Mohammed Hichem Hakka

Hayet Bennadji

Joffrey Biet

Mohammed Yahyaoui

Baptiste Sirjean

Valérie Warth

Lucie Coniglio

Olivier Herbinet

Pierre-Alexandre A Glaude

Francis Billaud

Frédérique Battin-Leclerc

Oxidation of methyl and ethyl butanoates

Keywords: Benzene, Toluene, Decane, Low-temperature oxidation, Jet-stirred reactor

la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Environmental concerns have led to an increased interest in the use of fuels containing a larger fraction of components that have been derived from biomass, such as methyl or ethyl esters in biodiesel (1,2). Biodiesel is composed of monoalkyl esters (methyl/ethyl esters) obtained from long chain fatty acids derived from renewable lipid sources (e.g., rapeseed oil in Europe and soybean oil in the United States) by transesterification with methanol or ethanol (2,3). It should be mentioned that the presence of additional oxygenated compounds could reduce the formation of soot in diesel engines (4,5) but may also promote the formation of some toxic pollutants, such as aldehydes (6).

The need to develop more efficient, but cleaner, engines requires the development of validated detailed kinetic models for the oxidation of fuels. If such mechanisms start to be available for surrogates of gasoline and diesel fuel, there are few kinetic models for the oxidation of methyl and ethyl esters. Despite rapeseed and soybean oils are mainly composed of compounds containing more than 16 atoms of carbon, it is interesting to better understand the reactivity of the oxygenated part of these molecules by studying first a small chain methyl/ethyl ester. The first detailed modeling of the oxidation of methyl esters has been proposed by Fisher et al. (7) for methyl formate and methyl butanoate with validation using experimental results obtained in static reactors below 900 K (8). More recently, a mechanism of the oxidation of methyl butanoate has been proposed by Gaïl et al. (9) with validations over a wide range of operating conditions, including results obtained in a jetstirred reactor from 800 to 1350 K (no significant conversion was obtained below 950 K), in a flow reactor, from 500 to 900 K (no significant conversion was obtained below 750 K) and in an opposedflow diffusion flame. Metcalfe et al. (10) have experimentally and theoretically studied the hightemperature ignition of methyl butanoate and ethyl propanoate using their shock tube at temperatures between 1100 and 1670 K. The proposed model has recently been updated to simulate experimental results obtained in a jet-stirred reactor from 750 to 1100 K for ethyl propanoate (11). Dooley et al. (12) have studied the low-temperature ignition of methyl butanoate in their rapid compression machine over the temperature range 640-949 K. These authors have also proposed a model able to reproduce the rapid compression machine data, but also the measurements of Gail et al. 9 in a jet-stirred reactor, a flow reactor, and an opposed-flow diffusion flame. Walton et al. (13) have experimentally studied the ignition of methyl butanoate and ethyl propanoate using their rapid compression machine at temperatures between 935 and 1117 K and slightly modified the model proposed by Metcalfe et al. (10). Theoretical calculations were performed by Huynh and Violi (14) for some reactions of importance for the thermal decomposition of methyl butanoate and applied successfully by Faroq et al. (15) to model experimental data obtained behind reflected shock waves (temperatures from 1260 to 1653 K). Hayes and Burgess (16) made theoretical calculations for some reactions important in the oxidative decomposition of methyl butanoate. No data have been yet reported for ethyl butanoate.

The first purpose of this paper is to present new experimental data about the oxidation of smallsaturated esters, including a comparative study of the ignition delay times of methyl and ethyl butanoate. A second objective is to describe new detailed kinetic models for the oxidation of these species generated using an automatic method and validated over a wide range of experimental conditions.

Experimental

This experimental study has been performed by using two different devices: a jet-stirred reactor and a shock tube. Methyl butanoate (99% pure) and ethyl butanoate (98% pure) were provided by Fluka (Saint Quentin Fallavier, France). Oxygen (99.5% pure) and argon and helium (both 99.995% pure) were supplied by Messer (Folschwiller, France).

Shock Tube

As the measurement of ignition delay times in the used shock tube has been described in several papers (17)(18)(19)(20), the main features of this experimental device will just be recalled here. Autoignition delay times have been measured in a stainless steel shock tube; the reaction and the driver parts were, respectively, 400.6 and 89 cm in length and 7.8 and 12.82 cm in diameter and were separated by two terphane diaphragms. These diaphragms were ruptured by suddenly decreasing the pressure in the space separating them, that allowed us to keep the same pressure (5.3 bar) in the highpressure part for all experiments. The driver gas was helium. The incident shock velocities were measured by four piezoelectric pressure transducers located along the reaction section (the distance between each transducer was 15 cm and the last one was located at 1 mm from the end-plate of the tube). The pressure P 5 and temperature T 5 of the test gas behind the reflected shock wave were derived from the values of the initial pressure (P 1 ) in the low-pressure section (ranging from 10 to 40 kPa) and of the incident shock velocity (V) by using ideal one-dimensional shock equations. The error on the temperature was estimated about 20 K.

The onset of ignition was detected by OH radical emission at 306 nm through a quartz window with a photomultiplier fitted with a monochromator at the end of the reaction part (the center of the window was located at 1 mm from the end-plate of the tube at the same place as the last pressure transducer). It is worth noting that the experimental OH emission at 306 nm is related to electronically excited OH* concentration.

Fresh reaction mixtures were prepared every day and mixed using a recirculation pump. Before each introduction of the reaction mixture (vacuum in low-pressure part obtained by a primary pump for a pressure around 1×10 -3 kPa), the reaction section was flushed with pure argon and evacuated, to ensure the residual gas to be mainly argon.

Jet-Stirred Reactor

The oxidation of methyl butanoate was carried out in a jet-stirred reactor (internal volume about 92 cm 3 ) made of quartz and operated at a constant temperature and pressure. This type of spherical reactor is well adapted for kinetic studies because the gas phase inside the reactor has been proved to be well stirred and concentrations are homogeneous therein (21). It has already been used many times in our laboratory for studying the oxidation of organic compounds with satisfactory modeling of the obtained results (e.g., 22,23). The heating of the reactor was achieved by means of electrically insulated resistors directly coiled around the vessel. Temperature was measured by using a thermocouple located inside the reactor; reactants were preheated at a temperature close to the reaction temperature. Corresponding residence time in the preheating section was approximately 1% of the total residence time.

The liquid fuel was contained in a glass vessel pressurized with helium. After each load of the vessel, helium bubbling and vacuum pumping were performed to remove oxygen traces dissolved in the liquid hydrocarbon fuel. The liquid reactant flow rate was controlled by using a liquid mass flow controller, mixed to the carrier gas, helium, and then evaporated by passing through a single pass heat exchanger whose temperature is set above the boiling point of the mixture. Carrier gas and oxygen flow rates were controlled by gas mass flow controllers located before the mixing chamber. The fuel/oxygen/helium mixtures were premixed prior the introduction into the reactor.

Owing to the formation of compounds, which were either gaseous or liquid at room temperature, the analyses of the products leaving the reactor were performed in two steps:

 For the analysis of heavy products, the outlet flow was directed toward a trap maintained at liquid nitrogen temperature during a determined period of time. The use of helium instead of nitrogen as diluent prevents trapping of the carrier gas and has a negligible effect on the obtained results compared to the use of nitrogen. At the end of this period (typically 10 min), the trap was removed and, after the addition of acetone and of an internal standard (n-octane), progressively heated up. When the temperature of the trap was close of 273 K the mixture was poured into a small bottle and then injected by an autosampler in a gas chromatograph with flame ionization detection (FID) for quantification. The column used for the separation was a HP-1 capillary column with helium as carrier gas. Calibrations were performed by analyzing a range of solutions containing known amounts of n-octane and of the species to be analyzed. Species heavier than methyl butanoate have not been analyzed.

