Diclofenac – PMX 205

Ferrate self-decomposition in water is also a self-activation process: Role of Fe(V) species and enhancement with Fe(III) in methyl phenyl sulfoxide oxidation by excess ferrate

Zhuang-Song Huang a, Lu Wang a,∗, Yu-Lei Liua, Hong-Yan Zhanga, Xiao-Na Zhaoa, Yang Baib, Jun Maa
a State Key Laboratory of Urban Water Resource and Environment, School of Environment, Harbin Institute of Technology, Harbin 150090, China
b Civil Engineering, College of Engineering and Informatics, National University of Ireland, Galway, Ireland

Abstract
To reveal the role of ferrate self-decomposition and the fates of intermediate iron species [Fe(V)/Fe(IV) species] during ferrate oxidation, the reaction between ferrate and methyl phenyl sulfoxide (PMSO) at pH 7.0 was investigated as a model system in this study. Interestingly, the apparent second-order rate constants (kapp) between ferrate and PMSO was found to increase with ferrate dosage in the condition of excess ferrate in borate buffer. This ferrate dosage effect was diminished greatly in the condition of excess PMSO where ferrate self-decomposition was lessened largely, or counterbalanced by adding a strong complexing ligand (e.g. pyrophosphate) to sequester Fe(V) oxidation, demonstrating that the Fe(V) species derived from ferrate self-decomposition plays an important role in PMSO oxidation. A mechanistic kinet- ics model involving the ferrate self-decomposition and PMSO oxidation by Fe(VI), Fe(V) and Fe(IV) species was then developed and validated. The modeling results show that up to 99% of the PMSO oxidation was contributed by the ferrate self-decomposition resultant Fe(V) species in borate buffer, revealing that ferrate self-decomposition is also a self-activation process. The direct Fe(VI) oxidation of PMSO was im- pervious to presence of phosphate or Fe(III), while the Fe(V) oxidation pathway was strongly inhibited by phosphate complexation or enhanced with Fe(III). Similar ferrate dosage effect and its counterbalance by pyrophosphate as well as the Fe(III) enhancement were also observed in ferrate oxidation of microp- ollutants like carbamazepine, diclofenac and sulfamethoxazole, implying the general role of Fe(V) and promising Fe(III) enhancement during ferrate oxidation of micropollutants.

Keywords:
Ferrate
Intermediate iron species Oxidation Micropollutants
Kinetics

1. Introduction
Ferrate has been considered as a green and potent chemi- cal with multiple functions in water treatment for many years (Sharma et al. 2015, Ma and Liu 2002a, Ma and Liu 2002b, Chen et al. 2018a, Chen et al. 2018b). As a powerful oxidant, ferrate is effective in abating micropollutants from water, espe- cially organic compounds with electron-rich moieties like phe- nols, oleﬁns, anilines and amines (Lee et al. 2009, Liu et al. 2018, Sun et al. 2018). Ferrate is also a promising disinfectant, eﬃca- cious for inactivating bacteria and viruses. Meanwhile, it has a sat- isfactory control of halogenated disinfection byproducts (DBPs) for- mation (Schink and Waite 1980, Hu et al. 2012, Fan et al. 2018, Cui et al. 2020, Gombos et al. 2012, Wang et al. 2019a). Further, the resultant iron(III) oxide/hydroxide particles from ferrate reduction show great capacity in removing arsenic, selenite, heavy metals and total organic compounds (Yang et al. 2018a, Viktor et al. 2020, Liu et al. 2017, Yang et al. 2018b).
The intrinsic drawback of ferrate might be its instability in aqueous solution, which causes great challenge and dif- ﬁculty in the ferrate preparation, storage and transportation (Sharma et al. 2015). The ferrate self-decomposition is highly pH- and dosage-dependent, which is accelerated at acidic condi- tion and high dosage (Lee et al. 2014). During the ferrate self- decomposition, Fe(VI) is reduced to Fe(III) by water via the in- termediacy of Fe(IV) and Fe(V) species, of which reactivity was reported to be several orders of magnitude higher than that of the parent Fe(VI) and might contribute to the micropollutants elimination during ferrate oxidation (Sharma 2011, Sharma 2013, Sharma et al. 2001). However, the Fe(V)/Fe(IV) species are also highly unstable and short-lived in aqueous solution, resulting in low oxidant exposure (Rush and Bielski 1989, Melton and Biel- ski 1990). Therefore, whether ferrate self-decomposition is just a self-degradation process consuming oxidation capacity or a self-activation process transforming Fe(VI) into the more reactive Fe(V)/Fe(IV) species for oxidation has remained unclear. It depends on whether the Fe(V)/Fe(IV) species are taking part into the target compounds oxidation and to what extent they contribute to the overall ferrate oxidation.
Exploring the reaction properties of the Fe(V)/Fe(IV) species could help to understand their roles and fates during the ferrate oxidation process. In a previous study, we found that the oxida- tive reactivity of Fe(V) species could be greatly reduced upon phos- phate complexation, which depressed the overall ferrate oxidation performance (Huang et al. 2018). On one hand, we concluded that the actual oxidation ability of ferrate was underestimated because of the prevalent use of phosphate buffer in lab experiments rel- evant to ferrate. On the other hand, based on the chemical char- acteristic that the Fe(V) species oxidation could be sequestered upon phosphate or pyrophosphate ligand complexation, we hy- pothesized that the reaction selectivity and relative contribution of Fe(V) species might be investigated by comparing the ferrate ox- idation performance in solution with or without the presence of phosphate ligand.
To accurately obtain the relative contribution of a speciﬁc species during a complex reaction involving multiple active species, a normal way is to develop a chemistry kinetic model con- sisting of major elementary reactions and corresponding rate con- stants. In this model approach, the selection of target compound is crucial for studying the fates of Fe(V)/Fe(IV) species during fer- rate oxidation. Good candidate compounds are those whose re- action mechanisms are known as one- or two-electron transfer, which indicate that Fe(V) or Fe(IV) species is primarily produced from Fe(VI) reduction. ABTS is a typical compound of one-electron transfer mechanism and its initial oxidation product (ABTS·+) is easy to be monitored spectrophotometrically at wavelength of 415 nm. However, ABTS·+ would be further oxidized to other un- known products in the excess of ferrate (Xue et al. 2020), mak- ing the (excess) ferrate-ABTS system too complicated. It was re- ported that some sulfoxide compounds, such as dimethyl sulfox- ide (DMSO) and methyl phenyl sulfoxide (PMSO), could be oxidized by ferrate with a two-electron transfer mechanism, generating the corresponding sulfones as products, which would not be further oxidized by excess ferrate (Pang et al. 2011, Shao et al. 2019). Besides, both PMSO and PMSO2 (methyl phenyl sulfone) could be readily analyzed by liquid chromatography (Pang et al. 2011, Wang et al. 2018).
The enhanced ferrate oxidation of organic pollutants (e.g. di- clofenac (Zhao et al. 2018a, Zhao et al. 2018b) and sulfamethoxa- zole (Shao et al. 2019)) with Fe(III) addition have been reported in unbuffered or borate buffered systems. The catalytic effect of Fe(III) particles on ferrate self-decomposition (Jiang et al. 2015) and the concomitant accelerated formation of active intermediate iron species (Lee et al. 2014) were proposed as the underlying mecha- nism. However, the discussion was rather general and no solid ev- idence or quantitative analysis is available by now.
In this study, the ferrate-PMSO reaction was systematically in- vestigated as a model system of two-electron transfer mechanism, to provide basic information on the fates of Fe(V)/Fe(IV) species and the role of ferrate self-decomposition during ferrate oxidation. The oxidation kinetics of PMSO by varying dosage of ferrate were comparatively investigated in the condition of excess ferrate or ex- cess PMSO in borate buffer or phosphate buffer at pH 7.0. A mech- anistic kinetic model was then developed to quantitatively explain the oxidant dosage effect observed and gain further insights into the Fe(III) enhanced effect.

