Matteo Pelucchi
email: matteo.pelucchi@polimi.it

Sylvain Namysl

Eliseo Ranzi

Alessio Frassoldati

Olivier Herbinet

Frédérique Battin-Leclerc

Tiziano Faravelli

An experimental and kinetic modelling study of n -C 4 C 6 aldehydes oxidation in a jet-stirred reactor

Keywords: Aldehydes, Low-temperature kinetics, Jet stirred reactor, Kinetic modeling

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Introduction

Pursuing a sustainable energy scenario for transportation requires the blending of renewable oxygenated fuels (e.g. alcohols) into commercial hydrocarbon fuels. Alcohol combustion is univocally associated with an increase in the emission of toxic compounds such as aldehydes and ketones [1,2]. The synergistic development of new fuels and engine technologies [3], as well as the optimization of pyrolysis and gasification processes of biomass derived bio-oils, requires the assessment of the influence of different functional groups on the reactivity of a given compound [4]. This motivates recent research efforts devoted to a better understanding of long chain aldehydes combustion [START_REF] Veloo | Proc. Comb. Inst[END_REF][START_REF] Veloo | [END_REF][7][START_REF] Pelucchi | Proc. Comb. Inst[END_REF][START_REF] Rodriguez | [END_REF][10]. Veloo et al. [START_REF] Veloo | Proc. Comb. Inst[END_REF][START_REF] Veloo | [END_REF] presented laminar flame speeds and jet-stirred reactor (JSR) measurements for C3-C4 aldehydes, together with a kinetic model. Pelucchi et al. [7], [START_REF] Pelucchi | Proc. Comb. Inst[END_REF] developed and validated a kinetic mechanism covering pyrolysis, high and low-temperature oxidation conditions for different aldehydes (Rn-(C O)-H) [START_REF] Pelucchi | Proc. Comb. Inst[END_REF]. Propanal, n-butanal and n-pentanal pyrolysis and high temperature oxidation were investigated in shock tubes [7]. The kinetic model was then extended to low temperature conditions for propanal and n-butanal. The dominant Habstraction channel at the aldehydic site forms a carbonyl radical (Rn-CO), which rapidly decomposes to an alkyl radical (Rn) and CO. The low-temperature oxidation of the generic Cn aldehyde then falls into the low-temperature pathways typical of Cn-1 alkyl radicals. A further confirmation to this assumption was recently given by Serinyel et al. [10], analyzing the oxidation of two branched C5 aldehydes (i.e. 2-and 3-methylbutanal) in a JSR at 500-1200 K and p = 10 atm. Indeed, sec-butyl and iso-butyl radicals were found to rule the low-temperature reactivity of 2-and 3-methylbutanal, respectively.

Recently Rodriguez et al. [START_REF] Rodriguez | [END_REF] studied the oxidation of n-hexanal in an atmospheric pressure JSR at 475-1100 K, measuring reaction products using a GC and continuous wave cavity ring-down spectroscopy (CRDS). These advanced analytical techniques allowed identifying specific lowtemperature oxidation products such as cyclic ethers with a C5 skeleton and multi-oxygenated C6 species. The kinetic model used, despite correctly capturing the overall reactivity, was not able to explain the formation of some minor species such as acetone, propanal and acrolein.

This study aims at presenting new experimental data of n-butanal and n-pentanal oxidation, complemented by previous data on n-hexanal oxidation [START_REF] Rodriguez | [END_REF], and at refining the previous kinetic models [7][START_REF] Pelucchi | Proc. Comb. Inst[END_REF][START_REF] Rodriguez | [END_REF] in order to better describe aldehydes low-temperature oxidation.

Experimental

Experiments were carried out in a heated isothermal quartz jet-stirred reactor [11,[START_REF] Herbinet | Cleaner Combustion[END_REF]. Experiments were performed under steady state conditions, at 1.05 atm, at a residence time of 2 s, at temperatures ranging from 500 to 1100 K, and at three equivalent ratios of 0.5, 1 and 2 with initial fuel mole fraction of 0.005. The reactive gases, diluted in helium, entered the spherical JSR through four nozzles, positioned in the center of the vessel, and designed in order to ensure a perfect gas mixing through turbulent jets. Thermal gradients inside the reactor were reduced by using a quartz annular pre-heating zone prior its entrance. The residence time in this zone was negligible compared to that in the reactor. Helium and oxygen were provided by Messer (purities of 99.99% and 99.999%, respectively) with flows controlled using flow rate controllers. The liquid flow (aldehydes were provided by Sigma Aldrich, with a minimal purity of 99.5% for butanal and 97% for pentanal) was controlled using a liquid-Coriolis-flow-controller, mixed with helium and passed through an evaporator before being mixed with oxygen. The relative uncertainty in gas flow rates was assumed to be around 5%.

Using heated (at 423 K) on-line connections to avoid condensation, the gases leaving the reactors were quantified using three gas chromatographs (GCs): • O2, CO, CO2 and CH4 were analyzed by a GC equipped with a thermal conductivity detector, a flame-ionization detector, and a Carbosphere packed column, • Molecules containing up to five carbon atoms were analyzed by a GC equipped with a flameionization detector preceded by a methanizer and a PlotQ capillary column, • Heavier molecules were analyzed by a GC equipped with a flame-ionization detector and a HP-5 capillary column.

Identification was made using a fourth off-line GC fitted with a Plot Q or a HP-5MS column, and coupled with a mass spectrometer. Response factors were determined by injecting calibration mixtures or using the effective carbon number method. Relative uncertainties in mole fractions were estimated to be ± 5% for species calibrated using standards (the typical uncertainty on GC measurements). For species concentrations calculated with the effective carbon number method, uncertainties are estimated to be around 10%.

Kinetic modelling

The detailed model of C3-C4 aldehyde oxidation [7,[START_REF] Pelucchi | Proc. Comb. Inst[END_REF] was lumped according to procedures already discussed and adopted for many fuels [START_REF] Ranzi | [END_REF]14]. Comparisons between the original detailed mechanism and the lumped one are reported in the Supplementary Material. The derived model, was systematically extended to describe n-pentanal and n-hexanal oxidation. Figure 1 shows the effectiveness of the lumped approach in terms of reduction of number of species. The assumption of the fast decarbonylation of carbonyl radicals [START_REF] Pelucchi | Proc. Comb. Inst[END_REF] already allows a first reduction. Figure 1 schematically shows the lumped low-temperature oxidation mechanism of n-hexanal. Although, names of lumped isomers and samples of molecular structures are therein reported, Figure 1: Lumped kinetic mechanism of n-hexanal oxidation. Names and structures of some lumped C6 isomers.

Supplementary Material better summarizes names and molecular structures. Horizontal lumping of isomers permits to describe aldehydes mechanism with only 8 species, whereas the detailed mechanism of n-hexanal would need ∼80 species. This reduction within the global CRECK model is of particular interest as this model is specifically conceived to describe oxidation of real fuels, up to diesel fuels, large methyl esters (C16), biomass components [14], and also heavy PAHs (C20) precursors of soot particles.

Assuming the fast decarbonylation reaction of Rn-CO, a single radical (RALDnX) lumping all of the Cn aldehyde radicals carrying the unpaired electron on the alkyl moiety has been accounted for. Again, one lumped unsaturated aldehyde (CnH2n-2O) coming from dehydrogenation reactions (RALDnX = H + CnH2n-2O) or from intermediate temperature pathways has been considered. At low temperatures, successive oxygen addition and isomerization reactions produce carbonyl peroxy radicals (RALDnOOX), alkyl carbonyl hydroperoxide radicals (QAnX), peroxy carbonylhydroperoxide radicals (ZAnX) and di-carbonylhydroperoxides (KEAnX). Intermediate low-temperature decomposition pathways of QAnX radicals can lead to the formation of smaller aldehydes together with smaller olefins. Moreover, QAnX can decompose to form lactones (ETALDnX) and OH.

