## 3 Results and Discussion
### Initial Concentration of TCE and KMnO\({}_{4}\)
These values align with previously reported ranges where \(\varepsilon\) values were found between \(-26.3\)\(\pm\) 2.4% and \(-20.9\)\(\pm\) 1.1% [40], while [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] [42] reported \(-25.1\)\(\pm\) 0.4% for excess KMnO4 (1250 mg/L) and \(-26.8\)\(\pm\) 1.1% under limited KMnO4 (67-157 mg/L) supply. While previous studies concluded that \(\varepsilon\) values remain unaffected by excess or insufficient TCE, our results suggest a subtle dependence on the n(KMnO4)/n(TCE) ratio (Figure 2). As this ratio increases, \(\varepsilon\) values also tend to increase, possibly due to the shifts in relative contributions of KMnO4 and MnO2 in the oxidation process. Under KMnO4-limited conditions (n(KMnO4)/n(TCE) \(<\) 2), MnO2 colloids formed during the reaction may oxidize residual TCE, slightly altering the carbon isotope effect [41; 55]. When TCE was excess, KMnO4 was quickly consumed by TCE, and the proportion of MnO2 oxidizing TCE was elevated. There may be a difference between the \(\varepsilon\) values of KMnO4 oxidized TCE and MnO2 oxidized TCE, resulting in a small change in the overall \(\varepsilon\) values at a higher degree of participation of MnO2 oxidized TCE, which needs to be further investigated. Another potential explanation is that insufficient KMnO4 leads to incomplete oxidation, which could affect \(\varepsilon\) values. Although earlier studies overlooked this, [PERSON] and [PERSON] [40] observed a lower \(\varepsilon\) value (\(-26.3\)\(\pm\) 2.4%) in a system with incomplete oxidation compared to one with sufficient oxidant, supporting our observations. To further evaluate these effects under extreme TCE loading, we examined the isotope behavior of DNAPL-phase TCE and a near-saturated aqueous TCE solution (950 mg/L). Compared to 75 mg/L TCE degraded by 250 mg/L KMnO4, TCE degradation was significantly lower in the DNAPL and 950 mg/L conditions, even when using 500 mg/L KMnO4 (Figure 3a). Furthermore, Figure 3b shows a corresponding decrease in \(\delta^{13}\)C values with increasing TCE concentrations. Figure 3c shows that \(\varepsilon\) = \(-24.4\)\(\pm\) 0.9% for 75 mg/L TCE and \(-23.4\)\(\pm\) 2.1% for 950 mg/L TCE. However, the \(\varepsilon\) value for DNAPL TCE was significantly higher at \(-13.0\)\(\pm\) 1.7%. This discrepancy likely results from the slow dissolution of the DNAPL phase, which skews the \(\delta^{13}\)C value of the reacting TCE pool. As heavier  
Figure 2: The comparison of \(\varepsilon\) values reported in this study on the oxidative degradation of TCE by KMnO4 at different n(KMnO4)/n(TCE). The purple solid round data was cited from reported study [40] and the wine color solid triangle data was cited from reported study [42]. TCE accumulates in the aqueous phase and lighter isotopes are continuously supplied via dissolution, the headspace \(\delta^{13}\)C deviates from the Rayleigh model, producing an apparent increase in \(\varepsilon\) values. The evolution of TCE degradation of DNAPL indicated that the TCE is obviously overdosed, but the TCE concentration of headspace gradually decreased for a long time. This may be because the rate of liquid TCE dissolved into the high concentration of TCE solution was slow. The concentration of TCE is still high even if the KMnO\({}_{4}\) oxidized a part of the TCE. Compared with the degradation curve of 950 mg/L TCE, the same concentration of KMnO\({}_{4}\) can only react with about half of the saturated solution of TCE. The saturated solution could not be reached within the time of the experiment. These findings suggest that in a fully dissolved system, increasing TCE concentrations have a small impact on the isotope effect. However, in DNAPL-contaminated zones where dissolution is rate-limiting, isotope effects are more pronounced and may serve as indicators of source zone contamination where TCE persists in the non-aqueous phase.