2. Material and Methods

2.1. Chemicals and Reagents
Potassium ferrate (K2FeO4) was prepared according to a wet chemical oxidation method described previously (Thompson et al. 1951, Liu et al. 2016), having a purity as high as 88% in term of Fe(VI) (w/w). One of the main impurity in ferrate powder is Fe(III) (oxyhydr)oxides (>10%), which could be removed by ﬁltration. Preparation of stock solutions of ferrate, FeCl3, and Fe(VI)-origin Fe(III) was described in SI-Text-1. Methyl phenyl sulfoxide (PMSO), methyl phenyl sulfone (PMSO2), 2,2-azino- bis(3-ethylbenzothiazoline-6-sulfonate) (ABTS), sulfamethoxazole (SMX), carbamazepine (CBZ) and diclofencac sodium (DCF) were purchased from Sigma-Aldrich with purity >97%. Other reagents, including sodium tetraborate decahydrate, sodium hydrogen phos- phate, sodium dihydrogen phosphate, sodium pyrophosphate, ferric chloride, hydrogen peroxide, were all reagent pure and obtained from Sinopharm Chemical Reagent Co., Ltd. All aqueous solutions were prepared with ultrapure water produced by a Milli-Q system (Millipore, Billerica, MA) except that the stock solutions of SMX and CBZ were prepared in an acetonitrile-water mixture (10/90%). Authentic water sample (Songhua River at Harbin, Heilongjiang province, China) has been ﬁltered through glass-ﬁber membrane (0.7 μm) prior to use. Relevant parameters are shown in Table S2.

2.2. Kinetic Experiments
Kinetic studies of PMSO oxidation by ferrate were investigated in different buffer conditions at pH 7.0. The batch experiments were conducted in glass ﬂasks with rapid magnetic stirring (500 r/min) at room temperature (25±0.2°C) maintained by a water bath. An aliquot of PMSO stock solution (10 mM) was spiked into the 150 mL system for a target concentration of 10 or 104 μM. Var- ious calculated volumes of ferrate stock solution for different fer- rate dosages (20, 30, 50 μM) were added to start the kinetic runs. Two sample aliquots were sampled simultaneously at proper time intervals. One sample was immediately quenched with excess hy- droxylamine [20 μL of 10%(w/w) NH2OH•HCl] (Johnson and Horn- stein 2003, Feng et al. 2018) and ﬁltered through a PTFE membrane (0.22 μm pore size) before PMSO and PMSO2 concentration mea- surement with liquid chromatography (SI-Text-2). Another sample was quenched with an ABTS solution to determine the residual fer- rate concentrations (Lee et al. 2014). The experimental procedures of the investigation of Fe(III) effect on ferrate oxidation of PMSO were similar to the ones described above. Speciﬁcally, since Fe(III) stock solution is acid, the pH of borate buffer was re-adjusted to 7.0 with NaOH after the spike Fe(III) stock solution. After that, PMSO and ferrate stock solutions were added in sequence to start the reaction. All the kinetic experiments were independently re- peated twice at least. The average values were presented and the error bars represent the range observed in the two replicates. The ﬁnal solution pH was measured and the pH variations were within the range of ±0.2 pH unit.

2.3. Stoichiometry Experiments
The reaction stoichiometry of ferrate and PMSO was determined by measuring the generated PMSO2 concentration after the com- plete reaction of ferrate with far excess of PMSO at pH 6.0, 7.0, 8.0 and 9.0. Serial glass beakers containing 10 mL of borate buffer so- lution were spiked with 20 μL pure PMSO liquid (melting point, 32°C) and the resulting PMSO concentration was around 17 mM. Various calculated volumes of ferrate stock solution (~4 mM) were added to the beakers with magnetic stirring (150 r/min) to start the reaction, with a resultant ferrate concentration ranging from 5 to 50 μM. After the reaction completed, an aliquot of 1 mL was sampled and ﬁltered with a PTFE membrane (0.22 μm pore size). The ﬁnal solution pH was measured with a Leici pH-meter (PHS- 3C, Shanghai) and the pH variations were within the range of ±0.2 pH unit. The concentration of PMSO2 was then analyzed by liquid chromatography.