 Oxygen, carbon oxides, and C 1 -C 2 hydrocarbons were analyzed online by a chromatograph fitted with both thermal conductivity detector (TCD) for oxygen and carbon oxides detection and FID for methane and C 2 hydrocarbons detection and using a CARBOSPHERE packed column with helium as carrier gas. Species identification and calibration was realized by injection of gaseous standard mixtures provided by Air Liquide (Metz, France). Using helium as carrier gas both in the reactor and in this gas chromatograph facilitates the quantification of oxygen.

Water, formaldehyde, hydrogen, and C 3 -C 4 hydrocarbons have not been analyzed. Calculated uncertainties on the species quantifications were about ±5% with the online analysis of oxygen and C 1 -C 2 hydrocarbons and about ±10% for the analysis of other species.

It is worth noting that important problems were encountered in performing these experiments due to reactions between methyl butanoate and seals inside the flowmeters. Methyl butanoate dissolved both Kalrez and Viton seals damaging the flowmeters and producing leakages. Since experiments were only performed with well functioning flowmeters, these problems have not affected the present measurements, but they have prevented us from testing more experimental conditions.

Results

Shock Tube

This study was performed under the following experimental conditions after the reflected shock wave:

 temperature range from 1280 to 1990 K,  pressure maintained around 8 atm, ranging from 7.6 to 9.1 atm, and  argon/ester/oxygen mixtures corresponding to three different equivalence ratios (φ = 0.25, 1

and 2) and to three different concentrations of esters (0.417 (only in the case of ethyl butanoate), 0.5 and 1%) and allowing delay times from 5 up to 700 μs to be obtained.

Figure 1 presents the record of the signal of the last pressure transducer and of the OH emission for a typical experiment in the case of ethyl butanoate. The pressure profile displayed three rises, which were due to the incident shock wave, 1; the reflected shock wave, 2; and the ignition. This last pressure rise is sharp enough for determining the delay time, while the rise of OH emission, 3, is much steeper and allows the delay time to be known with an accuracy better than 10%. The ignition delay time (τ) was defined as the time interval between the pressure rise measured by the last pressure transducer due to the arrival of the reflected shock wave and the rise of the optical signal by the photomultiplier up to 10% of its maximum value as shown in Figure 1. As shown in Figure 1, all the obtained pressure signals display a slight rise prior to ignition, even in the lowest temperature cases. As this rise is reproduced by modeling, it is probably more due to kinetics than to nonideal shock tube effects or premature ignition. Note that this rise was not usually observed when studying other hydrocarbons (e.g., 19,20). Tables I and II present the complete set of experimental conditions and measurements performed in this study for methyl butanoate and ethyl butanoate, respectively. We usually consider that the range of ignition delay times that can be measured in this shock tube while maintaining ideal conditions (adiabaticity for long ignition delay times and reasonable uncertainties for short ignition is the pressure of the mixture before the shock, V is the velocity of the incident wave, P 5 and T 5 are pressure and temperature behind the reflected shock wave, and τ is the ignition delay time. Italic corresponds to ignition delay times below 10 μs and then to a larger uncertainty. is the pressure of the mixture before the shock, V is the velocity of the incident wave, P 5 and T 5 are pressure and temperature behind the reflected shock wave, and τ is the ignition delay time. Italic corresponds to ignition delay times below 10 μs and then to a larger uncertainty. b Conditions of the signals displayed in Figure 1.

Figures 2 and3 present the experimental results obtained for the ignition of methyl butanoate and ethyl butanoate, respectively. Figures 2a and3a correspond to mixtures containing 0.5% of ester, for three equivalent ratios. Figures 2b and3b display the experimental results obtained for different ester concentrations with stoichiometric mixtures. These results show that in each case, ignition delay times increase when equivalence ratio increases and decrease when dilution decreases. Figure 2. Ignition delay times of methyl butanoate in a shock tube for (a) equivalence ratios of 0.25, 1, and 2 and a concentration of ester of 0.5% and (b) an equivalence ratio of 1 and concentrations of ester of 0.5% and 1%. Points correspond to experimental results and lines to simulations.

Figure 3. Ignition delay times of ethyl butanoate in a shock tube for (a) equivalence ratios of 0.25, 1, and 2 and a concentration of ester of 0.5% and (b) an equivalence ratio of 1 and concentrations of ester of 0.417%, 0.5%, and 1%. Points correspond to experimental results and lines to simulations. The two series corresponding to stoichiometric mixtures and a concentration of ester of 0.5% for methyl butanoate and 0.417% for ethyl butanoate have been made to obtain a direct comparison between both compounds with the same concentration of carbon atoms and the same C/O ratio. Figure 4 displays these results and shows a very small difference of reactivity between both esters. The ignition delay times for ethyl butanoate are slightly lower than for methyl butanoate above 1600 K. The results obtained by Metcalfe et al. (10) concerning the ignition of methyl butanoate and ethyl propanoate also show the ethyl ester to be the more reactive, but the difference in reactivity is more important at low temperature.

Figure 4. Comparison between autoignition delay times of methyl and ethyl butanoate in a shock tube for an equivalence ratio of 1 and a concentration of ester of 0.5% for methyl butanoate and of 0.417% for ethyl butanoate (corresponding to the same concentration of atoms of carbon). Points correspond to experimental results and lines to simulations.

For organic compound/oxygen/argon mixtures, the determination of power dependences is often proposed from the overall statistical correlation between τ and the gas concentrations:

 = A exp(E/RT) [OC] a [O 2 ] b [Ar] c
where A is the preexponential factor, E the apparent "activation energy," and R the gas constant (24). For a restricted range of pressure and temperature, a, b, and c are usually constant. Such a statistical correlation has been derived from the present experiments, but since the mole fraction of argon had limited variations under the different initial conditions (from 83.5% to 97.785%) and seems not to affect the delay times, it was chosen to keep c = 0. A multilinear regression gave the following relationships, with the concentrations behind the reflected shock wave in mol cm These statistical correlations show a strong negative O 2 power dependence, whereas the fuel power dependence is very small. Previous work with other organic compounds has also shown large negative O 2 power dependence and much smaller positive fuel power dependence (19,25). The apparent activation energy is slightly larger for the ethyl ester compared to the methyl one. This difference is in agreement with what can been seen in Figure 4.

Jet-Stirred Reactor

Table III presents the complete set of experimental conditions and measurements performed in this study for methyl butanoate. These results are displayed in Figures 5 to 7. As shown in Figure 5, the oxidation of methyl butanoate leads to the formation of similar amounts of two unsaturated esters, namely methyl crotonate (methyl 2-butenoate; Figure 5b) and methyl acrylate (methyl propenoate; Figure 5c). Concerning the oxygenated products displayed in Figure 6, the formation of carbon dioxide (Figure 6c) is larger than what should be obtained only from the reactions of carbon monoxide (Figure 6b) at the low temperatures used in this study, i.e., 800 and 850 K. Among C 1 -C 2 hydrocarbons (Figure 7), methane (Figure 7a) and ethylene (Figure 7b) are the most abundant ones, whereas the levels of acetylene and ethane (Figure 7c) are lower than 30 ppm. 1.08 × 10 -5

1.17 × 10 -5

1.16 × 10 -5

1.24 × 10 -5

1.30 × 10 -5

1.27 × 10 -5

1.28 × 10 -5

1.25 × 10 -5

1.29 × 10 -5

1.28 × 10 -5

1.34 × 10 -5 Figure 5. Time evolution profiles for the consumption of the ester and the formation of methyl crotonate and methyl acrylate measured during the oxidation of methyl butanoate in a jet-stirred reactor at 800 K for an equivalence ratio of 0.5 and at 850 K for an equivalence ratio of 1. Points correspond to experimental results, full lines to simulations with the complete mechanism, and dotted lines to simulations with a mechanism without the low-temperature reactions. . Time evolution profiles for the consumption of oxygen and the formation of carbon oxides measured during the oxidation of methyl butanoate in a jet-stirred reactor at 800 K for an equivalence ratio of 0.5 and at 850 K for an equivalence ratio of 1. Points correspond to experimental results and lines to simulations.

