# Extraction of Antioxidants from Grape and Apple Pomace: Solvent Selection and Process Kinetics
## 3 Results and Discussion
### Kinetic Modeling of Extraction Process  
All extraction results concerning TPC and AC have been used to fit a second-order kinetic model with two phases: an almost immediate washing or dissolution process followed by a slow extraction step, as indicated by Equation (1). After the adjustment of the mentioned kinetic equation to the relevant experimental data employing a Levenberg-Marquardt nonlinear regression algorithm, the kinetic constants and correlation values  
Figure 10: Antioxidant activity (DPPPH) results, and their kinetic analysis, obtained during the extraction processes applied to GP using several solvents: (**A**) glycols at 70 \({}^{\circ}\)C; (**B**) acetone at 25 \({}^{\circ}\)C, (**C**) acetone 80%: water 20% at 25 \({}^{\circ}\)C, and (**D**) water at 25 \({}^{\circ}\)C. The lines show the second-order kinetic model (Equation (1)) fitting to data. When fitting Equation (1) to the TPC results from the AP extraction (Table 1), the first observation is that q\({}_{0}\), the initial TPC value, dramatically increases with temperature, suggesting that the solubility of the compounds that are dissolved during this initial phase increases exponentially with this variable. After calculating an apparent extraction rate (r\({}_{0}\)) in this phase by dividing q\({}_{0}\) by the first sampling time, a finer study, representing ln(r\({}_{0}\)) versus the inverse value of absolute temperature (1/T)--Arrhenius equation--an exponential trend is again observed (as for q\({}_{0}\) with T), but, in this case, the apparent activation energy (E\({}_{\text{a}}\)) can be calculated, being equal to 19.92 kJ/mol, a value that should be considered essentially empirical, as it shows the exponential increase of solubility with temperature for this particular case: apple pomace and ethanol 70%: water 30% solution as solvent. This is also evident when fitting this same second-order equation to AC results; in this case, the E\({}_{\text{a}}\) is 10.68 kg/mol, so temperature affects the extraction of phenolic compounds more than the extraction of their antioxidant activity during the washing phase. Thus, the nature of the compounds being dissolved could change with the temperature, suggesting that most active compounds in AP are more polar (for q\({}_{0}\), time values are so low that no thermal deactivation exists). For q\({}_{1}\) and for q\({}_{e}\), there are maximum TPC values at 70 \({}^{\circ}\)C (10.6 \(\pm\) 0.7 and 14.5 \(\pm\) 1.1 mg GAE/gds, respectively) with a decrease between this temperature and 90 \({}^{\circ}\)C. This trend can be ascribed to a reduction in redox potential or to a certain collapse of the inner porous structure as the temperature approaches the boiling point of the extraction liquid. Again, there is no trend with temperature for the kinetic constant k\({}_{\text{d}}\) for TPC analysis, possibly indicating that there is a trade-off between accelerating effects due to increased diffusivity and phenolics desorption rate from pore surface and decelerating effects possibly due to pore structure collapse. Considering the experimental error, this idea can be extended to the analysis of AC k\({}_{\text{d}}\) values. If we compare the results for different solvents at room temperature to extract active components from AP, we can observe that acetone 80% \(\
u\)/\(\
u\) is the best extractant for a fast extraction of total phenolics (q\({}_{0}\) value similar to that of ethanol 70% or 96% at 70 \({}^{\circ}\)C); curiously, the addition of water to either ethanol or acetone reduces q\({}_{0}\), suggesting a lower solubility of phenolics extracted during the washing phase when water is added. Values for q\({}_{1}\) are similar for all acetone and ethanol mixtures, irrespective of water concentration, suggesting that the total amount of phenolics extracted is essentially constant for these solvents.