## 4 Discussion
Similarly, the feasibility of the reaction with respect to DPPH radicals (Equation (3)) was determined using the electrode potentials determined by [PERSON] et al. [33]. Both reactions were found to be thermodynamically feasible with a positive overall electromotive force. Similarly, in the case of CUPRAC, the redox potential of Cu(II,I) chelated to neocuproine was found to be E\({}^{0}\) = 0.6 V (Equation (2)), as determined by [PERSON] et al. [18] This is close to that of ABTS\({}^{\bullet+}\)/ABTS (E\({}^{0}\) = 0.68 V); hence, the electron transfer from the TiO\({}_{2}\)-NT surface conduction band was also thermodynamically feasible. \[\text{ABTS}^{\bullet+}+\text{e}^{-}\rightarrow\text{ABTS}\ [0.68\text{V}] \tag{1}\]  
\[\text{Cu(Nu)}^{2+}+\text{e}^{-}\rightarrow\text{Cu(Nu)}^{+}\ [0.60\text{V}] \tag{2}\]  
\[\text{DPPH}^{\bullet}+\text{e}^{-}\rightarrow\text{DPPH}^{-}[0.62\text{V}] \tag{3}\]  
\[\text{TiO}_{2}+\text{e}^{-}\rightarrow\text{TiO}_{2}\ (\text{e}^{-})\ [-0.50\text{V}] \tag{4}\]  
\[\text{ABTS}^{\bullet+}+\text{TiO}_{2}\ (\text{e}^{-})\rightarrow\text{TiO}_{2}+ \text{ABTS}\ [1.18\text{V}] \tag{5}\]  
\[\text{Cu(Nu)}^{2+}+\text{TiO}_{2}\ (\text{e}^{-})\rightarrow\text{TiO}_{2}+ \text{Cu(Nu)}^{+}\ [1.10\text{V}] \tag{6}\]  
\[\text{DPPH}+\text{TiO}_{2}\ (\text{e}^{-})\rightarrow\text{TiO}_{2}+ \text{DPPH}^{-}\ [1.12\text{V}] \tag{7}\]  
The variation in the rates of reaction for the different TiO\({}_{2}\) morphologies can be explained in terms of both (1) the structural variation caused by the electrolyte being used and (2) the manipulation of the structural growth on the surface influenced by the different process parameters, namely the potential. In TiO\({}_{2}\), the absorption of light containing sufficient energy results in electrons being promoted from the valence band to the conduction band leaving behind voids, or photoholes (h+), in the valence band. The promoted electrons migrate to the surface and can later react with other chemical compounds. However, the most reactive form of TiO\({}_{2}\), anatase, has a low quantum yield and the promoted electrons can rapidly recombine with the void holes generated in the valence band. The scope of controlling or \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **DPPH (s\({}^{-1}\))** & **ABTS (s\({}^{-1}\))** & **CUPRAC (M\({}^{-1}\)s\({}^{-1}\))** \\ \hline
**Blank** & \(-1.12\times 10^{-3}\pm 5.80\times 10^{-5}\) & \(3.82\times 10^{-3}\pm 6.12\times 10^{-5}\) s\({}^{-1}\) & \(1.68\times 10^{-3}\pm 4.76\times 10^{-4}\) \\
**TiO\({}_{2}\)NT** & \(-2.63\times 10^{-2}\pm 2.13\times 10^{-3}\) s\({}^{-1}\) & \(-1.03\times 10^{-2}\pm 4.30\times 10^{-4}\) s\({}^{-1}\) & \(1.15\times 10^{-2}\pm 9.64\times 10^{-4}\) \\
**TiO\({}_{2}\)NT-Ag** & \(-2.19\times 10^{-2}\pm 9.87\times 10^{-4}\) s\({}^{-1}\) & \(-1.07\times 10^{-2}\pm 1.17\times 10^{-3}\) s\({}^{-1}\) & \(1.21\times 10^{-2}\pm 4.62\times 10^{-4}\) \\
**TiO\({}_{2}\)NT-S** & \(9.73\times 10^{-3}\pm 9.87\times 10^{-4}\) s\({}^{-1}\) & \(-7.24\times 10^{-3}\pm 3.34\times 10^{-4}\) s\({}^{-1}\) & \(7.09\times 10^{-3}\pm 5.01\times 10^{-4}\) \\
**TiO\({}_{2}\)NT-P** & \(-1.29\times 10^{-2}\pm 5.22\times 10^{-3}\) s\({}^{-1}\) & \(-8.58\times 10^{-3}\pm 4.12\times 10^{-4}\) s\({}^{-1}\) & \(6.29\times 10^{-3}\pm 6.25\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Rate constant \(k\) for the various electron-transfer-based methods tested using first-order kinetics for DPPH and 2,2\({}^{\prime}\)-azino-bis (3-ethylbenzothazoline-6-sulfonic acid) (ABTS), while second-order kinetics were used for cupric ion reducing antioxidant capacity (CUPRAC). obtaining a specific morphology is to increase the reactivity of the TiO\({}_{2}\) through enhancing the ability of the surface to interact more with the pollutant or the light. The results obtained showed that layer thickness, rather than wall thickness, and tube diameters had the largest effect on the rate of reaction.