Figure 7. Time evolution profiles for the formation of C 1 -C 2 hydrocarbons measured during the oxidation of methyl butanoate in a jet-stirred reactor at 800 K for an equivalence ratio of 0.5 and at 850 K for an equivalence ratio of 1. Points correspond to experimental results and lines to simulations.

Description of the Detailed Kinetic Model

The detailed chemical kinetic reaction mechanisms presented here have been developed using EXGAS software. As the use of EXGAS to model the oxidation of alkanes and ethers has already been extensively described (23,(26)(27)(28)(29), we will recall here only its main features. However, we will provide more detail on the reactions and rate constants specific to the two small esters studied here.

General Features of EXGAS

The system provides reaction mechanisms made of three parts that are used together:  A comprehensive primary mechanism in which the only molecular reactants considered are the initial organic compounds and oxygen (see Table IV in the case of methyl butanoate). For modeling results obtained above 1000 K, the mechanism can include only high-temperature reactions, which are in the case of saturated hydrocarbons:  unimolecular initiations involving the breaking of a C-C bond,  bimolecular initiations with oxygen to produce alkyl (R•) and hydroperoxy (•OOH) radicals,  isomerizations of alkyl radicals involving a cyclic transition state and the transfer of an Hatom,  decompositions of radicals by β-scission involving the breaking of C-C, C-O or C-H bonds for all types of radicals,  oxidations of alkyl radicals with O 2 to form alkenes and •HO 2 radicals,  metatheses between radicals and the initial reactants (H-abstractions), and  combinations and dismutations of radicals.

Table IV. Primary Mechanism for the Oxidation of Methyl Butanoate.

Reactions

A n E a Equation Number

Unimolecular initiations C 5 H 10 O 2 S → • CH 2 CH 2 C(=O)OCH 3 + • CH 3 1.7 × 10 17 0.0 86,911 (1)
C 5 H 10 O 2 S → • CH 2 C(=O)OCH 3 + • C 2 H 5 3.8 × 10 16 0.0 81,705 (2)
C 5 H 10 O 2 S → CH 3 O • CO + nC 3 H • 7
7.9 × 10 16 0.0 92,781

C 5 H 10 O 2 S → CH 3 O • + C 3 H • 7 CO 1.5 × 10 16 0.0 96,856 (3)
C 5 H 10 O 2 S → • CH 3 + C 3 H 7 C(=O)O • 3.5 × 10 15 0.0 84,439 (4)
Bimolecular initiations

C 5 H 10 O 2 S + O 2 → HO • 2 + • CH 2 C 2 H 4 C(=O)OCH 3 2.1 × 10 13 0.0 53,030 (6)
C 5 H 10 O 2 S + O 2 → HO • 2 + C 3 H 7 C(=O)OCH • 2 2.1 × 10 13 0.0 51,130 (7)
C 5 H 10 O 2 S + O 2 → HO • 2 + C 2 H • 5 CHC(=O)OCH 3 1.4 × 10 13 0.0 46,508 (8)
C 5 H 10 O 2 S + O 2 → HO • 2 + CH • 3 CHCH 2 C(=O)OCH 3 1.4 × 10 13 0.0 50,586 (9)
Additions with oxygen

nC 3 H • 7 + O 2 = C 3 H 7 (OO • ) 9.0 × 10 18 -2.5 0 ( 10
)
nC 4 H • 9 + O 2 = C 4 H 9 (OO • ) 9.0 × 10 18 -2.5 0 (11) • CH 2 C 2 H 4 C(=O)OCH 3 + O 2 = CH 2 (OO • )C 2 H 4 C(=O)OCH 3 9.0 × 10 18 -2.5 0 (12) C 3 H 7 C(=O)OCH • 2 + O 2 = C 3 H 7 C(=O)OCH2(OO • ) 1.0 × 10 18 -2.5 0 (13) C 2 H • 5 CHC(=O)OCH 3 + O 2 = C 2 H 5 CH(OO • )C(=O)OCH 3 1.0 × 10 19 -2.5 0 ( 14
) CH • 3 CHCH 2 C(=O)OCH 3 + O 2 = CH 3 CH(OO • )CH 2 C(=O)OCH 3 1.7 × 10 19 -2.5 0 ( 15
) • CH 2 C(=O)OCH 3 + O 2 = CH 2 (OO • )C(=O)OCH 3 1.0 × 10 18 -2.5 0 ( 16
) CH • 3 CHCH 2 (OOH) + O 2 = CH 3 CH(OO • )CH 2 (
C 3 H • 7 CH(OOH) + O 2 = C 3 H 7 CH(OO • )(OOH) 1.0 × 10 19 -2.5 0 ( 33
) CH 2 (OOH)C 2 H 4 C(=O)OCH • 2 +O 2 = CH 2 (OOH)C 2 H 4 C(=O)OCH 2 (OO • ) 1.0 × 10 18 -2.5 0 ( 34
) CH 2 (OOH)C(=O)OCH • 2 + O 2 = CH 2 (OOH)C(=O)OCH 2 (OO • ) 1.0 × 10 18 -2.5 0 ( 35
) • CH(OOH)C(=O)OCH 3 + O 2 = CH(OO • )(OOH)C(=O)OCH 3 2.0 × 10 18 -2.5 0 (36) C 2 H • 5 C(OOH)C(=O)OCH 3 + O 2 = C 2 H 5 C(OO • )(OOH)C(=O)OCH 3 1.1 × 10 19 -2.5 0 ( 37
) CH • 3 C(OOH)CH 2 C(=O)OCH 3 + O 2 = CH 3 C(OO • )(OOH)CH 2 C(=O)OCH 3 1.8 × 10 19 -2.5 0 ( 38
) • CH(OOH)C 2 H 4 C(=O)OCH 3 +O 2 = CH(OO • )(OOH)C 2 H 4 C(=O)OCH 3 1.0 × 10 19 -2.5 0 ( 39
) • CH 2 C(=O)OCH 2 (OOH) + O 2 = CH 2 (OO • )C(=O)OCH 2 (OOH) 1.0 × 10 18 -2.5 0 ( 40
) • CH 2 C 2 H 4 C(=O)OCH 2 (OOH) + O 2 = CH 2 (OO • )C 2 H 4 C(=O)OCH 2 (OOH) 9.0 × 10 18 -2.5 0 (41) C 2 H • 5 CH(OOH) + O 2 = C 2 H 5 CH(OO • )(OOH) 1.0 × 10 19 -2.5 0 (42) CH 3 CH(OOH)CH • 2 + O 2 = CH 3 CH(OOH)CH 2 (OO • ) 1.5 × 10 18 -2.5 0 ( 43
)
iC 3 H • 7 + O 2 = CH 3 CH(OO • )CH 3 1.6 × 10 19 -2.5 0 (44) Isomerizations • CH 2 C 2 H 4 C(=O)OCH 3 = C 3 H 7 C(=O)OCH • 2 2.5 × 10 7 1.0 17,900 (45)
C 3 H 7 (OO

