Axel Horst

Magali Bonifacie

Gérard Bardoux

Hans Hermann Richnow

Geŕard Bardoux

Isotopic Characterization ( 2 H, 13 C, 37 Cl, 81 Br) of Abiotic Degradation of Methyl Bromide and Methyl Chloride in Water and Implications for Future Studies

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■ INTRODUCTION

Methyl chloride (CH 3 Cl, chloromethane) and methyl bromide (CH 3 Br, bromomethane) together contribute about 30% to halogen induced ozone loss even though atmospheric concentrations are very low: 540 pptv and 7 pptv, respectively. [START_REF] Engel | Update on ozone-depleting substances (ODS) and other gases of interest to the Montreal Protocol[END_REF] CH 3 Cl and CH 3 Br are emitted by both anthropogenic and natural sources such as fumigation for quarantine and preshipment treatment (for CH 3 Br), [START_REF] Fields | Alternatives to methyl bromide treatments for stored-product and quarantine insects[END_REF] marine macroalgae, [START_REF] Laturnus | Marine macroalgae in polar regions as natural sources for volatile organohalogens[END_REF] salt marshes, [START_REF] Rhew | Natural methyl bromide and methyl chloride emissions from coastal salt marshes[END_REF] soils, [START_REF] Rhew | Methyl halide and methane fluxes in the northern Alaskan coastal tundra[END_REF] biomass burning, [START_REF] Reinhardt | Factors affecting methyl chloride emissions from forest biomass combustion[END_REF] and tropical plants. [START_REF] Saito | Stable carbon isotope ratio of methyl chloride emitted from glasshouse-grown tropical plants and its implication for the global methyl chloride budget[END_REF] Main degradation processes for both of these compounds are reaction with OH and Cl radicals in the troposphere, [START_REF] Rudolph | The stable carbon isotope fractionation for reactions of selected hydrocarbons with OH-radicals and its relevance for atmospheric chemistry[END_REF] degradation in oceans [START_REF] Hu | An improved oceanic budget for methyl chloride[END_REF] and soils. [START_REF] Rhew | Sources and sinks of methyl bromide and methyl chloride in the tallgrass prairie: Applying a stable isotope tracer technique over highly variable gross fluxes[END_REF] The atmospheric budgets of both compounds are unbalanced with known degradation processes exceeding the best estimates of known emissions by approximately 20% for CH 3 Cl and 30% for CH 3 Br. [START_REF] Engel | Update on ozone-depleting substances (ODS) and other gases of interest to the Montreal Protocol[END_REF][START_REF] Yvon-Lewis | Recent trends in atmospheric methyl bromide: analysis of post-Montreal Protocol variability[END_REF] A better understanding of emission and degradation processes will be necessary in order to better quantify emission and degradation of CH 3 X and to improve budget estimates.

Previous studies suggested that degradation in oceans is primarily driven by the abiotic processes hydrolysis and halide exchange as well as microbial degradation. [START_REF] Hu | An improved oceanic budget for methyl chloride[END_REF][START_REF] Tokarczyk | Methyl bromide loss rates in surface waters of the North Atlantic Ocean, Caribbean Sea, and eastern Pacific Ocean (8°-45°N)[END_REF][START_REF] Yvon-Lewis | The potential effect of oceanic biological degradation on the lifetime of atmospheric CH3Br[END_REF] To a minor extent, hydrolysis may also contribute to degradation of CH 3 Br in soils. [START_REF] Papiernik | Mechanism of degradation of methyl bromide and propargyl bromide in soil[END_REF] Hydrolysis and halide exchange of CH 3 X (CH 3 Cl and CH 3 Br) are both nucleophilic substitution reactions (S N 2) following second order reaction kinetics. The attacking nucleophiles are either water (H 2 O), hydroxide ions (OH -), or halide ions such as Cl -and Br -(Y -): [START_REF] Elliott | Nucleophilic substitution rates and solubilities for methyl halides in seawater[END_REF][START_REF] Jeffers | On the degradation of methyl bromide in sea water[END_REF][START_REF] King | Removal of methyl bromide in coastal seawater: Chemical and biological rates[END_REF] CH X H O CH OH H X 3 2 3

+ → + + + - (r1)
CH X OH CH OH X 3 3

+ → + - - (r2)
CH X Y CH Y X 3 3

+ → + - - (r3)
In principle, hydrolysis of chlorinated aliphatic compounds may occur due to neutral (R1) and/or alkaline hydrolysis (R2) depending on the pH and the reacting organic compound. For instance, solely neutral hydrolysis (R1) was detected for CCl 4 whereas some chlorinated ethenes only reacted with hydroxide ions (R2). [START_REF] Jeffers | Homogeneous hydrolysis rate constants for selected chlorinated methanes, ethanes, ethenes, and propanes[END_REF] For CH 3 X it was shown that alkaline hydrolysis required a hydroxide concentration of more than 0.1 mol L -1 (pH > 13) and hence only neutral hydrolysis is considered to be relevant in most environments. [START_REF] Jeffers | On the degradation of methyl bromide in sea water[END_REF] Consequently, reactions R1 and R3 were suggested to constitute important degradation processes for methyl bromide in the environment. [START_REF] Moore | The relationship between methyl bromide and chlorophyll α in high latitude ocean waters[END_REF][START_REF] Lobert | A net sink for atmospheric CH3Br in the East Pacific Ocean[END_REF][START_REF] Yvon | An improved estimate of the oceanic lifetime of atmospheric CH3Br[END_REF] For methyl chloride, microbial degradation seems to be more important, especially in subarctic and arctic ocean waters due to slow degradation rates of abiotic processes. [START_REF] Hu | An improved oceanic budget for methyl chloride[END_REF] Still, the overall importance of these reactions compared to microbial degradation of methyl halides in oceans and soils is generally not well understood.

Stable isotope analysis was suggested as a diagnostic tool to overcome the limitations of solely quantifying concentration levels of these compounds. [START_REF] Hunkeler | A Guide for Assessing Biodegradation and Source Identification of Organic Ground Water Contaminants Using Compound Specific Isotope Analysis (CSIA)[END_REF] Several studies measured the carbon isotope composition of various sources and degradation processes and an overview of these isotopic signatures was published for CH 3 Br [START_REF] Bill | Stable carbon isotope composition of atmospheric methyl bromide[END_REF] and CH 3 Cl, [START_REF] Keppler | New insight into the atmospheric chloromethane budget gained using stable carbon isotope ratios[END_REF] respectively. Isotopic source signatures and existing isotopic enrichment factors for degradation processes were used to calculate an isotopic mass balance which was compared to the measured isotopic composition of tropospheric CH 3 X. Both studies revealed that the modeled atmospheric isotopic composition differed considerably from the measured isotopic composition. This discrepancy might be due to several reasons. Unknown sources and their isotopic composition could not be included in the models and also enrichment factors for degradation processes were partly not considered or known. In order to improve future atmospheric budget estimates of CH 3 X both emissions and degradation processes need to be characterized more precisely.

