## 3 Results and Discussion
### Effect of Milling Conditions on BDE 209 Degradation and Debromination  
The impact of milling conditions is illustrated in Figure 2 through quantification of the decomposition and debromination efficiency of BDE 209. Further details are provided in the Supplementary Materials (Figures S1-S3). As seen in Figure 2a, the effect of the grinding reagent molar ratio between LiCoO\({}_{2}\) and Fe (\(n_{\text{LiCoO}2}/n_{\text{Fe}}\)) was investigated, and BDE 209 exhibited a faster degradation with a higher \(n_{\text{LiCoO}2}/n_{\text{Fe}}\) ratio after 240 min co-milling. When \(n_{\text{LiCoO}2}/n_{\text{Fe}}\) increased from 0.36 to 0.9, the reduction of BDE 209 was rapidly and significantly escalated from 23.5% to 99.9%, while the debromination rate was varied from 21.0% to 92.0%. However, with \(n_{\text{LiCoO}2}/n_{\text{Fe}}\) reaching 1.08, the removal of BDE 209 remained almost constant, while the debromination decreased to 79.0%. In the low \(n_{\text{LiCoO}2}/n_{\text{Fe}}\) range, the higher LiCoO\({}_{2}\) load enhanced the oxidation of BDE 209. Conversely, in the high \(n_{\text{LiCoO}2}/n_{\text{Fe}}\) range, the excessive LiCoO\({}_{2}\) oxidized the Br\({}^{-}\) yielded in the MC process to Br\({}_{2}\), leading to a low Br\({}^{-}\) concentration being detected, and consequently the debromination rate being decreased [36].  
Figure 2b presents the influence of the rotational speed on the abatement and debromination of BDE 209 within 240 min. As the rotational speed varied from 300 to 600 rpm, both the removal and debromination of BDE 209 increased, reaching a maximum of 99.9% and 92.0% at 600 rpm, correspondingly. These results suggest that a higher ball milling speed could lead to a better degradation and debromination of BDE 209. Previous studies confirmed that the impact energy is a key factor in the MC treatment of pollutants, (see Equation (3)) [37; 38]. The faster rotation speed increases the collision velocity and collision number per unit time, leading to a higher impact energy of the MC process [38]. Hence, the C-C and C-Br bonds in BDE 209 are broken more easily with higher impact energy. When the rotation speed increased to 700 rpm, the degradation and debromination rates remained stable. This indicates that an excessively high rotation speed is unnecessary in this combined system, thus saving energy consumption:  
\[E=\sum_{\mathrm{j=1}}^{\mathrm{n}}\frac{m_{\mathrm{b}}}{2m_{\mathrm{p}}}v_{ \mathrm{j}}^{2} \tag{3}\]  
where \(E\) is the impact energy of milling balls, \(v_{\mathrm{j}}\) is the relative speed of the impact between the ball and the tank wall or the balls, \(m_{\mathrm{b}}\) is the mass of milling balls, n is the collision number per unit time, and \(m_{\mathrm{p}}\) is the mass of sample powders charged into the mill pots.  
Figure 2c depicts the effect of the ball-to-powder ratio (\(m_{\mathrm{b}}/m_{\mathrm{p}}\)) on the removal and the debromination of BDE 209 during MC treatment. The results indicate a positive correlation between the degradation rate and the yield of \(\mathrm{Br}^{-}\) with \(m_{\mathrm{p}}/m_{\mathrm{p}}\). As \(m_{\mathrm{b}}/m_{\mathrm{p}}\) was set at 50, the removal of BDE 209 was 52.1%, and the debromination was 48.9%; as \(m_{\mathrm{b}}/m_{\mathrm{p}}\) increased to 100, 150, and 200, the removal rate reached nearly 100%, and the debromination was 93.1% when \(m_{\mathrm{b}}/m_{\mathrm{p}}\) was at 200. The swift removal of BDE 209 was attributed to the large number of balls at high \(m_{\mathrm{b}}/m_{\mathrm{p}}\), increasing the collision frequency per unit time, and consequently, the amount of impact energy transferred to the solid particles becoming higher (Equation (3)) [39]. It is important to note that the higher the \(m_{\mathrm{b}}/m_{\mathrm{p}}\) ratio, the higher is the energy consumption [37; 38; 39]. Hence, the \(m_{\mathrm{b}}/m_{\mathrm{p}}\) value of 100 was selected as the optimal experimental parameter, considering operability and cost of practical application.