## 2 Materials and Methods
### Potentiometry and Spectrophotometry  
The potentiometric arrangement and the titrations were conducted with the same apparatus described previously [12]. The glass electrodes were from Metrohm. Following the addition of the reagents, they acquired a constant potential (within \(\pm\)0.01 mV) by 30 min. To prevent any interference due to carbonate formation, nitrogen gas was gently introduced into the test solutions, which were magnetically stirred throughout titrations. Figure 1: Chemical structure of the investigated natural antioxidants: quercetin (**a**), luteolin (**b**) and L-ascorbic acid (**c**). Nitrogen commercial cylinders were used, and the gas was further purified by passing it through 1 M NaOH, 1 M H\({}_{2}\)SO\({}_{4}\), double-distilled water and 0.16 M NaCl. The cell apparatus was kept in a thermostatic bath at (37.0 \(\pm\) 0.1) \({}^{\circ}\)C.  
The acid-base equilibria were investigated by performing potentiometric titrations, at 37 \({}^{\circ}\)C and in 0.16 M NaCl, and by measuring, with a glass electrode (GE), the electromotive force (EMF) of cell:  
REFTest SolutionGE  
where RE corresponds to the reference electrode (Ag I AgCl 0.01 M NaCl1 0.16 M NaCl), while the test solution was made of \(C_{\mathrm{L}}\) M of H\({}_{n}\)L, \(C_{\mathrm{A}}\) M HCl, \(C_{\mathrm{B}}\) M NaOH and 0.16 M NaCl. The primary \(C_{\mathrm{L}}\), \(C_{\mathrm{A}}\), \(C_{\mathrm{B}}\) and [H\({}^{+}\)] represent the basic data in the treatment to obtain the acidic constants. The EMF of the cell can be expressed, in mV, at the temperature of 37 \({}^{\circ}\)C, as Equation (1):  
\[E=E^{\circ}+61.54\log[\mathrm{H}^{+}]+E_{j} \tag{1}\]  
where \(E^{\circ}\) was constant for each series of measurements and \(E_{j}\) is the liquid junction potential, which depends on [H\({}^{+}\)] only [26]. The \(E_{j}\) value at 37 \({}^{\circ}\)C and 0.16 M NaCl was determined by acid-base titration using cell (G) without H\({}_{n}\)L. The obtained results for [H\({}^{+}\)] \(\leq\) 0.100 M could be accurately fitted by the linear slope \(E_{j}\) ([H\({}^{+}\)]) \(I=-j\)\(I\) [H\({}^{+}\)]. The value of \(j\) (mV/M) was 631 \(\pm\) 1. All titrations were separated into two parts. In the first one, \(E^{\circ}\) constant value (within \(\pm\)0.05 mV), was determined in accordance with the [PERSON]'s method [27; 28] in the [H\({}^{+}\)] range 10\({}^{-4}\)-10\({}^{-2}\) M and without H\({}_{n}\)L. [H\({}^{+}\)] was stepwise reduced by coulometrically generating OH\({}^{-}\) ions with the circuit C:  
\[-\mathrm{Pt/Test\ Solution/\AE+}\]  
where AE is the auxiliary electrode of general composition: 0.16 M NaCl/0.1 M NaCl, (0.16-0.1) M NaCl/\(\mathrm{Hg_{2}Cl_{2}/Hg}\). Under the chosen experimental condition, the only electroreducible species was water. Hence, suppose that at the cathode the only reaction that occurs is the water reduction (Equation (2)):  
\[\mathrm{H_{2}O+e^{-}\rightleftarrows 1/2\ H_{2}+OH^{-}} \tag{2}\]  
In the test solution of a known volume, \(V\), \(C_{\mathrm{B}}\) can be expressed as (\(\mathrm{\SIUnitSymbolMicro F\cdot}10^{-6}\)/V) M, where \(\mathrm{\SIUnitSymbolMicro F}\) stands for the microfaradays passed through the cell. In the second part, after the addition of H\({}_{n}\)L, the acidity was gradually decreased by adding known volumes of the standard NaOH solution. All titrations were conducted with a programmable computer-controlled data acquisition switch unit 34,970 A from Hewlett and Packard. The constant-current source of the coulometric circuit was a system DC power supply 6614 C by Hewlett and Packard. The EMF values were measured at a precision of \(\pm\)10\({}^{-5}\) V using an OPA 111 low-noise precision DIFET operational amplifier. Given the low solubility of quercetin and luteolin in water [12; 14] and by using the same experimental approach tested in a previous study [29], all the titrations were carried out by adding an exactly known and weighed amount of solid in the cell apparatus.