## 3 Results and Discussions
### \(\text{NO}_{3}\text{${}^{-}$}\) and DOC Release  
The results of the \(\text{NO}_{3}\text{${}^{-}$}\) and DOC concentrations monitoring suggested that Graphene performed well in comparison with the other soil improvers, despite the fact that Graphene was applied with a lower amount respect to the other improvers. CS batches showed higher release of \(\text{NO}_{3}\text{${}^{-}$}\). This was due to the higher pH that corresponds to a higher number of negative charges on the surface of the solid phase, which increases the solubility of the cations [39]. In the Graphene batches \(\text{NO}_{3}\text{${}^{-}$}\) concentration in water was significatively lower than in the Control for both CS and SS soils (Figure 7), with statistically different means respect to Control except for CS and SS L/S = 1 and L/S = 2. This suggested that possible adsorption reactions might occur, as already found by [PERSON] et al. [3] and [PERSON] et al. [12]. In addition, it has been recently highlighted that Graphene can enhance denitrification performance [40], significantly reducing the concentration of \(\text{NO}_{3}\text{${}^{-}$}\) in the liquid phase. Based on the results obtained by the sorption isotherm experiments (data in Supplementary Materials), the \(\text{NO}_{3}\text{${}^{-}$}\) decrease in Graphene's batches was likely due to denitrification. This is due to the fact that the percentage of adsorption, especially in the solution with 10 mg/L of \(\text{NO}_{3}\text{${}^{-}$}\), was almost negligible (\(\approx\)0.2% of \(\text{NO}_{3}\text{${}^{-}$}\) adsorbed). Compost batches showed significative higher values of \(\text{NO}_{3}\text{${}^{-}$}\) concentration in water for both CS and SS soils, above the admissible limit of 50 mg/L [41] for all L/S ratios, with statistically different means respect to Control. This was due to organic N mineralization which produced a large amount of \(\text{NO}_{3}\text{${}^{-}$}\) that was brought into solution approaching an asymptotic value of approximately 100 mg/L for CS batches and 200 mg/L for SS ones. For instance, the inorganic N reported by the manufacturer was 270 mg/kg, which was similar to the asymptotical value for the SS batches, meaning that nearly all of the inorganic N was brought into solution. In CS batches, \(\text{NO}_{3}\text{${}^{-}$0}\) was probably denitrified by the excess of labile organic substrates available in the Compost. Indeed, the manufacturer reported 29.4% of humidified organic matter. Biochar batches showed a slight but unsignificant increase of \(\text{NO}_{3}\text{${}^{-}$1}\) in CS batches respect to the Control (except for L/S = 1), while no differences in comparison to the Control was recorded in SS batches (except for L/S = 1 and L/S = 2). This highlights no release, no sorption, and no degradation of \(\text{NO}_{3}\text{${}^{-}$2}\) in all Biochar batches. Zeolites batches showed significative lower \(\text{NO}_{3}\text{${}^{-}$3}\) concentration in water than in the Control for CS L/S = 5 and L/S = 10 and for SS L/S = 5, since the clinoplolite has a moderately good \(\text{NO}_{3}\text{${}^{-}$4}\) adsorption capacity at neutral and basic pH [30]. ${}^{-}$5 ORP values in SSE batches CS (**left panels**) and SS (**right panels**) soils versus L/S ratios values at the end of the monitoring period. Error bars denote standard deviation calculated on three replicates, while lines are the best fit natural logarithmic curves. Different letters indicate statistically different means at 0.05 confidence. ${}^{-}$6 NO\({}_{3}\)– concentrations in SSE batches with CS (**left panels**) and SS (**right panels**) soils versus L/S ratios values at the end of the monitoring period. Error bars denote standard deviations calculated on three replicates, while lines are best fit natural logarithmic curves. Different letters indicate statistically different means at 0.05 confidence. The DOC concentrations were similar among CS and SS batches (Figure 8).