C 3 H 7 C(=O)OCH 2 (OO • ) = CH • 3 CHCH 2 C(=O)OCH 2 (OOH) 1.7 × 10 7 1.0 23,700 (56)
C 2 H 5 CH(OO • )C(=O)OCH 3 = CH • 3 CHCH(OOH)C(=O)OCH 3 3.3 × 10 9 1.0 32,500 (57)
C 2 H 5 CH(OO • )C(=O)OCH 3 = • CH 2 CH 2 CH(OOH)C(=O)OCH 3 8.6 × 10 8 1.0 28,500 (58)
C 2 H 5 CH(OO • )C(=O)OCH 3 = C 2 H 5 CH(OOH)C(=O)OCH • 2 (59)
1.5 × 10 The rate constants are given at 1 atm (k = AT n exp(-E a /RT)) in cm 3 . mol. s. cal units.  a lumped secondary mechanism, containing reactions consuming the molecular products of the primary mechanism that do not react in the reaction bases. To have a manageable size, the lumped secondary mechanisms (26) involved lumped reactants: the molecules formed in the primary mechanism, with the same molecular formula and the same functional groups, are lumped into one unique species without distinction between the different isomers. The rules used for writing the reactions of hydroperoxides, aldehydes, ketones, alkenes, and cyclic ethers bearing an ester function have been derived from those recently proposed for alkanes by Biet et al. (23). The writing of the secondary reaction is made to promote the formation of C 2+ alkyl radicals, the reactions of which are already included in the primary mechanism.  A C 0 -C 2 reaction base, including all the reactions involving radicals or molecules, contains less than three carbon atoms (30), which is periodically updated. As this part of the mechanism concerns small species, pressure-dependent rate constants follow the formalism proposed by Troe (31) and efficiency coefficients have been included, which is not the case in the primary and secondary mechanisms.

Thermochemical data for molecules or radicals are automatically computed using software THERGAS (32) based on group additivity [START_REF] Benson | Thermochemical kinetics[END_REF], and stored as 14 polynomial coefficients, according to the CHEMKIN II formalism [START_REF] Kee | Sandia Laboratories Report[END_REF]. The only change made in the case of esters, was that the bond dissociation energy of the C-H bonds carried by the atom of carbon just neighboring the ester function has been taken equal to 95.6 kcal/mol as the value proposed by Luo [START_REF] Luo | Handbook of bond dissociation energies in organic compounds[END_REF] for ethyl propanoate.

The kinetic data of isomerizations, combinations, and the unimolecular decompositions are calculated using software KINGAS (26), based on the thermochemical kinetics methods (33) using the transition state theory or the modified collision theory. The kinetic data, for which the calculation is not possible by KINGAS, are estimated from correlations, which are based on quantitative structurereactivity relationships and obtained from a literature review (26)(27)(28)(29) or are estimated from quantum calculations.

The Primary Mechanism of the Oxidation of Methyl Butanoate

Since no mechanism generated by EXGAS in the case of the oxidation of esters has been yet published, Table IV presents the primary mechanism for the oxidation of methyl butanoate, which contains 334 reactions of this ester or of the produced free radicals. This detailed kinetic model was build in a comprehensive way and contains all reactions pertinent at both low and high temperatures, although experimental data from the literature (12,[START_REF] Hadjali | [END_REF] gave no evidence of lowtemperature phenomena such as cool flame or negative temperature coefficient for methyl esters smaller than methyl pentanoate.

The stable molecules obtained by decompositions by β-scission, decomposition to give cyclic ethers, oxidations, and terminations are lumped. For instance, the two isomers of methyl crotonate are not distinguished and both written C 5 H 8 O 2 ZS. For the additions to oxygen molecules (reactions (10)- (44) in Table IV), the combinations (reactions (318)-(325)) and the disproportionations (reactions (326)-(334)), the kinetic data have directly been derived from those proposed for alkanes and alkyl radicals by Buda et al. 29. For the other types of reactions, the following changes have been considered:

 Initiations by Breaking a C-C or a C-O Bond (Reactions (1)-(5))

In the case of esters, the initiations by breaking of a C[BOND]O bond need also to be taken into account (reactions (4) and ( 5)) in addition to those by breaking of a C-C bond (reactions (1)-( 3)). The activation energy of reaction (3), which involves the breaking of the C-C bond located in α-position from the ester function, has been taken equal to 93 kcal/mol according to the value recently calculated by El-Nahas et al. (37). For the other reactions, the values proposed by El-Nahas et al. (37) and those calculated using KINGAS (26) were in agreement to about ± 2 kcal/mol.  Bimolecular Initiations (Reactions ( 6)-( 9)), Oxidations (Reactions (250)-( 257)), and

Metatheses (Reactions (258)-(317))

Bimolecular initiations and metatheses involve an H-abstraction from the initial reactant by oxygen molecules or small radicals, respectively. The small radicals taken into account in metatheses were

•O• and •H atoms and •OH, •HO 2 , •CH 3 , •CHO, •CH 2 OH, •CH 3 O, •CH 3 O 2 , •C 2 H 5 ,
•iC 3 H 7 , and the four peroxy radicals deriving from the first addition to oxygen. The oxidation of an alkyl radical deriving from a saturated ester leads to •HO 2 radicals and to the conjugated unsaturated esters. The correlations used for bimolecular initiations and oxidations are the same as for alkanes (29). For the abstraction of an H-atom from a carbon atom located in α-position of the ester function (the fastest of the H-abstraction reactions for this type of molecules), the correlations were taken the same as those used for the abstraction of a tertiary H-atom from alkanes, except in the case of the abstractions by •O• and •H atoms and by •OH, •HO 2 , and •CH 3 radicals (reactions 260, 264, 268, 272, and 276). In this case, the rate parameters have been evaluated using an Evans-Polanyi-type correlation from Dean and Bozzelli [START_REF] Dean | Combustion Chemistry of Nitrogen[END_REF], developed for the abstraction of H-atoms from hydrocarbons:

k = n H A T n exp (-{E 0 -f(H 0 -H)}/RT)
where n H is the number of abstractable H-atoms; A, n, and E 0 are the rate parameters for the case of a metathesis by the considered radical from ethane; ΔH 0 is the enthalpy of the metathesis by the considered radical from ethane; ΔH is the enthalpy of the metathesis by the considered radical from the reacting molecule; f is a correlation factor, the values of which were given by Dean and Bozzelli [START_REF] Dean | Combustion Chemistry of Nitrogen[END_REF] for each considered radical. For the abstraction of an H-atom from a carbon atom neighboring the O-atom, the correlations were taken the same as those used for the abstraction of a primary H-atom from alkanes, except in the case of the abstractions by •O• and •H atoms and by •OH, •HO 2 and •CH 3 radicals (reactions 259, 263, 267, 271, and 275). In this case, the rate parameters have also been evaluated using the Evans-Polanyi-type correlation from Dean and Bozzelli [START_REF] Dean | Combustion Chemistry of Nitrogen[END_REF].

 Radical Intramolecular Isomerizations (Reactions (45)-(81)) and Decompositions of •OOQOOH Radicals into Branching Agents (Reactions (82)-(142))

According to Glaude et al. [START_REF] Glaude | [END_REF], the isomerization of each •OOQOOH radical and the decomposition of the obtained radicals to give hydroperoxide species are globalized into a single step. As in our previous work (26), the activation energy is set equal to the sum of the activation energy for H-abstraction from the substrate by analogous radicals and the strain energy of the cyclic transition state. The activation energy for abstracting an H-atom from the atom of carbon located in α-position from the ester function has been taken equal to that for the abstraction of a tertiary H-atom in an alkyl radical. The strain energy of the cyclic transition state including seven members among which three oxygen atoms has been increased of about 3 kcal/mol compared to that with only two oxygen atoms.