The CRECK kinetic model, obtained by extending the lumped version of C3-C4 aldehydes oxidation [7,[START_REF] Pelucchi | Proc. Comb. Inst[END_REF] to n-pentanal and n-hexanal, consists of 416 species and 11500 reactions. In the attempt to pursue and encourage a complete unification of core mechanisms, the CRECK model was recently updated and implements a C0-C3 core mechanism obtained by coupling the H2/O2 and C1/C2 from Metcalfe et al. [15], C3 from Burke et al. [16], and heavier fuels from Ranzi et al. [14,17]. The thermochemical properties were adopted, when available, from [18]. The thermodynamic properties of additional fuels specific species are taken from [START_REF] Veloo | Proc. Comb. Inst[END_REF][START_REF] Veloo | [END_REF][START_REF] Rodriguez | [END_REF]. The mechanism is provided in the Supplementary Material, together with transport and thermodynamic properties.

All simulations have been performed using the OpenSMOKE+ + software [19].

Results and discussion

Figure 2 compares experimental and predicted mole fraction profiles of the three aldehydes, at different stoichiometries. Additional comparisons are reported in the Supplementary Material (Figures S1-S10). CRECK mechanism predicts experimental conversions quite satisfactorily. In particular, the relative reactivity both at high and low temperatures is well captured: n-hexanal > n-pentanal > n-butanal. In addition to the higher O2 concentration at fixed fuel content, the low-temperature reactivity is higher for heavier aldehydes also because of enhanced RO2= QOOH isomerization possibilities. As an example, at ϕ = 0.5 experimental fuel conversions at T = 625 K are ∼32%, ∼70% and ∼75% for n-butanal, n-pentanal and n-hexanal, respectively. The model slightly over-predicts n-butanal conversion (∼40% vs ∼33%) and accurately captures n-hexanal low-temperature peak conversion. Conversely, the model slightly under-predicts n-pentanal conversion (∼61% vs. ∼68 %). Although commercial n-pentanal was delivered with a declared 97% minimal purity, a GC analysis revealed a 98.8% purity. The fuel contained 0.8% of n-butanal and other minor impurities. Model simulations proved the negligible effect of even larger n-butanal impurities. The equivalence ratio effect on the global reactivity is also correctly reproduced by the model, predicting decreasing low-temperature extents for decreasing oxygen concentrations. Aiming at a further reduction of the number of species, the dotted line in 𝜑 = 1.0 case of Figure 2 shows pentanal fractions as obtained through the vertical lumping approach [14]. n-pentanal has been simply assumed as a combination of n-butanal (50%) and n-hexanal (50%). The minor discrepancies between these two predictions encourage the application of vertical lumping, when modeling heavy homologous species [20].

Results from sensitivity analyses (T = 600 K, 𝜑 = 1.0) of aldehyde conversion to rate parameters are reported in Figure 3 highlighting interesting features. Conditions where the low temperature reactivity of the three fuels is enough pronounced to allow for significant insights were selected. As already discussed in [START_REF] Pelucchi | Proc. Comb. Inst[END_REF], low-temperature reactions of alkyl radicals control aldehyde lowtemperature reactivity. However, H-abstraction reactions by OH and HO2 radicals, from both the carbonyl and the alkyl moieties increase overall reactivity. The higher impact of H-abstractions by HO2 radical for n-butanal is explained on the basis of a less pronounced low-temperature reactivity, as discussed above. When increasing carbon chain length, the importance of aldehyde specific low-temperature pathways increases, as it is the case for n-hexanal. Namely, internal isomerization (RALD6XOO = QA6X) and peroxy-carbonyl hydroperoxide radical (ZA6X) decomposition to di-carbonyl-hydroperoxides significantly impact n-hexanal conversion. Most of the remaining reactions fall within propane and pentane subsets, respectively for n-butanal and n-hexanal.

To better assess model predictions, Figure 4 shows the effects of perturbations of n-propylperoxy radicals isomerization rate constant (nC3H7O2= nC3-QOOH) on n-butanal conversion at 𝜑 = 1.0, for P = 1 atm and 10 atm. The model over-predicts fuel conversion at atmospheric pressure, whereas under-predictions are observed at higher pressure [START_REF] Veloo | [END_REF]. An improved agreement could be obtained only by increasing and reducing the rate constant at high and low pressures, respectively. As expected from the limited pressure dependence of the isomerization reactions in the temperature range 550-750 K, this observation seems to indicate the presence of some inconsistencies within the two sets of measurements. Therefore, it is reasonable to accept a similar extent of over-and under-predictions for both datasets. Figure 5 shows comparisons between experimental data and model predictions for selected species from the stoichiometric oxidation of the three fuels.

The model correctly predicts oxygen consumption, with largest deviations for n-pentanal case.

Major species formation (CO, CO2, H2O, CH4, C2H4, C3H6) is also accurately reproduced. Deviations of up to a factor of ∼2 are observed for CH2O at T > 750 K, and mainly in n-butanal case. In these conditions, ∼80% of formaldehyde comes from the decomposition of propyl hydroperoxide radical: nC3-QOOH = > OH + C2H4+ CH2O, whose kinetic parameters have been already assessed for propane oxidation [22]. The same reaction is responsible for ∼50% of formaldehyde formation at 10 atm (Figures S3-S6). Better agreement is obtained for n-pentanal and n-hexanal. When a single model is adopted for different fuels, as it is the case for the CRECK kinetic model, ad hoc modifications of rate parameters according to a specific dataset strongly reduces the physical meaning of the model itself. For this reason, parameters belonging to a different kinetic subset have not been subject to modification within this study. Acetaldehyde formation is correctly predicted in the three cases, mainly at low temperatures where its formation is controlled by ketohydroperoxide decompositions.

At high temperatures, the same pathways control methane formation (CH3 + HO2 = O2 + CH4) and consumption (CH4 + OH = CH3 + H2O) for the three fuels. Contributions from H-abstractions by CH3 account only for ∼5-10%. Good agreement is found for n-butanal and n-hexanal, whereas the model over predicts methane yields in n-pentanal case.

Oxirane formation is also over-predicted at T > 800 K, in particular for n-butanal. Once again the controlling reaction is not aldehyde specific. Formation of oxirane (C2H4O1-2) mostly occurs via C2H4 + HO2 = OH + C2H4O1-2, therefore it is related to ethylene yields generally accurately predicted. Considering the uncertainties in the measurements of H2O2 [START_REF] Rodriguez | [END_REF]21,22] the model provides relatively good predictions, mainly at low temperatures. A factor of ∼10 deviation is observed for rich cases (Figure S10). Similar deviations were also discussed by Rodriguez et al. [START_REF] Rodriguez | [END_REF].

Cyclic ethers and olefins, mostly coming from low-temperature oxidation pathways of alkyl radicals are well captured for the three fuels. Concerning cyclic ethers, some deviations are observed for methyl-oxirane, properly predicted in propane oxidation [21].

Methanol is under-predicted by ∼2.5 times, and is controlled by H-abstractions by metoxy radical at high temperatures. At low temperatures, contributions come from recombination disproportionation of aldehyde peroxy radicals. The importance of such reactions also for alkanes oxidation has been previously discussed [21,22]. Relatively large deviations (factor of ∼2) are observed for cyclopentene formation in n-hexanal oxidation. This species is mostly formed by the decomposition of pentyl-hydroperoxy radical (NC5-QOOH) to HO2 and n-pentene (nC5H10) that is oxidized through typical low temperature pathways whose refinement is outside the scope of this study.