In the current study we focused on isotopically characterizing the major abiotic degradation processes in oceans. Isotopic enrichment factors (ε) for the isotopes of all three elements in each compound were measured for the two nucleophilic substitution reactions (SN 2 ) hydrolysis and halide exchange. Significant improvements may be expected if the isotopic compositions of several elements are measured in one compound. Such multielement isotopic approaches have recently become available with improved measurement techniques and were successfully applied to describe, for instance, the fate of organic contaminants in groundwater. [START_REF] Kuder | 3D-CSIA: carbon, chlorine, and hydrogen isotope fractionation in transformation of TCE to ethene by a Dehalococcoides culture[END_REF][START_REF] Franke | Triple-element compound-specific stable isotope analysis of 1,2dichloroethane for characterization of the underlying dehalogenation reaction in two Dehalococcoides mccartyi strains[END_REF] For CH 3 Cl, hydrogen isotope measurements were presented recently [START_REF] Nadalig | Hydrogen and carbon isotope fractionation during degradation of chloromethane by methylotrophic bacteria[END_REF][START_REF] Keppler | Mass spectrometric measurement of hydrogen isotope fractionation for the reactions of chloromethane with OH and Cl[END_REF][START_REF] Jaeger | Chloromethane formation and degradation in the fern phyllosphere[END_REF] and bromine isotope analysis was demonstrated in two studies for CH 3 Br 30,31 but overall no multielement isotope studies have been published yet for methyl halides. Here we determined the isotope fractionation caused by the two SN 2 reactions for all available stable isotopes in each compound; that is, hydrogen and carbon isotopes in both compounds and chlorine as well as bromine isotopes for methyl chloride and methyl bromide, respectively. To our knowledge, the presented data are the first three-dimensional isotope measurements for each of these substances. The results are compared to isotope fractionation pattern of other potentially important processes and implications toward a future use of multidimensional isotope studies of methyl halides are discussed.

■ MATERIALS AND METHODS

Chemicals. Methyl chloride and methyl bromide were purchased as compressed gases and with a purity of more than 99%. Methyl chloride was obtained from Linde (Germany) whereas methyl bromide was purchased from Gerling, Holtz & Co (Germany). A commercially available sea salt without any additives (Aquasale, Heilbronn, Germany, major ion composition given in Supporting Information Table S1) was purchased to prepare brines with a concentration of 35 g kg -1 (psu) which is similar to the average salt content of seawater.

Preparation of Samples and Experiments. Stock solutions with a concentration of 10 mmol L -1 CH 3 Br and CH 3 Cl were prepared for hydrolysis experiments and 5 mmol L -1 CH 3 X for halide exchange experiments by injecting the corresponding amount of gas into the headspace of a 1L crimpsealed glass bottle filled with distilled water and brine (3.5%), respectively. Additionally, a stock solution of 0.2 mmol L -1 CH 3 Br was prepared to carry out a hydrolysis experiment at a lower concentration. The brine was prepared by mixing distilled water with the sea salt and boiling this solution for 10 min. All experiments were carried out in unbuffered solution (see also Results and Discussion for further explanations). After preparation, stock solutions were shaken overnight for equilibration before further usage. For each experiment, 6-10 septum bottles (60 mL) were filled with 40 mL of solution, crimp-sealed and all bottles shaken for at least 3 h. Then, the starting concentration was determined by injecting aliquots of the headspace of all samples. At least three standards were analyzed to quantify the sample concentrations via a threepoint calibration (Supporting Information 3). To avoid gasleakage through the pinched septa, the sample bottles were kept upside-down throughout the entire experiment. Furthermore, samples were kept at a dark place maintaining a temperature of 23 ± 1 °C. Sampling of the bottles took place in different time intervals. For methyl bromide, sampling occurred every 3-5 days whereas for methyl chloride up to two months passed before another sample was collected. After sampling, each bottle was frozen to -18 °C for conservation and stored until the end of the experiment at this temperature. Before analysis, all samples of one experiment were heated simultaneously to 25 °C in a water bath and subsequently shaken for 2 h to ensure equal treatment of all samples and complete equilibration in the sample bottles.

Stable Isotope Analysis of Carbon, Hydrogen, Chlorine, and Bromine. Stable isotope analysis was carried out by injecting aliquots of the headspace gas (50-1000 μL depending on concentration and element) into the injector (split mode) of the gas chromatographic systems (GC) using a gastight syringe with push-button valve (VICI Precision Sampling). The GC was either connected to gas source isotope ratio mass spectrometry (IRMS) for hydrogen and carbon isotope analysis or to multiple collector inductively coupled plasma mass spectrometry (MC-ICPMS) for chlorine and bromine isotope analyses. The analytical procedures followed closely the methods described and published in previous studies for carbon, [START_REF] Chevallier | Distinct carbon isotope fractionation signatures during biotic and abiotic reductive transformation of chlordecone[END_REF] hydrogen, [START_REF] Renpenning | Compound-specific hydrogen isotope analysis of heteroatom-bearing compounds via gas chromatography-chromiumbased high-temperature conversion (Cr/HTC)-isotope ratio mass spectrometry[END_REF] chlorine, [START_REF] Horst | Compound specific stable chlorine isotopic analysis of volatile aliphatic compounds using gas chromatography hyphenated with multiple collector inductively coupled plasma mass spectrometry[END_REF][START_REF] Renpenning | Online isotope analysis of 37Cl/35Cl universally applied for semi-volatile organic compounds using GC-MC-ICPMS[END_REF] and bromine [START_REF] Horst | Compound-specific bromine isotope analysis of methyl bromide using gas chromatography hyphenated with inductively coupled plasma multiple-collector mass spectrometry[END_REF] isotopes. Descriptions of the methods are provided for each method in the Supporting Information 1, including also a cross calibration for bromine isotopes following previously published protocols [START_REF] Eggenkamp | Rediscovery of classical methods and their application to the measurement of stable bromine isotopes in natural samples[END_REF][START_REF] Louvat | Determination of Bromine Stable Isotope Ratios from Saline Solutions by "Wet Plasma" MC-ICPMS Including a Comparison between High-and Low-Resolution Modes, and Three Introduction Systems[END_REF] (Supporting Information 2).

Results from isotopic measurements are reported in delta values (δ) for all isotopes. Delta values are calculated according to the following expression: 39

E Ur R R ( ) ( )sample ( )standard 1 i δ = - (1)
delta values are given in Ur (urey) according to recent IUPAC recommendations. [START_REF] Brand | Assessment of international reference materials for isotope-ratio analysis (IUPAC Technical Report)[END_REF] Urey, if expressed in milli-urey (mUr), and the more commonly used permil scale (‰) are interchangeable: 1 mUr = 0.001 = 1‰, but Ur is, in contrast to permil a SI unit and hence common SI prefixes such as milliand micro-become available. Other terms for the expression of isotopic ratios such as ppm and permeg may also be reported in Ur. Thus, the unit urey provides a single unified approach for the expression of all stable isotope ratios. The overall uncertainties of the analytical procedures, including reproducibility, linearity, and scale normalization are usually better than 5 mUr (hydrogen), 0.5 mUr (carbon), 0.2 mUr (chlorine), and 0.1 mUr (bromine).

Enrichment factors and dual element isotope ratios. The isotopic enrichment factor describes the change of the isotopic composition between the substrate and the instantaneous product caused by a reaction or a process. [START_REF] Scott | Optimal methods for estimating kinetic isotope effects from different forms of the Rayleigh distillation equation[END_REF] It further characterizes the constant change of the isotopic composition of the substrate reservoir due to the preferential loss of heavy or light isotopes during a reaction or process. In the current study, isotopic enrichment factors (ε H , ε C , ε Cl, ε Br ) for CH 3 Cl and CH 3 Br were determined by using the Rayleigh equation: [START_REF] Mariotti | Experimental determination of nitrogen kinetic isotope fractionation: Some principles; illustration for the denitrification and nitrification processes[END_REF] i k j j j j j y

{ z z z z z E E f ln 1000 1000 ln( ) i i x 0 δ δ ε + + ≈ (2)
where δ i E is the isotopic signature (δ 2 H, δ 13 C, δ 37 Cl, δ 81 Br) of the organic after partial degradation, δ i E 0 indicates the initial delta value (δ 2 H 0 , δ 13 C 0 , δ 37 Cl 0 , δ 81 Br 0 ), and f is the fraction of organic remaining after partial degradation. The procedure for quantifying f is provided in the Supporting Information 3. The Rayleigh equation is appropriate to derive the isotopic enrichment factors for first-order or pseudo-first-order reactions. [START_REF] Van Breukelen | Extending the Rayleigh equation to allow competing isotope fractionating pathways to improve quantification of biodegradation[END_REF] Λ-values (lambda) describe the ratio of the enrichment factors of isotopes of two different elements. [START_REF] Van Breukelen | Extending the Rayleigh equation to allow competing isotope fractionating pathways to improve quantification of biodegradation[END_REF] Λ-values are determined as the slope of a linear regression of isotopic signatures of two elements (e.g., H and C) determined from samples of the same experiment. Λ-values may also be estimated according to the following relationship: 43

x y x y / ε ε Λ ≈ (3)
where ε x and ε y are the enrichment factors of two different elements determined for the same mechanism in a certain compound.

