## 3 Results and Discussion
### Release Study  
The results of the oxidized-quercetin-release study for all the systems are shown in Figure 11. The graph in Figure 10a shows how quercetin release varies in the SQ5 and SP(6-50)Q5 systems.  
Figure 10: \({}^{1}\)H-\({}^{29}\)Si CP-MAS NMR spectra of S (**a**); SP50 (**b**); and SP50Q20 (**c**).  
Figure 9: \({}^{1}\)H-\({}^{13}\)C CP-MAS NMR spectra of SP50Q5 (**a**); SP50Q10 (**b**); SP50Q15 (**c**); and SP50Q20 (**d**). The reported FWMH refers to the peak at \(\delta\) 69.9.  
When P is absent in the system, approximately 50% of the quercetin present is released after about 1 h. During the following hours, the release of quercetin increases until reaching, after about 6 h, an overall release of about 63%, which remains constant over time, up to the monitored 24 h. When P is added to the system, regardless of the amount of P added, the release always reaches lower percentages, and the trend appears slower and more controlled. Quercetin, thanks to the presence in its structure of -OH and C=O groups, is able to form both hydrophobic bonds with other querectein and hydrogen bonds with the -OH groups of the sol-gel matrix [59, 60, 61]. When the amount of quercetin in the system is low, the probability of quercetin-quercetin hydrophobic bonds decreases, so most of the interactions are hydrogen bonding with the SiO\({}_{2}\) network (Figure 11a). However, these interactions are weak and in solution, they tend to break down, thus leading to the release of most of the quercetin. When P is added to the system, the possible interactions that can occur increase, and P can interact with both the SiO\({}_{2}\) matrix and quercetin [38, 60]. In this type of system, Q could in any case bind to the SiO\({}_{2}\) matrix and to P, the latter being constituted of long chains that might entrap the quercetin, which would therefore no longer be released (Figure 11b). This hypothesis could explain why, at low quantities of quercetin, the system in which the polyethylene glycol is present favors slow and sustained release over time in comparison to the system without P.  
This reasoning also seems to be consistent with the SQ10 and SP(6-50)Q10 systems; however, the trend was not found in the SQ(15 and 20 wt%) and SP(6-50 wt%)Q(15 and 20 wt%) systems. In these cases, in fact, the release is lower when P is absent and higher when P is added. In this scenario, the hypothesis is that an increase in the amount of quercetin within the system enhances the likelihood of greater interaction between quercetin molecules through hydrophobic bonds. These quercetin clusters could therefore remain blocked in the SiO\({}_{2}\) matrix and consequently not be available for release in solution  
Figure 11: Release of quercetin in function of the P percentage and with (**a**) 5 wt% of Q, (**b**) 10 wt% of Q, (**c**) 15 wt% of Q, and (**d**) 20 wt% of Q.  
(Figure 11c). On the contrary, when P is added to the system, it may interact with the sol-gel network through its long chains, which could hamper the trapping, which in the absence of P, would lead to quercetin clusters inside the SiO\({}_{2}\) matrix. Consequently, quercetin would be linked in part with itself, in part with the network, and in part with P through hydrogen bonds (Figure 11d). All these hypotheses are depicted in Figure 12.