Figure 6 shows rate of production analysis carried out for n-butanal and n-hexanal at ϕ = 1.0, P = 1 atm, T = 600 and 700 K. Flux analysis for n-pentanal is not reported as, from the hierarchical nature of this study, the same reaction classes explain its oxidation. Selectivity of H-abstraction reactions on the carbonyl moiety decreases from more than 70% for n-butanal to less than 60% for n-hexanal. These percentages also reflect the relative weight of the Cn-1 alkyl radical low-temperature oxidation. At T = 600 K, the alkyl moiety is completely oxidized by addition to O2, while for increasing temperature a limited contribution also comes from the isomerization to directly form the carbonyl radical (Rn-1+ CO). Carbonyl peroxy radicals (RALDnOOX) isomerize to different extents to form QAnX. At low temperature, 23% of RALDnOOX isomerizes to QAnX for n-hexanal, while only ∼5% successfully propagates the low-temperature branching in n-butanal case. This difference depends on molecule size and on importance of RALDnOOX decomposition pathways.

The isomerization produces QOOH species carrying the radical at the carbonyl position, these radicals rapidly produce Rn-1 and CO. Depending on the relative position of the -OOH group with respect to the carbonyl moiety, this step produces the QOOH radical of the Cn-1 alkane or a Cn-1 aldehyde and OH. The two possible channels in n-hexanal oxidation mechanism are depicted in Figure 7. This pathway accounts for ∼11-16% in n-butanal, and ∼6-11 % in n-hexanal oxidation. Figure 8 shows the relative importance of the second channel leading to the formation of the Cn-1 aldehyde, i.e. propanal and pentanal for n-butanal and n-hexanal, respectively. The higher concentration of RALDnOOX in n-hexanal oxidation sustains the production of pentanal, whose yield does not exhibit the double maximum observed for propanal from n-butanal. Because of the presence of n-butanal as an impurity in n-pentanal feed (Section 3), experimental data are not reported, whereas n-butanal simulation profile in Figure 8 refers to a 100% purity n-pentanal feed.

Figure 8: Cn-1 aldehydes formation from Cn aldehyde oxidation. Symbols: Experimental data from this study and in [START_REF] Rodriguez | [END_REF]. Lines: simulation results.

Decomposition channels of QAnX are of limited impact under the conditions investigated in Figure 6. The analogous cyclization reaction producing cyclic ethers in alkanes low-temperature oxidation, explains the formation of lactones (ETALDnX) in the case of aldehydes. Figure 9 shows the pathways responsible for the formation of 6-methyl-tetrahydropyranone and 5-ethyldihydrofuranone as observed in [START_REF] Rodriguez | [END_REF]. Because of the lumped approach, the comparisons with model predictions refer to the sum of these species. The peak of lactones concentration is reproduced reasonably, despite the scarce sensitivity of model predictions to stoichiometric ratios.

Figure 9: n-hexanal oxidation. Caprolactone formation pathways and comparison between model predictions (lines) and experimental measurements (symbols) [START_REF] Rodriguez | [END_REF].

A significant formation of ketones is observed for n-pentanal and n-hexanal oxidation. Figure 10 shows acetone profiles at three different equivalence ratios for n-hexanal. Acetone is mainly formed via the Korcek mechanism of keto-hydroperoxide decomposition, as shown in Figure 10. This pathway was not accounted for in Rodriguez et al. [START_REF] Rodriguez | [END_REF]. The largest deviations are observed in the intermediate temperature range (T = 700-800 K) and mostly for the stoichiometric and the lean mixtures. The relative importance of keto-hydroperoxide decomposition via OOH bond breaking and via the Korcek mechanism already discussed by Ranzi et al. [22] (∼10:1 at 750 K) directly impacts acetone yields. Clearly, a modification of this ratio toward a higher importance of the Korcek mechanism would strongly impact the low temperature branching thus worsening the agreement for fuel conversion (Figure 2). It is worth noting that only n-pentanal and heavier aldehydes are expected to produce high yields of acetone as the formation of a primary alkyl radical (e.g. pent-1-yl) able to effectively isomerize to a secondary (e.g. pent-2-yl) is necessary. Moreover, a pronounced low temperature reactivity (i.e. higher ketohydroperoxide yields) favors its formation through the Korcek mechanism [22]. Finally, recombination/disproportionation reactions of peroxy radicals from Cn-1 alkyl radicals can explain butanone formation (Figure S11 of Supplementary Material).

Conclusions

n-butanal and n-pentanal oxidation was experimentally investigated in a JSR. Coupled with the previous measurements of n-hexanal oxidation [START_REF] Rodriguez | [END_REF], this study extends and completes the existing gaps in experimental targets available for the validation of aldehydes kinetic models, of relevance for the combustion of alternative fuels such as alcohols. Based on a previous study [START_REF] Pelucchi | Proc. Comb. Inst[END_REF], and on the recent update of the core mechanism of the CRECK kinetic framework, the detailed model of aldehyde low-temperature oxidation was lumped and extended from n-butanal, to n-pentanal and n-hexanal, providing overall good agreement with experimental data. Aldehydes specific reaction classes were found to be responsible for some of the detected species (i.e. Cn lactones, ketones, Cn-1smaller aldehydes and olefins etc.). This work further constrains pathways relevant to aldehyde oxidation, and highlights the influence of the carbonyl moiety on intermediate species formation.

Figure 2 :

 2 Figure 2: Comparison of experimental (symbols) and predicted (lines) mole fraction profiles of 0.5% n-butanal, n-pentanal and n-hexanal [9] oxidation in an isothermal JSR, 𝜑 = 0.5, 1.0, 2.0, P = 1.05 atm, 𝜏 = 2.0 s. Dotted line: vertical lumping, n-pentanal = 50%/50% (n-butanal/n-hexanal). Reported error bars: 5%.

Figure 3 :

 3 Figure 3: Sensitivity analysis of aldehyde conversion to rate constants at T = 600 K, 𝜑 = 1.0, P = 1 atm.

Figure 4 :

 4 Figure 4: Stoichiometric n-butanal oxidation in isothermal JSR. Experimental (symbols) [6] and predicted (lines) conversion. Red: 0.5% n-butanal/O2/He, P = 1.05 atm, 𝜏 = 2.0 s. Black: 0.15% n-butanal/O2/N2, P = 10 atm, 𝜏 = 0.7 s. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Figure 5 :

 5 Figure 5: n-butanal, n-pentanal and n-hexanal [9] oxidation in JSR at 𝜑 = 1.0, P = 1 atm and 𝜏 = 2.0 s. Comparison between experimental (symbols) and predicted (lines) mole fraction profiles of major species.

Figure 6 :

 6 Figure 6: Rate of production analysis of the lumped low-temperature mechanism of n-butanal (black) and n-hexanal (blue) at T = 600 K (bold) and T = 700 K (italics). Species in brackets are not explicitly accounted for in the kinetic model. Examples of specific pathways are reported in the Supplementary Material. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Figure 7 :

 7 Figure 7: Decomposition pathways of QAnX radicals with a radical position at the carbonyl moiety.

Figure 10 :

 10 Figure 10: n-hexanal oxidation. Acetone formation pathways and comparison between model (lines) and experimental measurements (symbols) [9].

Acknowledgments

The authors acknowledge the financial support of IMPROOF project (H2020-IND-CE-2016-17/H2020-SPIRE-S016) European Union's Horizon 2020 research and innovation program (grant agreement no. 723706). Support from COST CM1404 SMARTCATs Action through the Short Term Scientific Mission is also acknowledged.

Supplementary Material

-Kinetic mechanism (kinetics.CHEMKIN, text format) -Thermodynamics properties (thermo.CHEMKIN, text format) -Supplementary_Material.doc: additional comparisons of model and experiments, additional explanations of kinetic pathways, lumped low temperature mechanism and species nomenclature, comparison between detailed and lumped mechanism.