 Decompositions of Radicals by β-Scission (Reactions (143)-(227)) and Decompositions of R•CO Radicals (Reactions (228)-(231))

The presence of oxygen atoms in the involved radicals can have a significant impact on the values of the activation energies of the decomposition by β-scission. Quantum calculations were performed for model reactions at the CBS-QB3 level of theory using Gaussian03 [START_REF] Frisch | Gaussian03, revision B05[END_REF] to estimate these data with a given accuracy of ± 1 kcal/mol. Intrinsic reaction coordinate (IRC) calculations have been systematically performed at the B3LYP 6-31G(d) level of theory on transition states, to ensure that they are correctly connected to the desired reactants and products. Table V displays the values that have been used for the activation energies of the decompositions of oxygenated radicals by β-scission. The kinetic data for the decompositions of R•CO radicals have been taken equal to the values proposed by Baulch et al. [START_REF] Baulch | [END_REF] for the decomposition of CH• 3 CO radicals. Table V. Activation Energies (kcal/mol) Used for the Decompositions by β-Scission of Oxygenated Radicals Involved in the Oxidation of Methyl and Ethyl Esters.

Types of Reaction

E a R/C(//O)/O • → R • + CO 2 a 5.1 R/C(//O)/O/CH • 2 → R/C • //O + CH 2 //O a 31.9 R/CH • /C(//O)/O/CH 3 → R/CH//C//O + CH 3 O •b,c 49.0 R/CH • /CH 2 /C(//O)/O/CH 3 → R/CH//CH 2 + CH 3 O/C • //O b,c 30.7 R/CH 2 /C • //O → R • + CH 2 //C//O d 39.9 R/CH • /CH 2 /C(//O)/O/CH 3 → H • + R/CH//CH/C(//O)/O/CH 3 b,c 34.9 R/C(//O)/O/CH 2 /CH • 2 → R/C(//O)/O • + C 2 H 4 a
25.1 a The calculation was performed for R • = CH • 3 . b,c The calculation was performed for R • = H • . c The same value is used in the case of ethyl esters. d The calculation was performed for R

• = C 2 H • 5 .
 Formation of Cyclic Ethers (Reactions ( 232)-( 249))

The different obtained cyclic ethers are lumped according to the size of the included ring. As illustrated by Figure 8, two types of ethers can be obtained according to the presence or not of the ester function inside the ring. However the kinetic data have directly been derived from those proposed by Buda et al. (29) for the formation of cyclic ethers in the mechanism of the oxidation of alkanes.

Figure 8. Examples of cyclic ethers that can be obtained from methyl butanoate.

The Mechanism of the Oxidation of Ethyl Butanoate

The primary and secondary mechanisms for the oxidation of ethyl butanoate have been generated using rules very similar to those described in the case of methyl butanoate. However, since this mechanism can only be validated by modeling shock tube data, only high-temperature reactions have been considered. The activation energies used for the decompositions by β-scission of oxygenated radicals have also been taken from Table V.

The only significant differences with the mechanism of methyl butanoate is the inclusion of the molecular elimination leading to the formation of ethylene and butanoic acid from ethyl butanoate and of the secondary reactions of butanoic acid, for which new rules of generation have to be considered.

O O O O O O C 5 H 8 O 3 ES#5 C 5 H 8 O 3 E#3S O O O
This molecular elimination is favored since it occurs through a transition state including a six-membered ring as shown in Figure 9. Molecular eliminations from methyl esters and other channels from ethyl esters can also be envisaged, but theoretical calculations by El-Nahas et al. (37) have shown them to be negligible due to higher energy barriers. The most investigated reaction between the molecular eliminations from ethyl esters giving ethylene and organic acids is that involving ethyl acetate. First kinetic measurements about this reaction in a flow system (42) have led to a A-factor of 3.2×10 12 s -1 with an activation energy of 47.8 kcal/mol. These values are in good agreement with more recent ones measured in a shock tube (43) (A = 10 12 s -1 and Ea = 47.7 kcal/mol) and with the A-factor estimated by Benson (33) (A = 6.2×10 12 s -1 at 700 K). Fewer values have been proposed for heavier ethyl esters. Barnard et al. 44 have measured for ethyl propanoate an A-factor of 5 × 10 12 s -1 with an activation energy of 48.5 kcal/mol, whereas the calculations of El-Nahas et al. (37) led to an activation energy of 50 kcal/mol. Finally, Kairaitis and Stimson (45) have measured for ethyl butanoate a A-factor of 2 × 10 12 s -1 with an activation energy of 47.3 kcal/mol, which are the values that we have used in the present mechanism since they are in agreement with the average rate parameters for this type of reaction. As it will be shown further in the text, the formation of butanoic acid is the main channel consuming ethyl butanoate under the conditions of our shock tube study. To be more accurate for modeling its reactivity, the secondary reactions of this oxygenated species have been generated as if it was an initial reactant: i.e., a comprehensive primary mechanism and a globalized secondary one have been written. The rules of generation of the primary mechanism for the high-temperature oxidation of carboxylic acids are the same as in the case of esters. Only the rate constants used for the abstraction of the H-atom linked to an O-atom by bimolecular oxidation and metatheses have been taken equal to those proposed for a tertiary alkylic H-atom (29). The unimolecular initiation involving the breaking of the O-H bond has been taken into account. The primary reactions of butanoic acid lead to the formation of unsaturated acids, butenoic acids, globalized into one single species (C 4 H 6 O 2 ZB), which can react by H-abstractions with small radicals R• (•H, •OH, •HO 2 , •CH 3 , •CH 3 OO, and •C 2 H 5 ) to give RH, CO 2 , and allyl radicals.

Comparison between Experimental and Computed Results

Simulations were performed using SENKIN and PSR softwares of CHEMKIN II (34) using the mechanisms previously described, which are available as supplementary material. The mechanism for the oxidation of methyl butanoate (C 5 H 10 O 2 S-1) involves 203 species and globally contains 1317 reactions (462 reactions are in the reactions bases, 334 in the primary mechanism and 521 in the secondary mechanism). That for the oxidation of ethyl butanoate (C 6 H 12 O 2 S-1) and butanoic acid ( mechanism and 378 in the secondary mechanism). While two organic reactants have been considered, the number of reactions in this second mechanism is smaller because only high-temperature reactions are considered. Simulated ignition delay times have been taken as the time at 10% of the maximum concentration of excited OH* radicals using the mechanism for excited species developed by Hall et al. (46).

 Autoignition and Oxidation of Methyl Butanoate

Figure 2 shows that the agreement between experimental and simulated ignition delay times of methyl butanoate is satisfactory. Figure 10 shows that our model can also correctly predict the experimental results previously obtained both by Metcalfe et al. (10) and by Walton et al. (13) (within a factor less than 2). Figures 567present a comparison between our experimental results and simulations in the case of the oxidation of methyl butanoate in a jet-stirred reactor. While the consumption of oxygen is well reproduced, that of methyl butanoate is overestimated. The formation of methyl acrylate, methyl crotonate, and methane is for the most part correctly modeled, but the agreement deteriorates for other products. While the production of carbon oxides is considerably overestimated in most cases, that of ethylene is underestimated. 12) considered only high-temperature reactions and the reactions of methyl butanoate alkyl radicals with O 2 and RO 2 radicals. All the four models sensibly overestimate the consumption of methyl butanoate (Figure 3a), especially for the short residence times, and underestimate the production of ethylene (Figure 3c). The underestimation of ethylene is of a factor up to 8 for the models of Fisher et al. (7) and Gaïl et al. (9), while it is only up to 3 for the present model and that of Dooley et al. 12. The production of carbon oxides (Figure 3b) and methane (Figure 3c) are captured by the four models within a factor better than 1.5. The present model and that of Dooley et al. (12) reproduces the best the time profile of methyl acrylate (Figure 3a), which is overestimated by a factor above 2 for the two other models. That is certainly due to the fact that the more recent models better consider the reactions of unsaturated esters.

