## 2 Material and Methods
### Safrole Residue Persistence in Cowpea Beams  
Considering the insecticidal potential of safrole, the developed and validated method was used to assess the degradation/persistence rate of its residue in samples of cowpea beans which PHEO was applied with two different methods: contact or fumigation. The beans were treated by contact with PHEO at 208.52 uL kg\({}^{-1}\) of grains, corresponding to a safrole concentration of 194.77 ug kg\({}^{-1}\). Another batch of grains were subjected to fumigation with PHEO at 242.59 uL L\({}^{-1}\) of air, equivalent to a safrole concentration of 226.62 uL L\({}^{-1}\). These values represent the lethal PHEO dose to kill 95% of a \(C\). _maculatus_ population (CL\({}_{95}\)), as determined by preliminary bioassays.  
In the treatment by contact, PHEO was sprayed with a gravity-fed double-action airbrush with an internal mixing system (model BC 60, Steula, Sao Paulo, Brazil). The working pressure used for spraying was 15 psi. In this case, the experimental units consisted of 0.8-L glass flasks (8 cm diameter \(\times\) 15 cm height), each containing 200 g of cowpea beans. The treatment by fumigation was performed in 300-milliliter glass flasks containing 200 g of cowpea beans per flask. To guarantee no contact of the liquid phase of the PHEO with the grains, PHEO was applied on filter paper (2.5 \(\times\) 8.0 cm) surrounded by a metallic screen (12.3 \(\times\) 5.6 \(\times\) 0.5 cm) with a 4-mm mesh. Organza fabric (15 \(\times\) 15 cm) was placed upright among the beans. The bottles were closed with a metallic screw lid and sealed with parafilm (PM996, American, Neenah, WI, USA).  
After the treatments, the cowpea beans remained exposed for 24 h (contact test) or 96 h (fumigation test)--times determined by previous toxicity bioassays with \(C\). _maculatus_. After that, the grains were transferred to nylon bags (12 \(\times\) 16 cm) and stored under constant conditions of temperature (25 \(\pm\) 2 \({}^{\circ}\)C) and relative humidity (70 \(\pm\) 5%). Safrole residue analysis used the validated HS-SPME-GC/FID method, considering storage periods of 5, 10, 26, 60, and 90 days. Safrole persistence was calculated through the analytical curve of the method. All assays were performed in triplicates.  
Different mathematical models were tested to fit the degradation of safrole residue. Choosing the best model considered the coefficient of determination (\(R^{2}\)), the estimate of the root-mean-square error (RMSE, the closest to zero), and the significance level (\(P<0.05\)).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Experiments**} & \multicolumn{2}{c}{**Time (min) a**} & \multicolumn{2}{c}{**Temperature (\({}^{\circ}\)C) b**} \\ \cline{2-5}  & **Real** & **Codified** & **Real** & **Codified** \\ \hline
1 & 3 & \(-\) & 30 & \(-\) \\
2 & 3 & \(-\) & 60 & \(+\) \\
3 & 10 & \(+\) & 30 & \(-\) \\
4 & 10 & \(+\) & 60 & \(+\) \\
5 & 3 & \(-\) & 30 & \(-\) \\
6 & 3 & \(-\) & 60 & \(+\) \\
7 & 10 & \(+\) & 30 & \(-\) \\
8 & 10 & \(+\) & 60 & \(+\) \\ \hline \hline \end{tabular} a
[FOOTNOTE:a]Footnote a: Exposure time of the fiber; b  
\end{table}
Table 1: Complete 2\({}^{2}\)-factorial design for optimization of the safrole extraction conditions from cowpea beans.