Nicolas Vin

Frédérique Battin-Leclerc

Olivier Herbinet
email: olivier.herbinet@univ-lorraine.fr

A STUDY OF THERMAL DECOMPOSITION OF BROMOETHANE

Keywords: bromoéthane, pyrolysis, molecular reaction, detailed kinetic modeling JSR: Jet-Stirred-Reactor, TR: Tubular Reactor, FTIR: Fourier Transform InfraRed Spectroscopy, GC: Gas Chromatography, GC-MS: Gas Chromatography -Mass Spectrometry, PFR: Plug Flow Reactor, Pe: Peclet criterion

The pyrolysis of bromoethane under dilute atmosphere and quasi-atmospheric pressure was studied at temperatures from 600 to 975 K using a fused silica jet-stirred reactor (JSR) and an alumina tubular reactor (TR). In the JSR, a complete conversion was observed at a residence time of 2 s, a temperature of 975 K and an inlet mole fraction of bromoethane of 0.01. In the TR, the full conversion was observed from 925 K. In both reactors, the following species were quantified: methane, ethylene, acetylene, ethane, 1,3butadiene, vinylacetylene and vinyl bromide. A new detailed kinetic model was developed and gave a good prediction for both reactors of the global reactivity and the major products. Flow rate and sensitivity analyses have been performed to better understand the important reaction pathways during bromoethane pyrolysis. They showed, in contrast to previous studies, that the radical mechanism is far from being negligible and that the sole analysis of reaction products can be misleading as the radical mechanism mainly lead to ethylene and HBr which are also the two products from the molecular decomposition reaction of bromoethane.

Introduction

Brominated flame retardants (BFRs) has become of increasing concern to scientists because of their widespread use in large quantities in consumer products such like electronic devices (computers, televisions…) [START_REF] Kodavanti | Chapter 38 -Brominated Flame Retardants[END_REF]. As a result, several BFRs were found in quantifiable levels in human bodys and many of these chemicals are now recognized as global contaminants and are associated with health effects [START_REF] Shaw | Brominated Flame Retardants and Their Replacements in Food Packaging and Household Products: Uses, Human Exposure, and Health Effects[END_REF]. The recycling of these electronic wastes by combustion requires a better knowledge about the thermal decomposition of BFRs and more generally about the brominated compounds [START_REF] Ma | Chemical recycling of brominated flame retarded plastics from e-waste for clean fuels production: A review[END_REF], since the combustion and thermal decomposition of these compounds can lead to the formation of dioxin and furan like species [START_REF] Zhang | Brominated flame retardants and the formation of dioxins and furans in fires and combustion[END_REF]. Bromoethane (C2H5Br) is a haloalkane which could be used as a model molecule for aliphatic BFRs. This molecule is used for the production of other organic compounds by alkylation [START_REF] Jungk | Kinetics of Methylation and Ethylation of Benzene and Toluene in 1,2,4-Trichlorobenzene under the Influence of Aluminum Bromide; Mechanism of the Alkylation Reaction1,2[END_REF] and for the treatment of agricultural soils, by fumigation or the treatment of foodstuffs [START_REF] Taylor | Methyl bromide-Is there any future for this noteworthy fumigant?[END_REF].

The pyrolysis of bromoethane was already investigated several times in literature. The first study was performed in 1931 by Lessig et al. [START_REF] Lessig | The Decomposition of Ethyl Bromide, Alkyl Halides, and Acetal in the Gas Phase at 300°-400[END_REF] using a glass static vessel at temperatures between 573 and 673 K.

HBr and ethylene were identified as the main products and the existence of an unimolecular decomposition reaction was discussed:

𝐶 𝐻 𝐵𝑟 𝐶 𝐻 + 𝐻𝐵𝑟 (Reaction I)
Table 1 presents a summary of the previous studies of the thermal decomposition of bromoethane where the rate expression of reaction 1 was determined.

In 1933, Vernon et al. [START_REF] Vernon | Kinetics of the Unimolecular Dissociation of Gaseous Ethyl Bromide1[END_REF] have studied the thermal dissociation of bromoethane using a Pyrex vessel and proposed a first expression for the rate constant of reaction I at temperatures from 670 and 693 K and for pressures below 0.48 bar. Daniels et al. [START_REF] Daniels | The Decomposition of Ethyl Bromide and the Collision Theory of First-Order Reactions[END_REF] in 1938 determined the rate expression of reaction I above 0.13 bar and for temperatures between 643 and 693 K. At pressures below 0.13 bar, the value of the rate constant, kI, decreased as the pressure decreased. Except ethylene and HBr, the major products, the formation of small amounts of hydrogen, ethane, propane, butane was also observed in decreasing order of abundance. Authors also found that the addition of oxygen or bromine enhanced the decomposition of bromoethane, while the addition of NO has no influence on the reactivity. The effect of hydrogen and nitrogen addition on bromoethane pyrolysis has also been investigated by Fugassi et al. [START_REF] Fugassi | A Study of the Decomposition of Gaseous Ethyl Bromide[END_REF] in 1938 at 670 K. The addition of both additives led to a decrease of the reactivity. In 1952, Blades et al. [START_REF] Blades | The Kinetics of the Decompositions of Ethyl, Isopropyl and n-Propyl Bromides[END_REF] studied the decomposition of bromoethane in a tubular reactor with toluene as carrier gas to detect a free radical mechanism. Since no hydrogen, ethane or dibenzyl nor any products other than ethylene and HBr were found, they concluded to an only molecular mechanism. They measured a rate expression for reaction I at atmospheric pressure between 800 and 900 K. In 1956, Goldberg et al. [START_REF] Goldberg | Kinetics of the Pyrolysis of Ethyl Bromide1[END_REF] studied the kinetics of the pyrolysis of bromoethane in a batch reactor between 583 and 749 K and also determined the rate expression of reaction I. They reported that the over-all reaction is not a simple unimolecular reaction. Thomas et al. [START_REF] Thomas | 234. Studies in the pyrolysis of organic bromides. Part XII. The unimolecular decompositions of ethyl bromide and 4-bromopent-1-ene[END_REF] determined in 1959 in a batch reactor the rate expression of reaction I during the pyrolysis of bromoethane between 653 and 703 K at 0.48 bar. Later in 1964, Tsang et al. [START_REF] Tsang | Thermal Decomposition of Some Alkyl Halides by a Shock-Tube Method[END_REF] measured again the rate expression of reaction I. Experiments were performed in a shock tube at temperatures between 740 and 940 K and at pressures between 0.7 and 1.7 bar. Park et al. [START_REF] Park | Thermal unimolecular decomposition reactions of ethyl bromide at 724[END_REF] studied in 1980 the pressure dependence of reaction I. A rise of the pressure from 0.001 bar to 0.076 bar (at 724, 744 and 755 K) led to an increase of the value of the rate constant of reaction I by a factor of around 4. Finally, Jung et al. [START_REF] Jung | Collisional energy transfer in the two-channel thermal unimolecular reaction of bromoethane-2-d[END_REF] in 1987 studied the kinetics of reaction I using deuterated bromoethanes over the temperature range of 660-706 K in the presence of CF4 and He as bath gases at 0.07 bar. The pressure dependence of the rate constant was investigated in the fall-off region at three temperatures (660.2, 693.2, and 706.4 K).

In 2014, Ahubelem et al. [START_REF] Ahubelem | Dehydrohalogenation of ethyl halides[END_REF] theoretically investigated the unimolecular decomposition of selected ethyl halides, including bromoethane, using high level computational chemistry methods. The high pressure limit rate expression has been calculated for temperatures between 300 and 2000 K as: 𝑘 = 5.7 × 10 T . e , / s .

Figure 1 shows the temperature dependence of the rate constants of reaction I determined since 1959.