■ RESULTS AND DISCUSSIONS Reaction Rates. Experiments were performed to investigate the abiotic degradation of CH 3 Br and CH 3 Cl dissolved in water. Experiments in distilled water were carried out to study hydrolysis reactions only. In brines (seawater) degradation may be due to both, hydrolysis and halide exchange. All experiments were performed at a temperature of 23 ± 1 °C. No buffer was added to the stock solutions because buffer catalysis was reported as a complicating factor in previous studies. [START_REF] Jeffers | On the degradation of methyl bromide in sea water[END_REF][START_REF] Perdue | Prediction of buffer catalysis in field and laboratory studies of pollutant hydrolysis reactions[END_REF][START_REF] Elliott | Methyl halide hydrolysis rates in natural waters[END_REF] Moreover, hydrolysis of CH 3 Cl and CH 3 Br is expected to primarily follow reaction R1 in the environment. Theoretically, when taking into account the nucleophilicities of the nucleophiles (Supporting Information 4), alkaline (R2), and neutral hydrolysis (R1) should be equally important at a pH of 11.6. [START_REF] Schwarzenbach | Environmental Organic Chemistry[END_REF] Another study showed that alkaline hydrolysis of singly halogenated compounds was not sustained, if OH -concentrations dropped below 0.1 mol L -116 (pH 13). Consequently, reaction R2 is supposed to be unimportant at pH 10 and below. [START_REF] Schwarzenbach | Environmental Organic Chemistry[END_REF] Therefore, all hydrolysis reactions in this study, which were performed at pH values smaller than 7, were assumed to be independent of the pH and to predominantly follow reaction R1. Results for the determined rate constants of the individual experiments are summarized in Table 1 and are compared to previously published values.

For hydrolysis of CH 3 Br two experiments were carried out at different concentrations. Rate constants of both experiments varied between 0.035 ± 0.008% d -1 at 10 mmol L -1 CH 3 Br and 0.013 ± 0.002% d -1 at 0.2 mmol L -1 CH 3 Br. The rate constant obtained at high concentrations may, however, be influenced by an additional equilibration effect with Br -ions in the solution also represented by unusual bromine isotope values (see discussion below). During hydrolytic degradation of CH 3 Br, Br -ions are released into the solution according to reaction R1. Schwarzenbach et al. [START_REF] Schwarzenbach | Environmental Organic Chemistry[END_REF] summarized previously published relative nucleophilicities of nucleophiles reacting with CH 3 Br. [START_REF] Hine | Physical Organic Chemistry[END_REF] Taking into account these nucleophilicities and the CH 3 Br concentration of 10 mmol L -1 , released Br -ions reached indeed a concentration high enough to compete with water as a nucleophile. Both hydrolysis and Br -exchange are equally important when about 75% of Br -is released due to transformation of CH 3 Br (Supporting Information 4). A second experiment was run at a lower concentration to avoid any of such additional reactions. At 0.2 mmol L -1 CH 3 Br the release of Br -ions due to transformation only reached about 2% of the amount necessary to compete with hydrolysis (Supporting Information 4) and no additional effect on the Br isotopic composition was detected. Consequently, hydrolysis of methyl bromide at 0.2 mmol L -1 CH 3 Br followed pseudo first-order kinetics (Supporting Information Figure S4), a prerequisite to reliably apply the Rayleigh equation for quantification of isotopic enrichment factors. The experimentally determined rate constant of 0.013 ± 0.002 d -1 was lower than at high concentrations but the magnitude was close to the rate constant of 0.021 ± 0.002 d -1 reported by Jeffers and Wolfe. [START_REF] Jeffers | On the degradation of methyl bromide in sea water[END_REF] For experiments with added sea salt the rate constant was about 1 order of magnitude larger (0.115 ± 0.023 d -1 ) compared to hydrolysis in distilled water and followed pseudo first-order kinetics (Supporting Informaiton Figure S5). This experimentally determined rate constant agrees, within analytical uncertainty, with 0.154 ± 0.06 d -1 published by a previous study. [START_REF] King | Removal of methyl bromide in coastal seawater: Chemical and biological rates[END_REF] The ten-times higher rate constant due to the [START_REF] Elliott | Methyl halide hydrolysis rates in natural waters[END_REF] nucleophilic strength of Cl (Supporting Information 4) suggests that halide exchange dominates the abiotic degradation of CH 3 Br in seawater with hydrolysis only contributing to a minor extent to the overall combined degradation rate.

For hydrolysis of methyl chloride in distilled water the experimentally determined rate constant of 0.0015 ± 0.0005 d -1 is in good agreement with 0.0014 ± 0.0002 d -1 reported previously. [START_REF] Elliott | Methyl halide hydrolysis rates in natural waters[END_REF] The reaction of CH 3 Cl with H 2 O and salt yielded a rate constant of 0.12 ± 0.02% d -1 which is indistinguishable from hydrolysis in distilled water. Data from both reactions of CH 3 Cl follow pseudo first-order kinetics (Supporting Information Figures S6 andS7). The similar reaction rate constants obtained from both experiments may indicate that halide exchange of CH 3 Cl at ambient temperatures does not have any measurable effect on the combined degradation rate and hence hydrolysis should be the main abiotic degradation mechanism in natural waters.

Hydrolysis and Associated Isotope Effects. Isotopic enrichment factors derived from hydrolysis experiments were determined for stable carbon, hydrogen, and bromine isotopes of CH 3 Br. At high concentrations (10 mmol L -1 CH 3 Br) additional equilibration with Br -influenced the reaction rate constant and the Rayleigh equation may only possess a limited validity for this experiment. Despite this limitation, the carbon isotopic data followed a linear regression with an ε C of -49.6 ± 5.6 mUr (Supporting Information Figure S9). This value is close to -58.3 ± 6.8 mUr (Figure 1b) which was determined for the low-concentration experiment (0.2 mmol L -1 CH 3 Br) where no significant Br -exchange occurred. Both ε C are consistent with a published carbon isotope enrichment factor of -51.0 ± 6.0 mUr. [START_REF] Baesman | Laboratory determination of the carbon kinetic isotope effects (KIEs) for reactions of methyl halides with various nucleophiles in solution[END_REF] The same authors investigated the pH Enrichment factors are derived from the Rayleigh plots in Figure 1 and Figure 2. Lambda values are determined graphically from dual-elemental isotope plots (Supporting Information Figure S11-S14). Errors are given as the 95% confidence interval of the regressions. Values in italics indicate that these reactions might not strictly follow pseudo-first-order kinetics and epsilons only serve as an approximation despite acceptable correlation coefficients; nd means "not determined"; * indicates that this value was calculated using eq 3. independence of carbon isotope fractionation by carrying out experiments at different pH (4.6, 7.3, and 8.8) and additionally in unbuffered solutions (pH 3.6-6.0). No significant difference was observed in that study for isotopic enrichment factors obtained from unbuffered solutions compared to those with a fixed pH confirming that hydrolysis primarily occurs via one reaction (R1). Hence enrichment factors obtained in the current study should be valid for the conditions found in relevant environmental compartments such as surface waters and soils.