2.4. Kinetic Fitting
The kinetic ﬁtting and simulation of the mechanistic model for ferrate-PMSO reaction were carried out by a kinetic simulation software, Kintecus (www.kintecus.com) (Ianni 2003). Speciﬁcally, a Powell ﬁtting algorithm (Vetterling et al. 1992) with a proprietary function as the comparison operator was selected to run the opti- mization. A bootstrapping method (iteration amount = 1000) was applied to determine the standard deviations of the ﬁt-derived pa- rameters (Ianni 2003, Efron 1992).

3. Results and Discussion

3.1. Reaction Kinetics of Ferrate and PMSO at pH 7.0: Buffer Effect and Ferrate Dosage Effect

3.1.1. In the condition of excess ferrate
Herein, the reaction kinetics between ferrate and PMSO were conducted comparatively in 10 mM borate and 10 mM phosphate at pH 7.0. The initial concentration of PMSO was kept at 10 μM with varying excess ferrate concentration ([ferrate]0 = 20, 30, 50 μM). The second-order rate constant is obtained by plotting the natural logarithm of the target compounds concentration vs. the Fe(VI) exposure according to the equation shown as follows: where [PMSO] and [Fe(VI)] represent the target compounds and ferrate concentration at time t; kapp represents the apparent second-order rate constant of reaction between ferrate and PMSO. As shown in Fig. 1, the PMSO consumption and PMSO2 for- mation as a function of time were determined and found to be equivalent along the reaction. The ferrate decay was simultane- ously monitored (Figure S1). In borate buffer [Fig. 1 (a-c)], after 10 min of reaction, the PMSO consumption increased from 6.1 to 9.4 μM as the ferrate dosage increased from 20 to 30 μM. As the ferrate dosage further increased to 50 μM, the oxidation rate in- creased dramatically where the 10 μM of PMSO was completely oxidized to PMSO2 within only 1 min. Similar trend was also ob- served in phosphate buffer [Fig. 1 (e-g)], but the reaction rates were much slower.
Theoretically, the increase of ferrate dosage would promote the organic compounds’ elimination rate but should not alter the ap- parent second-order rate constants (kapp) if Fe(VI) species was the only responsible oxidant (House 2007). However, as shown in Fig. 1 (d, h), the kapp value in borate buffer increased from (1.3±0.1) × 102 to (3.6±0.1) × 102 and (1.5±0.1) × 103 M−1s−1 as ferrate dosage increased from 20 to 30 and 50 μM, respectively.
The kapp values in phosphate buffer were also increased with fer- rate dosage increasing, but the values were smaller (34±1, 39±1 and 54±1 M−1s−1 for ferrate dosages of 20, 30, 50 μM, respec- tively) and the trend was milder (the maximum variation factor for kapp value reduced from 11.5 in borate buffer to 1.6 in phosphate buffer). Similar oxidant dosage effect was also reported for fer- rate oxidation of taste and odor compounds (including 1-penten- 3-one, cis-3-hexen-1-ol and β-ionone) in phosphate buffered solu- tions at pH 7.0, but the underlying mechanism had not been re- vealed (Shin et al. 2018). The results above show that increasing ferrate dosage could self-enhance ferrate oxidation of PMSO, but the dosage effect was diminished to some extent by the presence of phosphate ligand.

3.1.2. Initial instant oxidation
It should be noted that three kinetic lines for 20, 30, 50 μM ferrate dosage did not pass the zero point in Fig. 1 (d, h). Also, sudden drops or lifts were found at the beginning of the PMSO or PMSO2 kinetic curves in Fig. 1 (a-c) and (e-h). The above phe- nomena indicate that an instant oxidation had occurred upon the ferrate addition, which might be caused by the relative high con- centration of ferrate at the dosing point when the oxidant diffu- sion proceeded. To verify this speculation, equal volume of ferrate solution and PMSO solution were mixed together to start the ki- netics experiment, where the dosed ferrate solution concentration was lower to only 2 times of the ﬁnal concentration and the dif- fusion process could be greatly shortened, compared with the con- ventional ferrate dosing method of injecting concentrated ferrate stock solution. Figure S2 shows that the kapp values determined by these two methods were identical within experimental error but the initial rapid PMSO loss was eliminated in the 1:1 mixing group and the ﬁtting line of ln(C/C0) vs Fe(VI) exposure plot was nearly across the zero point. The above result veriﬁes that the instant ox- idation gap during ferrate oxidation of PMSO was caused by the initial insuﬃcient mixing. Hence, the slope of kinetic line exclud- ing zero point would reﬂect the true kapp value that did not cover the instant oxidation caused by initial insuﬃcient mixing.

3.1.3. In the condition of excess PMSO
Ferrate self-decomposition is inevitable when PMSO is oxidized by excess ferrate. In order to reveal the relationship between fer- rate self-decomposition and ferrate oxidation, the reaction kinet- ics was also investigated comparatively in the condition of excess PMSO, where the ferrate self-decomposition was lessened largely