Since the rate constants measured before were all higher by a factor of at least 11 than the more recent values, they are not plotted in Figure 1. In the temperature range 650-700 K, there is an excellent agreement between the expressions measured by Jung et al [START_REF] Jung | Collisional energy transfer in the two-channel thermal unimolecular reaction of bromoethane-2-d[END_REF] (P = 0.07 bar) and Thomas et al. [START_REF] Thomas | 234. Studies in the pyrolysis of organic bromides. Part XII. The unimolecular decompositions of ethyl bromide and 4-bromopent-1-ene[END_REF] (P = 0.48 bar) and the high pressure limit calculated by Ahubelem et al. [START_REF] Ahubelem | Dehydrohalogenation of ethyl halides[END_REF]. At higher temperatures, the expression measured by Tsang et al. (0.7 < P < 1.7 bar) leads to rate constants for reaction I lower by a factor of 2 than the calculated values. The objective of this study is to investigate the bromoethane pyrolysis using two different types of continuous flow reactors, from which reaction products can be easily analyzed, to better understand the chemistry of brominated compounds: a Jet-Stirred Reactor (JSR), which is a type of Continous Stirred Tank Reactor (CSTR) with an homogenous gas phase composition favoring radical reactions, and a Tubular Reactor (TR) which is characterized by a gas phase composition space evolution along the tube. To our knowledge, no previous study of the pyrolysis of bromoethane was performed in a JSR. A new detailed kinetic model has been developed to reproduce these experimental results, using for reaction I the high pressure limit rate expression calculated by Ahubelem et al. [START_REF] Ahubelem | Dehydrohalogenation of ethyl halides[END_REF].

Experimental procedure

Experiments were carried out in two continuous flow reactors: a jet-stirred-reactor (JSR) and a tubular reactor (TR). In both reactors, species were sampled at the outlet and analyzed using gas chromatography and a Fourier Transform InfraRed (FTIR) spectrometer. The features of the two reactors and analytical

-6 -4 -2 0 2 Log (k(s-1)) 1.6x10 -3 1.5 1.4 1.3 1.2 1.1 1/T(K)
Thomas et al. [START_REF] Taylor | Methyl bromide-Is there any future for this noteworthy fumigant?[END_REF] Jung et al. [START_REF] Vernon | Kinetics of the Unimolecular Dissociation of Gaseous Ethyl Bromide1[END_REF] Tsang et al. [START_REF] Goldberg | Kinetics of the Pyrolysis of Ethyl Bromide1[END_REF] Ahubelem et al. [START_REF] Thomas | 234. Studies in the pyrolysis of organic bromides. Part XII. The unimolecular decompositions of ethyl bromide and 4-bromopent-1-ene[END_REF] procedure are described in the following paragraphs. A scheme of the experimental setup and a picture of gas chromatographs are shown in Figures S1 and S2 in SM.

Reactants entered the spherical fused silica JSR (volume of 85 cm 3 ) though an injection cross made of four nozzles which was located at its center and created high turbulence to produce homogeneity in composition and temperature of the gas phase [START_REF] David | Règies de construction et d'extrapolation des réacteurs auto-agités par jets gazeux[END_REF]. The isothermal JSR is preceded by a quartz annular preheating zone (made of two concentric tubes) in which the temperature of the gas is increased up to the reactor temperature to ensure the temperature homogeneity in the reactor, but also to ensure a good mixing of the inlet mixture. The gas residence time inside the annular preheater is very short compared to its residence time inside the reactor (a few percent). Both the reactor and the preheating zone are heated by the means of Thermocoax resistances rolled up around the reactor. The reaction temperature is measured by a K-type thermocouple located inside the intra-annular space of the preheating zone (the inlet mixture flows in the inter-annular space); its extremity being placed at the level of the injection cross (reaction temperature uncertainty estimated to ± 5 K). Experiments in the JSR were performed at a constant pressure of 1.067 bar (800 Torr), at a residence time of 2 seconds and at temperatures ranging from 600 to 975 K.

Experimental studies in the tubular reactor have been performed using a horizontal 60 cm long alumina tube (volume of 294 cm 3 ) with an inner diameter of 20 mm and an outer diameter of 25 mm. The ends of the reactor is connected to 2.54 cm (1-inch) diameter Swagelok unions and sealed with high temperature epoxy resin from Final Crotonics. The tubular reactor is heated by an electrical furnace from Vecstar equipped with an S-type thermocouple. For each set reaction temperature, a temperature profile (temperature versus position in the tubular reactor) in absence of reaction was measured using a R-type thermocouple (see measured profiles in Figure 2). The uncertainty in measured temperatures was estimated to ± 5 K. Experiments were performed at a constant pressure of 1.067 bar, at a residence time in the set-point temperature zone around 2 seconds and at temperatures ranging from 600 to 975 K.

The two setups used in this study allow the minimization of wall effects which were observed in some former studies [START_REF] Daniels | The Decomposition of Ethyl Bromide and the Collision Theory of First-Order Reactions[END_REF], [START_REF] Goldberg | Kinetics of the Pyrolysis of Ethyl Bromide1[END_REF], [START_REF] Fugassi | A Study of the Decomposition of Gaseous Ethyl Bromide[END_REF]. These studies were performed in reactors made of Pyrex which is known for its propensity to catalyze reactions, whereas the jet-stirred reactor used in the present study was made of fused silica and the tubular reactor of alumina. Contrary to previous studies in batch reactors working under low pressure, our setup use continuous flow reactors and work at pressures close to the atmosphere, which also helps minimizing wall effects.

6

Simulations were performed assuming that the TR can be modeled as a plug flow reactor and using the measured temperature profiles in absence of reaction. The values of the Peclet criterion depending on temperature are given in Table 2. In our operating conditions, the Peclet criterion is always above 100 and we can consequently consider our tubular reactor as a Plug Flow Reactor. It is possible to assimilate a plug flow reactor as a cascade of J jet-stirred reactors [START_REF] Levenspiel | Chemical Reaction Engineering[END_REF]. To determine this number J, Residence Time Distributions (RTD) were measured in this study by an online mass spectrometer (Omnistar from Pfeiffer) after a pulse injection of argon at the reactor inlet (at 800, 900, 1000 and 1100 K). We then performed simulations with MATLAB [START_REF]and Natick, MATLAB and Statistics Toolbox Release[END_REF] to determine the number J of jet-stirred reactors needed to reproduce the experimental results between 800 and 1100 K. The number J obtained for each temperatures investigated are given in Table 2. As is shown by Figures S5-S8 in Supplementary Material, the higher the temperature or the residence time, the lower J, and the lower the ideality of the plug flow reactor. This is in agreement with the data displayed in Table 2 where the Peclet number decreases significantly when the temperature or the residence time increases.

Helium, methane and hydrogen were provided by Messer (purity of 99.999 %) and the brominated reactant was purchased from Sigma-Aldrich (purity of 98.0 %). Gas flow rates were controlled by mass flow controllers and the liquid flow rate by a Coriolis flow controller. The uncertainty in the flow measurements was around 0.5% for each controller, so about 1% on the residence time.

As described previously [START_REF] Vin | A study of chlorobenzene pyrolysis[END_REF], using a heated transfer line maintained at 433 K to avoid product condensation, the gases sampled at the outlet of the reactors were analyzed using:

 Gas chromatography (GC): methane, ethylene, acetylene and ethane were quantified by a first chromatograph fitted with a PlotQ capillary column, a thermal conductivity detector (TCD) and a flame ionization detector (FID); other types of molecules were quantified using a second chromatograph, fitted with a HP-1 capillary column and a FID. A gas chromatograph equipped with a Plot-Q capillary column and coupled to a mass spectrometer was used to identify the reaction products (mass spectra of the fuel and of species which were not calibrated using standards are given in Figure S4 in SM). Response factors were determined by injecting calibration mixtures or using the effective carbon number method. Relative uncertainties in mole fractions were estimated to be ±5% for species which were calibrated using standards and ±10% for other ones. Two typical chromatograms obtained during this study are provided as examples in SM (Figure S3).

 A Fourier Transform InfraRed (FTIR) spectrometry: bromoethane and HBr were analysed using a FTIR spectrometer from Thermo Scientific Antaris equipped with a Mercure Cadmium Telluride photoelectric detector. FTIR spectroscopy calibrations were obtained by injecting standards and the relative uncertainties in mole fractions were estimated to be ±10%. A typical spectrum recorded using this technique is shown in the results and discussion section of this paper.

