## 3 Results and Discussion
### Antioxidant Capabilities of TCDs  
The antioxidant power of TCDs was evaluated with the DPPH inhibition assay (Table 1) and compared to that of carbon dots with well-established antioxidant activity, as was that obtained hydrothermally from glutathione (GCD) [18]. The determination is based on the action of the free radical DPPH on the antioxidant, which hands a hydrogen atom to it over, shown in the case of CDs from the surface functional groups -OH and -COOH (Figure 6). This causes a respective radical on the nanoparticle, which has two possible pathways of stabilization: delocalization of the unpaired electron by resonance in the aromatic environment of the CD core or the rearrangement of the chemical bonds of the surface functional groups themselves. Five different concentrations of CDs were tested, ranging from 4 to 20 ppm. TCDs show a strong inhibition even at the lowest concentration, whereas GCD needs at least four-times more concentration to achieve the same antioxidant power. In terms of EC\({}_{50}\) (needed concentration to obtain 50% of DPPH inhibition), EC\({}_{50}\) estimation for TCD is below 4 ppm (0.16 ppm\(\cdot\)n nmol DPPH\({}^{-1}\)), whereas it is around 14 ppm for GCD (0.56 ppm\(\cdot\)n nmol DPPH\({}^{-1}\)). It is known that the co-existence of several antioxidants in a sample may show synergism, exhibiting stronger antioxidant activity as a mixture than when acting \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**[CDs]/ppm** & **4** & **8** & **12** & **16** & **20** \\ \hline \% inhibition TCDs & 54.7\% & 59.6\% & 61.0\% & 63.1\% & 63.8\% \\ \% inhibition GCDs & 21.0\% & 39.0\% & 46.0\% & 53.0\% & 60.0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: DPPH% inhibition at different concentrations of CDs. Figure 5: (a) Tauc plots for estimation of the TCDs bandgap and (b) Urbach energy estimation for GCDs. Figure 6: Mechanism of DPPH-/ROS reduction by antioxidant TCD in aqueous media. separately [29]; taking into account the presence of a wide variety of antioxidants in tomato juice, this synergism may explain the stronger antioxidant activity compared to GCD. The stronger antioxidant activity of TCDs is related to their higher size, as bigger particles potentially have a higher number of surface antioxidant functionalities, which can interact with the environment to a greater extent. Since TCD and GCD are of a different size, the same mass of both materials has a different number of particles and, therefore, the total surface is not comparable. In order to check whether the total available surface of TCD is bigger than GCD, we have to compare the total surface ratio \(n_{\mathrm{T}}\cdot A_{\mathrm{T}}/(n_{\mathrm{G}}\cdot A_{\mathrm{G}})\), where \(n_{\mathrm{T}}\) and \(n_{\mathrm{G}}\) are the number of TCD and GCD nanoparticles, respectively, and \(A_{\mathrm{T}}\) and \(A_{\mathrm{G}}\) are the surface of a single TCD or GCD, respectively. The number of nanoparticles can be estimated from the mass of material used and the material's density. For a fixed mass of TCD, \(m_{\mathrm{T}}\), the number of TCD nanoparticles, \(n_{\mathrm{T}}\), will be represented by:  
\[n_{\mathrm{T}}=\frac{m_{\mathrm{T}}}{\frac{4}{3}\pi n_{\mathrm{T}}^{3}\rho_{ \mathrm{T}}} \tag{6}\]  
where \(r_{\mathrm{T}}\) is the TCD radius and \(\rho_{\mathrm{T}}\) is the TCD density. Here, we suppose an identical density for TCD and GCD and use the same mass of both materials (\(m_{\mathrm{T}}=m_{\mathrm{G}}\)), meaning the ratio of nanoparticles is \(n_{\mathrm{T}}/n_{\mathrm{G}}=(r_{\mathrm{G}}/r_{\mathrm{T}})^{3}\). Similarly, we take into account the equation for the surface of a sphere, \(A_{\mathrm{T}}/A_{\mathrm{G}}=(r_{\mathrm{T}}/r_{\mathrm{G}})^{2}\).