 Autoignition of Ethyl Butanoate

Figure 3 shows that the agreement between experimental and simulated ignition delay times of ethyl butanoate is correct, apart from the least diluted mixtures in the upper part of the temperature range studied. While the agreement is slightly worse for ethyl butanoate than for methyl butanoate, Figure 4 shows that the increasing difference of reactivity between both esters when temperature increases, which is experimentally observed, is modeled. However, the simulated difference of reactivity is less marked than the experimental behavior.

Discussion

Autoignition in a Shock Tube

Figure 12 displays a reaction flux analysis performed for both esters under the conditions of Figure 2, at 1370 K, the lowest temperature studied, for an equivalence ratio of 1 and for 50% conversion of ester. Figure 13 displays a sensitivity analysis showing the relative change in ignition delay times obtained when multiplying by 10 the rate constant of the main reactions consuming methyl butanoate, ethyl butanoate, and butanoic acid (a negative value means that the ignition delay time calculated with the change in rate constant is shorter). Figure 14 presents the computed temporal evolution of the initial organic reactant, the main products and •OH radicals. Figures 13 and14 have been obtained for both esters and under the same conditions as in Figure 12. Under the conditions of Figure 12, methyl butanoate is mainly consumed by H-abstractions by hydrogen atoms and hydroxyl radicals, which accounts for globally 75% of the ester consumption. As the abstraction of an H-atom from the atom of carbon located in α-position from the ester function has been considered as the easiest, the main radicals obtained by H-abstractions are R MB -1 radicals (34% of the ester consumption) that decompose to give methyl radicals and methyl acrylate. Methyl acrylate (see Figure 14a) is the major C 2+ -oxygenated product obtained during the autoignition of methyl butanoate. The three other isomer radicals are obtained in similar amounts. R MB -2 radicals decompose to give formaldehyde and smaller radicals that ultimately lead to ethylene, carbon monoxide, and methyl radicals. Ethylene (see Figure 14a) is the major intermediate product obtained from methyl butanoate. R MB -3 radicals can either produce methyl crotonate and H-atoms or propene and radicals the decomposition of which lead to carbon dioxide and methyl radicals. Methyl crotonate (see Figure 14a) is the second main C 2+ -oxygenated product obtained during the autoignition of methyl butanoate, but it is formed in lower amounts than methyl acrylate. As shown in Figure 14a, carbon dioxide is both formed during induction time before the autoignition, and as a final product during the autoignition of methyl butanoate. R MB -4 radicals yield ethylene and R MB -5 radicals, which can isomerize, decompose, and ultimately lead to formaldehyde, carbon monoxide, and methyl radicals.

(a) (b) R MB -2 R MB -3 R MB -4 R MB -6 R MB -5 R EB -1 R EB -3 R EB -5 R EB -4 R EB -2 O O + CH 3 + CH 3 2 C 2 H 4 + CO 2 + CH 3 OH O + CH 3 + CH 3
The second type of reactions consuming methyl butanoate is unimolecular decompositions. There are two important channels with close reaction flux and accounting for globally 25% of the ester consumption. The first one requires to break a C-C bond and leads to ethyl and R MB -5 radicals (15% of the ester consumption). The decomposition of ethyl radicals leads almost only to ethylene and H-atoms. The second one involves the breaking of a C-O bond and yields methyl and R MB -6 radicals, the decomposition of which is a source of carbon dioxide, ethylene and methyl radicals.

As shown in Figure 13, unimolecular decompositions of methyl butanoate to give R MB -5 and ethyl radicals or R MB -6 and methyl radicals have a large promoting effect as an increase of their rate constants noticeably decreases ignition delay times. This promoting effect is slightly larger in the case of the formation of R MB -5 and ethyl radicals, as the decomposition of these last radicals is a source of the branching agents, H-atoms. Since the four H-abstraction channels compete with unimolecular decompositions for the ester consumption, they have a retarding effect. The important inhibiting effect of the formation of R MB -3 radicals, the decomposition of which is a source of H-atoms, is certainly due to the fact that these radicals also produce unsaturated species, such as propene and methyl crotonate, which can lead by H-abstractions to resonance stabilized radicals. On the contrary, the formation of R MB -2 and R MB -4 radicals, which are a source of formaldehyde, which leads to •HCO radicals and then to H-atoms, has lower inhibiting effects.

The ways of consumption of ethyl butanoate are very different from those of methyl butanoate as it is mainly consumed by a molecular reaction to give butanoic acid (75% of its consumption), which is the major C 2+ -oxygenated product obtained (see Figure 14b). As shown in Figure 14b, the formation of ethylene is twice during the oxidation of the ethyl ester (a maximum mole fraction of 6×10 -3 ) than during that of the methyl ester (a maximum mole fraction of 3.5×10 -3 ). The importance of this channel decreases when temperature increases, e.g., it accounts for only 40% of the ester consumption at ϕ = 1 and T = 1635 K, at 50% ester conversion. It slightly increases when equivalence ratio increases, as it represents 78% of the ester consumption at ϕ = 2 and T = 1370 K, at 50% ester conversion. It can be observed in Figure 14b that contrary to the case of methyl butanoate, the ignition of ethyl butanoate does not occur at the end of the consumption of ester, but when butanoic acid is completely consumed.

Minor channels involve H-abstractions (22% of the ester consumption) by hydrogen atoms and hydroxyl radicals to give mainly R EB -1 radicals and unimolecular decomposition (3% of the ester consumption). R EB -1 radicals mainly isomerize to produce radicals that decompose to ethylene and radicals that in turn decompose to carbon dioxide and propyl radicals. These last radicals yield ethylene and methyl radicals. A small part of R EB -1 radicals directly decomposes to give methyl radicals and ethyl acrylate, the second main C 2+ -oxygenated product obtained from ethyl butanoate (see Figure 14b).

Butanoic acid is mainly consumed by H-abstractions (56% of its consumption) and yields mainly R EB -2 radicals and to a lower extent R EB -3, R EB -4, and R EB -5 radicals. R EB -2 radicals are decomposed to give methyl radicals and acrylic acid, another very minor C 2+ -oxygenated product obtained from ethyl butanoate. R EB -3 radicals decompose to produce carbon dioxide and propyl radicals, a source of ethylene and methyl radicals. The decomposition of REB-4 radicals leads to propene and radicals, the decomposition of which gives carbon monoxide and hydroxyl radicals. Finally, the breaking of a C-C bond in R EB -5 radicals produces ethylene and radicals, the decomposition of which yields carbon dioxide and methyl radicals. As in the case of methyl butanoate, carbon dioxide is both formed during the induction time and as a final product of the autoignition of ethyl butanoate (see Figure 14b). Unimolecular initiations, which lead to ethyl radicals, a source of H-atoms, and radicals the decomposition of which produces methyl radical and carbon dioxide, are responsible for 32% of the consumption of butanoic acid. The unimolecular initiation yielding ethyl radicals is made easier in the acid due to a lower activation energy (78.9 kcal/mol) compared to those for the ethyl (81.2 kcal/mol) and methyl (81.7 kcal/mol) esters and also to a larger A-factor in the case of the acid. As shown in Figure 13b, this reaction has a large promoting effect, whereas the concurrent H-abstraction have an inhibiting one.

The fact that about 24% of the consumption of ethyl butanoate leads to unimolecular initiations involving the production of branching agents, H-atoms, while it is only the case for 15% from methyl butanoate certainly explains the higher reactivity observed for the ethyl ester. The fact that the importance of unimolecular initiations increases with temperature explains that the higher the temperature, the larger this difference is.

