Rate constants for the reactions of chloride monoxide radical (ClO^•) and organic molecules of environmental interest

In their classic paper, Alfassi et al. (1988) used Reactions (7) and (8) to produce ClO^• and determined the rate constants in pulse radiolysis experiments. The radiolysis of water supplied ^•OH. In transient measurements carried out by pulse radiolysis or (laser) flash photolysis ClO^• exhibits weak light absorption with the maximum at 280 nm and molar absorbance of ∼900 mol⁻¹ dm³ cm⁻¹ (Alfassi et al. 1988). Due to the very weak absorbance of ClO^•, in transient kinetic measurements the product absorbance is used in rate constant determination. However, there is a complication: HClO/ClO⁻ (pK_a = 7.5) is also an oxidant, which reacts with many organic molecules. Alfassi et al. (1988) selected several organic molecules/ions (among others 4-cyanophenoxide ion, 4-nitrophenoxide ion, 4-methoxybenzyl alcohol) which had low reactivity with ClO⁻ and determined their rate constants at high pH. The reactivity of ClO⁻ is smaller than that of HClO. In the later rate constant determinations, the authors usually disregarded this reaction possibility, although many rate constant measurements were made at slightly alkaline pH (8.4).

Li et al. (2021a), Peng et al. (2022) and An et al. (2022) used quantum chemical calculations (DFT, density functional theory) for the determination of rate constants for a large number of organic molecules. Guo et al. (2018), besides experimental rate constant determinations, also used structure-reactivity correlations, applying the Hammett substituent constants to predict k_ClO• values. The same technique was employed by Sun et al. (2016) and Huang & Zhang (2022). The reduction potentials were also used for estimations of rate constants in ClO^• reactions.

Zhou et al. (2019) determined the rate constants for the reaction with substituted benzoic acids by modeling calculations with the involvement of a large number of reactions of the active chlorine species during the UV/chlorine process. This technique was also applied for rate constant determination in several other works.

Compilation of the published rate constants collected from original publications is given in the tables. The pH values and the accuracies are indicated as they were published in the original works. The error bounds in tables represent the σ-level uncertainty. All of the rate constant determinations were made around room temperature. The tables show also the pK_a values of compounds collected from several publications, e.g., Perrin (1965), Babic et al. (2007), and Shalaeva et al. (2008). The methods of k_ClO• determinations are indicated by the following abbreviations: PR, pulse radiolysis; FP, flash photolysis; Comp., competitive method; Model./Fit./Simul., modeling/fitting/simulation in complex reaction systems often taking into account large numbers of reactions (usually UV/chlorine), Est./Pred./Assum. estimated/predicted/assumed based on the rate constant of structurally similar compounds (e.g., using the Hammett substituent constants), Calc., quantum chemical calculations.

The reaction is made possible by the lower standard reduction potential of the N₃^•/N₃⁻ couple (1.33 V vs. NHE, Armstrong et al. 2015) than that of the ClO^•/ClO⁻ couple (1.39 V). However, due to the small difference in the reduction potentials, the electron transfer rate constant is relatively small, 2.5 ± 0.5 × 10⁸ mol⁻¹ dm³ s⁻¹. The azide radical is considered to be a highly selective one-electron oxidant (Alfassi & Schuler 1985). The rate constant of carbonate ion with ClO^• is very low, 6 × 10² mol⁻¹ dm³ s⁻¹ (Reaction (-9), Huie et al. 1991). The reaction leads to an equilibrium in the electron transfer (Reactions (9) and (-9)) (Huie et al. 1991; Armstrong et al. 2015). As it was mentioned previously, the low rate constant of Reaction (-9), 6 × 10² mol⁻¹ dm³ s⁻¹, has special importance. The reactions of ^•OH, Cl^• and Cl₂^•− with carbonate ion (Reactions (14)–(16)) increase the importance of ClO^• reaction in the UV/chlorine process (Zhu et al. 2021).

Formate ions (HCOO⁻) have low reactivity with ClO^•, Alfassi et al. (1988) gave only an upper limit for the rate constant value, <1 × 10⁶ mol⁻¹ dm³ s⁻¹. Wu et al. (2017) using the competitive technique determined k_ClO• = 1.3 ± 0.1 × 10⁷ mol⁻¹ dm³ s⁻¹ for the reaction with tert-butanol. This rate constant value seems to be highly overestimated. Wang et al. (2020) reported only a minimal effect of a high concentration of tert-butanol on the ClO^• induced degradation of primidone. No effect of tert-butanol was found in the degradation of iopamidol (Kong et al. 2018a).