Hydrogen isotope enrichment factors could only be measured for samples at high concentrations. CH 3 Br concentrations of 0.2 mmol L -1 were too low to meet the isotopic detection limit for hydrogen isotope measurements. Despite the mentioned uncertainties regarding the rate law, the enrichment factor of +42 ± 20 mUr is consistent with a secondary isotope effect resulting from reaction R1 (Figure 1a, Table 2). Secondary effects are usually smaller than primary isotope effects and occur in elements located adjacent to a reactive position due to the changing structure of the molecule or influences of bond vibrations, for example. [START_REF] Melander | Reaction Rates of Isotopic Molecules[END_REF] Furthermore, the positive ε H indicates an inverse isotope effect. The remaining CH 3 Br in water becomes successively depleted in deuterium throughout the reaction. Secondary inverse isotope effects of hydrogen are in fact a common feature for nucleophilic substitution reactions of methyl derivatives and this was investigated in several experimental studies in the gas phase as well as in computational studies. [START_REF] Gronert | Deuterium isotope effects in gas-phase reactions of alkyl halides -Distinguishing E2 and SN2 pathways[END_REF][START_REF] Viggiano | Temperature-dependence of the kinetic isotope effect for a gas-phase SN2 reaction -Cl-+ CH3[END_REF][START_REF] Wolfe | Secondary H/D isotope effects in methyltransfer reactions decrease with increasing looseness of the transition structure[END_REF][START_REF] Hennig | Secondary kinetic isotope effect in nucleophilic substitution: a quantum-mechanical approach[END_REF] Accordingly, the inverse isotope effects may be explained with transition state theory. During S N 2 reactions the nucleophile (H 2 O, Y -) approaches the carbon atom from the side opposite to the halogen atom. In the transition state both the nucleophile and the leaving halogen atom are partly bound to the carbon atom. The tetrahedral geometry of the methyl halide molecule changes to a trigonal bipyramidal geometry in the transition state where the hydrogen atoms are located in a single plane. [START_REF] Schwarzenbach | Environmental Organic Chemistry[END_REF] This structural change is associated with an increase of the bending and stretching force constants, the latter caused by a tightening of the C-H bonds. [START_REF] Wolfe | Secondary H/D isotope effects in methyltransfer reactions decrease with increasing looseness of the transition structure[END_REF] This increase is represented by a symmetric excitation of the stretching vibration which increases the reaction probability of the molecules containing a C-D bond to a larger extent than for molecules containing a C-H bond. [START_REF] Hennig | Secondary kinetic isotope effect in nucleophilic substitution: a quantum-mechanical approach[END_REF] As a result, CH 3 Br in the solution becomes enriched in [START_REF] Yvon-Lewis | The potential effect of oceanic biological degradation on the lifetime of atmospheric CH3Br[END_REF] C and 81 Br (see below) but depleted in 2 H. Even though our measured enrichment factor of +42 mUr was smaller than those in the cited articles (up to +200 mUr in gas phase experiments), it qualitatively confirms these inverse effects for different nucleophiles (see also discussion further below) reacting with methyl halides dissolved in water.

For bromine isotopes in CH 3 Br an ε Br of -1.2 ± 0.4 mUr was measured for the experiment carried out at 0.2 mmol L -1 CH 3 Br (Figure 1c). At high concentrations (10 mmol L -1 CH 3 Br) a nonlinear behavior of the δ 81 Br values could be observed which was not in agreement with the Rayleigh equation (Supporting Information Figure S8). At first, the δ 81 Br of the substrate became more enriched but then started to converge toward the starting value again. Apparently, the rising concentrations of bromine ions released into the solution started to equilibrate with the CH 3 Br substrate. At low concentrations no such effect was observed because Br - concentrations in solution were too low to compete with H 2 O as a nucleophile (Supporting Information 4). Hence, this equilibration is unlikely to occur in most freshwaters and soils, environments where CH 3 Br and Br -concentrations are low and where hydrolysis may contribute to degradation. Even in ocean waters the Br -content only reaches 25% of the concentration required to compete with H 2 O (1.8 mmol L -1 , Supporting Information 4), which might explain why no indications of such an equilibration effect were observed in experiments with brines, as discussed further below.

For hydrolysis of CH 3 Cl, stable hydrogen, carbon, and chlorine isotope enrichment factors were determined. The degradation experiment of CH 3 Cl in distilled water (hydrolysis) was carried out over 232 days and sampling occurred in time steps of 1-3 months. Isotopic enrichment factors of +25 ± 6 mUr ( 2 H), -41.7 ± 10.2 mUr ( 13 C), and -5.3 ± 1.3 mUr ( 37 Cl) were derived from the Rayleigh plots (Figure 2a-c). No equivalent data is available in the literature for comparison. Compared to hydrolysis of CH 3 Br, enrichment factors for hydrogen and carbon showed a similar magnitude and direction; that is, carbon isotope effects were relatively large and normal whereas hydrogen isotope effects were small and inverse due to a secondary isotope effect caused by the nucleophilic substitution reaction. The chlorine isotope enrichment factor is about 3 times larger than the measured bromine isotope effect in CH 3 Br which is consistent with a previous estimate based on theoretical calculations for primary kinetic isotope effects for halogens. [START_REF] Willey | Capacitive integration to produce high precision isotope ratio measurements on methyl chloride and methyl bromide samples[END_REF] Isotope Effects Caused by Halide Exchange Reactions. The nucleophilic substitution reaction of halide ions was the second abiotic degradation process investigated in this study. The enrichment factors obtained from experiments with CH 3 Br dissolved in brine were +22 ± 13 mUr, -63.3 ± 5.1 mUr, and -1.2 ± 0.2 mUr for 2 H, [START_REF] Yvon-Lewis | The potential effect of oceanic biological degradation on the lifetime of atmospheric CH3Br[END_REF] C, and 81 Br, respectively (Figure 1d-f and Table 2). The measured carbon isotope enrichment factor (-63.3 ± 5.1 mUr) agrees well with -57.0 ± 5.0 mUr reported by Baesman and Miller. [START_REF] Baesman | Laboratory determination of the carbon kinetic isotope effects (KIEs) for reactions of methyl halides with various nucleophiles in solution[END_REF] Another study published an ε C of -41.2 mUr for this reaction which is by about 20 mUr smaller. [START_REF] Kalin | Continuous flow stable isotope methods for study of delta(13)C fractionation during halomethane production and degradation[END_REF] Compared to the hydrolysis experiments carried out in the current study, enrichment factors for halide exchange are indistinguishable if the analytical uncertainty is taken into account (Table 2). Chlorine ions dominated the exchange reaction with CH 3 Br because Cl - concentrations were about nine times higher than necessary to compete with water as a nucleophile (Supporting Information 4). The product of this reaction was CH 3 Cl which could be identified during δ 13 C-CH 3 Br measurements (Supporting Information 5). The measured δ 13 C values of the generated CH 3 Cl were indistinguishable from the δ 13 C predicted by the Rayleigh equation for the cumulative product (Supporting Information Table S3, Figure S10) and CH 3 Cl is considered the major product of this reaction.

Exchange of chlorine with bromine is a degradation process for CH 3 Br but simultaneously constitutes a source for CH 3 Cl. Still, oceanic concentrations of CH 3 Br are very low compared to CH 3 Cl. Hu et al. [START_REF] Hu | Coastal emissions of methyl bromide and methyl chloride along the eastern Gulf of Mexico and the east coast of the United States[END_REF] reported average concentrations of 2 pM which is much lower than the 88 pM found for CH 3 Cl during the same cruise in the Atlantic Ocean. Thus, the transformation of CH 3 Br would only marginally (<2%) increase the total CH 3 Cl concentration in seawater even if all CH 3 Br were completely transformed to CH 3 Cl. Chlorine exchange in CH 3 Br is therefore not a significant source of CH 3 Cl despite its importance as an abiotic degradation process for CH 3 Br.

