## 3 Results and Discussion
### Characterization of the Phase Transition
We performed repeated temperature scans at different scan rates to evaluate whether and how the shape of the thermograms was affected by the thermal history of the sample and the scanning rate. During a scan of five consecutive heating-cooling cycles for the polymer pEFS8-26, we observed that \(T_{\text{onset}}\) and \(T_{\text{max}}\) decreased until reaching convergence after three cycles (Figure 5). This behavior, as well as the downshift of the heat capacity before the transition, concurred in indicating an overall increase in the hydrophobicity of the system [55]. In addition, the shape of the curve became more complex and irregular, and the presence of a shoulder immediately after the onset appeared more evident as the number of repeated cycles increased. A similar behavior was also found for the longer polymer chain, pEFS8-46 (Figure S2). The lack of full reversibility shown by the calorimetric measurements is similar to that observed in some PNIPAM-based polymers [13; 24] and seems in general to be a common feature in thermoresponsive polymers when they are investigated by calorimetric techniques. A deeper investigation was performed by repeated heating/cooling scans, increasing the final scan temperature by 2-3 \({}^{\circ}\)C for every two scans. We observed that the transition of pEFS8-26 was reversible up to 76 \({}^{\circ}\)C, which was the maximum reversibility temperature (\(T_{\text{rev}}\)). Small differences visible only at the onset temperature of the last two scans revealed the presence of kinetic phenomena (Figure 6a). The calorimetric findings were confirmed by turbidimetry measurements (Figure 6b), which highlighted the absence of hysteresis in heating-cooling cycles. On the other hand, the thermal profiles obtained for pEFS8-26 by performing the same procedure described above were different from each other at temperature above \(T_{\text{rev}}=78\)\({}^{\circ}\)C (Figure S3a). Consistently, turbidimetry measurements showed hysteresis in repeating heating-cooling cycles (Figure S3b). Overall, we can speculate that when the polymer aqueous solution is heated at \(T\leq T_{\rm rev}\) but above \(T_{\rm onset}\), the unimers in a more globular structure self-assemble into multichain aggregates that reversibly regenerate the original unimer conformation when cooling back below \(T_{\rm onset}\) (Figure 7 top). Differently, when the polymer aqueous solution is heated at \(T>T_{\rm rev}\) a more marked dehydration process occurs that possibly leads to conformational changes in the multichain aggregates in which stronger interactions among the perfluorinated main chains are favored in a sort of \"melted\" hydrophobic core. Such a conformation might therefore prevent the multichain aggregate from regenerating unimers in their original globular structure while promoting the formation of a more opened and extended shape (Figure 7 bottom). This would result in a major exposure of the perfluorinated main chains in contact with water and an increase in the hydrophobicity of the overall polymer system, which in turn causes a reduction in \(T_{\rm onset}\) and \(T_{\rm max}\), and a downshift of the heat capacity before the transition, as discussed above. Figure 5: Reversibility of the aggregation process for pEFS8-26 aqueous solutions (1 g/L), studied by nano-differential scanning calorimetry (n-DSC). The first three scans were carried out at 1 \({}^{\circ}\)C/min, and the last two at 0.5 \({}^{\circ}\)C/min. Figure 6: Reversibility of the aggregation process for pEFS8-26 aqueous solution studied by n-DSC (changing the final temperature by 3 \({}^{\circ}\)C every two heating scans) (**a**) and turbidity measurements (**b**).