## 3 Results and Discussion
### Kinetic and Release Models
Among them, the presence of \(\beta\)-Linalool (33.5%), \(\beta\)-Isosafrole (17.39%), eucalypt (15.6%), and methyleugenol (10.33%) was highlighted. According to the chemical structure of these molecules (Figure 6), the main interactions with functionalized samples (Figure 3) could be electrostatic interactions and Van der Waals forces. These compounds presented poor interaction with the oxidized surface of nPSi-Ox, which justifies the fast step-like release profile observed and denotes poor temporal regulation of the release with those structures. A similar behavior was observed for nPSi-\(\beta\)CD samples. However, the compatible hydrocarbonized surface of the \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{2}{c}{**Zero-Order**} & \multicolumn{2}{c}{**First-Order**} & \multicolumn{2}{c}{**Korsmeyer-Peppas**} & \multicolumn{2}{c}{**Higuchi**} & \multicolumn{2}{c}{**Hixson–Crowell**} \\ \cline{2-10}  & \(\text{R}^{2}_{\text{adj.}}\) & \(\text{K}_{\text{0}}\) & \(\text{R}^{2}_{\text{adj.}}\) & \(\text{K}_{\text{1}}\) & \(\text{R}^{2}_{\text{adj.}}\) & \(\text{K}_{\text{KP}}\) & \(n\) & \(\text{R}^{2}_{\text{adj.}}\) & \(\text{K}_{\text{H}}\) & \(\text{R}^{2}_{\text{adj.}}\) & \(\text{K}_{\text{HC}}\) \\ \hline nPSi-Ox & \(-2.1228\) & 33.01 & 0.9650 & 12.83 & 0.9329 & 90.66 & 0.050 & \(-0.4705\) & 65.08 & 0.4441 & 0.39 \\ nPSi-UAc & \(-0.7239\) & 30.72 & 0.9237 & 3.59 & 0.8699 & 75.77 & 0.173 & 0.3759 & 58.61 & 0.4859 & 0.37 \\ nPSi-APTS & \(-0.2184\) & 33.27 & 0.9875 & 3.11 & 0.8944 & 76.91 & 0.233 & 0.6330 & 62.12 & 0.7253 & 0.38 \\ nPSi-Chi & \(-2.4854\) & 28.87 & 0.7481 & 11.75 & 0.9156 & 82.10 & 0.016 & \(-0.7720\) & 57.75 & \(-0.7630\) & 0.37 \\ nPSi-BCD & \(-1.5574\) & 34.35 & 0.9897 & 9.07 & 0.9225 & 90.49 & 0.096 & \(-0.0869\) & 66.72 & \(-0.0515\) & 0.40 \\ \hline \hline \end{tabular}  
\(\text{R}^{2}_{\text{adj.}}=\) regression coefficient adjusted; \(K_{0}=\) Zero-order release rate constant (\(\text{h}^{-1}\)); \(K_{1}=\) First-order release rate constant (\(\text{h}^{-1}\)); \(K_{\text{KP}}=\) Korsmeyer–Peppas release rate constant (\(\text{h}^{-n}\)); \(n=\) drug release exponent; \(K_{\text{H}}=\) Higuchi rate constant (\(\text{h}^{-1/2}\)) and \(K_{\text{HC}}=\) cube root law release constant (\(\text{h}^{-1/3}\)).  
\end{table} 
Table 2: Essential oil kinetic release models using different functionalizates of nPSi. nPSi-UAc sample could interact more effectively via hydrogen bonds with these volatile compounds, thus controlling the kinetic release of the essential oil. Likewise, it is suggested that amino groups present on the nPSi-APTS surface could also interact electrostatically due to the amine groups of APTS to control the release profile of the essential oil. In the case of nPSi-Chi, which also presents amine groups, it is important to mention that this functionalization was weaker by adsorption and that APTS was covalently. This could also explain the higher variations in release profiles. Overall, this experimental strategy has the potential to control the volatility of _Laureliopsis philippiana_ essential oil on the road to develop long-term antibacterial applications.