## 3 Results and Discussion
### Extraction Kinetics and Temperature Effects  
The optimization of the extraction process revealed significant changes in the extraction variables as a consequence of ultrasonication pretreatment, but to portray the ultrasound effect on the process in an integrated frame, information pertaining to the kinetics of the extraction and the effect of temperature was indispensable. Towards this objective, extraction kinetics were traced over a wide breadth of temperatures, ranging from 40 to 80 \({}^{\circ}\)C (Figure 5). In each case, the optimized conditions were used to carry out the extractions (Table 5). A modification of a previously proposed kinetic model was employed for both non-pretreated and ultrasound-pretreated samples [34]:  
\[Y_{TP(t)}=Y_{TP(0)}+\frac{Y_{TP(s)}t}{t_{0.5}+t}. \tag{4}\]  
The term \(Y_{TP(t)}\) represents the extraction yield in total polyphenols (mg GAE g\({}^{-1}\) dm) at any time \(t\), \(Y_{TP(0)}\) is a fitting parameter, \(Y_{TP(s)}\) the yield in total polyphenols at equilibrium (saturation), and \(t_{0.5}\) half the time (min) required for the extraction to enter the regular regime. The phase of the regular regime refers to the period within which small increases in \(Y_{TP}\) are achieved within relatively large \(t\)[35]. In all cases examined, fitting of the kinetic model to the experimental data gave \(\text{R}^{2}>0.98\) (\(p<0.0001\)), suggesting that the model implemented could very effectively describe extraction kinetics. Determination of the initial rate of the extraction, \(h\), and the second-order extraction rate, \(k\), was accomplished using the following equations:  
\[h=\frac{Y_{TP(s)}}{t_{0.5}}, \tag{5}\]  
\[k=\frac{1}{Y_{TP(s)}\ t_{0.5}}. \tag{6}\]  
The data generated from the kinetic assay are analytically presented in Table 6. The effect exerted by the ultrasonication pretreatment was shown to be temperature-dependent, since acceleration of the extraction (increased \(k\)) was seen only at 70 and 80 \({}^{\circ}\)C. This trend was corroborated by the values determined for \(h\), which were increased for the ultrasound-pretreated samples at temperatures higher than 60 \({}^{\circ}\)C. Likewise, \(t_{0.5}\) was shorter for the extractions received ultrasonication pretreatment at temperatures higher than 60 \({}^{\circ}\)C. Furthermore, for every temperature tested, \(Y_{\text{TP}}\) of the ultrasonication-pretreated samples was always significantly higher than that of the non-pretreated ones. However, in both cases, temperature had a non-significant effect on \(Y_{TP(\mathrm{s})}\), since it varied between 82.03 to 83.90 mg GAE g\({}^{-1}\) dm for the non-pretreated extractions and from 91.24 to 93.97 mg GAE g\({}^{-1}\) dm for the ultrasound-pretreated extractions. Figure 5: Kinetics of polyphenol extraction from \(M\). _deifera_ leaves, with and without prior ultrasonication pretreatment. Extraction conditions for the non-pretreated sample: \(\mathrm{C}_{\mathrm{DES}}=85\%\) (_uv/v_); \(\mathrm{R}_{\mathrm{LS}}=20\) mL. \(\mathrm{g}^{-1}\); \(\mathrm{S}_{\mathrm{S}}=800\) rpm. Extraction conditions for the ultrasonication-pretreated sample: \(\mathrm{C}_{\mathrm{DES}}=75\%\) (_uv/v_); \(\mathrm{R}_{\mathrm{LS}}=100\) mL. \(\mathrm{g}^{-1}\); \(\mathrm{S}_{\mathrm{S}}=200\) rpm. Pretreatment with ultrasonication is likely to solubilize all polyphenols occurring at and near the surface of the solid particles. This assumption could justify the fact that at temperatures 40-60 \({}^{\circ}\)C the stirred-tank extraction of the ultrasound-pretreated samples proceeded at a lower rate. On the other hand, the non-pretreated samples had a higher load of polyphenols at the exterior of the solid particles and exhibited apparently increased \(k\) and \(h\).