The degradation of CH 3 Cl dissolved in brine generated similar enrichment factors as for hydrolysis of CH 3 Cl in distilled water: + 24 ± 19 mUr for hydrogen, -40.6 ± 13.9 mUr for carbon and -5.2 ± 1.0 mUr for chlorine (Figure 2df, Table 1). In contrast to CH 3 Br, the addition of sea salt did not increase the degradation rates of CH 3 Cl (see discussion above) and it can be assumed that only hydrolysis took place. Furthermore, chlorine isotope measurements did not deliver any evidence for equilibrium exchange of Cl -with CH 3 Cl. The CH 3 Cl dissolved in the brine had a starting δ 37 Cl of +6.02 mUr SMOC [START_REF] Horst | Compound specific stable chlorine isotopic analysis of volatile aliphatic compounds using gas chromatography hyphenated with multiple collector inductively coupled plasma mass spectrometry[END_REF] whereas Cl -in the added sea salt should be close to 0.0 mUr SMOC. [START_REF] Kaufmann | Natural chlorine isotope variations[END_REF] In our experiments we observed a shift of δ [START_REF] Eggenkamp | Rediscovery of classical methods and their application to the measurement of stable bromine isotopes in natural samples[END_REF] Cl toward more enriched values following clearly pseudo first-order kinetics (Supporting Information Figure S7). In contrast, exchange of CH 3 Cl with Cl -, if occurring at ambient temperatures, should have caused a shift of δ 37 Cl in the direction of the lighter values of the added sea salt. Thus, halide exchange in CH 3 Cl may be considered negligible at ambient temperatures and should not affect the δ 37 Cl of methyl chloride in most environments.

Overall, the results of the current study give further insights into the importance of these two reactions for degradation of CH 3 X in water and provide first isotopic enrichment factors for hydrogen and halogens. For CH 3 Br, halide exchange should be the dominant abiotic degradation mechanism in seawater which confirms the findings of previous studies. [START_REF] Elliott | Nucleophilic substitution rates and solubilities for methyl halides in seawater[END_REF][START_REF] Baesman | Laboratory determination of the carbon kinetic isotope effects (KIEs) for reactions of methyl halides with various nucleophiles in solution[END_REF][START_REF] Zafiriou | Reaction of Methyl Halides with Seawater and Marine Aerosols[END_REF] Hydrolysis may have a rather minor role in degrading CH 3 Br in freshwaters and soils. Hydrolysis of CH 3 Br also occurs in oceans at a 10 times slower rate and isotopic enrichment factors are similar to those obtained from halide exchange reactions due to the same reaction mechanism (S N 2 reaction). Consequently, the two processes cannot be individually characterized and quantified with isotopic methods and both reactions may be included as a combined abiotic degradation process in future isotope-based budget estimates. Still, if necessary, degradation by the individual processes can be estimated from the relative rate difference of these abiotic processes which should be constant at relevant temperatures in seawater. For CH 3 Cl, only hydrolysis may occur as an abiotic mechanism in most environments with degradation rates being 1 order of magnitude lower than for hydrolysis of CH 3 Br. Consequently, hydrolysis should only marginally contribute to degradation of CH 3 Cl in oceans, freshwater, and soils as confirmed by previous studies. [START_REF] Elliott | Methyl halide hydrolysis rates in natural waters[END_REF][START_REF] Tokarczyk | Methyl chloride and methyl bromide degradation in the Southern Ocean[END_REF] Dual-Element Isotope Ratios. Λ-values provide a more precise parameter than ε values to characterize and compare reaction mechanisms because these ratios are insensitive to masking and rate limitation by additional processes. [START_REF] Elsner | Stable isotope fractionation to investigate natural transformation mechanisms of organic contaminants: principles, prospects and limitations[END_REF] For the current study, lambda values were derived from dual-element isotope plots provided in Supporting Information Figures S11-S14. The resulting Λ H/C , Λ C/Cl , and Λ C/Br are given in Table 2. Λ H/C values ranged from -0.3 to -0.7 for both compounds and both reaction pathways. The Λ C/Cl for CH 3 Cl ranged from 6.9 to 7. 3

F

The Λ H/C of -0.6 for hydrolysis of CH 3 Cl shows a similarly small absolute value as degradation by methylotrophic bacteria [START_REF] Nadalig | Hydrogen and carbon isotope fractionation during degradation of chloromethane by methylotrophic bacteria[END_REF] (Λ H/C = 0.7, SI Table S4), differing by the algebraic sign due to an inverse ε H for hydrolysis. Consortia of soil microbes showed slightly larger Λ H/C which ranged from 1.3 up to 4.6 due to a decreasing ε C with decreasing CH 3 Cl concentrations. [START_REF] Jaeger | Chloromethane degradation in soils: a combined microbial and two-dimensional stable isotope approach[END_REF] These small lambdas for abiotic and biotic reactions in water are the result of relatively small secondary hydrogen isotope effects (<-50 mUr) due to rupture of the C-X bond. Abiotic and biotic reactions in water are, however, still distinguishable by opposing positive and negative Λ H/C .

In contrast, the main abiotic degradation pathways of CH 3 Cl in the gas phase (OH•, Cl• radical reactions) are characterized by larger Λ H/C of 23.6 to 27.5 (SI Table S4) based on the enrichment factors published by two recent studies. [START_REF] Keppler | Mass spectrometric measurement of hydrogen isotope fractionation for the reactions of chloromethane with OH and Cl[END_REF][START_REF] Bahlmann | Evidence for a major missing source in the global chloromethane budget from stable carbon isotopes[END_REF] Radical reactions cleave the C-H bond and therefore primary isotope effects for both C and H can be observed causing an overall larger Λ H/C which is clearly distinguishable from reactions in water, even though only two isotopic systems are used.

Implications for Future Isotope-Based Studies of CH 3 X. The results presented in this paper provide a first glimpse of the capabilities of triple-element isotope analysis of CH 3 X for identification and characterization of degradation processes of methyl halides. Specifically, the pattern of isotopic shifts defined by enrichment factors and lambda values will be a useful tool to distinguish abiotic degradation processes from other removal processes of CH 3 X. A comparison of isotope effects measured for degradation mechanisms of CH 3 Cl demonstrates that basically all known relevant abiotic and biotic degradation mechanisms in water (and soils) are due to a C-Cl bond cleavage in CH 3 Cl (Figure 3). Resulting Λ C/Cl are relatively similar for all these reactions but Λ H/C may still be used to distinguish abiotic from biotic degradation due to opposing inverse and normal hydrogen isotope fractionation, respectively (Table 2, SI Table S4). Methylotrophic bacteria, for instance, were identified as the main biotic degraders in water and soils because these organisms are capable of consuming considerable amounts of methyl halides. [START_REF] Schafer | Bacterial cycling of methyl halides[END_REF] Large carbon isotope enrichment factors (-38 to -41 mUr) were reported for this biotic reaction but rather small secondary hydrogen isotope enrichment factors (-27 to -29 mUr) due to cleavage of the C-Cl bond. [START_REF] Nadalig | Hydrogen and carbon isotope fractionation during degradation of chloromethane by methylotrophic bacteria[END_REF] Halogen isotope effects for aerobic microbial degradation of CH 3 Cl (or CH 3 Br) have not been published yet but it is conceivable that they show a similarly large isotope fractionation as reported for other halogenated alkanes. Aerobic microbial degradation of 1,2dichloroethane, for instance, caused an ε Cl of at least -3.8 mUr [START_REF] Palau | Hydrogen isotope fractionation during the biodegradation of 1,2-dichloroethane: Potential for pathway identification using a multi-element (C, Cl, and H) isotope approach[END_REF] which was similar to the ε Cl reported for anaerobic microbial degradation (-4.2 mUr). [START_REF] Franke | Triple-element compound-specific stable isotope analysis of 1,2dichloroethane for characterization of the underlying dehalogenation reaction in two Dehalococcoides mccartyi strains[END_REF] In contrast, CH 3 X in the troposphere mainly degrades via OH and Cl radical reactions 1 which cause a C-H bond dissociation. Consequently, reported hydrogen isotope effects for CH 3 Cl were large [START_REF] Keppler | Mass spectrometric measurement of hydrogen isotope fractionation for the reactions of chloromethane with OH and Cl[END_REF] (>-264 to -280 mUr) and carbon isotope effects were moderate (-10.2 to -11.2 mUr). [START_REF] Bahlmann | Evidence for a major missing source in the global chloromethane budget from stable carbon isotopes[END_REF] Halogens present in CH 3 X should only show small secondary isotope effects because they are not involved in radical reactions. [START_REF] Melander | Reaction Rates of Isotopic Molecules[END_REF] Consequently, gas phase reactions of CH 3 Cl show a completely different pattern of isotopic shifts compared to reactions in water and soils (Figure 3). This separation of fractionation patterns of aqueous and gas phase reactions may also be conceivable for CH 3 Br because biotic and abiotic degradation mechanisms are largely the same. [START_REF] Engel | Update on ozone-depleting substances (ODS) and other gases of interest to the Montreal Protocol[END_REF] The possibility to clearly distinguish degradation in water from degradation in the gas phase may considerably simplify the characterization and probably even allow for quantification of degradation processes of methyl halides when applying triple-element isotope analysis.

