## 3 Results
### E Dependence on the Regeneration of Trp from Trp\({}^{\bullet+}\)  
We further examined the reducing capacities of various plant phenols toward tryptophan cations. To explore the effect of driving force (\(\Delta E\)) on the reduction of Trp\({}^{\bullet+}\) by plant phenols, we selected six phenols with differing \(\Delta E\) values: salicylic acid (Sal, \(\Delta E=-0.13\) V), m-hydroxyl-benzoic acid (m-hyd, \(\Delta E=-0.02\) V), Van (\(\Delta E=0.08\) V), Pyr (\(\Delta E=0.32\) V), caffeic acid (Caf, \(\Delta E=0.36\) V), and catechin (Cat, \(\Delta E=0.62\) V). The kinetic curves of Trp\({}^{\bullet+}\) at 560 nm are shown in Figure 5. As shown in Figure 5A, the rate constants listed in Table 3 cover a broad range. These values indicate that tryptophan participates in a second-order reaction, with rate constants consistent with a diffusion-controlled bimolecular process.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**pH** & **2** & **5.6** & **7.2** & **9** & **10** \\ \hline \(\varphi\)-OH & 98.84\% (99.31\%) & 2.1\% (3.47\%) & 0.05\% (0.09\%) & 0.00\% (0.00\%) & 0.00\% (0.00\%) \\ \hline \(\varphi\)-O\({}^{-}\) & 1.16\% (0.69\%) & 97.88\% (96.53\%) & 99.5\% (99.79\%) & 78.02\% (93.18\%) & 26.20\% (57.74\%) \\ \hline \(\varphi\)-O\({}^{2-}\) & 0.00\% (0.00\%) & 0.01\% (0.00\%) & 0.44\% (0.12\%) & 21.98\% (6.82\%) & 73.80\% (42.26\%) \\ \hline \end{tabular} \({}^{a}\) Calculated with Marvin Calculator Plugins. Marvin 18.24.0 2018, ChemAxon ([[http://www.chemaxon.com](http://www.chemaxon.com)]([http://www.chemaxon.com](http://www.chemaxon.com)), accessed on 10 January 2024).  
\end{table}
Table 2: Percentages of deprotonated forms of plant phenols in Pyr (and Van) from pH 2 to 10 \({}^{a}\).  
Figure 4: pH influences the regeneration of Trp from Trp\({}^{\bullet+}\). Kinetic traces of Trp\({}^{\bullet+}\) were recorded at 560 nm in the pH range from 2 to 10 with (**A**) syringic acid (Syr) and (**B**) vanillic acid (Van). Thicker solid lines are derived from curve fitting. (**C**) Effect of pH on pseudo-first-order rate constant for regeneration of Trp from Trp\({}^{\bullet+}\) as calculated by radical decay at 560 nm.  
The second-order rate constants for electron transfer (ET) from the plant phenols to the Trp\({}^{\bullet+}\) increase with the driving force, approaching rates near the diffusion limit for bimolecular reactions [26]. At pH 9, the reaction rate with Trp\({}^{\bullet+}\) increases from 2.2 \(\times\) 10\({}^{7}\) M\({}^{-1}\).s\({}^{-1}\) for Sal to 1.3 \(\times\) 10\({}^{8}\) M\({}^{-1}\).s\({}^{-1}\) for Caf. However, as the driving force continues to increase, the rate constants for ET with Trp radical cation (Trp\({}^{\bullet+}\)) decrease. For instance, the reaction rate with Trp\({}^{\bullet+}\) for catechchin is 7.5 \(\times\) 10\({}^{7}\) M\({}^{-1}\).s\({}^{-1}\). This bell-shaped dependence of ET rates on the driving force is consistent with predictions from [PERSON] theory [27], which was later experimentally confirmed for various processes, including ET from phenolate ions [28; 29; 30; 31; 32]. In accordance with this framework, we analyzed the rate data using [PERSON] theory [27; 32], which describes the ET rate as being controlled by the driving force, a matrix coupling element (\(V\)), and the reorganization energy (\(\lambda\)) for the reaction: [32; 33]  
\[k_{\text{ET}}=\sqrt{\frac{4\pi^{3}}{h^{2}\lambda RT}}V^{2}\text{exp}-\left\{ \frac{\left(\Delta E^{0}+\lambda\right)^{2}}{4\lambda RT}\right\} \tag{6}\]  
The plot of Figure 5B is based on a reorganization of Equation (6) and yields \(\lambda\) = 0.43 \(\pm\) 0.08 eV for the reorganization energy for ET from the plant phenols to the Trp radical cation at pH 9. The matrix coupling element has the value of \(V\) = 3.75 \(\pm\) 0.35 cm\({}^{-1}\) for the plant phenols. The values for the relative coupling elements represent the coupling between each of the Trp radical cations and the plant phenolates investigated.