3.2. Role of Fe(V) Species in the PMSO Oxidation by Ferrate

3.2.1. The cause of buffer effect and ferrate dosage effect
No signiﬁcant buffer effect was observed on the PMSO oxida- tion kinetics for ferrate reaction with excess PMSO, contrast to the obvious inhibition effect of phosphate on PMSO oxidation by ex- cess ferrate. This distinct buffer effect indicates that i) the major iron species responsible for PMSO oxidation are different in the conditions of excess PMSO and excess ferrate; ii) the buffer inﬂu- ence/ligand effect on PMSO oxidation are varied with Fe(VI), Fe(V) and Fe(IV) species.
The inﬂuence of buffer nature on reaction between Fe(VI) species and PMSO was investigated by monitoring the Fe(VI) de- cay kinetics at varying excess dosage of PMSO. The Fe(VI) decay kinetics could be described by the following rate law: the PMSO concentration increased from 10 to 104 μM, the reac- tions proceeded more rapidly but the experimental determined kapp value turned out to be decreased. For example, the kapp values for 20, 30 and 50 μM ferrate dosage in borate buffer was lowered from (1.3±0.1) × 102, (3.6±0.1) × 102 and (1.5±0.1) × 103 M−1s−1 to 43±2, 54±2 and 74±3 M−1s−1 by factor of around 3, 7 and 20 times respectively. The corresponding kapp values in phosphate buffer were decreased to be 33±4, 36±2 and 39±2 M−1s−1 for fer- rate dosage of 20, 30 and 50 μM, only a little smaller than the values in borate buffer. Compared to the condition of excess fer- rate, both the buffer effect and ferrate dosage effect on PMSO oxi- dation kinetics were diminished greatly in the condition of excess PMSO, suggesting these two effects in excess ferrate are strongly related to ferrate self-decomposition, of which decomposition in- termediate products [i.e. Fe(V)/Fe(IV) species] might be involved in the PMSO oxidation. where kappr represents the apparent second-order rate constant and kobs represents the pseudo ﬁrst-order rate constant of reaction between ferrate and PMSO.
As shown in Fig. 3, since the PMSO concentration is not in far excess, the kobs -[PMSO]0 plot is not across the zero point and the intercept corresponds to the ferrate self-decomposition. The observed Fe(VI) decay rate was positively dependent on PMSO dosage, where the slope yields a consistent second-order rate con- stant (kappr) of ~40 M−1s−1 in both phosphate buffer and borate buffer. The identical slopes in borate buffer and phosphate buffer reveal that the speciﬁc PMSO oxidation by Fe(VI) species was not inﬂuenced by phosphate. The Fe(VI) oxidation of ABTS, a one- electron transfer model compound, was also found not inﬂuenced by phosphate in our previous study (Huang et al. 2018). Figure S4 shows that the Fe(VI) oxidation of micropollutants like CBZ and DCF were also not affected by phosphate. The results above suggest that the imperviousness of Fe(VI) species oxidation to phosphate is likely universal.
Fe(VI) reacted with PMSO via a two-electron transfer mecha- nism, producing equimolar of Fe(IV) and PMSO2. The initial reac- tion of ferrate self-decomposition was also reported to produce Fe(IV) species and H2O2 (Lee et al. 2014). Therefore, suﬃcient amount of Fe(IV) intermediate would be formed during the ferrate- PMSO reaction in both conditions of excess ferrate and excess PMSO. If the observed buffer effect in excess ferrate was caused by the ligand inhibition on Fe(IV) oxidation of PMSO, then a remark- able buffer effect should be also observed in the condition of ex- cess PMSO, which is in contrast to the experimental result. Hence, both Fe(VI) and Fe(IV) species could be excluded for causing the buffer effect.
Then, the only possible iron species responsible for the ob- served buffer effect was Fe(V) species, of which oxidation would be greatly suppressed by phosphate complexation (Huang et al. 2018). In ferrate-PMSO reaction system, Fe(V) was generated from the one-electron reduction of Fe(VI) by Fe(II), the reaction product of Fe(IV) species with H2O2 or PMSO. Since Fe(V) was directly pro- duced from Fe(VI) species, the Fe(V) formation was dependent on the availability of Fe(VI) species. In the condition of excess PMSO, most Fe(VI) was consumed by PMSO and thus less Fe(V) formation and Fe(V) contribution for PMSO oxidation was expected. Compar- atively, in the condition of excess ferrate, more Fe(VI) species were available to produce Fe(V) species via ferrate self-decomposition process for PMSO oxidation. As a result, buffer effect is obvious in excess ferrate condition where the Fe(V) concentration and contri- bution is prominent and no signiﬁcant buffer effect was observed in excess PMSO condition due to the much less Fe(V) occurrence. In this fashion, the ferrate dosage effect observed in the condi- tion of excess ferrate could be also explained by the involvement of Fe(V) species derived from ferrate self-decomposition, which would be enhanced at higher ferrate dosage and concomitantly the Fe(V) contribution. On the other hand, the ferrate dosage effect was weakened in phosphate buffer as the Fe(V) oxidation would be inhibited by phosphate presence.
The role absence of Fe(IV) species in buffer effect suggests that:i) Fe(IV) reacted sluggishly with PMSO at pH 7.0 and contributed barely to the overall PMSO oxidation no matter in which buffer condition or ii) the Fe(IV) oxidation of PMSO was not inﬂuenced by the phosphate presence like Fe(VI) species. The former conse- quence implies that Fe(IV) was not involved in the PMSO oxida- tion, then there was no place for Fe(IV) to cause the ferrate dosage effect on PMSO oxidation. The latter one was against the phe- nomenon that ferrate dosage effect was eliminated by a large ex- tent in phosphate buffer. Therefore, Fe(IV) would not be the cause of ferrate dosage effect at pH 7.0.

