## Results
### Kinetic Evaluation of Caroenoid Extraction
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Matrix** & **T (\({}^{\circ}\)C)** & **P (MPa)** & \multicolumn{2}{c}{**(k) \(\times\) 10\({}^{4}\) (s\({}^{-1}\))**} & \multicolumn{2}{c}{**(H\({}^{*}\times\left[\text{Cs}\right]\)\(\times\) 10\({}^{3}\)**} \\  & & & **(c.i. \(\leq\) 0.01\(\times\) 10\({}^{-4}\))** & **(c.i. \(\leq\) 0.01\(\times\) 10\({}^{-3}\))** & **(c.i. \(\leq\) 0.01\(\times\) 10\({}^{-6}\))** & **r\({}^{2}\)** \\ \hline \multirow{4}{*}{_C. annuum L._} & 40 & 40 & 11.98 & 0.97 & 1.16 & 0.95 \\  & 40 & 70 & 21.32 & 0.99 & 2.11 & 0.97 \\  & 60 & 40 & 17.76 & 0.99 & 1.75 & 0.95 \\  & 60 & 70 & 27.26 & 1.01 & 2.74 & 0.98 \\  & Soxhlet extraction & 7.69 & 0.98 & 0.98 & 0.75 \\ \hline \multirow{4}{*}{_L. esculentum L._} & 40 & 40 & 6.79 & 3.13 & 2.12 & 0.98 \\  & 40 & 70 & 10.65 & 3.13 & 3.33 & 0.98 \\ \cline{1-1}  & 60 & 40 & 8.86 & 3.14 & 2.78 & 0.98 \\ \cline{1-1}  & 60 & 70 & 12.93 & 3.16 & 4.09 & 0.99 \\ \cline{1-1}  & Soxhlet extraction & 6.00 & 3.11 & 1.87 & 0.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Extraction of carotenoids from pepper and tomato. Values were assumed by Rmax and the equation parameters k and H\({}^{*}\times\left[\text{Cs}\right]\) as a function of the working conditions. T = temperature; P = pressure; \(r^{2}\) = square of correlation coefficient (\(p\) = 0.05). Figure 1: _Cont._  
On the basis of the reported data, regardless of the raw material used, the following remarks can be made:  
1. The increase in pressure and temperature does not significantly influence the total amount of carotenoids extractable at equilibrium (extraction time = \(\infty\)), as shown by the values assumed by the H* \(\times\) [Cs] parameter. Indeed, this product--which represents the yield in milligrams of carotenoids extracted from one gram of lyophilized material when the equilibrium is reached--assumes that for all the SFE runs, the values used were close to the concentration of carotenoids in the starting material (1016 mg/kg for pepper and 3125 mg/kg for tomato peels) and also to the concentrations obtained with percolation with n-hexane;
2. P highly affects the extraction kinetics, as confirmed by the values of the k constant when working at the same T;
3. Secondarily, T also affects the kinetics of the SFE, as shown by the value that k assumes when working at the same P;
4. The binomial pressure-temperature combination is more crucial than T and P alone in determining the kinetics of the SFE process. In particular, transitioning from the mildest (40 \({}^{\circ}\)C and 40 MPa) to the most intense (60 \({}^{\circ}\)C and 70 MPa) working conditions, the value of k increases 2.3- and 1.9-fold for chili peppers and tomato peels, respectively. 5. In all conditions, extraction with Sc-CO\({}_{2}\) was completed faster than percolation with n-hexane, as shown by the values assumed by k and/or R\({}_{\rm max}\). For example, the ratio between the value of k obtained at the most intense SFE conditions and that of the Soxhlet extraction was about 3.5 and 2.2 for chili pepper and tomato peels, respectively. These considerations, together with the high values of the square of the correlation coefficient, demonstrate the suitability of the hypotheses introduced and give a measure of validity for the mathematical model proposed. Figure 1: **(a)** Evolution of the experimental and calculated points related to carotenoid extraction from lyophilized fruits of _C. annuum_ L. as a function of extraction time and working conditions (\(\blacksquare\) 40 \({}^{\circ}\)C, 40 MPa; \(\times\) 40 \({}^{\circ}\)C, 70 MPa; \(\blacklozenge\) 60 \({}^{\circ}\)C, 40 MPa; \(\blacklozenge\) 60 \({}^{\circ}\)C, 70 MPa; + Soxhlet extraction n-hexane); **(b)** Evolution of the experimental and calculated points related to carotenoid extraction from lyophilized peels of _L.