## 2 Materials and Methods
### Characterization
#### 2.3.4 Evaluation of the Elastocaloric Effect
The characteristic time of temperature dampening, i.e., the time in which the temperature difference between the NR samples and the air drops, in absolute value, at a fraction equal to 1/e (\(\approx\)37\(\%\)) of the initial value, was calculated for both the stretching and retraction phases. This parameter is of fundamental importance since it provides information about the kinetics of the heat exchange process [32]. The thermal analysis adopted to determine \(\tau_{\text{c}}\), and to describe how the temperature of the NR sample evolved over time due to the convective heat transfer with the surrounding fluid, is described below. Assuming that the NR samples during the elastocaloric test were immersed in a fluid at constant temperature T\({}_{f}\), and on their surfaces touched by the fluid there was a uniform and constant convective heat transfer coefficient h (W/(m\({}^{2}\)K)), the temperature variation of the material, initially at a temperature T\({}_{0}\), was estimated with the temporal law reported in Equation (5) [32]:  
\[T(t)=T_{f}+\Big{(}T_{0}-T_{f}\Big{)}e^{-hA/\rho V_{\text{c}}\rho t}=T_{f}+\Big{(} T_{0}-T_{f}\Big{)}e^{-t/\tau_{\text{c}}} \tag{5}\]  
where A is the area of heat exchange (m\({}^{2}\)), T is the temperature of the sample assumed at time t, V is the volume of the material (m\({}^{3}\)), \(\rho\) is the density (g/m\({}^{3}\)) and c\({}_{\text{P}}\) is the specific heat capacity of the material (J/(g\(\cdot\)K)). The initial temperature of the sample (T\({}_{0}\)) refers to the temperature assumed immediately after the stretching/releasing phase (points 2 and 4 in Figure 1). Considering a negligible radiative heat transfer phenomena, the characteristic time of heat exchange was determined by fitting the experimental temperature variation curves, related to the stretching and retraction phase, by using Equation (5). Figure 2 shows an example of the fitting procedure. Figure 2: Example of the fitting procedure adopted to determine the characteristic time dampening. Once we had determined the characteristic time of temperature dampening, the heat transfer coefficient was evaluated by using a reverse procedure. From Equation (5), \(\tau_{c}\) could be expressed as  
\[\tau_{c}=\rho Vc_{p}/hA \tag{6}\]  
Consequently, as all the other parameters are known, the heat transfer coefficient (h) could be determined via Equation (7) as  
\[h=\rho Vc_{p}/A\tau_{c} \tag{7}\]  
and the heat extracted from the environment per unit volume of material was calculated via Equation (8) as  
\[Q_{ab}=\left(h*A*\int_{t1}^{t2}T(t)dt\right)/V \tag{8}\]  
where h is the heat transfer coefficient of natural rubber determined experimentally, as previously explained; A is the surface of the sample between the specimen grips; t1 and t2 define the time interval in which the heat absorption from the environment occurred (see Figure 3), while T(t) is the experimental temperature variation of the samples. Finally, the COP\({}_{\text{mat}}\) value was calculated as the ratio between the heat absorbed during the retraction phase (Q\({}_{\text{ab}}\)) and the mechanical work per unit volume of material (W) employed to deform the samples during the elastocaloric tests (integral of the stress-strain curves normalized by the volume of tested rubber), as reported in Equation (9),  
\[COP_{mat}=\frac{Q_{ab}}{W} \tag{9}\]  
The COP\({}_{\text{mat}}\) parameter is qualitative and was introduced solely to compare the performances of the produced samples and to identify the most promising formulation [19]. Once a prototype is developed, all energy consumption terms will be taken into account, as well as fluid temperature and humidity. Figure 3: Example of the integration procedure followed to determine the heat extracted from the environment during the retraction phase.