## 3 Results and Discussion
### Extraction Kinetics--Temperature Effects  
Previous studies on the extraction of polyphenols from _S. fruticosa_ using methyl \(\beta\)-cyclodextrinrin (m-\(\beta\)-CD) showed that extracts with increased polyphenol concentration and improved antioxidant characteristics could be obtained at 80 \({}^{\circ}\)C [14]. However, a following investigation with a 60% (_w/v_) hydroglycerolic mixture demonstrated that Y\({}_{\text{TP}}\) displayed a gradual decrease when extraction temperature varied from 50 to 80 \({}^{\circ}\)C [42], although differences were non-significant (_p_ < 0.05). Therefore, to obtain a reliable picture of the effect of temperature, extraction kinetics was traced within the range of 40 to 80 \({}^{\circ}\)C (Figure 6), under optimized conditions, that is, S\({}_{\text{S}}\) = 900 rpm, C\({}_{\text{DES}}\) = 77% (_w/v_), and \(t_{\text{US}}\) = 15 min. Figure 6: Kinetics of polyphenol extraction from _S. fruticosa_, traced under optimized conditions (S\({}_{\text{S}}\) = 900 rpm, C\({}_{\text{DES}}\) = 77% (_w/v_), and \(t_{\text{US}}\) = 15 min). YTP exhibited an increasing trend, and at 80 \({}^{\circ}\)C the YTP(s) determined was 113.39 mg GAE g\({}^{-1}\) dm (Table 3). Likewise, the initial extraction rate, \(h\), increased from 2.314 mg g\({}^{-1}\) min\({}^{-1}\) at 40 \({}^{\circ}\)C to 6.439 mg g\({}^{-1}\) min\({}^{-1}\) at 80 \({}^{\circ}\)C, and \(t_{0.5}\) showed a declining tendency over this range, which manifested acceleration of the extraction. In a similar manner, the second-order extraction rate, \(k\), increased from \(0.356\times 10^{-3}\) g mg\({}^{-1}\) min\({}^{-1}\) at 40 \({}^{\circ}\)C to 0.501 \(\times 10^{-3}\) g mg\({}^{-1}\) min\({}^{-1}\) at 80 \({}^{\circ}\)C, and \(k\) values correlated well with \(T\) (R\({}^{2}\) = 0.96, \(p\) = 0.0413), using the exponential model described by the Equation (4) (Figure 7). Comparison with extraction using hydroglycerolic solvent [42] showed that the fitting parameter b (Equation (4)), which is a measure of the sensitivity of \(k\) with regard to \(T\) changes, was 0.0136 for the extraction with LA-SCDB15 and 0.0765 for the extraction with hydroglycerolic solvent. This finding suggested that the extraction with hydroglycerolic solvent was more energy-demanding. To corroborate this hypothesis, the activation energy (\(E_{\text{a}}\)) of the process was estimated using the Equation (5). The barrier level of 7.64 kJ mol\({}^{-1}\) found was significantly lower than 47.67 kJ mol\({}^{-1}\) determined for the extraction with 60% (_w/v_) glycerol [42], thus affirming the higher efficiency of the extraction with LA-SCDB15. At this point, it should be stressed that in both cases stirred-tank extraction took place after ultrasonication pretreatment. This pretreatment stage resulted in washing out the most readily extracted compounds, a phenomenon also observed in other cases [16; 21] and therefore the \(E_{\text{a}}\) determined corresponded to the extraction of the remaining solute, whose dissolution and entrainment into the liquid phase is governed by internal diffusion. The fact that the stirred-tank stage was far less energy-demanding using LA-SCDB15 than 60% (_w/v_) glycerol, evidenced that this \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{\(T\) (\({}^{\circ}\)C)} & \multicolumn{4}{c}{**Kinetic Parameters**} \\ \hline  & \(k\) (\(\times\)10\({}^{-3}\)) (g mg\({}^{-1}\) min\({}^{-1}\)) & \(H\) (mg g\({}^{-1}\) min\({}^{-1}\)) & \(Y_{\text{TPU}}\) (mg GAE g\({}^{-1}\)) & \(t_{\text{a,5}}\) (min) & \(E_{\text{a}}\) (k) mol\({}^{-1}\)) \\ \hline
40 & 0.356 & 2.314 & 80.64 \({}^{\text{a}}\) & 34.85 & \\
50 & 0.407 & 2.994 & 85.73 \({}^{\text{a}}\) & 28.63 & \\
60 & 0.424 & 3.508 & 90.95 \({}^{\text{a}}\) & 25.93 & 7.64 \\
70 & 0.471 & 5.388 & 107.01 \({}^{\text{a}}\) & 19.86 & \\
80 & 0.501 & 6.439 & 113.39 \({}^{\text{b}}\) & 17.61 & \\ \hline \hline \end{tabular} Values with different letters within the same column are statistically different (\(p<0.05\)).  
\end{table}