## 3 Results
### Design of Experiments (DoE) and Process Optimization  
Table 4 shows the combinations of the SFE conditions for _MeOH_ and \(q_{CO2}\) used in the DoE, which comprised a 2 factor, 2 level Central Composite Design (CCD). The results were expressed both as TPR and as CFA recovery, since this is the main phenolic compound in the extracts. The extraction temperature and pressure were fixed at 80 \({}^{\circ}\)C and 350 bar, respectively, due to the higher recoveries observed in the screening runs under these conditions. Additionally, other preliminary runs showed that increasing both parameters further had no effects on recovery (data not shown). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Run**} & \multirow{2}{*}{**MeOH (\%)**} & \multirow{2}{*}{**q\({}_{\text{CO2}}\) (g/min)**} & \multirow{2}{*}{**CFA (\%)**} & \multirow{2}{*}{**TPR (\%)**} & **Antioxidant Activity (\%)** \\ \hline
**01** & 10 & 8 & 5.6 & 3.4 & 83.1 \(\pm\) 3.3 \({}^{\text{a}}\) \\
**02** & 10 & 18 & 29.4 & 12.1 & 84.0 \(\pm\) 2.9 \({}^{\text{a}}\) \\
**03** & 20 & 8 & 67.3 & 27.1 & 83.8 \(\pm\) 3.6 \({}^{\text{a}}\) \\
**04** & 20 & 18 & 82 & 37 & 73.0 \(\pm\) 2.7 \({}^{\text{b}}\) \\
**05** & 7.9 & 13 & 19.3 & 9.8 & 56.8 \(\pm\) 2.1 \({}^{\text{c}}\) \\
**06** & 22.1 & 13 & 63.6 & 33.6 & 69.0 \(\pm\) 2.2 \({}^{\text{b}}\) \\
**07** & 15 & 5.9 & 11.2 & 7.7 & 65.1 \(\pm\) 1.8 \({}^{\text{d}}\) \\
**08** & 15 & 20.1 & 62.2 & 33 & 73.5 \(\pm\) 3.1 \({}^{\text{b}}\) \\
**09** & 15 & 13 & 35.3 & 21.8 & 78.6 \(\pm\) 2.8 \({}^{\text{b}}\) \\
**10** & 15 & 13 & 32.2 & 19.2 & 78.7 \(\pm\) 3.1 \({}^{\text{b}}\) \\
**11** & 15 & 13 & 23.9 & 14 & 77.1 \(\pm\) 3.1 \({}^{\text{b}}\) \\ \hline \hline \end{tabular} \({}^{\text{a}}\)Concerning antioxidant activity, identical superscript letters indicate no significant difference among results.  
\end{table} 
Table 4: Experimental conditions for the optimization study regarding the supercritical fluid extraction (SFE) of potato peels. The responses were analyzed as a function of % of total phenolic recovery (TPR), caffe acid recovery, and antioxidant activity. Fixed independent variables: T: 80 \({}^{\circ}\)C, P: 350 bar, \(\text{t}_{\text{ext}}\): 60 min. CFA: Caffe acid. The maximum TPR and CFA recoveries observed were 37% and 82%, respectively, obtained in run 04; and the minimum, 3.4% and 5.6%, in run 01 (under the lowest \(MeOH\%\) and \(q_{CO2}\)). The Pareto charts of effects show the variables that significantly influenced the TPR (Figure 1a) and CFA (Figure 1b) recovery at a significance level of 95%. As observed, both linear variables affect the responses but, judging by the magnitude of the positive coefficients of both variables, it is clear that \(MeOH\%\) is the governing parameter, i.e., the polarity of the solvent is the most important factor to consider in the phenolic extraction of potato peels. This can be directly noted in run 01, performed under the same \(q_{CO2}\) conditions as run 03, but the latter at double the MeOH concentration of the first. As a result, the TPR increased from 3.4% to 27.1%, and the CFA recovery from 5.3% to 67.3%. Similarly, the positive effect of \(q_{CO2}\) can be seen by comparing runs 01 and 02, for example, which have the same \(MeOH\%\), but the latter had a higher \(q_{CO2}\). In this case, the TPR increased from 3.4% to 12.1%, and the CFA from 5.6% to 29.4%, due to the higher convective mass transfer rates imparted by increasing the solvent flow rate [38]. A mathematical model describing the extraction of both components was generated (Equations (3) and (4)), and to validate them statistically, an F-test (lack of fit) was performed. Table 5 shows the results of the analysis of variance (ANOVA) performed for both models. \[\text{TPR}(\%)\ =\ 0.218*[\text{MeOH}]\ +\ 0.0561*[\text{MeOH}]^{2}\ +\ 0.423*[\text{Q}]\ +\ 0.029*[\text{Q}^{2}]\ +\ 0.012*[\text{MeOH}]*[\text{Q}]-10.31 \tag{3}\]  
where: TPR(%): Total Phenolic Recovery; [MeOH]: Methanol concentration (%); [Q]: CO2 flow rate (g/min).