## 3 Results and Discussion
### PFG-NMR Investigation  
The proton transport properties and the molecular dynamics of water confined inside the hydrophilic clusters of the PEMs have been investigated by \({}^{1}\)H-NMR spectroscopy, and, in particular, the direct measurements of the water self-diffusion coefficients (D) and the longitudinal relaxation times (T\({}_{1}\)) [38]. The water self-diffusion coefficients (D) measured on completely swollen PEMs in the temperature range of 20-130 \({}^{\circ}\)C are shown in Figure 5. In the 20-60 \({}^{\circ}\)C temperature range, we can observe a similar behavior of D among the samples, where the few different values are due to the initial water contents in the membranes. However, above 60 \({}^{\circ}\)C, the diffusivity trend begins to diverge abruptly. In fact, pristine sPEEK shows a brusque decrease of D and at 130 \({}^{\circ}\)C the D value is about one order of magnitude lower than the initial ones at room temperature. On the other hand, the nanocomposite PEMs show only a slight decrease in diffusivity only above 100 \({}^{\circ}\)C or even invariability for the sample at 3 wt% of filler loading. It is worth pointing out that during these measurements, the relative humidity on the NMR tube is not controlled and no hydration system is provided, but the tube is simply sealed. Therefore, during heating, the water confined in the membranes can evaporate above 90-100 \({}^{\circ}\)C. The data clearly show that the pristine sPEEK membrane cannot retain water above 60-80 \({}^{\circ}\)C, while the PSLM nanomaterial is able to maintain a certain degree of hydration at a high temperature. Among the nanocomposite membranes, the sPEEK_LDH\({}_{3}\) sample displayed the best behavior, as the water diffusivity continues to grow slightly up to 130 \({}^{\circ}\)C. This result indicates that the dispersion of a correct amount of PSLM creates the right condition for the electrolyte membrane to be able to work at high temperatures and low humidity, addressing one of the crucial requirements for PEMCs. The analysis of spin-lattice relaxation times (T\({}_{1}\)) was able to shed more light on aspects of water distribution within the ionic clusters of PEMs. Compared to D, T\({}_{1}\) refers to more localized motions, including both translation and rotation on a time scale comparable to the reciprocal of the NMR angular frequency (few nanoseconds). Generally lower T\({}_{1}\) values suggest stronger electrostatic interactions, which inhibit the molecular rotational and translational motion. Figure 6 reports the temperature behavior of T\({}_{1}\) in the range 20-130 \({}^{\circ}\)C. We can observe a significant difference between the trend in the filler-free sample and the nanocomposite membranes. In fact, while in the three composite PEMs, T\({}_{1}\) slightly increases during the heating with a typical expected temperature behavior [39], where the pristine  
Figure 5: Self-diffusion coefficients (D) as a function of the temperature (from 20 \({}^{\circ}\)C to 130 \({}^{\circ}\)C) of the water confined in sPEEK-based membranes. sPEEK sample shows higher T\({}_{1}\) values at the beginning, which then fall rapidly and largely above 60 \({}^{\circ}\)C, meaning that a fundamental change at the molecular level is taking place in the hydrophilic clusters of the membrane. Actually, the water molecules in sPEEK pristine, having lower interactions, are more susceptible to evaporation, therefore, above 60 \({}^{\circ}\)C, the only water left in the membrane is that of the first hydration spheres, and therefore is strongly bound to the sulfonic groups of the polymer. Such water molecules suffer from much stronger electrostatic interactions, so that their rotational and/or translational motions are severely restricted, and T\({}_{1}\) goes down.