The calculated k_ClO• value of 1,4-dimethoxybenzene (8.04 × 10⁸ mol⁻¹ dm³ s⁻¹, Li et al. 2021a) was found to be smaller than the experimental rate constant (2.1 × 10⁹ mol⁻¹ dm³ s⁻¹) of Alfassi et al. (1988). The calculated ClO^• initiated reaction rate constants of aromatic compounds are in the range of 10²–10¹⁰ mol⁻¹ dm³ s⁻¹. ClO^• was found to be highly reactive to phenolates, anilines and alkoxy/hydroxyl aromatic compounds. Upon the deprotonation of phenol to phenolate, the k_ClO• value increased by four orders of magnitude, from 6.3 × 10⁶–1 × 10⁷ mol⁻¹ dm³ s⁻¹ to 1 × 10⁹–3.71 × 10¹⁰ mol⁻¹ dm³ s⁻¹ (Li et al. 2021a; An et al. 2022; Huang & Zhang 2022). (The latter value seems to be unrealistic since it is much higher than the diffusion-limited rate constant of ∼1 × 10¹⁰ mol⁻¹ dm³ s⁻¹ (Kovács et al. 2022).) The deprotonation of the phenolic OH resulted in the sudden increase of the rate constant in the reactions of a number of other phenol type compounds as shown in Table 4. E.g., in the case of 2,4,6-tribromophenol k_ClO• increased from 1.95 × 10⁵ to 3.71 × 10¹⁰ mol⁻¹ dm³ s⁻¹ (Li et al. 2022). The k_ClO• values of alkoxybenzenes are higher for compounds with shorter alkyl side chains and more alkoxy substituents.

Due to the electrophile character of k_ClO• reactions the calculated rate constants highly increase upon deprotonation of aniline cation. Li et al. (2021a) calculated values of 2.07 × 10³ and 1.11 × 10¹⁰ mol⁻¹ dm³ s⁻¹ for aniline cation and the neutral molecule, respectively. The calculated values of An et al. (2022) are closer to each other: 3.28 × 10⁵ and 1.47 × 10¹⁰ mol⁻¹ dm³ s⁻¹, respectively.

p-Aminophenol has two dissociable places, the amino group and the hydroxyl group. In the pH range between 0 and 14, the ionization state changes in the order: cation, neutral, zwitterion and anion. The calculated rate constants gradually increase with the pH. For p-aminophenol cation and anion, An et al. (2022) calculated k_ClO• values of 8.05 × 10⁵ and 5.35 × 10¹⁰ mol⁻¹ dm³ s⁻¹, respectively, the rate constant of the neutral species lies between the two. Acetaminophen (paracetamol, used as a non-steroidal anti-inflammatory drug, NSAID) is a derivative of p-aminophenol. Giang et al. (2017) by using the competitive technique published k_ClO• = 3.53 × 10⁹ mol⁻¹ dm³ s⁻¹, while the theoretical calculations of Li et al. (2021a) and Wang et al. (2021b) based on the TST yielded one and three orders of magnitude smaller values: 4.61 × 10⁸ and 7.74 × 10⁶ mol⁻¹ dm³ s⁻¹, respectively. The chemical structure of N-phenacetin (N-(4-ethoxyphenyl)acetamide, also used as NSAID) is similar to that of acetaminophenen. The calculated rate constant values for the two medicines, for the neutral acetaminophen and phenacetin (Li et al. 2021a) are also close to each other.