Kinetic model

Simulations were performed using the OpenSmoke package [START_REF] Cuoci | OpenSMOKE++: An object-oriented framework for the numerical modeling of reactive systems with detailed kinetic mechanisms[END_REF] and a newly developed detailed chemical kinetic reaction mechanism for bromoethane pyrolysis including 214 species in 1443 reactions.

The model is based on mechanism proposed by Husson et al. [START_REF] Husson | New experimental evidence and modeling study of the ethylbenzene oxidation[END_REF] for the oxidation of ethyl-benzene, containing the reactions from C0 to C8 species. Reactions specific to bromoethane have been added to this base mechanism. The mechanism added to the one of Husson et al. [START_REF] Husson | New experimental evidence and modeling study of the ethylbenzene oxidation[END_REF] is given in Table 3.

In the mechanism of Table 3, the following types of reactions were added to account for the reactant consumption:

 Unimolecular initiation reactions by breaking a C-H, C-C or a C-Br bond (reactions 1 to 4 in Table 3); the C-Br bond (70 kcal/mol [START_REF] Luo | Comprehensive Handbook of Chemical Bond Energies[END_REF]) is the weakest one in the bromoethane molecule (C2H5Br).

 Molecular reactions (reaction 5 to 7), especially reaction I, the decomposition of bromoethane into

HBr and ethylene with the rate expression proposed by Ahubelem et al. [START_REF] Ahubelem | Dehydrohalogenation of ethyl halides[END_REF].

Table 3: reactions added to the base mechanism [START_REF] Husson | New experimental evidence and modeling study of the ethylbenzene oxidation[END_REF] to account for the chemistry of the bromoethane pyrolysis

Note: The rate constants are given in the form k = A T n exp(-Ea/RT) where A has units of cm  Reactions of β-scission of the CH2CH2Br and CH3CHBr radicals (reactions 28 to 32).

 Reactions of termination yielding HBr and Br2 (reactions 32 to 34).

When possible, calculations using quantum methods were carried out for kinetic constants when no data were available using the Gaussian 09 revision B.01 suite of programs [START_REF] Frisch | Gaussian 09[END_REF] (at CBS-QB3 level [START_REF] Montgomery | A complete basis set model chemistry. VI. Use of density functional geometries and frequencies[END_REF]). The conformational analysis was performed to check that optimized structures well corresponded to global minima (at the B3LYP/6-31G(d) level [START_REF] Becke | Density-functional thermochemistry. III. The role of exact exchange[END_REF]). Internal rotations of moieties around simple bonds in optimized species have been treated like hindered rotors and their contribution were considered in kinetic parameter calculations through the calculation of partition functions. Intrinsic reaction coordinate calculations were performed to check that transitions states well connected both reactants and products.

Kinetic constants were calculated thanks the transition state theory using Gibbs energies of species involved in the considered reaction. They were corrected to take into account the tunneling (using the asymmetric Eckart potential). The gpop software suite from Miyoshi [31] was used to perform the posttreatment of the Gaussian calculations. Comparisons were made with literature data when available for rate constant calculation strategy assessment (Figures S9 andS10). An excellent agreement was obtained between the rate constants calculated by Ahubelem et al. [START_REF] Blades | The Kinetics of the Decompositions of Ethyl, Isopropyl and n-Propyl Bromides[END_REF] and that calculated in this work for the molecular reaction of decomposition of bromoethane to ethylene and HBr (Figure S9). This is not surprising given that calculations were performed using a similar strategy at the same level (CBS-QB3).

Overall the agreement is good with other literature data. A good agreement was also obtained for the reaction of Br-atom abstraction from bromoethane to HBr and the ethyl radical (Figure S10). To our knowledge, there are no other data in literature available for comparisons.

The thermodynamic data were taken from the database of Burcat et al. [START_REF] Burcat | Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion with Updates from Active Thermochemical Tables[END_REF] or calculated by the Thergas software [START_REF] Muller | THERGAS: a computer program for the evaluation of thermochemical data of molecules and free radicals in the gas phase[END_REF] based on group additivity method.

Results and discussion

This part presents the main results obtained during the pyrolysis of bromoethane in the JSR and the TR. It also displays the comparison with data computed using the detailed kinetic model developed in this study.

A kinetic study of the model is then performed to highlight the specificities of the chemistry of the pyrolysis of bromoethane. shows that the molecule starts to be consumed at 600 K in both reactors. Furthermore, the type of reactor has an influence on bromoethane conversion. Indeed, the reactivity is larger in the TR than in the JSR (full conversion at 925 K in the TR and at 975 K in the JSR). This is in line with the theory of ideal reactors since it can be shown that, for a simple reaction A  products, the conversion in a plug flow is larger than in a perfectly stirred reactor, under equal operating operations [START_REF] Levenspiel | Chemical Reaction Engineering[END_REF]. The model predicts well the evolution of bromoethane conversion with temperature in both reactors.

Bromoethane conversion

Figure 3 (b) shows that a rise of the residence time from 2 to 8 seconds leads to an increase of the conversion from 12.6 to 32.1 %. The model is in agreement with the experimental results for small residence times (between 2 and 4 seconds) but overestimates the conversion for the highest residence times. The fact that a larger deviation between simulation and experiments was observed when residence time increases is in agreement with the fact that the PRF is less ideal as is shown by the smaller Peclet numbers and J (Table 2).

Product formation

This part presents the experimental and computed results for the products obtained during the pyrolysis of bromoethane in both reactors. Since HBr has been measured during the experiments in TR, it is clear now that the major products during the pyrolysis of bromoethane are HBr and ethylene in both reactors. This highlights the importance of the molecular reaction (reaction I) and confirms the results of the previously listed studies The kinetic model predicts well the formation of ethylene and 1,3-butadiene. The formations of ethane and vinyl bromide are well predicted at low temperatures (between 700 and 850 K) and overestimated at higher temperatures. Methane and vinylacetylene formations are underestimated whatever the temperature.

JSR product formation

Figure 4 shows that ethylene is by far the major product identified, even if HBr has not been measured

during the experiments in the JSR.

TR product formation

HBr has been quantified in the TR using FTIR spectroscopy. To determine its mole fraction, an hypothesis has been made: supposing that all the main bromine species have been quantified, the mole fraction of HBr can be determined by using the bromine balance during the pyrolysis of bromoethane for each temperatures.

Discussion

In previous studies Blades et al. [START_REF] Blades | The Kinetics of the Decompositions of Ethyl, Isopropyl and n-Propyl Bromides[END_REF] postulated that the reaction of decomposition of bromoethane is intramolecular as well as Thomas et al. [START_REF] Thomas | 234. Studies in the pyrolysis of organic bromides. Part XII. The unimolecular decompositions of ethyl bromide and 4-bromopent-1-ene[END_REF]. However, Daniels et al. [START_REF] Daniels | The Decomposition of Ethyl Bromide and the Collision Theory of First-Order Reactions[END_REF] have detected small amounts of hydrogen, ethane, propane, butane (in addition to ethylene) in decreasing amount of abundance. They specify in their paper that the dissociation of bromoethane into ethyl radical and Br-atom is possible and propose three different mechanisms and two of them are radical mechanisms. Goldberg et al. [START_REF] Goldberg | Kinetics of the Pyrolysis of Ethyl Bromide1[END_REF] also reported that the thermal decomposition of bromoethane cannot be explained by a simple molecular reaction. The large variety of detected reaction products detected in the present study confirms that the radical mechanism does exist and is very important under operating conditions used in experiments.

Furthermore, the formation of vinyl bromide as well as vinyl acetylene and 1,3-butadiene has been detected for the first time during this study under our operating conditions. Modeling efforts were made in the present study to develop the first detailed kinetic model for the pyrolysis of bromoethane. This model was used to run kinetic analyses and better understand the chemistry of the pyrolysis of bromoethane.

