# Thermal Energy Storage Performance of Tetrabutylammonium Acrylate Hydrate as Phase Change Materials
## 3 Results and Discussion  
### The System without Any External Forces (Static System)  
Initially, we reported the thermographs of Tetrabutylammonium Acrylate (TBAAc) hydrate obtained by a differential scanning calorimeter (DSC). Figure 2 shows the thermographs, which were measured at \(w_{TBAAc}\) = 0.33 and 0.36. A single peak was observed, and the existence of ice was not identified at \(w_{TBAAc}\) = 0.33. As for the system without any external forces (static system), we performed thermal energy storage experiments. We measured \(T_{\text{in}}\), \(T_{\text{out}}\), and \(T_{\text{PCM}}\). Figure 3 shows the time evolution of each temperature. Time zero indicates the time at which the circulating water is started to flow inside the coil. As shown in Figure 3, \(T_{\text{PCM}}\) decreased until t = 1.5 h and increased from t = 1.5 to t = 4 h. When \(T_{\text{PCM}}\) is increasing, TBAAc hydrate formation would occur because the \(T_{\text{PCM}}\) was 10 K lower than its equilibrium temperature, 291.5 K [35]. After the hydrate formation, the heat generation from the hydrate formation occurred and exceeded the endothermic of the heat exchanger. This was why \(T_{\text{PCM}}\) rose from t = 1.5 to t = 4 h. \(T_{\text{PCM}}\) moderately decreased again at t = 4 h when \(T_{\text{PCM}}\) was 288 K. At this moment, the formed TBAAc hydrate gradually grew around the heat exchanger as shown in Figure 4d. This adhesion would be the thermal resistance between the heat exchanger and thermal energy storage medium much lower than before. Then, the hydrate formation rate decreased due to the increased thermal resistance, and \(T_{\text{PCM}}\) decreased because the endothermic of the heat exchanger exceeds the heat generation from hydrate formation. Figure 4a-d illustrates the optical observation of the time evolution of the hydrate formation. The hydrate was formed on the surface of the heat exchanger. Heat exchange occurs on the heat exchanger surface, which leads to hydrate formation occurring there. From t = 1.5 h to t = 2 h, the hydrate gradually grew and started covering the coil surface. The surface of the coil was fully covered by the hydrate around t = 4 h. After t = 7 h, optical changes could not be observed. In addition, we found that the TBAAc hydrate  
Figure 1: Schematic diagram of the apparatus. kept growing from the surface of the coil to the bulk of the solution. There was a 3 cm gap between the surface of the coil and the wall of the container. This discovery of the hydrate growth length can be a tip to design a static thermal energy storage system. Thermal energy storage rate, \(\dot{q}\), and density, \(\overline{q}\), were calculated by the formulas (1) and (2). What every character stands for is written in Table 2. On the right-hand side of (2), the thermal energy storage density due to sensible heat is subtracted from the thermal energy storage density, which is obtained by integrating the thermal energy storage rate. \[\dot{q} =\rho_{w}\dot{V}_{w}c_{w}(T_{out}-T_{in})/V_{PCM} \tag{1}\] \[\overline{q} =\sum_{t=0}^{t}\dot{q}dt-\rho_{PCM}c_{PCM}(T_{PCM,\;0}-T_{PCM}) \tag{2}\]  
Figure 3: Time evolutions of the temperature at inlet of the chiller (T\({}_{\rm in}\)), outlet (T\({}_{\rm out}\)) of the chiller and thermal energy storage medium (T\({}_{\rm PCM}\)) in the static system. The obtained thermal energy storage density represents the heat storage density due to heat of hydrate formation and decomposition. The density of the PCM is assumed to be 1.0 kg m\({}^{-3}\). The value of each parameter used in the calculation is shown in Table 2. The physical property of water was referred to REFPROP ver. 9.1 [36]. Figure 5a illustrates the time evolution of the thermal energy storage rate in the static system. Since \(\dot{q}\) is proportional to the gap between T\({}_{\text{in}}\) and T\({}_{\text{out}}\), \(\dot{q}\) varied the same way with T\({}_{\text{out}}\).