In Table 5, the rate constant values for benzoic acids taken from the works of Li et al. (2021a), An et al. (2022) and Peng et al. (2022) were obtained in quantum chemical calculations using the TST. The values of Zhou et al. (2019) were estimated through a complex fitting procedure to the concentration changes of the compound investigated in UV/chlorine process. Only the values of Alfassi et al. (1988) were obtained in direct pulse radiolysis experiments. The latter authors for the k_ClO• of the benzoate ion gave an upper limit of <3.0 × 10⁶ mol⁻¹ dm³ s⁻¹. The calculated rate constant of An et al. (2022), 8.88 × 10⁴ mol⁻¹ dm³ s⁻¹, and that of Li et al. (2021a), 6.68 × 10⁴ mol⁻¹ dm³ s⁻¹ are also very low. Peng et al. (2022) calculated three orders of magnitude higher value for the anion: 2.32 × 10⁷ mol⁻¹ dm³ s⁻¹. The values given for the neutral molecule, 7.26 × 10³ and 3.13 × 10³ mol⁻¹ dm³ s⁻¹, published by Li et al. (2021a) and An et al. (2022), respectively, are much smaller than the values for the anion.

As the calculated results for p-hydroxybenzoic acid and p-aminobenzoic acid show, similarly to benzoic acid, deprotonation, and thereby the increase of electron density on the benzene ring greatly increases the rate constant. According to the estimations of Zhou et al. (2019) electron donating substituents on the ring of benzoate increase, electron-withdrawing substituents decrease the rate constants.

Li et al. (2021a) mention that ClO^• reactions likely to play an important role in the UV/chlorine process when k_ClO• is greater than 10⁶ mol⁻¹ dm³ s⁻¹. The k_ClO• values of many aromatic compounds were found above this limit: the order was: anilines ≈ phenolate > trimethoxy-benzenes > dimethoxybenzenes > phenylamides > phenol > phenylmethanol > mono-alkoxybenzenes. Among these, the k_ClO• values of anilines, phenolate, dimethoxy- and trimethoxy-benzenes were greater than 10⁸ mol⁻¹ dm³ s⁻¹.

Erythromicin is an often applied macrolide-type antibiotic. Kim et al. (2020) investigated the pH dependence of its reaction with ClO^•. The rate constant increased in the pH range 6–10 from 3.1 × 10⁹ to 1 × 10¹⁰ mol⁻¹ dm³ s⁻¹, due to deprotonation with pK_a 8.9. The authors established that in the UV-LED(275 nm)/chlorine process at high pH the Cl^• and ClO^• radicals played the key role in the degradation.

Wang et al. (2021a) carried out pH dependence studies on the reaction of trimethoprim. This medicine is often used in combination with sulfa drugs, e.g., sulfamethoxazole or sulfadiazine. At low pH both N-atoms in the heterocyclic ring are protonated, at high pH the neutral form dominates (pK_a1 3.1, pK_a2 7.1). Under the usual conditions there is a pH determined equilibrium between the dication (Trim²⁺), the monocation (Trim⁺) and the neutral forms. From the fitted results of Wang et al. (2021a) it seems that the neutral form has the smallest rate constant, 1.93 × 10⁶ mol⁻¹ dm³ s⁻¹. The rate constant of Guo et al. (2018) predicted for the ClO^• + trimethoprim reaction, 4.46 × 10¹⁰ mol⁻¹ dm³ s⁻¹, is out of the range of rate constants of chlorine monoxide reactions shown in the tables in this paper.

Both 2-phenylbenzimidazole-5-sulfonic acid (PBSA) and sulfamethoxazole are derivatives of sulfonic acid. PBSA as a personal care product (PCP) is used as an organic filter of UV radiation. Therefore, its concentration is often high in swimming pools and recreation waters, it appears also in lakes and rivers. In swimming pools usually, chlorination is used for disinfection. Therefore, under the effect UV light in open-air swimming pools PBSA is attacked by different chlorine radicals, among them ClO^•. Yin et al. (2022) using competitive experiments published a rate constant of 1.5 × 10⁵ mol⁻¹ dm³ s⁻¹. Based on similar experiments the k_ClO• value of Hu et al. (2022) is 8.6 × 10⁷ mol⁻¹ dm³ s⁻¹. Considering the rate constants of similar compounds, we tend to believe that the k_ClO• value of Yin et al. (2022) is closer to reality than the rate constant of Hu et al. For sulfamethoxazole (antibiotic), Guo et al. (2018) calculated an unrealistically high upper limit for the rate constant: <2.23 × 10⁹ mol⁻¹ dm³ s⁻¹. Zheng et al. (2022) suggested that rate constant of sulfamethoxazole is very low; they observed very slow degradation of the target compound when the ClO^• dominated in the reaction mixture.

