## 3 Results and Discussion
### Extraction Kinetics and Temperature Effects
At higher temperatures, polyphenol extraction was more rapid for the ultrasonicated samples, most probably because the pretreatment brought about disruption of the cell walls of the plant material, which enabled more facile penetration of the solvent into the solid particles and easier entrainment of the solute (polyphenols) in the liquid phase. Concerning \(Y_{TP(s)}\), the variation as a response to \(T\) was non-significant, a fact indicating the \(T\) had virtually no effect on \(Y_{TP(s)}\). This outcome is a paradox, in light of previous investigations, which demonstrated that increasing \(T\) had a proportional effect on \(Y_{TP(s)}\)[36; 37]. However, earlier studies on polyphenol extraction from _M. oleifera_ leaves with a glycerol/sodium acetate DES revealed that switching \(T\) from 50 to 80 \({}^{\circ}\)C resulted in a constant decline in \(Y_{TP(s)}\)[13]. The fact that increasing \(T\) did not contribute in attaining higher \(Y_{TP(s)}\) might suggest that extraction could reach equilibrium after a given period of time, irrespective of the \(T\). The increase in \(k\) as a response to increasing \(T\) was found to obey the Arrhenius law:  
\[k=k_{0}e^{-\frac{E_{a}}{RT}}. \tag{7}\]  
where \(k_{0}\), \(R\), \(T\), and \(E_{a}\) correspond to the temperature-independent factor (min\({}^{-1}\)), the universal gas constant (8.314 J K\({}^{-1}\) mol\({}^{-1}\)), the absolute temperature (K), and the activation energy (J mol\({}^{-1}\)). The linear expression of Equation (7) would be:  
\[lnk=lnk_{0}+(-\frac{E_{a}}{R})\frac{1}{T}. \tag{8}\]  
Thus, \(E_{a}\) could be determined graphically, by the slope (\(-\frac{E_{a}}{R}\)) of the straight line obtained by plotting \(lnk\) as a function of 1/\(T\) (Figure 6). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**T (\({}^{\circ}\)C)**}} & \multicolumn{6}{c}{**Kinetic Parameters**} \\ \cline{2-6}  & \(k\) (\(\times\)10\({}^{-3}\)) (g & \(h\) (mg g\({}^{-1}\) & Y\({}_{\text{TP(s)}}\) (mg & \(t_{0.5}\) (min) & \(E_{a}\) (kJ mol\({}^{-1}\)) \\  & **mg\({}^{-1}\) min\({}^{-1}\))** & **min\({}^{-1}\))** & **GAE g\({}^{-1}\))** & **t\({}_{0.5}\) (min)** & **\(E_{a}\) (kJ mol\({}^{-1}\))** \\ \hline No pretreatment & & & & & \\
40 & 2.68 & 18.03 & 82.03 & 4.55 & \\
50 & 3.17 & 21.71 & 82.71 & 3.81 & \\
60 & 3.58 & 22.15 & 78.62 & 3.55 & 11.24 \\
70 & 3.95 & 26.32 & 81.60 & 3.10 & \\
80 & 4.40 & 30.96 & 83.90 & 2.71 & \\ \hline Ultrasonic & & & & & \\ pretreatment & & & & & \\
40 & 1.46 & 12.12 & 91.24 & 7.53 & \\
50 & 1.76 & 14.58 & 91.01 & 6.24 & \\
60 & 3.29 & 28.78 & 93.52 & 3.25 & 34.02 \\
70 & 4.52 & 36.79 & 90.14 & 2.45 & \\
80 & 5.72 & 50.52 & 93.97 & 1.86 & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Kinetic data and the effect of temperature. The \(E_{\rm a}\) values for the extractions without and with ultrasonication pretreatment were 11.24 and 34.02 kJ mol\({}^{-1}\), respectively (Table 6), clearly showing that the extraction of the ultrasonication-pretreated samples was more energy-demanding by almost 4 times. Based on this outcome, it would appear that ultrasonication prior to batch stirred-tank extraction does not lower the requirements in energy for accomplishing an efficient extraction of polyphenols from _M. oleifera_ leaves, but the energetic needs are even higher. Yet, such observation could be rather misleading and the increased of \(Y_{TP(s)}\) of the ultrasonication-pretreated samples should not be overlooked. The increased \(E_{\rm a}\) value found for the ultrasonication pretreated extraction was most probably because during pretreatment the most readily extracted polyphenols were dissolved in the liquid phase (solvent), leaving behind (inside the solid particles) polyphenols that were more difficult to extract, since solubilization of these polyphenols would depend on internal diffusion, which is the rate-determining step in diffusion-controlled extractions [30; 38]. Therefore, the following stirred-tank extraction was apparently more energy-demanding.