3.2.2. Counterbalance of ferrate dosage effect by pyrophosphate
If the mechanism proposed above is true, the oxidant dosage effect in borate buffer is expected to be counterbalanced with the presence of an appropriate amount of a much stronger ligand, like pyrophosphate.
As shown in Figure S5, in the condition of excess ferrate, 0.1 mM pyrophosphate greatly inhibited the reaction between ferrate and PMSO compared with oxidation kinetics in borate buffer [Fig. 1 (a-d)] but was not suﬃcient to completely diminish the ferrate dosage effect (kapp = 31±1, 34±3, 43±2 M−1s−1 for 20, 30, 50 μM ferrate dosage, respectively). Increasing the pyrophosphate concen- tration to 1 mM, the kapp values were reduced to a relatively con- stant level around 30 M−1s−1 for all ferrate dosages of 20, 30, 50 μM [Fig. 4 (a, b)]. In the condition of excess PMSO [Fig. 4 (c, d)], the kapp values were also obtained at a similar level around 30 M−1s−1 with the presence of 1 mM pyrophosphate. The consistent values (~30 M−1s−1) in pyrophosphate buffer prove that the Symbols represent the average values of two independent experiments and the error bars represent the range observed in the two replicates. Dash lines represent the kinetic model simulations. Solid lines represent the linear ﬁtting ferrate dosage effect was induced by Fe(V) oxidation, which was completely sequestered in 1 mM pyrophosphate buffer.
At pH 8.0, 1 mM pyrophosphate could also diminish the fer- rate dosage effect, reducing the kapp values from 16±1, 18±1, and 25±1 M−1s−1 for 20, 30 and 50 μM ferrate to a consistent value around 9 M−1s−1 (Figure S6). Compared with that at pH 7.0, the reaction was much slower and the ferrate dosage effect was also much weaker at pH 8.0. The results above could be rationalized by the fact that ferrate self-decomposition is faster at lower pH, which favors the generation of Fe(V) species from ferrate self- decomposition and thus the PMSO oxidation (Lee et al. 2014). Besides, the Fe(V) reactivity was also dependent on solution pH, which was reported to be more reactive at lower pH (Sharma and O’Connor 2000, Sharma 2002, Sharma et al. 2004). Therefore, the ferrate dosage effect is more prominent at lower pH.

3.3. Mechanistic Kinetic Modeling

3.3.1. Model development
Based on the experimental results and analyses above, a ki- netic model involving the ferrate self-decomposition, PMSO oxida- tion by Fe(VI), Fe(V) and Fe(IV) species was proposed to simulate the ferrate-PMSO reaction at pH 7.0 (Fig. 8 and Table 1). The kinetics and mechanism of ferrate self-decomposition have been investigated in depth recently (Lee et al. 2014, Jiang et al. 2015). Lee et al. reported that the self-decomposition kinetics of ferrate was second-order at pH 7.0 in phosphate buffer (Lee et al. 2014). It started with the rate-limiting dimer- ization of two Fe(VI) species to form a di-ferrate(VI) intermedi- ate, which ﬁnally hydrolyzed into two Fe(IV) species and H2O2 (eq 1). The Fe(IV) species further oxidized H2 O2 to O2 , produc- ing Fe(II) as product (eq 2). Fe(II) then reduced Fe(VI) species via one-electron transfer, generating Fe(V) species and Fe(III) (eq 3). The Fe(V) species then underwent self-decomposition reaction, including ﬁrst-order reaction and second-order reaction, both of which generated Fe(III) and H2O2 as products (eq 5, 6). Both Fe(VI) species and Fe(V) species could also oxidize H2O2 into O2 through a two-electron transfer process (eq 4, 7). Jiang reported that the heterogeneous ferrate self- decomposition catalyzed by Fe(III) particles could be described by ﬁrst-order reaction and thus ferrate self-decomposition in borate buffer followed mixed ﬁrst- and second-order kinetics (Jiang et al. 2015). However, we found that the reaction order of ferrate self-decomposition was dependent on pH but not on buffer condition (SI-Text-3, Figure S7 and Table S1). In both phosphate buffer and borate buffer, a second-order kinetics could describe the ferrate decomposition well at pH 6.0 and 7.0 while a ﬁrst-order kinetics ﬁt successfully at pH 9.0. For pH 8.0, a mixed ﬁrst- and second-order kinetics has to be used. The reaction order of fer- rate self-decomposition seems related to different ferrate species (HFeO4- and FeO42−), of which distribution is pH-dependent (Sharma 2011), but not due to the homogeneous or heterogeneous reaction. The recent work on ferrate self-decomposition in alkaline condition by Luo et al also observed the ﬁrst-order decay of FeO42− species and demonstrated by density functional theory (DFT) calculation that the FeO42− species favored unimolecular decay mechanism through water attack (WA) other than the dimerization through oxo-coupling (OC) (Luo et al. 2020). Nev- ertheless, the enhance effect of the Fe(III) particles on ferrate self-decomposition was conﬁrmed here, on the basis of the larger rate constant at higher ferrate dosage or with increasing external Fe(III) dosage in borate buffer (Figures S8-S9 and Table S1). There- fore, only a second-order ferrate self-decomposition reaction (eq 1) was included in the kinetic model at pH 7.0. The corresponding rate constant (k1) in phosphate and pyrophosphate buffer was set as 22 M−1s−1, a value determined from ferrate self-decomposition kinetics experiment (Figures S10-S11, Table S1). In borate buffer, considering the possible varying heterogeneous Fe(III) catalytic effect on ferrate self-decomposition, the rate constant of eq 1 was set as a pending parameter (k1).
PMSO was oxidized to PMSO2 by Fe(VI), Fe(V) and Fe(IV) species via two electron transfer mechanism, with Fe(IV), Fe(III) and Fe(II) as the iron products (eq 9-11). The corresponding rate constants are denoted as k2, k3 and k4, respectively. All the other rate constants of reactions in Table 1 under different buffer con- ditions were determined/estimated based on kinetic information from literatures and more details are provided in SI-Text-4, Figures S12-S27.