Nalidixic acid is a narrow-spectrum antibacterial agent used for treating urinary tract infections. The second-order rate constant of reaction with ClO^• is published as <8.9 × 10⁶ mol⁻¹ dm³ s⁻¹ (Wu et al. 2017) and 1.79 × 10⁷ mol⁻¹ dm³ s⁻¹ (Guo et al. 2018). The chemical structure of nalidixic acid reminisces that of the fluoroquinolone antibiotics, e.g., that of flumenique. The rate constant of the latter compound was published as 2.75 × 10⁷ mol⁻¹ dm³ s⁻¹ (Guo et al. 2018). Chloramphenicol is effective against a wide variety of microorganisms, but due to serious side-effects in humans, it is usually reserved for the treatment of serious and life-threatening infections (e.g., typhoid fever). It is rather inactive in reaction with ClO^• due to the electron-withdrawing nitro group and the chlorine atoms in the molecule (Guo et al. 2018).

Fluconazole (medicine used to treat fungal infections) has two triazole rings. Radical addition is suggested as the main reaction of ClO^• with fluconazole (Cai et al. 2020). The experimentally obtained rate constant is 4.0 × 10⁷ mol⁻¹ dm³ s⁻¹, the value obtained by DFT calculations, 9.48 × 10⁷ mol⁻¹ dm³ s⁻¹ is two times higher than the experimental one. There is another medicine, ribavirin, in Table 6 with a triazole ring. Ribavarin is an antiviral agent that is used, for instance, to treat hepatitis C. The rate constant obtained in competitive experiments (5.58 × 10⁷ mol⁻¹ dm³ s⁻¹, Sun et al. 2022) is close to the value published for fluconazole.

Ibuprofen and naproxen are propionic acid-based non-steroidal anti-inflammatory drugs (NSAIDs). The rate constant of ClO^• reaction with ibuprofen based on competitive experiments was published as 5.49 × 10⁶ mol⁻¹ dm³ s⁻¹ (Guo et al. 2018). For naproxen, competitive experiments in three laboratories suggest k_ClO• values in the 10⁹ mol⁻¹ dm³ s⁻¹ order of magnitude range (Guo et al. 2018; Pan et al. 2018; Liu et al. 2021). The three orders of magnitude higher value for naproxen than for ibuprofen is certainly due to the naphthalene unit in the molecule which offers an excellent possibility for electrophile attack. An increase in the rate constant upon replacing benzene with the naphthalene unit caused an increase also in the rate constants of reactions of other one-electron oxidants, e.g., in the reactions of β-blockers (Kovács et al. 2022). Diclofenac is also an NSAID. In the molecule, an amino group connects two aromatic rings. The k_ClO• value predicted for this medicine (Guo et al. 2018), 3.54 × 10⁸ mol⁻¹ dm³ s⁻¹, is similar to those of rate constants given for compounds with two aromatic rings.

The k_ClO• value of caffeine reaction with ClO^• was published in several papers. Actually, caffeine often served as a model compound in investigations of the UV/chlorine process. The published rate constants range from the value estimated based on structure-reactivity relations, 1.4 × 10³ mol⁻¹ dm³ s⁻¹ (Sun et al. 2016) to the calculated value (quantum chemistry) of Li et al. (2021b), 1.4 × 10⁹ mol⁻¹ dm³ s⁻¹. The experimentally obtained values are around 1 × 10⁸ mol⁻¹ dm³ s⁻¹ (Guo et al. 2017, 2018; Wu et al. 2017). Theoretical calculations showed that the basic reaction is ClO^•-adduct formation, just like in the cases of ^•OH and BrO^• reactions (Li et al. 2021a).

Atenolol, metoprolol, salbutamol and ractopamine as β-blockers are used to treat cardiovascular diseases. These compounds are propionamide derivatives, all containing benzene or naphthalene unit. There are two main vulnerable sites for a radical attack in these molecules, the aromatic ring(s) and the amino group (Kovács et al. 2022). Guo et al. (2018) in competitive experiments determined rate constants of 8.68 × 10⁷ and 1.34 × 10⁸ mol⁻¹ dm³ s⁻¹, respectively, for atenolol and metoprolol. They predicted k_ClO• values of 1.21 × 10⁸ and 8.59 × 10⁹ mol⁻¹ dm³ s⁻¹ for salbutamol and ractopamine, respectively. The high value of the latter may be rationalized by the two aromatic rings in the molecule. Both rings have electron releasing hydroxyl group in para position.