Figure 7 shows the carbon selectivity product obtained during bromoethane pyrolysis in both reactors. At approximately the same conversion, the carbon product selectivity seems to be quite similar even if more methane, vinyl bromide and ethane are produced in the TR than in the JSR. Ethylene is by far the major carbon containing reaction product (its selectivity is divided by 10 in Figure 7). The formation of Br2 was not observed during this study although this species can be detected with the thermal conductivity detector of the gas chromatograph used in this study. This is likely due to concentrations below the detection limit. This is in agreement with data computed using the detailed kinetic model (maximum As the model reproduces in an acceptable way the JSR and the TR experimental results, Figure 8 presents a flow rate analysis performed at 833 K using the OpenSmoke package [START_REF] Cuoci | OpenSMOKE++: An object-oriented framework for the numerical modeling of reactive systems with detailed kinetic mechanisms[END_REF] during the pyrolysis of bromoethane in JSR. The major consumption pathways of bromoethane decomposition are:

concentration
 Reaction I, by molecular reaction giving ethylene and HBr (43.0 %).

 by H-atom abstraction with bromine atoms (51.3 %) producing HBr and the bromoethane radical (CH2CH2Br).

Reaction I is then not the only pathway to be considered during bromoethane thermal decomposition, it is not even the most important one under the conditions of this study. The sequence of reactions composed of the fuel H-atom abstraction by bromine atoms forming CH2CH2Br and the reaction of decomposition by scission of CH2CH2Br to ethylene and HBr forms a propagation loop (sequence of reaction consuming a radical in the first step and regenerating this radical in the last step) which is characteristic of straight chain radical mechanisms. These propagation loops are responsible for the large reactivity of organic compounds during gas phase pyrolysis reactions. At 833 K, the overall rate of consumption of bromoethane though this propagation loop is about 320 times larger than the rate of consumption of bromoethane though the breaking of C-Br bond which is the weakest bond in the fuel (70.0 kcal.mol -1 [START_REF] Luo | Comprehensive Handbook of Chemical Bond Energies[END_REF]).

The flow rate analysis also confirms that bromine atoms mainly react with the fuel by reactions of H-atom abstraction (leading to the formation of HBr) rather than by reactions of termination and addition. This is in agreement with the non-detection of Br2 and dibrominated compounds during experiments. To better understand the most influential reactions, a sensitivity analysis at 833 K was performed. It is shown in Figure 9. The reactions with the largest promoting effect at 833 K are (by decreasing importance):

 The H-atom abstraction with the bromine atom giving CH2CH2Br and HBr  The molecular reaction (reaction I) leading to the two main products: ethylene and HBr.

 The H-atom abstraction with ethyl radical producing the reactant radical and ethane This brings to light the fact that, in addition to the molecular reaction, the H-atom abstraction with the bromine atom (producing CH2CH2Br) is also important. The radical mechanism is thus far from being negligible compared to the molecular decomposition pathway. The sole analysis of reaction product can be misleading as the radical mechanism mainly leads to the same products (ethylene and HBr) as the molecular decomposition reaction of bromoethane (reaction I).

However, the radical CH3CHBr decomposition to create vinyl bromide has an inhibiting effect as well as the Br-atom abstraction with hydrogen radical on bromoethane leading to HBr and ethyl radical.

Conclusion

A study of bromoethane pyrolysis has been carried out in two different reactors: a jet-stirred reactor and a tubular reactor. Temperatures ranged from 600 to 975 K. The residence time was in both reactors equal to 2 s with a bromoethane inlet mole fraction of 0.01 (dilution in helium). All experiments were performed at a pressure of 1.067 bar. The following products were identified: ethylene, HBr, vinyl bromide, methane, ethane, acetylene, 1,3-butadiene, vinyl acetylene. HBr could be quantified during the experiments in the TR thanks the use of FTIR spectroscopy. As in previous literature studies, ethylene and HBr were detected as the major reaction products. The numerous minor products detected in this study show that the molecular decomposition of bromoethane to ethylene and HBr is not the only consumption pathway and that the radical mechanism play an important role under the studied conditions. This confirms the conclusion made in previous literature studies by Daniels et al. [9] and Goldberg et al. [START_REF] Goldberg | Kinetics of the Pyrolysis of Ethyl Bromide1[END_REF].

Since there is a lack of kinetic data in the literature about brominated compounds, a detailed kinetic model has been developed based on theoretically calculated rate parameters. This model gives satisfactory predictions of the reactivity and formation of major compounds (HBr, ethylene) in both reactors. Ethane and vinyl bromide profiles are better predicted by the kinetic model in the TR than in the JSR. Model refinements are needed to better account for the formation of minor products. This will require the experimental studies of these intermediates to better understand their pyrolysis chemistry.

The kinetic analysis performed using the detailed kinetic model developed in this study showed that there are two major decomposition pathways of bromoethane: the molecular reaction giving ethylene and HBr, and the H-atom abstraction by bromine atom on the bromoethane producing CH2CH2Br and HBr, with quasi equal importance. This observation could not be deduced from the sole interpretation of experimental results as the two pathways produce the same reaction products. It confirms that the radical mechanism plays an important role in the thermal decomposition of bromoethane in the conditions of the present study.

Figure 1 :

 1 Figure 1: Temperature dependence of the rate constant of reaction I determined since 1959.

Figure 2 :

 2 Figure 2: Measured temperature profile in TR in absence of reaction.

Figure 3

 3 Figure 3 presents experimental and simulated evolutions with temperature of bromoethane conversion obtained in the jet-stirred reactor (JSR) and in the tubular reactor (TR) under the same operating conditions.

Figure 3 :Figure 3

 33 Figure 3: Evolution of bromoethane conversion with (a) temperature in both reactors, (b) residence time in the tubular reactor (TR) (Symbols are experiments and lines simulations, 775 K, 1 % bromoethane inlet mole fraction, τ = 2 s, P = 1.067 bar). Circles are GC measurements, crosses are FTIR ones

Figure 4

 4 Figure 4 presents the experimental and simulated evolution with temperature of the mole fractions of ethylene, vinyl bromide, ethane, acetylene, 1,3-butadiene, methane and vinyl acetylene measured in the JSR.

Figure 4 :

 4 Figure 4: JSR mole fraction evolution with temperature of (a) ethylene (b) vinyl bromide, (c) ethane (d) acetylene (e) 1,3-butadiene (f) methane (g) vinyl acetylene with 1.0% bromoethane inlet mole fraction at τ = 2 s and P = 1.067 bar. Symbols are experiments and lines simulations.

Figure 5

 5 Figure 5 gives an infrared spectrum measured by FTIR at 825 K during the pyrolysis of bromoethane. The reactant and the 2 main products (HBr and ethylene) are well visible on the spectrum.

Figure 5 :Figure 6 :

 56 Figure 5: Infrared spectrum obtained by FTIR spectroscopy during the pyrolysis of bromoethane in the tubular reactor (825 K, 1.0% bromoethane inlet mole fraction at τ = 2 s and P = 1.067 bar).

  of 8,6 ppm at 1016 K in the tubular reactor). No dibrominated aliphatic compounds were detected in these experiments. HBr and vinyl bromide are the only brominated products observed during this study. The bromine atom balance (comparing the Br atom number in HBr, vinyl bromide and unreacted bromoethane against that in bromoethane at the inlet of the reactor) was performed in the tubular reactor and is satisfactory. It oscillates around 100% with a standard deviation of ± 4,8% over the whole temperature range, similarly to the carbon atom balance (see Tables S1-S2 in supplementary material).

Figure 7 :

 7 Figure 7: Carbon atom containing product selectivity obtained during bromoethane pyrolysis in the TR (850 K, 1.0 % bromoethane inlet mole fraction, τ = 2s, P = 1.067 bar, 81.9 % conversion) and in the JSR (875 K, 1.0 % bromoethane inlet mole fraction, τ = 2s, P = 1.067 bar, 82.8 % conversion).