Oxidation in a Jet-Stirred Reactor

The large overestimation of the reactivity (Figure 5) and the underestimation of the formation of ethylene (Figure 7) are all the more surprising since the jet-stirred reactor has been used under conditions for which it has been proved to have a very good mixing (21) and with a temperature gradient inside the vessel below 5 K. These discrepancies could be due to possible molecular decomposition paths of the fuel, which are not taken in account in the model and which could compete with more reactive radical consumption routes. El-Nahas et al. (37) performed ab initio calculations to investigate the possible molecular decomposition paths of methyl butanoate. To explain the formation of ethylene, which is underpredicted by our model, we tried to include these new reactions but with almost no effect on both the reactivity and the ethylene formation in our conditions. The easiest pericyclic elimination involved an activation energy of 68 kcal mol -1 and has no influence on our calculations. The study of the thermal decomposition of methyl butanoate would help to better understand the specific molecular decomposition chemistry of this kind of species. Dooley et al. (12) investigated the possible heterogeneous wall-catalyzed decomposition of methyl butanoate in order to reproduce the formation of methanol. The inclusion of this reaction in their model induced higher concentrations of methanol but also higher conversions of the fuel. In our case, all models predict higher conversions, which could also be explained by a wall-catalyzed paths forming unreactive species.

The overestimation of the reactivity is responsible for the displacement toward the smallest residence times and the larger magnitude of the maximum in the profiles of methyl crotonate and methyl acrylate. However, the ratio between the mole fractions of these two compounds is correctly predicted by our model.

Figure 15 displays a reaction flux analysis performed for methyl butanoate under the conditions of Figure 5, at 800 K, the lowest temperature studied, and for a residence time of 1.9 s corresponding to a 50% conversion of ester. Note that our model is too reactive compared to the experiments and some consumption routes are likely more important than they are in the reality due to this to high reactivity (e.g., low-temperature reactions). radicals and methyl acrylate and their addition to oxygen molecules to form peroxy radicals. Subsequent isomerizations and decomposition from these peroxy radicals lead to hydroxyl radicals and a C 5 methyl ester including an oxirane. The important flux of formation of methyl crotonate by oxidation explains the more important prediction by the model compared to that of methyl acrylate.

The second most abundant radicals obtained are R MB -2 radicals (17% of the ester consumption), which react mainly by addition to oxygen molecules to give after isomerization hydroxyl radicals and a C 5 methyl ester including a pyran. The formation of R MB -3 radicals accounts for 16% of the ester consumption. These radicals also react mainly by addition to oxygen molecules to give after isomerization hydroxyl radicals and a C 5 methyl ester including an oxirane. A smaller channel involves their reaction with oxygen molecules to give methyl crotonate. The last radicals, R MB -4 radicals, which derive from the abstraction of a primary H-atom (8% of the ester consumption), are consumed by addition to oxygen molecules followed by isomerizations and decomposition to give hydroxyl radicals and a C 5 methyl ester including an oxetane. The formation of methyl esters including a cyclic ether has not been experimentally observed in the present study, whereas such compounds with a fivemembered ring have been analyzed in a recent study of the oxidation of methyl palmitate, a large ester showing reactivity in the low-temperature region, performed at similar conditions with the same experimental facility (47).

While Figure 15 shows that the reactions of additions to oxygen molecules and the derived channels (low-temperature reactions) have an important influence on the formation of products, Figure 5a shows that simulations using a mechanism in which these reactions have been removed lead to a small decrease of the reactivity at 800 K compared to the full mechanism. This influence is much lower at 850 K.

Conclusion

This paper presents new measurements concerning ignition delay times of methyl and ethyl butanoate in a shock tube behind reflected shock wave between 1130 and 1620 K and about the oxidation of methyl butanoate in a jet-stirred reactor at 800 and 850 K, as well as a detailed kinetic model allowing us to correctly reproduce these results under most studied conditions.

Shock tube experiments showed that ethyl butanoate is slightly more reactive than methyl butanoate. Reaction flux and sensitivity analyses let us think that this difference of reactivity would be due to easier unimolecular initiations involving the production of branching agents, H-atoms, in the case of the ethyl ester. The ways of consumption of both esters are very different due to the considerable importance of the molecular reaction yielding ethylene and butanoic acid in the case of ethyl butanoate. This molecular reaction makes ethyl esters a potential important source of carboxylic acid, which could contribute to the acidity of gas and aqueous phases of the atmosphere, and would most certainly exclude this type of molecules from the list of advisable fuel components.

Jet-stirred experiments have shown that the major C 2+ -oxygenated products obtained during the oxidation of methyl butanoate are methyl crotonate and methyl acrylate. While simulations for shock tube conditions predict larger amounts of methyl acrylate compared to those of methyl crotonate, simulations for the jet-stirred reactor shows larger amounts of the C 5 unsaturated methyl ester.

Simulations of the oxidation at 800 K show also the possible formation of C 5 molecules involving three oxygen atoms in both ester and cyclic ether functions. Our model, as well as those in the literature, cannot correctly reproduce the conversion of methyl butanoate and the formation of ethylene observed in the jet-stirred reactor; this discrepancy can either be due to wall-catalyzed paths forming unreactive species or to misunderstood channels important for the chemistry of the oxidation of methyl butanoate under the studied range of temperatures. More studies in the same range of temperature but using a different type of reactor or of diagnostic should allow us to better understand this discrepancy.

Figure 1 .

 1 Figure 1. Typical experimental profiles of pressure and OH* emission in the case of ethyl butanoate.

Figure 6

 6 Figure 6. Time evolution profiles for the consumption of oxygen and the formation of carbon oxides measured during the oxidation of methyl butanoate in a jet-stirred reactor at 800 K for an equivalence ratio of 0.5 and at 850 K for an equivalence ratio of 1. Points correspond to experimental results and lines to simulations.

  C(=O)OCH 3 = CH 3 CH(OOH)CH 2 C(=O)

bNotes:

  For molecules, the letters in italics indicate the chemical functions carried by the molecule. c A aldehyde function (-CH=O) d E ether function (-O-) e K ketone function (-C(=O)-) f L alcohol function (-O-H) g P hydroperoxide function (-O-O-H) h S ester function (-CO-O-CH 3 ) i U peroxy function (-O-O-) j Z unsaturation (C=C) k #x cyclic molecule with a cycle containing x atoms l Owing to the lumping of the products, several reactions are written in duplicate with different rate parameters as they correspond to distinct channels. For studies at temperature below 1000 K, it is necessary to also consider low-temperature reactions:  additions of alkyl and hydroperoxyalkyl (•QOOH) radicals to an oxygen molecule,  isomerizations of alkylperoxy and hydroperoxyalkylperoxy radicals (ROO• and •OOQOOH) involving a cyclic transition state and the transfer of an H-atom,  decompositions of hydroperoxyalkyl and dihydroperoxyalkyl •U(OOH) 2 radicals to form cyclic ethers and •OH radicals, and  disproportionations of alkylperoxy radicals with •HO 2 to produce hydroperoxides and O 2 .

Figure 9 .

 9 Figure 9. Molecular elimination from ethyl butanoate.

  C 4 H 8 O 2 B-1) involves 115 species and globally includes 1011 reactions (171 reactions in the primary

Figure 10 .

 10 Figure 10. Comparison of model predictions (lines) using the present model with the experimental results (points) of Metcalfe et al. (10) for stoichiometric mixtures at 1 and 4 bar and of Walton et al. (13) for an equivalence ratio of 0.4 at 10 bar.

