. To find a trend of aging, the latent heat for non-singular data were fitted by an exponential decrease law (dashed curve), given in Equation (4). \[\frac{dL(x)}{dt}=-b\ L(x) \tag{4}\]  
where \(L(x)\) is the latent heat for any cycle \(x\). The crystallization temperatures are also plotted at the bottom (Figure 11b). Thus, the relation between singular crystallization temperatures (below the black dashed curve) and lower latent heat values on the next cycle (open symbol) would be highlighted. In addition to the 5 th cycle that was cooled more slowly (2.5 \({}^{\circ}\)C\(\cdot\)h\({}^{-1}\) instead of 20 \({}^{\circ}\)C\(\cdot\)h\({}^{-1}\)) and crystallized at a higher temperature (50 \({}^{\circ}\)C), several singular points (\(T_{C}<41.7\)\({}^{\circ}\)C) were observed. The gap between those temperatures and the mean one seems to increase throughout cycles. Indeed, it was low at the beginning, with a crystallization temperature of 38 \({}^{\circ}\)C (a supercooling degree \(\Delta T\approx 28\)\({}^{\circ}\)C) different from the mean value of 45 \({}^{\circ}\)C (\(\Delta T\approx 13\)\({}^{\circ}\)C). Then, an increase in the gap was found over the number of cycles as a crystallization temperature of 30 \({}^{\circ}\)C (\(\Delta T=28\)\({}^{\circ}\)C) is reached after the 15 th cycle and is minimal after the 34 th cycle (crystallization temperature of 20 \({}^{\circ}\)C (\(\Delta T\approx 38\)\({}^{\circ}\)C)). This increase of the gap directly impacts the latent heat and may be related to aging as the quantity of material presenting a stoichiometric concentration (\(w_{AS}=0.603\)) decreases over cycles. It is assumed that this reduction of volume would lead to the reduction of the number of potential sites for nucleation of the SAT and the rise of the supercooling degree. This was supported by the work of [PERSON] et al. [31], who noticed an increase of this supercooling degree throughout the aging cycle of the SAT. Without considering these singular crystallizations, the latent heat on the second cycle was about 240 \(\cdot\)g\({}^{-1}\), close to literature data [25; 32]. Then, the latent heat decreases and stabilizes around 213 \(\cdot\)g\({}^{-1}\) after 35 cycles, which represents a drop of about 10%. A comparison was done with the results from other studies, performed over more cycles. Figure 12 presents the evolution of latent heat throughout aging from [PERSON] et al. [10] and [PERSON] et al. [33], combined with the results obtained from SAT60%. The exponential decrease fits from the data of the different authors are represented by dashed curves. Figure 10: Probability distribution of crystallization temperatures for SAT60%. The sample tested here presents an initial latent heat around 240 J\(\cdot\)g\({}^{-1}\) that reaches approximately 213 J\(\cdot\)g\({}^{-1}\) (\(-11\%\)) after 35 cycles applied between 20 and 70 \({}^{\circ}\)C. In comparison, an analysis performed by [PERSON] et al. [8] (green curve) showed that the latent heat of the SAT technical-grade sample seemed to stabilize around 200 J\(\cdot\)g\({}^{-1}\) (\(-17.4\%\)) after 300 cycles applied between 40 and 70 \({}^{\circ}\)C. The results were comparable for [PERSON] et al. [10] (red curve) where a drop of the latent heat from 280 to 200 J\(\cdot\)g\({}^{-1}\) (\(-28.5\%\)) of a SAT technical grade  
Figure 11: Evolution of (**a**) the latent heat and (**b**) the supercooling degree over 35 cycles of a raw SAT sample (\(w_{AS}=0.603\)). Values for the 5 th and 6 th symbol (from different thermal history) are plotted as stars. The open symbols (following a low-temperature crystallization) will not be considered for exponential fit and aging analysis. \(T_{M}\) and \(T_{C}\) respectively represent melting and crystallization temperatures. Figure 12: Evolution of latent heat adapted from [PERSON] et al. [10] (in red), [PERSON] et al.