Figure 8 :

 8 Figure 8: Flow rate analysis at 833 K (0.01 bromoethane inlet mole fraction, τ = 2s, P = 1.067 bar). Numbers on arrows represent the consumption rates normalized by the total bromoethane consumption rate. Red thick arrows correspond to the main ways of decomposition of bromoethane.

Figure 9 :

 9 Figure 9: Sensitivity analysis on bromoethane mole fraction at 833 K (0.01 bromoethane inlet mole fraction, τ = 2s, P = 1.067 bar). Reactions with a negative coefficient have a promoting effect on the reactivity.

Table 1 :

 1 Summary of conditions used in the previous studies of the thermal decomposition of bromoethane where a rate expression was measured for reaction I. Activation energies are in kcal/mol.

	Instrument	Experimental Conditions	Bath gas	kI (s -1 )	Reference
		T = 670 -693 K; 0.016 < P < 0.48 bar	/	3.85 × 10 𝑒 . /	Vernon et al., 1933 [8]
		T = 643 -693 K; P > 0.13 bar	/	1.16 × 10 𝑒 . /	Daniels et al., 1938 [9]
	Batch reactor	T = 653 -703 K; P = 0.4 bar	/	6 × 10 𝑒 . /	Goldberg et al., 1956 [10]
		T = 653 -703 K; P = 0.48 bar	/	2.8 × 10 𝑒 . /	Thomas et al., 1959 [11]
		T = 660 -706 K ; P = 0.07 bar	He	4.17 × 10 𝑒 . /	Jung et al., 1987 [12]
	Tubular reactor	T = 800 -900 K; P = 1 bar	Toluene 7.3 × 10 𝑒 .

/ Blades et al. 1952 [13]

Shock Tube T = 740 -940 K ; 0.7 < P < 1.7 bar Ar 10 . 𝑒 . / Tsang et al. 1964

[START_REF] Tsang | Thermal Decomposition of Some Alkyl Halides by a Shock-Tube Method[END_REF]

Table 2 :

 2 Values of the Peclet number, Pe, during the pyrolysis of bromoethane in the TR (1.0%

	(a)

bromoethane inlet mole fraction, P = 106.7 kPa): (a) versus temperature (T) at a residence time () of 2 s; (b) versus  at T= 975 K.

  Rate constants taken equal to the values proposed by Campbell et al.[START_REF] Campbell | Reaction Kinetics, Thermodynamics, And Transport In The Hydrogen-Bromine System -A Survey Of Properties For Flame Studies[END_REF]. f Rate constants taken equal to the values proposed by Baulch et al.[START_REF] Baulch | Homogeneous Gas Phase Reactions of Halogen-and Cyanide-Containing Species[END_REF].

	 The H-atom abstraction reactions by H-atoms (reactions 9 to 13), by Br-atoms (reactions 24 to 27),
		by methyl radicals (reactions 15 to 19) and by ethyl radical (reactions 20 to 23) with reverse
	Reaction	reactions.	A	N	Ea	Footnote	No.
	Reactions of bromoethane  Br-atom abstraction reactions by H-atoms (reaction 8) and methyl radical (reaction 14). Reactions of unimolecular initiation
	CH3+CH2Br = C2H5Br	3.6 × 10 13	0.0	0.0	a	(1)
	C2H5 + Br = C2H5Br	3.6 × 10 13	0.0	0.0	a	(2)
	CH3CHBr + H = C2H5Br	1.0 × 10 14	0.0	0.0	a	(3)
	CH2CH2Br + H = C2H5Br	1.0 × 10 14	0.0	0.0	a	(4)
	Molecular reactions
	C2H5Br = C2H4 + HBr	5.7 × 10 10	1.03	54600	b	(5)
	CH2CHBr => C2H2 + HBr	1.86 × 10 12	3.715	63308	c	(6)
	C2H2 + HBr => CH2CHBr	1.422 × 10 -2	4.397	34306	c	(7)
	Reactions of H-atom abstraction
	C2H5Br + H => HBr + C2H5	2.94 × 10 9	1.678	5594	c	(8)
	HBr + C2H5 => C2H5Br + H	1.74 × 10 7	1.889	22737	c	(9)
	C2H5Br + H => H2 + CH3CHBr	7.18 × 10 8	1.583	9555.7	c	(10)
	H2 + CH3CHBr => C2H5Br + H	5.94 × 10 2	2.777	12191	c	(11)
	C2H5Br + H => H2 + CH2CH2Br	2.24 × 10 4	2.944	8477	c	(12)
	H2 + CH2CH2Br => C2H5Br + H	1.0 × 10 3	2.751	6760	c	(13)
	C2H5Br + CH3 => CH3Br + C2H5	9.76 × 10 6	1.838	15508	c	(14)
	CH3Br + C2H5 => C2H5Br + CH3	2.12 × 10 7	1.967	14956	c	(15)
	C2H5Br + CH3 => CH4 + CH3CHBr	1.52 × 10 7	1.78	16797	c	(16)
	CH4 + CH3CHBr => C2H5Br + CH3	6.4 × 10 6	1.82	21603	c	(17)
	C2H5Br + CH3 => CH4 + CH2CH2Br	6.39 × 10 7	1.963	16602	c	(18)
	CH4 + CH2CH2Br => C2H5Br + CH3	8.12 × 10 7	1.901	20456	c	(19)
	C2H5Br + C2H5 => C2H6 + CH3CHBr	1.87 × 10 -4	5.05	7880	d	(20)
	C2H6 + CH3CHBr => C2H5Br + C2H5	4.48 × 10 -5	5.29	15658	d	(21)
	C2H5Br + C2H5 => C2H6 + CH2CH2Br	3.33 × 10 4	3.1	13544	d	(22)
	C2H6 + CH2CH2Br => C2H5Br + C2H5	1.77 × 10 4	3.2	16796	d	(23)
	C2H5Br + Br = Br2 + C2H5	0.15 × 10 13	0.0	20800	c	(24)
	C2H5Br + Br => HBr + CH2CH2Br	0.36 × 10 6	2.73	9983	c	(25)
	HBr + CH2CH2Br => C2H5Br + Br	0.71 × 10 3	2.69	-4036	c	(26)
	C2H5Br + Br = HBr + CH3CHBr	0.58 × 10 13	0.26	13700	c	(27)
	Reactions of β-scission
	CH2CH2Br = C2H4 + Br	0.58 × 10 13	0.26	13700	c	(28)
	CH2CH2Br = CH2CHBr + H	9.94 × 10 13	-0.039	42704	c	(29)
	CH2CHBr + H = CH2CH2Br	1.96 × 10 8	1.89	2853	c	(30)
	CH3CHBr = CH2CHBr + H	3.39 × 10 8	1.70	36648	c	(31)
	CH2CHBr + H = CH3CHBr	1.72 × 10 8	2.06	50.7	c	(32)
	Reactions of termination
	H + Br = HBr	2.90 × 10 16	-1.5	0.0	e	(33)
	Br + Br = Br2	1.48 × 10 14	0.0	-1701	f	(34)

3

,mol, s, T has units of K, and Ea has units of cal/mol. a Rate constants estimated by analogy with values obtained for alkanes with the software EXGAS. b Rate constants taken equal to the values proposed by Ahubelem et al.

[START_REF] Ahubelem | Dehydrohalogenation of ethyl halides[END_REF]

. c Rate constants calculated using quantum methods. d Rate constants estimated by analogy with values of H-atom abstraction on bromoethane. e

Acknowledgements

This work has been supported by TERBIS, 943 rue Pasteur, 60700 Pont Sainte Maxence, France.

Perfectly-Stirred-Reactor; CSTR: Continous-Stirred-Tank-Reactor;