In the literature, we found four values for the k_ClO• of gemfibrozil reaction (a medicine used to regulate blood lipid level). All values were established in competitive experiments. The values of Guo et al. (2017, 2018) and Kong et al. (2018b) are ∼ 4.2 × 10⁸ mol⁻¹ dm³ s⁻¹, Liu et al. (2021) published higher value: 1.93 × 10⁹ mol⁻¹ dm³ s⁻¹. Bezafibrate is also used to control lipid levels in the blood. The rate constants published by Kong et al. (2018b) and Shi et al. (2018) differ by one order of magnitude, 3.6 ± 0.1 × 10⁷ and 5.0 × 10⁸ mol⁻¹ dm³ s⁻¹, respectively. Kong et al. (2018b) used competitive experiments, while Shi et al. (2018) applied modeling calculations in the UV/chlorine process.

In clenbuterol (veterinary drug) a similar side chain is attached to the aromatic ring as in salbutamol. There are two chlorine atoms and an amine group in the ring. Guo et al. (2018) gave a surprisingly high upper limit for the rate constant: <5.0 × 10⁹ mol⁻¹ dm³ s⁻¹. Because of the two electron-withdrawing Cl atoms on the ring, we expect a much smaller rate constant. The antidepressant medicine venlafaxine, similar to the β-blockers has also an aromatic ring and in the side chain a tertiary amine group. The rate constant is in the 10⁸ mol⁻¹ dm³ s⁻¹ order of magnitude range as those of the β-blockers (Guo et al. 2018).

Carbamazepine is used as an anticonvulsant or anti-epileptic drug. Guo et al. (2017, 2018) in two papers published two different rate constants based on competitive experiments, although the values are not very far from each other, 9.7 × 10⁷ and 1.97 × 10⁸ mol⁻¹ dm³ s⁻¹. The value of Zhu et al. (2021) obtained in UV/chlorine experiments, by using complex fitting procedure, 1.78 × 10⁶ mol⁻¹ dm³ s⁻¹, is two orders of magnitude smaller than the values of Guo et al. (2017, 2018). Primidone in the medical practice is also used to treat epilepsy. Guo et al. (2018) in competitive experiments determined a value of 5.51 × 10⁷ mol⁻¹ dm³ s⁻¹, while Wang et al. (2020) in simulation experiments estimated an order of magnitude smaller rate constant, 1.12 × 10⁶ mol⁻¹ dm³ s⁻¹.

Iopromide and iopamidol have similar structures, in both of them there is a central benzene ring with three iodine atoms. Due to the iodine heavy atoms, they are used as X-ray contrast media in organ imaging. Their k_ClO• values were established in competitive experiments and they differ by a factor of 17: 1.25 × 10⁹ and 7.3 × 10⁷ mol⁻¹ dm³ s⁻¹, respectively (Cha et al. 2022; Luo et al. 2022). It is hard to say the reason for this large difference, in spite of the similar structure. The different pH values applied during the measurements (pH 7 and 10) may influence k_ClO•. In UV/chlorine degradation of both contrast materials ClO^• reaction has the dominant role (Kong et al. 2018a).

Clothianidin (used as insecticide) contains a 5-member thiazole ring. The rate constant established in competitive experiments seems to be overestimated: 7.3 ± 0.1 × 10⁹ mol⁻¹ dm³ s⁻¹ (Lee et al. 2021). It is 4.3 times higher than the rate constant of ^•OH reaction: 1.7 ± 0.2 × 10⁹ mol⁻¹ dm³ s⁻¹. ClO^• is suggested to attack the C-atom on the C = N moiety to substitute the nitroamino moiety of the urea compound. Benzothiazoles and benzotriazoles have also 5-member haterocyclic rings. They are widely applied in various consumer and industrial products, e.g., as vulcanization additives in rubber industry or as corrosion inhibitors. Yang et al. (2021) using radical scavengers in the UV/chlorine process derived similar second-order rate constants for the ClO^• reaction of benzothiazole and benzotriazole: 2.22 × 10⁸ and 2.4 × 10⁸ mol⁻¹ dm³ s⁻¹, respectively. Choo et al. (2022) measured an increase in the rate constant for benzotriazole from 1.46 ± 0.09 × 10⁸ to 2.1 ± 0.1 × 10⁸ mol⁻¹ dm³ s⁻¹ as the pH increased from 8.4 to 8.8, the pK_a is at 8.3. These k_ClO• values are much smaller than the rate constant published for clothianidin (Lee et al. 2021).