3.3.2. Model ﬁtting in pyrophosphate buffer and phosphate buffer
As discussed in the above section on buffer effect, the Fe(V) ox- idation was completely sequestered in pyrophosphate buffer be- cause of strong ligand complexation. But it’s not clear whether Fe(IV) play a role in the PMSO oxidation at pH 7.0. Based on the role absence of Fe(IV) in the buffer effect of PMSO oxidation, it could be deducted that Fe(IV) might either react poorly with PMSO or its oxidation was not inﬂuenced by ligand presence. To gain in- sight into the role of Fe(IV) in PMSO oxidation, the mechanistic kinetic model proposed above was used to ﬁt the concentration- time proﬁles of Fe(VI), PMSO and PMSO2 acquired in pyrophos- phate buffer, through a global ﬁtting function with multiple data sets of varying ferrate dosages.
Firstly, rate constants between PMSO and Fe(VI), Fe(IV) species (k2 and k4) were set as pending parameters while reaction be- tween Fe(V) and PMSO was excluded from the kinetic model for mechanism reduction to run a preliminary model ﬁtting. The rate constant of Fe(VI) and PMSO was determined to be 25±6 M−1s−1, somewhat close to the experimental determined kapp value (~30 M−1s−1) in pyrophosphate buffer. Comparatively, an upper limit was derived for the rate constant of Fe(IV) species and PMSO, k4 <1.5 × 10−2 M−1s−1, instead of a precise value with standard de- viation, suggesting the reactivity between Fe(IV) and PMSO was extremely low at pH 7.0 and the Fe(IV) contribution to PMSO oxida- tion was negligible. Therefore, the role absence of Fe(IV) in buffer effect was likely due to the sluggish Fe(IV) reactivity towards PMSO at pH 7.0 rather than the alternative hypothesis that the Fe(IV) ox- idation of PMSO was impervious to ligand presence. This explana- tion was also in agreement with the reported poor oxidation per- formance on PMSO by Fe(II)/H2O2 (Bataineh et al. 2012), Fe(II)/PDS (Wang et al. 2018, Dong et al. 2020), Fe(II)/PMS (Wang et al. 2019b) and Fe(II)/PAA (Kim et al. 2019) system at circumneutral pH con- ditions, where Fe(IV) species was proposed as the major reactive species. In a recent study, it’s reported that Fe(IV) species did contribute to the PMSO oxidation at pH 8.0 in borate buffer (Zhu et al. 2020), contrast to the result at pH 7.0 in this study. To further investigate the role of Fe(IV) during ferrate oxidation, stoichiometry experi- ment of ferrate and PMSO was conducted at pH ranging from 6.0 to 9.0 in borate buffer. As shown in Fig. 5, the ∆[PMSO2]/∆[Fe(VI)] ratio was determined to be larger than one (~1.2) at pH 8.0 and 9.0, proving the Fe(IV) involvement in PMSO oxidation at alkaline condition (see SI-Text-5 for more details). Comparatively, the molar ratio reduced to around unity at pH 6.0 and 7.0, in agreement with the model ﬁtting result that Fe(IV) reacted sluggishly with PMSO at pH 7.0 and thus contributed barely to the PMSO oxidation. The results above reveals that the role of Fe(IV) species is strongly de- pendent on solution pH and Fe(IV) might be less reactive at near- neutral conditions. Hence, the reaction between Fe(IV) and PMSO (eq 11) is a re- dundant step in the kinetic model and could be excluded for mech- anism reduction in the following model ﬁtting. Further, the av- eraged value of kapp experimentally obtained in pyrophosphate buffer could be recognized as the speciﬁc rate constant (k2) of Fe(VI) species with PMSO, i.e. k2=30 M−1s−1, with negligible in- volvement of Fe(V) and Fe(IV) species. Then, the k3 value for Fe(V) and PMSO was estimated to be k3<2.5 × 105 M−1s−1 in pyrophos- phate by adopting the above parameter setting through model ﬁt- ting. Through the same approach, the k3 value was determined to be (1.5±34%) × 106 M−1s−1 in phosphate buffer, in agreement with the reported rate constant range of 105-106 M−1s−1 reported for Fe(V) species oxidizing organic compounds including phenol (Rush et al. 1995), amino acid (Rush and Bielski 1995) and car- boxylic acid (Bielski et al. 1994) in phosphate buffer from pulse- radiolysis studies. 3.3.3. Model ﬁtting in borate buffer Since the ferrate self-decomposition was self-enhanced with in- creasing ferrate dosage, due to the greater amount of Fe(III) formed at higher ferrate dosage, the k1 value was set as another pending parameter besides k3 considering the Fe(III) enhanced effect might vary in different conditions. Unlike the condition of pyrophosphate and phosphate, it was unsuccessful to simultaneously ﬁt the mul- tiple data sets of varying ferrate dosages with a global ﬁtting func- tion in borate buffer. Therefore, model ﬁtting was conducted indi- vidually at 20, 30 and 50 μM ferrate dosage. As shown in Fig. 1, the model ﬁtted all the data sets well and the ﬁtting results were summarized in Table 2. The k1 value was determined to be 38.1, 43.5 and 82.1 M−1s−1 for ferrate dosage of 20, 30 and 50 μM, respectively, consistent with the increasing trend of decomposition rate constants observed in sole ferrate self- decomposition experiments (Table S1). The k3 value of Fe(V) and PMSO was determined to be 1.52 × 107 M−1s−1 at 20 μM fer- rate, 6 orders of magnitude higher than that of Fe(VI) species (30 M−1s−1), and only 1~2 orders of magnitude lower than the corre- sponding rate constants of sulfate radical (3.17 × 108 M−1s−1) or hydroxyl radical (3.61 × 109 M−1s−1). The k3 value increased to 5.11 × 107 M−1s−1 at 30 μM ferrate and 1.07 × 108 M−1s−1 at 50 μM ferrate, approaching rates of typical radical reaction. The very high reactivity of Fe(V) species with PMSO corroborated the par- tial radical character of the oxide ligands bound to Fe(V) (Rush and Bielski 1989, 1995, Bielski 1992). Based on the ferrate dosage effect on k3 values, we speculated that the oxidation of PMSO by Fe(V) species was also enhanced by the in situ formed Fe(III) derived from ferrate reduction, similar to the ferrate self-decomposition (eq 1). The enhancement caused by Fe(III) is a heterogeneous process, which would be suppressed by ligand presence as ligand could form complexes with Fe(III) ions or cover the surfaces of Fe(III) particles. Therefore, a uniform ﬁtting result could be obtained for varying ferrate dosages in pyrophos- phate or phosphate buffer through a global ﬁtting function, but not in borate buffer, where Fe(III) particles play an important role in PMSO oxidation. 