In order to fully benefit from the advantages of tripleelement isotope analysis in the future, however, it will be Figure 3. Illustration of fractionation effects of CH 3 Cl in water and in the gas phase (troposphere). The δ 2 H, δ 13 C, and δ 37 Cl are expressed as the relative difference from δ 2 H 0 , δ 13 C 0 , and δ 37 Cl 0 of the undegraded sample. All isotopic values for abiotic reactions in water are taken from the current study whereas carbon and hydrogen isotope values are taken from the literature (SI Table S4). Fractionation for chlorine isotopes in biotic reactions has been estimated assuming a minimum isotope effect of -4 mUr based on previous studies on chlorinated alkanes as described in the text (average of aerobic/anaerobic reactions). For gas phase reactions an insignificant secondary chlorine isotope effect was assumed being smaller than analytical uncertainty of 0.2 mUr. The figure demonstrates a clear distinction between isotope fractionation in the gas phase (troposphere) and fractionation in water.

necessary to determine three-dimensional isotopic fingerprints of atmospheric samples and of the largest sources (macroalgae, salt marshes, biomass burning, plants, soils). Moreover, full sets of isotopic enrichment factors and lambda values for the main removal processes (OH radical reactions, microbial degradation in oceans and soils) must be determined. Once these tasks are completed, the isotopic data can be fed into models. Previous models relied exclusively on upscaled emission data, used together with the corresponding stable carbon isotopic signatures of the sources to create a weighted mean isotopic source signature for CH 3 Cl and CH 3 Br, respectively. [START_REF] Keppler | New insight into the atmospheric chloromethane budget gained using stable carbon isotope ratios[END_REF][START_REF] Bahlmann | Evidence for a major missing source in the global chloromethane budget from stable carbon isotopes[END_REF][START_REF] Mccauley | An isotopic approach for understanding the CH(3)Br budget of the atmosphere[END_REF] This weighted mean does however not reflect the atmospheric isotopic composition because degradation processes induce isotope fractionation in methyl halides during or shortly after emission (e.g., in oceans or soils) or in the well-mixed atmosphere. Previous models often only partly included the isotopic shifts induced by degradation processes or relied on estimates because enrichment factors were not available for each assumed degradation process. [START_REF] Bill | Stable carbon isotope composition of atmospheric methyl bromide[END_REF][START_REF] Keppler | New insight into the atmospheric chloromethane budget gained using stable carbon isotope ratios[END_REF][START_REF] Mccauley | An isotopic approach for understanding the CH(3)Br budget of the atmosphere[END_REF] A recent study provided a more refined carbon isotope mass balance which accounted for the effect of degradation in atmospheric CH 3 X and simultaneous mixing of continuous emissions of CH 3 X from sources. [START_REF] Bahlmann | Evidence for a major missing source in the global chloromethane budget from stable carbon isotopes[END_REF] The calculated budget, however, suggested an even larger imbalance between emissions and loss processes than previously thought.

The future use of two additional isotopic systems for each compound may substantially improve such mass balance approaches because of the different sensitivity of hydrogen and halogen isotopes for radical reactions in the atmosphere and degradation in water/soil respectively Figure 3). Hence, three different isotopic mass balances may be created which have to yield matching results for emissions and degradation rates derived from isotope enrichment factors thus providing a tool for verification of such a mass balance approach. Apart from these bottom-up approaches, inverse top-down models using isotopic data might be appropriate methods for source apportionment of atmospheric compounds. [START_REF] Crill | Whither methane in the IPCC process?[END_REF] These inverse models estimate emissions and degradation from variations in the atmospheric composition but require long-term monitoring using a relatively dense network of sampling stations. [START_REF] Houweling | Global inverse modeling of CH4 sources and sinks: an overview of methods[END_REF] Inverse models may, however, provide an alternative route to calculate the atmospheric budget, but for CH 3 X the application of these models is currently still out of reach because of the challenges to regularly measure the isotopic composition of atmospheric CH 3 X. Once these challenges are overcome, triple-element isotope analysis may provide a realistic chance to better quantify the unbalanced atmospheric budgets of CH 3 X and to identify the putatively missing sources.

■ ASSOCIATED CONTENT

* S Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.est.9b02165.

Additional information on analytical methods (isotope analysis, quantification), cross-calibration of standards for bromine isotope analysis, relative nucleophilicities of halogens and water, graphical determination of the rate laws of the different reactions, isotopic measurements of carbon and bromine for hydrolysis of CH 3 Br at high concentrations, determination of lambda values from the current and previous studies, and isotopic information on product-CH 3 Cl (PDF)

■ AUTHOR INFORMATION Corresponding Author *E-mail: axel.horst@ufz.de. ORCID Axel Horst: 0000-0002-3475-2425 Hans Hermann Richnow: 0000-0002-6144-4129 Notes

Figure 1 .

 1 Figure 1. Rayleigh plots for abiotic reactions of CH 3 Br in water. Panel (a), (b), and (c) show results of the reaction CH 3 Br + H 2 O (hydrolysis). Panel (d), (e), and (f) demonstrate isotope effects due to CH 3 Br + H 2 O + Y -(hydrolysis and halide exchange combined). The slope of the regression indicates the enrichment factor in Ur. Error bars represent the analytical uncertainty of 5 mUr (δ 2 H), 0.5 mUr (δ 13 C), and 0.1 mUr (δ 81 Br). For carbon isotopes, error bars are smaller than the used symbols. The quantification was carried out with an uncertainty of usually better than 5%.

Figure 2 .

 2 Figure 2. Rayleigh plots for reactions of CH 3 Cl. Panel (a), (b), and (c) show results of the reaction CH 3 Cl + H 2 O (hydrolysis). Panel (d), (e), and (f) represent isotope effects due to CH 3 Cl + H 2 O + Y-(combined hydrolysis and halide exchange). The slope of the regression indicates the enrichment factor in Ur. Error bars represent the analytical uncertainty of 5 mUr (δ 2 H), 0.5 mUr (δ 13 C), and 0.2 mUr (δ 37 Cl). For carbon isotopes, error bars are smaller than the used symbols. The quantification was carried out with an uncertainty of usually better than 5%.

Table 1 .