N,N-Diethyl-meta-toluamide (DEET) is used as an insect repellent. It is rather inert in reaction with ClO^•: k_ClO• <1.0 × 10⁶ mol⁻¹ dm³ s⁻¹ (Wu et al. 2017). The chlorophenoxy type herbicide mecoprop is widely used even now for weed control, while the other herbicide atrazine, often used in the past, is banned in many countries. In the UV/chlorine process, mecoprop decomposes to a large extent in ClO^• reactions (k_ClO• = 1.11 × 10⁸ mol⁻¹ dm³ s⁻¹, Kong et al. 2020b). At the same time, atrazine is rather unreactive in reaction with this radical (<10⁶ mol⁻¹ dm³ s⁻¹ (Kong et al. 2020b; Ye et al. 2021)). Contrary to this statement, in the bisulfite/chlorine dioxide system ClO^•and SO₄^•− were suggested as the main radical intermediates that destroy atrazine (Wang et al. 2022b).

Dissolved organic matter (DOM) or with other name natural organic matter (NOM) is a complex mixture of organic compounds with different structures. Fulvic and humic acids are the dominant DOM fractions in natural waters. Due to the undefined composition, the rate constants are generally given in mgC⁻¹ dm³ s⁻¹ units. Of course, the rate constant strongly depends on the source: in the literature, there are many values for DOM of different origins (e.g., Yuan et al. 2022). Here we mention only the value of Guo et al. (2017), 4.5 × 10⁴ mgC⁻¹ dm³ s⁻¹, which is often used in modeling studies.

Rate constants of ClO^• reactions were collected from the literature and were discussed together with the methods of determination and the reaction mechanisms. Only a small fraction of these rate constants was determined by the absolute method, pulse radiolysis combined with kinetic spectroscopy. The major part was determined by competitive techniques. In another group of experiments, the rate constants were derived in rather complex reaction systems using simulations/modeling or fitting procedures and often involving radical scavenging experiments in the determinations. Quantum chemical calculations were also frequently used to determine ClO^• rate constants. The latter methods often gave unrealistic rate constant values. Much fewer rate constants are available in the literature on the reaction of ClO^• with organic molecules as on the reactions of other main radical intermediates of the UV/chlorine process, Cl^•, ^•OH and Cl₂^•−.

For most compounds, we found only one published rate constant value. Therefore, we had little possibility to compare the values obtained in different laboratories, eventually employing different techniques. In cases when several rate constant values were published, we often observed large differences between the values obtained from different sources. The calculated values span a very large range from 10² to 10¹⁰ mol⁻¹ dm³ s⁻¹. The experimentally obtained ones are between 10⁵ and 10¹⁰ mol⁻¹ dm³ s⁻¹. With very few exceptions, the experimental values are well below 1 × 10¹⁰ mol⁻¹ dm³ s⁻¹. The latter value is considered to be the diffusion-controlled limit for ClO^• (Kovács et al. 2022). Therefore, the reaction rate constants are determined by the chemical reactivity, and diffusion limitation has little role. We know very little about the nature of chemical reactions. This is due to the small number of pulsed radiolysis investigations. The transient identification may give direct indications about the reaction mechanism. However, it seems that a basic mechanism is a radical addition to the double bonds (aromatic rings) of organic molecules. In some cases, evidence was given also for SET reaction. There are no direct indications for the participation of H-atom abstraction. The structure dependence of the rate constant values clearly shows an electrophile character similar to the other three radicals playing a major role in the UV/chlorine process. In reactions of phenols, benzoic acids, and anilines, the reactivity strongly increases with deprotonation, i.e. with the increase of electron density on the rings.

Since ClO^• reactions play a very important role in the emerging UV/chlorine technology, some standardization of the rate constant measuring techniques and more k_ClO• measurements are needed.

This work was supported by the National Office for Research and Development through the Hungarian-Chinese Industrial Research and Development Cooperation Project (No. 2017-2.3.6.-TÉT-CN-2018-00003).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.