3.3.4. Enhanced effect of Fe(III) on Fe(V) oxidation To verify the speculated enhanced effect of Fe(III) on Fe(V) oxi- dation of PMSO, varying dosages of FeCl3 were introduced into the system in advance to investigate the effect of external Fe(III) on the oxidation of PMSO by 20 μM ferrate in borate buffer at pH 7.0. As shown in Fig. 6, the addition of FeCl3 signiﬁcantly acceler- ated the oxidation of PMSO by ferrate. The apparent second-order rate constants (kapp) were determined to be 2.5 × 102, 3.7 × 102 and 5.1 × 102 M−1s−1 for the FeCl3 dosage of 5, 20 and 50 μM, respectively. These values were larger by factors of 1.92, 2.85 and 3.92 respectively, than the corresponding kapp value of single fer- rate dose. Besides, the addition of FeCl3 show no inﬂuence on the PMSO oxidation in phosphate buffer (data not shown), conﬁrm- ing the phosphate retardation on the Fe(III) enhancement proposed above. The speciﬁc effect of external Fe(III) on Fe(VI) species oxidation was also investigated by monitoring the Fe(VI) decay under varying dosages of excess PMSO. Fig. 3 shows that the kappr remain consistent around 40 M−1s−1 in borate buffer with or without external Fe(III) present, indicating that the speciﬁc Fe(VI) oxidation was not inﬂuenced by Fe(III). Since the role of Fe(IV) was excluded in PMSO oxidation at pH 7.0 in both borate and phosphate buffer, the Fe(III) enhancement mechanism was likely related to Fe(V) oxidation. Fe(V) species was generated from the serial reactions of fer- rate self-decomposition. The presence of Fe(III) might promote the Fe(V) generation from ferrate decomposition due to its catalytic ef- fect on ferrate self-decomposition (Jiang et al. 2015). In this sense, the decrease of Fe(VI) exposure would result in a corresponding increase of Fe(V) exposure as Fe(VI) species transformed into Fe(V) species during the ferrate decomposition and thus enhance the PMSO oxidation by Fe(V) oxidation. Fig. 5 (c) shows that ferrate decomposed faster as the external Fe(III) dosage increased. At re- action time of 10 min, the Fe(VI) exposure decreased from 6.04 to 3.57 mM•s as the Fe(III) dosage increased from 0 to 50 μM. In theory, the Fe(V) exposure would correspondingly increase by 1.69 times at most. However, the PMSO oxidation performance in terms of -ln([PMSO]/[PMSO]0) increased by 2.16 times, higher than the corresponding theoretical Fe(V) exposure augmentation factor. These results suggest that the reactivity of Fe(V) with PMSO was also enhanced by Fe(III), which accord precisely with the increas- ing k3 value at higher ferrate dosage derived from model ﬁtting in borate buffer (Table 2). When the external Fe(III) was prepared from ferrate self-decomposition, an oxidation enhancement with increasing Fe(VI)-origin Fe(III) dosage was also observed (Figure S28), revealing the self-enhanced nature of ferrate-PMSO oxidation process. 3.3.5. Model validation and relative contribution of Fe(VI) and Fe(V) species The rate constants derived from the data ﬁtting in the condition of excess ferrate (Table 2) was used to predict the kinetic data of excess PMSO by model simulation. As shown in Figs. 2 and 4 (c), the model successfully predicted the kinetic curves of PMSO and PMSO2 of varying ferrate dosages under excess PMSO in all buffer conditions, validating the model proposed above is robust and rea- sonable. The kappr value experimentally determined by monitoring the Fe(VI) decay under varying dosage of excess PMSO (~ 40 M−1s−1) turned out to be a little higher than the kapp value determined under excess ferrate in pyrophosphate buffer (~30 M−1s−1), which was recognized as the true rate constant between Fe(VI) species and PMSO at pH 7.0. This mismatch appears to be unexpected since the kapp’ value was determined in the condition where fer- rate self-decomposition was minimized and was also expected to reﬂect the true rate constant between Fe(VI) and PMSO. The ki- netic model in Table 1 was utilized to simulate the reaction of ferrate with varying dosage of excess PMSO. Interestingly, model simulation also yields a kappr value of around 40 M−1s−1 (Fig. 3c). In the ferrate-PMSO system, Fe(VI) was consumed by Fe(VI) self- decomposition (eq 1) and reaction with Fe(II) (eq 3), H2O2 (eq 4), PMSO (eq 11). Model simulation shows that in the excess of PMSO, the contributions of Fe(VI) self-decomposition and reaction with H2O2 were negligible (2% and 0%) while reactions with Fe(II) and PMSO were the major contributors (29% and 69%). That is to say, about 69% of the kappr determined by monitoring the Fe(VI) decay under excess PMSO reﬂect the true rate constant between Fe(VI) and PMSO, 69% × 40=27.6 M−1s−1, exactly close to the 30 M−1s−1 determined in pyrophosphate buffer. Although the Fe(II) concen- tration in ferrate-PMSO system was quite low (1.5 × 10−9 M), the reaction between Fe(II) and Fe(VI) was extremely fast (1 × 107 M−1s−1) (Lee et al. 2014) and thus contribute fairly to the Fe(VI) consumption even under excess PMSO. The contribution ratios of Fe(VI) and Fe(V) species on the PMSO oxidation under various conditions were calculated and shown in Fig. 7 (see SI-Text-S6 for calculation details). In the condition of excess ferrate, the contribution of Fe(V) species to the total PMSO oxidation in borate buffer was determined to be 73%, 90% and 98% at the ferrate dosage of 20, 30 and 50 μM, respectively. This re- sult reveals that Fe(V) was the prevailing active species when ex- cess ferrate oxidized PMSO in borate buffer at pH 7.0 and its dom- inant role was enhanced at higher ferrate dosage. On one hand, higher ferrate dosage would increase the competitiveness of Fe(VI) self-decomposition pathway (eq 1) over the direct Fe(VI)-PMSO oxidation pathway (eq 9), producing a greater amount of Fe(V) species and leading to a higher Fe(V) exposure. On the other hand, more Fe(III) generated from ferrate reduction would also be bene- ﬁcial for the Fe(V) oxidative reactivity through heterogeneous en- hancement. In phosphate buffer, the corresponding contributions of Fe(V) species reduced to 17%, 20% and 30%, respectively, where Fe(VI) species predominated the PMSO oxidation in turn. In py- rophosphate buffer, the contribution of Fe(VI) species increased to around 99% at 20, 30, 50 μM ferrate dosage whereas Fe(V) species contributed negligibly. As the condition switched from excess fer- rate to excess PMSO, the corresponding Fe(V) contributions de- creased in all buffer conditions. For example, the Fe(V) contribu- tions decreased from 73%, 90% and 98% to 40%, 47% and 66% in borate buffer for ferrate dosages of 20, 30 and 50 μM. This decreas- ing trend of Fe(V) contribution was in agreement with the decreas- ing kapp values and diminishing ferrate dosage effect from excess ferrate to excess PMSO. Overall, the above results were consistent with the dosage effect and buffer effect on the kapp variation ob- served in the kinetic experiments. A higher kapp value at raised fer- rate dosage or weaker ligand presence was clearly corresponded to a higher Fe(V) contribution. 