 1 Rate Constants for Hydrolysis and Halide Exchange of CH 3 Br and CH 3 Cl Rates constants were determined from linear regressions of ln[f] versus time and indicate the rate constant at 23 ± 1 °C. The errors are given as the 95% confidence interval. b Jeffers and Wolfe. 16 c King and Saltzman. 17 d Elliot and Rowland.

		rate constants a [d -1 ]	rate constants (previous studies) [d -1 ]
	CH 3 Br + H 2 O	0.013 ± 0.002	0.021 ± 0.002 b
	CH 3 Br + H 2 O + Y -	0.115 ± 0.023	0.154 ± 0.06 c
	CH 3 Cl + H 2 O	0.0015 ± 0.0005	0.0014 ± 0.00002 d
	CH 3 Cl + H 2 O + Y -0.0012 ± 0.0003

a

Table 2 .

 2 Isotopic Enrichment Factors (ε) and Lambda Values (Λ) of Abiotic Reactions in Water a

		ε H mUr	ε C mUr	ε Cl mUr	ε Br mUr	Λ H/C	Λ C/Cl	Λ C/Br
	CH 3 Br + H 2 O (10 mmolL -1 )	+42 ± 20	-49.6 ± 5.6	nd
	CH 3 Br + H 2 O (0.2 mmol L -1 )	n d	-58.3 ± 6.8	-1.16 ± 0.42	-0.7 ± 0.2*		46.1 ± 16.1
	CH 3 Br + H 2 O + Y -	+22 ± 13	-63.3 ± 5.1	-1.22 ± 0.23	-0.3 ± 0.2		48.2 ± 6.5
	CH 3 Cl + H 2 O	+25 ± 6	-41.7 ± 10.2	-5.3 ± 1.3		-0.6 ± 0.3	7.3 ± 0.9
	CH 3 Cl + H 2 O + Y -	+24 ± 19	-40.6 ± 13.9	-5.2 ± 1.0		-0.6 ± 0.2	6.9 ± 2.3
	a

  and the Λ C/Br of CH 3 Br ranged from 46.1 to 48.2. No other lambda values have been reported yet for both CH 3 Cl and CH 3 Br. Some Λ H/C for reactions of CH 3 Cl could be calculated from published ε H and ε C according to eq 3 because these enrichment factors were derived from the same experiment. The resulting Λ H/C are given in SI TableS4. For CH 3 Br no dual-element isotope studies are available yet and therefore lambda values of other reaction pathways could not be calculated.

	Environmental Science & Technology	Article
		DOI: 10.1021/acs.est.9b02165
		Environ. Sci. Technol. XXXX, XXX, XXX-XXX

DOI: 10.1021/acs.est.9b02165 Environ. Sci. Technol. XXXX, XXX, XXX-XXX C

DOI: 10.1021/acs.est.9b02165 Environ. Sci. Technol. XXXX, XXX, XXX-XXX E

DOI: 10.1021/acs.est.9b02165 Environ. Sci. Technol. XXXX, XXX, XXX-XXX G

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

The Laboratory for Stable Isotopes (LSI) at the Helmholtz Centre for Environmental Research -UFZ is acknowledged for providing support during measurements and access to the IRMS instruments at their facilities. The Centre for Chemical Microscopy (ProVIS) at the Helmholtz Centre for Environmental Research, supported by European Regional Development Funds (EFRE -Europe funds Saxony), is acknowledged for the use of the GC-MC-ICPMS at their analytical facilities. This is IPGP contribution 4045. This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 701350.


Marjorie Cavarroc

Maxime Mikikian

Yves Tessier

Laïfa Boufendi

Dust Successive Generations in Complex Plasmas: A Cyclic Phenomenon in the Void Region

Keywords:

Dust formation and growth in plasmas are in most cases continuous cyclic phenomena. We show that the growth of new dust generations takes place in a dust free region, usually called void, in the dust cloud. The three-step process of new dust generation is detailed thanks to the correlation between electrical, optical and ex situ diagnostics. The strong inhomogeneity of both the plasma and the dust cloud during this process is underlined.

Complex (or dusty) plasmas generated in radiofrequency (rf) discharges are widely studied since the 90's. First dust particle observations in processing plasmas were reported by [1] in 1985 for silicon deposition plasmas and by [2] in 1989 in silicon etching plasmas. A first burst of interest has been induced by those contamination phenomena in industrial plasma reactors. Since then, dust particle formation has been widely studied. Silane-based discharges have often been used as "standard systems" to investigate fundamental phenomena and mecanisms involved in dust particle formation and growth, and lots of publications have been produced on this topic (see for example the work of [3][4][5][6][7]). In the 90's the main aim of those studies was to understand dust particle formation to avoid it in industrial reactors. In the 2000's, a second burst of interest has been induced by potential applications of single-crystal and/or polycristalline dust particles. Indeed, single-crystal nanoparticles [8] can be incorporated in thin film layers in order to improve their mechanical and/or optoelectronical properties [9], or used for single electron device fabrication [10]. Dust forming plasmas are also used to produce analog aerosols of planet atmospheres like Titan as demonstrated by [11].

The aim of this paper is to set out the detailed mechanism of formation of dust particle successive generations. We especially show that their growth is a complex spatiotemporal phenomenon closely linked to the void region in the dust cloud. This region has never been clearly attested in spatially confined reactive plasmas due to the reduced optical accesses available to image this region, and to the small size of produced dust particles (giving few laser light scattering signal).The strong inhomogeneity of both the plasma and the dust cloud induced by the growth of dust successive generations can be a significant drawback when performing depositions.

The rf discharge is produced in a grounded cylindrical plasma box (13 cm inner diameter and 3.3 cm for interelectrode distance), enclosed in a vacuum vessel [4,12]. The powered electrode is a shower-head one in order to * Electronic address: marjorie.cavarroc@univ-orleans.fr ensure a homogeneous gas distribution at the entrance of the plasma zone. It is connected to a 13.56 MHz rf generator through a matchbox including a blocking capacitor. Typical experimental conditions are: argon-silane mixture (92:8) with a total pressure around 120 µbar and a rf power around 10 W. Dust particle formation and growth are monitored through the modifications they induce in the plasma parameters, by following the time evolution of the current third harmonic (3H) amplitude, that mainly correlates the variation of the free electron density in the plasma [13]. The successive generation process is a continuous phenomenon. As long as silane precursors are provided, new generations of dust are formed in the discharge [START_REF] Melzer | AIP Conference Proceedings[END_REF]. From the time evolution of 3H in figure 1 we can distinguish: (insert) nanocrystal formation and accumulation, aggregation instability ( [8,[START_REF] Cavarroc | [END_REF]), nanocrystal aggregation and growth by surface deposition, second and third generations.

Successive generations of dust particles appear as quasi-sinusoidal low-frequency oscillations of the 3H signal, with a period of the order of typically one minute (figure 1). The decrease of 3H corresponds to a decrease of the electron density: this can be explained both by the presence of big dust particles attaching lots of electrons, or by numerous small dust particles that could produce the same effect. The increase of 3H corresponds to an increase of the electron density, meaning that less electrons are attached by dust particles: big dust particles could be expelled from the plasma, or the density of smaller dust particles is weak. All classical parameters affecting dust particle formation have an influence on the time-period of these oscillations. As an example, when gas temperature is increased, dust particle formation is delayed and the time-period of these oscillations can rise above several minutes.

Thanks to correlations with Laser Light Scattering (LLS, performed in the plasma center as in [16] using a laser beam and a cooled photomultiplier) and Optical Emission Spectroscopy (OES) of an argon line at 750.38 nm (I 750.38 ), we can refine our hypothesis concerning the behavior of 3H (see figure 2). For this purpose, we need to assume the presence of a void region in the dust cloud as in [17]. We will see further that this assumption has been experimentally validated.

For the sake of clarity, figure 2 has been divided in several parts numbered from I to IV. The early stages of dust particle formation (between 0 and 10 s) have already been discussed previously in [16].

