## 3 Results and Discussion  
### The Effect of pH  
The thermal degradation of Qt at 90 \({}^{\circ}\)C was first assessed as a function of pH near neutrality, that is, within the range 6.5-7.5. The evolution of the decrease of Qt concentration, \(C\) (\(\mu\)mol L\({}^{-1}\)), was plotted against time, \(t\) (s), and at all three pH values tested (6.5, 7.0, and 7.5) it was observed that the curve obtained had a sigmoid trend (Figure 1). Therefore, a sigmoidal model was implemented, as follows:  
\[C_{t}=\frac{C_{0}}{1+\ e^{-(\frac{t-t_{1/2}}{p})}} \tag{1}\]  
where \(C_{0}\) and \(C_{t}\) are the initial molar Qt concentration and the concentration at any time, \(t\), respectively, \(t_{1/2}\) is the half-life of the degradation reaction (s), and \(-\frac{1}{p}\) the apparent first-order degradation rate, \(k\) (s\({}^{-1}\)). The examination was also carried out using first-order kinetics (Figure 2), as follows:  
\[\ln\left(\frac{C_{t}}{C_{0}}\right)=\ -kt \tag{2}\]The decline in absorbance is virtually stabilized after some time, which actually signified the end of the reaction within the time limits initially set. These points do not contribute in tracing kinetic curves, and they were, therefore, excluded from the linear representation in Figure 1.  
As can be seen in Table 1, the implementation of the sigmoidal model exhibited higher R\({}^{2}\), which indicated a better fitting to the experimental data compared to first-order model. However, for both sigmoidal and first-order models, the statistical significance was higher than 95% (\(p<0.05\)). Figure 1: Kinetics of Qt thermal degradation (100 \(\upmu\)mol L\({}^{-1}\)) at pH 7.5 and 90 \({}^{\circ}\)C (**upper plot**). Verification of the first-order kinetics are shown by a linear plot (**lower plot**). Determination of degradation rate constants, \(k\), and degradation half-lives, \(t_{1/2}\), revealed important discrepancies between models (Table 1). In particular, \(k\) determined that the sigmoidal model were 2.3 to 2.5 higher than those determined with the first-order model. However, for pH 7.5, \(t_{1/2}\) determined with the sigmoidal model was 1.55-times higher than that determined with the first-order model. This finding pointed to an underestimation of the degradation rate constant, when the first-order model was used, but also to a different relationship between \(k\) and \(t_{1/2}\) in the sigmoidal model, as implied by Equation (1). At this point, the issue that arises is the reason for which the sigmoidal model, which rather traces Qt degradation more accurately, delivers higher \(k\). The monitoring of Qt degradation is carried out by recording the decrease in \(\lambda_{\text{max}}\) (370 nm). Yet, decrease of absorbance at 370 nm occurs not when Qt starts to break down into simpler phenolics, but as soon as Qt is converted into the initial oxidation product, which is its quinone (Figure 3) [20]. Should this be the case, then initially, decrease in \(\lambda_{\text{max}}\) might be slower. This is because Qt quinone exhibits a \(\lambda_{\text{max}}\) at around 425-430 nm [21] and, thus, it may possess notable absorbance at 370 nm, which would affect monitoring of Qt disappearance. First-order kinetics fails to incorporate this stage, and the points included in tracing Qt degradation are those corresponding to rapid Qt disappearance, which takes place during quinone decomposition. Cleavage of the Qt quinone skeleton would lead to decreases at 370 nm, yielding degradation products (simpler phenolics) that possess practically no absorbance at this region of the spectrum [22]. This is most probably the rationale behind the differences