3.4. Practical Application The ferrate self-decomposition used to be considered as an un- desirable reaction which would consume signiﬁcant amount of ferrate and potentially decrease the oxidation eﬃciency for mi- cropollutants abatement. Taking PMSO as a model organic com- pound, this study reveals that without the presence of strong lig- ands, the oxidation of target compounds was mainly achieved by Fe(V) species generated from ferrate self-decomposition, especially at relative high ferrate dosage or with Fe(III) promotion. Therefore, ferrate self-decomposition is not just a self-degradation but also a During the ferrate oxidation of micropollutants like CBZ and DCF (Figure S30), apparent ferrate dosage effect was also observed in borate buffer, which was then counterbalanced in pyrophos- phate. Similar to ferrate oxidation of PMSO, it’s very likely that Fe(V) derived from ferrate self-decomposition contributed to the micropollutants oxidation and (partly) caused the ferrate dosage effect and buffer effect. Ferrate dosage effect on CBZ oxidation was also observed in river water matrix (DOC=17.0±0.5 mgC/L, Figure S31), revealing that the ferrate dosage effect as well as the fer- rate self-activation process was also present in actual water sam- ples. The kapp values in borate buffered river water samples were lower than the corresponding values in borate buffered pure wa- ter samples. This might be ascribed to the following two reasons: 1) the complexing components of natural organic matters (NOM) would inhibit the ferrate oxidation via complexing intermediate iron species (Adusei-Gyamﬁ et al. 2019); 2) the reductive compo- nents of NOM would competitively consume the active intermedi- ate iron species (Kappler and Haderlein 2003). As a highly reactive and unstable species, the oxidation re- activity of Fe(IV) species was reported to be lower than that of Fe(V) species (Sharma 2011, Sharma 2013). In this study, the rate constant of Fe(IV) with PMSO at pH 7.0 was found buffer conditions at pH 7.0. Experimental condition: [ferrate]0 [PMSO]0 = 10 μM (a) or 104 μM (b). oxidation. However, the reactivity of Fe(IV) with other micropollu- tants remains unknown. It is still unable to conﬁrm or negate the role of Fe(IV) during the ferrate oxidation of micropollutants. Get-self-activation process, during which Fe(VI) species is transformed into the more reactive Fe(V) species for oxidation. In this regard, accelerating the ferrate self-decomposition could be used to enhance the ferrate oxidation of micropollutants. Intro- ducing external Fe(III) (e.g. dosing FeCl3) could promote the Fe(V) species generation from ferrate self-decomposition for PMSO oxi- dation. More importantly, the heterogeneous Fe(III) enhancement on Fe(V) oxidation improved the competitiveness of Fe(V) oxida- tion pathway over Fe(V) auto-decomposition and thus elevated the utilization eﬃciency of ferrate oxidation capacity, reducing the fer- rate dosage required. The addition of external FeCl3 was proved to be able to enhance the ferrate oxidation of micropollutants like SMX over a wide pH range (Figure S29). The in situ formed Fe(III) particles in ferrate reaction are reported to be composed of both amorphous and crystalline Fe(III) (Lv et al. 2018) whereas the Fe(III) particles derived from direct Fe(III) hydrolysis is amor- phous (Ching et al. 1994, Duan and Gregory 2003), implying that the amorphous part of Fe(III) particles play the simulative role. Nevertheless, whether the crystal form of Fe(III) oxides and other transition metal oxides could also catalyze the ferrate oxidation, as well as the inﬂuence of other characteristics like particle size and morphology, deserves further investigation. ting knowledge of the ligand effect on Fe(IV) oxidation could help us to further distinguish the relative contributions of Fe(VI), Fe(V), Fe(IV) during the ferrate oxidation of micropollutants, and facilitate our understanding of ferrate chemistry. 4. Conclusions • The oxidant dosage effect on ferrate oxidation of PMSO, higher kapp values at higher ferrate dosage, could be counterbalanced by pyrophosphate addition. Similar phenomena were observed for ferrate oxidation of micropollutants like CBZ and DCF. • The Fe(V) species derived from ferrate self-decomposition was responsible for the ferrate dosage effect and was the major ox- idant during ferrate oxidation of PMSO. Therefore, ferrate self- decomposition was also a self-activation process forming Fe(V) species to oxidize target compounds. • Fe(VI) oxidation was impervious to phosphate while Fe(V) oxi- dation was strongly suppressed by phosphate complexation. • The in situ formed Fe(III) or external Fe(III) was found to en- hance the ferrate oxidation of PMSO by promoting the Fe(V) oxidation. Declaration of Competing Interest The authors declare that they have no known competing ﬁnan- cial interests or personal relationships that could have appeared to inﬂuence the work reported in this paper. Acknowledgements This work was ﬁnancially supported by the National Science and Technology Major Projects for Water Pollution Control and Treatment (Grant No. 2017ZX07201003), the National Key R&D Pro- gram of China (2017YFA0207203), and the National Natural Science Foundation of China (NSFC, 51808163). 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