In part I, from 10 to 60 s, 3H increases while I 750.38 first increases before reaching a maximum value and then decreases, and there is no detectable LLS signal. The increase in I 750.38 corresponds to the opening of a void region, where the ionization rate is enhanced [18,19]. This enhancement favors the growth of a new dust particle generation in the void region. Once this new generation started to grow, I 750.38 starts to decrease. In this part, new dust particles are neither big enough nor numerous enough to be detected by LLS, so the LLS signal is zero. However, new synthesized dust particles push away bigger ones from the discharge center. The expellation of bigger dust particles, which had attached numerous free electrons, causes an increase of the free electron density in the plasma. Newly created small dust particles attach far less electrons than expelled bigger ones. There is thus a net increase of the free electron density in the discharge, leading to 3H increase. This confirms the hypothesis of a void opening when 3H starts to increase [17].

In part II, from 60 to 80 s, 3H exhibits a slope modification and keeps on increasing but more smoothly. I 750.38 is still decreasing as in part I and a small increase in the LLS signal is detected. Newly created dust particles grow in the void region and become detectable by LLS. They also start to attach more and more free electrons due to their increasing size. They keep on pushing bigger dust particles away, and tend to fill the whole void region, leading to the decrease of I 750.38 . As new dust particles become bigger, and so more charged, the balance between free electrons lost by attachment and free electrons recovered due to dust expelling is modified. There is still an increasing amount of free electrons in the plasma, but the net increase is lower than in part I, and thus explain the slope modification in the increase of 3H.

In part III, from 80 to 110 s, 3H increases to its maximum value before starting to decrease. I 750.38 decreases to its minimum value, and the LLS signal increases until reaching a plateau. The new generation of grown dust particles is now clearly detected thanks to LLS. This new generation now almost fill the whole void region, leading to the decrease of I 750.38 that reaches its minimum value. The net increase in the free electron density is less and less important due to the strong attachment on the growing dust particles, leading 3H to reach a maximum value. Then, a plateau appears on the LLS signal and I 750.38 : the void region is now totally filled by the new generation of dust particles. As these grains are still growing, they keep on attaching more and more electrons, leading to the beginning of 3H decrease.

In part IV, from 110 to 140 s, the LLS signal suddenly falls to zero, while I 750.38 starts to increase. A new void is opening in the discharge center. 3H decreases until reaching a plateau: an equilibrium is reached between free electrons recovered from dust expellation and free electrons lost by attachment. I 750.38 keeps on increasing until a new dust particle generation starts to grow in the void region. The phenomenon is then cyclic and the following part is a new part II, followed by a part III and so on, as long as silane is provided in the discharge.

Voids are dust-free regions in the dust cloud. The assumed mechanism to explain these regions are related to the equilibrium between the inward electrostatic force and the outward ion drag force. Dust voids are still actively studied (see for example [20,21] and references therein). They are experimentally observed in various dusty plasmas both under microgravity conditions or in the laboratory. They have been observed in sputtering discharges [19,[22][23][24][25] or with calibrated injected dust particles [26,27]. In reactive plasmas, dust voids have not really been observed until now. However, they are strongly suspected in acetylene-based discharges [28], and some features described as "two layers" have already been observed in silane-based plasmas [29]. Moreover, some cases of dust particle successive generations growing in a void region have already been reported in sputtering plasmas [23,24]. In reactive gas plasmas, this hypothesis is often made in order to explain experimental results [17,28].

The correlation between 3H, LLS signal and I 750.38 , presented in figure 2, lets think that a void region could appear in the dust cloud and be the place where a new generation grow. In order to explore the validity of this assumption, we performed several observations of the plasma glow using a CCD camera focused in the plasma center. These experiments were very fussy to perform due to the lack of optical accesses on our reactor. Thus we used a discharge box pierced by a hole of 12 mm in diameter. Figure 3 shows a typical frame extracted from a movie: the center of the circle hardly corresponds to the center of the discharge, while the dark blue part corresponds to the plasma box. In this figure, a central area of higher glow emission (in red), meaning a higher ionization as well, is evidenced. This result confirms the one previously obtained by optical emission spectroscopy and the void region hypothesis. The assumed void region is off-center. The "red region" is obviously in the upper part of the dust cloud. This effect can be explained by the thermophoretic force on dust particles: the upper electrode is assumed to be 60 0 C while the lower one is at room temperature. The dust cloud is consequently attracted toward the lower electrode, thus exhibiting a void region closer to the upper electrode.

The three-step process assumed in this Letter is related to the formation of new dust particles generations in a void region. This scenario is consistant if an adequate dust particle size distribution is observed in the discharge. For this purpose, spatially resolved depositions have been performed during dust particle successive generations. Five substrates were located on the grounded (lower) electrode in the discharge box. The first one was in the center, and the others were evenly dissevered along the electrode radius. These samples have then been observed thanks to Scanning Electron Microscopy (SEM) using different magnifications. In the images with a scale of 5 µm (see figure 4), very few big dust particles (between few tens to few hundreds of nm) are detected in the discharge center (r = 0 mm), while more and more are present when the radius is scanned toward the plasma edge (r = 62 mm). On the other hand, the images with a scale of 200 nm (see figure 5) indicate that the constitution of the deposited layer is very dependent on its location in the discharge. In the discharge center, the sublayer is made of very numerous nanoparticles around 10 nm (giving a dense sublayer). The more we go away of the center, the less the sublayer is dense, and its smaller constituents tend to increase in size (up to around 20 nm). These results are totally consistent with a void region, where new dust generations would grow, pushing bigger ones toward plasma edge. plasma (three in this example). Each new generation grown in the void pushes away the previous one, leading to a concentric structure with the newest dust particles (i.e. smallest ones) in the discharge center, and "shells" made each ones of "older" (i.e. bigger) dust particles. The five colored blocks stand for the volume of deposition on each sample. Thus the collected dust particle populations are consistent with SEM results.

In this paper, thanks to a correlation between the time evolution of the current third harmonic, laser light scattering and optical emission spectroscopy, we brought to the fore the dust cloud dynamics during the growth of dust particle successive generations. It appears that as long as precursors are provided in the discharge, the plasma and the dust cloud never reach a stable state: all plasma parameters oscillate following a cycle that can be resolved in three main steps (refeered as part II, III and IV in the text). We inferred the presence of a void region in a spatially confined argon/silane plasma. This region has already been suspected but has never been rigorously attested before in spatially confined plasmas to the authors' knowledge. Moreover, new dust generations have been demonstrated to grow in this dust free region, pushing previously formed bigger dust particles toward the plasma edge. This last conclusion raises an interesting problem concerning spatially resolved optical measurements usually performed in the plasma center. Due to the presence of a void region in the center, those measurements are not representative of the global behavior of both the plasma and the dust cloud. Then, plasma characteristics or eventual dust presence can be misinterpreted, and correlation with other diagnostics is thus strongly advised. We finally suggest that the described mechanism for the growth of dust successive generations can be extended to the majority of dust forming plasmas.

FIG. 1 :

 1 FIG.1: Time-evolution of the third harmonic of the discharge current amplitude during dust formation for different timescales.

FIG. 2 :

 2 FIG.2: Time-evolution of 3H, I750.38 and LLS during dust particle successive generations in an Argon-Silane plasma.

FIG. 3 :

 3 FIG. 3: Typical glow of the discharge during dust formation. The colormap spreads from blue for low intensity to red for high intensity.

FIG. 4 :

 4 FIG. 4: SEM images of the spatially resolved depositions (scale = 5µm).

Figure 6

 6 Figure 6 gives a rough sketch of the proposed void region in the Ar/SiH 4 discharge. As proposed in our model, several dust particle populations coexist in the

The authors would like to acknowledge Annie Richard for her precious help in SEM imaging.