## 3 Results and Discussion  
### Investigation Based on the Model DPPH\({}^{\bullet}\) Radical  
The reaction of antioxidants with the stable radical DPPH\({}^{\bullet}\) is a non-competitive scheme to draw information regarding their radical scavenging potency [25]:  
\[\text{AH}+n\ \text{DPPH}^{\bullet}\rightarrow\text{products} \tag{3}\]  
Such a scheme has been widely used to build up several stoichiometric and kinetic hypotheses and evaluate a high number of naturally occurring polyphenols as antioxidants [25]. The phenolic acids investigated herein were assayed not only for stoichiometry, but also efficiency, by determining the efficient concentration (IC\({}_{50}\)), that is, the molar concentration of an antioxidant to provoke a 50% reduction in the initial molar DPPH\({}^{\bullet}\) concentration.  
To compute the total stoichiometry, the following equation was used [25; 26; 27]:  
\[n_{\rm t}=\frac{A_{\rm i}-A_{\rm f}}{\varepsilon\,C} \tag{4}\]  
where \(A_{\rm i}\) and \(A_{\rm f}\) are the initial and final absorbance of the reaction mixture (DPPH\({}^{\bullet}\) + antioxidant), at 517 nm, and \(\varepsilon\) the molar DPPH\({}^{\bullet}\) absorptivity in methanol (11,240 M\({}^{-1}\) cm\({}^{-1}\)). \(C\) is the antioxidant molar concentration, which in this case was set at 16 \(\upmu\)M, to give an approximate DPPH\({}^{\bullet}\)/antioxidant molar ratio of 6 [25; 28]. This was deemed necessary in order to eliminate variations arising from different concentrations, since \(n_{\rm t}\) was shown to be concentration dependent [29; 30]. The \(n_{\rm t}\) is a measure of how many radicals can be trapped by one antioxidant molecule and may provide valuable information regarding the effectiveness of an antioxidant.  
After \(n_{\rm t}\) determination, and assuming Equation (3) represents a complete reaction, the IC\({}_{50}\) was estimated using the following function [31]:  
\[\text{IC}_{50}\ (\upmu\text{M})\ =\ \frac{\left[\text{DPPH}^{\bullet}\right]_{0}}{2 n_{\rm t}} \tag{5}\]  
where [DPPH\({}^{\bullet}\)]\({}_{0}\) is the initial molar DPPH\({}^{\bullet}\) concentration (\(\upmu\)m). The \(n_{\rm t}\) and IC\({}_{50}\) values determined experimentally are analytically provided in Table 1. The IC\({}_{50}\) found for CA was in absolute accordance with 19.8 \(\upmu\)M previously reported [32], although other authors gave a value of 12.2 \(\upmu\)M [27]. Likewise, the IC\({}_{50}\) of 45.3 \(\upmu\)M [33], 41.8 \(\upmu\)M [34], and 44.6 \(\upmu\)M [35] determined for  
Regarding \(n_{\text{t}}\), the value determined in this study was 2.63, in near-perfect agreement with 2.65 found in an earlier investigation [25] and 2.6 determined in a recent study [30], but also in close match with the values of 2.3 [27] and 2.2 [29]. Similarly, the \(n_{\text{t}}\) of 1.10 for FA was in agreement with the values of 1.16 [23], 1.2 [29], and 1.3 [27; 30] found in previous studies. For CouA, discrepancies have been observed, with \(n_{\text{t}}\) values estimated to be either 1 [29] or \(>\)1 [23].  
Taking into account both \(n_{\text{t}}\) and IC\({}_{50}\), the ranking of the hydroxycinnamates tested was CA \(>\) FA \(>\) CouA. This outcome was in absolute agreement with previous findings, which demonstrated the same order of efficiency [35; 37; 38; 39; 40]. It should be noted that the ranking based on any testing with DPPH\({}^{\bullet}\) may be considered as merely indicative, since the quenching mechanisms of DPPH\({}^{\bullet}\) and ROO\({}^{\bullet}\) by a given antioxidant may differ significantly. In alcoholic solutions, such as methanol, where the DPPH\({}^{\bullet}\) test is usually carried out, phenols ionize and thus react with DPPH\({}^{\bullet}\) via electron transfer (ET) from their anions [41], whereas in lipids, antioxidants act as H-donating molecules [31]. Therefore, no direct extrapolation of the effectiveness of an antioxidant could be made for its lipid-stabilizing effect against oxidation.