## Results
### Kinetic Evaluation of Polyphenol Extraction  
The same approach based on [PERSON]'s law and used to describe the kinetics of carotenoid SFE, was used to optimize the working parameters related to the extraction of polyphenols from pepper and tomato by-products with pure EtOH or Sc-CO\({}_{2}\) coupled with EtOH (1:1, \(w/w\)). In particular, the following equation was used to determine the maximum extraction rate (R\({}^{\prime}\)max):  
\[\mathrm{R}^{\prime}_{\mathrm{max}}=\mathrm{k}^{\prime}\times\mathrm{H}^{ \prime*}\times\left[\mathrm{Ps}\right] \tag{9}\]  
where: k\({}^{\prime}\) = kinetic constant (s\({}^{-1}\)); H\({}^{\prime*}\) = an adimensional constant, ranging from zero to one, and related to the equilibrium constant H\({}^{\prime}\); [Ps] = polyphenolic concentration in the starting lyophilized material (adimensional). The values assumed by R\({}^{\prime}\)max and the functional parameters k\({}^{\prime}\) and H\({}^{\prime*}\times\left[\mathrm{Ps}\right]\) are reported in Table 4.  
Figure 2 shows the time evolution of polyphenols extracted from pepper (Figure 2a) and from tomato peels (Figure 2b) as a function of the working conditions, together with the data calculated on the basis of the kinetic parameters reported in Table 4. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Matrix**} & **EOH** & **Sc-CO\({}_{2}\)** & **T (\({}^{\circ}\)C)** & **P (MPa)** & **00 \(\times\) 10\({}^{4}\) (s\({}^{-1}\))** & **(H\({}^{\prime}\times\left[\mathrm{Cs}\right]\times\) 10\({}^{3}\))** & **(R\({}_{\mathrm{max}}\)) \(\times\) 10\({}^{4}\) (s\({}^{-1}\))** \\  & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** \\ \cline{3-8}  & 50 & 50 & 50 & 30 & 6.92 & 10.12 & 7.00 & 0.95 \\  & 50 & 50 & 80 & 30 & 7.48 & 28.73 & 21.48 & 0.97 \\ _C. autumn L_ & 100 & – & 80 & 30 & 9.16 & 31.96 & 29.28 & 0.98 \\  & 100 & – & 80 & 50 & 12.78 & 31.68 & 40.48 & 0.98 \\  & \multicolumn{3}{c}{Sovable extraction} & 5.38 & 30.90 & 16.63 & 0.99 \\ \hline  & 50 & 50 & 50 & 30 & 5.46 & 0.64 & 0.35 & 0.96 \\  & 50 & 50 & 80 & 30 & 9.84 & 2.42 & 2.34 & 0.92 \\ _L. esculentum L_ & 100 & – & 80 & 30 & 10.64 & 2.85 & 3.03 & 0.94 \\  & 100 & – & 80 & 50 & 14.02 & 2.83 & 3.96 & 0.98 \\  & \multicolumn{3}{c}{Sovable extraction} & 8.33 & 2.86 & 2.38 & 0.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Extraction of polyphenols from pepper and tomato by-products. Values assumed by R\({}^{\prime}\)max and the equation parameters k\({}^{\prime}\) and H\({}^{\prime*}\times\left[\mathrm{Ps}\right]\) as a function of the working conditions. T = temperature; P = pressure; r = correlation coefficient. Figure 2: _Cont._  
On the basis of the data reported in Table 4, regardless of the raw material utilized, the following remarks can be made:  
1. As previously observed with potato by-products [42], pure Sc-CO\({}_{2}\) was confirmed to be a poor solvent for polyphenols, even when high density values were used;
2. EtOH is a suitable co-solvent used to pilot the polarity of the solvent phase, provided that high percentages are utilized (\(\geq\)50%);
3. At an equal EtOH/Sc-CO\({}_{2}\) ratio (1:1) and P (30 MPa), T greatly affects the extraction process, with particular reference to the total amount of extractable polyphenols. Indeed, while the kinetic constant k\({}^{\prime}\) does not change markedly when T increases from 50 \({}^{\circ}\)C to 80 \({}^{\circ}\)C, the equation parameter H\({}^{\prime\prime}\)\(\times\) [Ps] increases almost three-fold for chili peppers and four-fold for tomato by-products, from 50 \({}^{\circ}\)C to 80 \({}^{\circ}\)C. This means that such temperature increases determine the solubilization of phenolic compounds that are otherwise not easily collectable;
4. To obtain the extraction of the whole phenolic fraction, pure EtOH at 80 \({}^{\circ}\)C, and 30 MPa or 50 MPa conditions were needed. In such conditions, the extraction process was faster than when it was carried out using the Soxhlet apparatus, as shown by the values of the kinetic constant k\({}^{\prime}\).