## 3 Results and Discussion
### Kinetic and Release Models  
Figure 5 shows the experimental release profiles of the essential oil obtained for each functionalization. The models were evaluated up to 4 h, the moment at which a constant cumulative release of essential oil into the solution was observed. In that sense, the controlled release reached a maximum at time of 0.5 h for nPSi-Chi (Figure 5D), 2 h for the cases of nPSi-Ox, nPSi-UAc and nPSi-\(\beta\)CD (Figure 5A,B,E, respectively), and 4 h for nPSi-APTS (Figure 5C). Variations in the release profiles were due to the volatile  
Figure 4: FT-IR spectra of the different functionalities of porous silicon nanostructures. chemical compounds from _L. philippiana_ essential oil, which easily evaporated at normal temperatures. Figure 5: Essential oil kinetic release profile with different functionalities of nanostructured porous silicon. (**A**) nPSi-Ox, (**B**) nPSi-UAc, (**C**) nPSi-APTS, (**D**) nPSi-Chi, and (**E**) nPSi-\(\beta\)CD. Moreover, to understand the release mechanism of each functionalization, kinetic profiles were fitted to five different models, including the Zero-order, First-order, Korsmeyer-Peppas, Higuchi, and Hixson-Crowell models, whose data are summarized in Table 2. All samples except for nPSi-Chi presented better adjustment with the First-order model, where the immediate-release dosage was dispersed in a single action [21]. In the case of nPSi-Chi, the essential oil release kinetics were more accurately described using the Korsmeyer-Peppas model. This result suggests that the governing factor of essential oil release could be attributed to the Fickian diffusion process [21; 23]. However, as the obtained \(\text{R}^{2}_{\text{adj}}\) values obtained by the First-Order and Korsmeyer-Peppas models are similar, the Akaike Information Criterion (AIC) was applied to determine a preferential model. This fined technique is based on in-sample fitting to estimate the likelihood of a model and predict future values. The best model is one that has a smaller AIC parameter [35]. These results showed that the essential oil kinetic release did not present significant differences among the samples determined by the F-test (Table 3). This parameter is used when comparing statistical models that have been fitted using the same underlying factors and data, and as a complement to the AIC parameter [36]. Only the nPSi-Chi samples showed significant differences, which is better described by the Korsmeyer-Peppas model. Therefore, according to the AIC results, both models, First-Order and Korsmeyer-Peppas, could accurately describe the release of _Laureliopsis philippiana_ essential oil from nPSi structures. In this sense, the parameters of both models were analyzed. The First-order release kinetic constant (\(K_{1}\)) was associated with the release rate. \(K_{1}\) values of the samples were nPSi-Ox \(>\) nPSi-Chi \(>\) nPSi-\(\beta\)CD \(>\) nPSi-UAc \(>\) nPSi-APTS, which indicated that the oxidized samples showed the fastest release profile, and nPSi-UAc and nPSi-APTS presented the most controlled release. Analyzing the Korsmeyer-Peppas release kinetic constant (\(K_{\text{KP}}\)), values presented a similar tendency: nPSi-Ox \(>\) nPSi-\(\beta\)CD \(>\) nPSi-Chi \(>\) nPSi-APTS \(>\) nPSi-UAc, suggesting that essential oil release was faster on oxidized samples and more controlled on nPSi-APTS and nPSi-UAc structures. Finally, concerning the release exponent \(n\) of the Korsmeyer-Peppas model, which determines the mechanism of diffusion, all samples presented a smaller value than 0.5. These values suggest that a quasi-Fickian diffusion mechanism governed the release of essential oil from all nPSi samples [21; 23; 37]. These results could be explained by the complex composition of _Laureliopsis philippiana_ essential oil, which involves diverse organic and aromatic molecules. These structures are characterized by low molecular weight volatile hydrocarbons.