Figure 11

 11 Figure11presents a comparison between our experimental data at 850 K and modeling results computed using the present model but also those of Fischer et al.(7), Gaïl et al.(9), and Dooley et al.(12). Models developed by Fischer et al.(7) and by Gaïl et al. (9) contain both low-and high-temperature reactions, whereas Dooley et al.(12) considered only high-temperature reactions and the reactions of methyl butanoate alkyl radicals with O 2 and RO 2 radicals. All the four models sensibly overestimate the consumption of methyl butanoate (Figure3a), especially for the short residence times, and underestimate the production of ethylene (Figure3c). The underestimation of ethylene is of a factor up to 8 for the models of Fisher et al.(7) and Gaïl et al.(9), while it is only up to 3 for the present model and that of Dooley et al. 12. The production of carbon oxides (Figure3b) and

= 1 ,

 1 P= 1 atm[10] = 1, P= 4 atm[10] = 0.4, P= 10 atm[13]

Figure 11 .

 11 Figure 11. Comparison between the experimental results obtained in a jet-stirred reactor under the conditions of Figure 5 at 850 K and values computed using the model described in this paper and the mechanisms of Fischer et al. (7) (broken lines), Gaïl et al. (9) (dotted lines), and Dooley et al. (12) (mixed lines).

  et al.[9] Model from Fischer et al.[7] Model from Dooley et al.[12]

Figure 12 .

 12 Figure 12. Reaction flux analysis performed under the conditions of Figure 2 at 1370 K for an equivalence ratio of 1 and for 50% conversion of ester in the case of (a) methyl butanoate and (b) ethyl butanoate. The size of the arrows is proportional to the relative flux. The channels involving a consumption of the esters below 5% are not shown. Dotted arrows represent several successive elementary reactions.

Figure 13 .

 13 Figure 13. Sensitivity analysis showing the relative changes obtained when multiplying by 10 the rate constant of the main reactions consuming (a) methyl butanoate (MB) and (b) methyl ethanoate (EB) and butanoic acid (AB). R represents the radicals involved in H-abstractions. R MB -x and R EB -y refer to the radicals shown in Figure 12.

Figure 14 .

 14 Figure 14. Temporal evolution of the initial ester, the main products, and •OH radicals under the same conditions as in Figure12in the case of (a) methyl butanoate and (b) ethyl butanoate.

Figure 15 .

 15 Figure 15. Reaction flux analysis performed under the conditions of Figure5at 800 K and for a residence time of 1.9 s corresponding to 50% conversion of methyl butanoate. The size of the arrows is proportional to the relative flux. The channels involving a consumption of the esters below 5% are not shown. Dotted arrows represent several successive elementary reactions.

Table 1 .

 1 However we present here a few points with ignition delay times shorter than 10 μs and then with a larger uncertainty. Mixture Compositions, Shock Conditions, and Ignition Delay Times for Methyl Butanoate.

		
	1-Incident wave
	2-Reflected wave
	3-OH peak
		
		τ

MB = 0.5%; X 02 = 13%; X Ar = 86.5% ϕ = 2; X MB = 0.5%; X 02 = 1.625%; X Ar 97.875%

  1

Table II .

 II Mixture Compositions, Shock Conditions, and Ignition Delay Times for Ethyl Butanoate.

	P 1 (kPa)	P 5 (atm)	V (m/s) τ (μs)	T 5 (K)	P 1 (kPa)	P 5 (atm) V (m/s) τ (μs)	T 5 (K)
		ϕ = 1; X EB = 1%; X = 8%; X Ar = 91%		ϕ = 1; X EB = 0.5%; X 02 = 4%; X Ar = 95.5%
	27	8.2	321.5	1296	29.3	8.5	788	111.7	1385
	29.3	7.8	259	1301	27.9	8.2	790	97	1390
	28.6	8.9	311	1313	27.3	8.2	797	71.3	1411
	28	9.2	114	1352 a	26.6	8.3	807	37.8	1442
	25.3	8.3	84.3	1358	25.9	8.2	813	36.5	1459
	23.3	7.9	34.4	1378	24.6	7.9	815	25.5	1468
	24.6	8.4	56.4	1384	25.3	8.5	831	26.7	1516
	26	9	42.3	1401	22.6	7.8	835	15.5	1530
	24	8.5	15.2	1412	23.9	8.2	836	13.3	1533
	22.6	8.3	16.6	1443	23.3	8.2	843	12.4	1555
	23	8.7	11	1474	-	-	-	-	-
	ϕ = 1; X EB = 0.42%; X = 3.33%; X Ar = 96.25%	ϕ = 0.25; X EB = 0.5%; X 02 = 16%; X Ar = 83.5%
	9.6	8.5	1485	1307	29.9	8.7	783	188.6	1282
	2	8.7	123.4	1388	29.3	8.5	785	101.4	1288
	42.8	8.9	153.7	1393	28	8.4	794	106.7	1311
	2.2	9.2	191.1	1398	27.7	8.5	799	75.6	1325
	15.2	8.7	87.2	1429	27.4	8.7	810	36	1356
	12.6	8.4	59.4	1441	26.6	8.8	820	20.3	1386
	5.6	7.9	31.9	1475	23.4	7.8	821	13.2	1386
	4.6	8.4	23	1498	25.3	8.4	823	14.5	1393
	34.4	8.6	22.3	1505	24.6	8.5	833	11.4	1422
	11.2	8.1	10.7	1543	23.9	8.3	833	6.8	1423
	41.4	7.8	10	1562	22.6	8.1	842	5.3	1448
	7.5	8.1	5.5	1573	-	-	-	-	-
	15	8.6	9.8	1574	-	-	-	-	-
			ϕ = 2; X EB = 0.5%; X 02 = 2%; X Ar = 97.5%
	25.5	8.6	88.3	1532	21.3	7.9	859	47.1	1628
	24.4	8.4	58	1555	19.3	7.9	894	14.9	1743
	22.3	7.7	40.4	1563	16.6	7.3	914	10.8	1814
	22.3	7.8	65.5	1566	17.3	7.6	915	9.7	1816
	22.6	7.9	39.4	1569	16.4	7.6	935	6.6	1888
	23.3	8.1	47.3	1571	-	-	-	-	-
	a P 1

Table 3 .

 3 Experimental Results Obtained in a Jet-Stirred Reactor for Methyl Butanoate.

	Residence

Times (s) 1.5 3 4.5 6 7.5 9 Compounds Mole Fraction φ = 0.5; X MB = 2%; X 02 = 26%; X He = 72%; T = 800 K

									Residence Times (s)
			1.5		3			4.5			6			7.5			9
	Compounds								Mole Fraction
	CH 4	2.78 × 10 -3	2.87 × 10 -3	4.82 × 10 -3	4.75 × 10 -3	4.66 × 10 -3	5.01 × 10 -3	5.08 × 10 -3	5.20 × 10 -3	5.47 × 10 -3	5.56 × 10 -3	5.07 × 10 -3	5.33 × 10 -3	5.50 × 10 -3	5.21 × 10 -3	5.63 × 10 -3	5.75 × 10 -3	-
	C 2 H 2	2.49 × 10 -6	2.87 × 10 -6	9.76 × 10 -6	9.37 × 10 -6
	O 2	2.57 × 10 -1	2.55 × 10 -1	2.10 × 10 -1	2.09 × 10 -1	2.09 × 10 -1	1.94 × 10 -1	1.94 × 10 -1	1.95 × 10 -1	1.89 × 10 -1	1.88 × 10 -1	1.89 × 10 -1	1.87 × 10 -1	1.82 × 10 -1	1.83 × 10 -1	1.87 × 10 -1	1.83 × 10 -1	1.84 × 10 -1
	CO	1.39 × 10 -4	1.45 × 10 -4	4.59 × 10 -3	5.26 × 10 -3	5.38 × 10 -3	1.78 × 10 -2	1.66 × 10 -2	1.55 × 10 -2	2.43 × 10 -2	2.51 × 10 -2	2.43 × 10 -2	2.81 × 10 -2	2.99 × 10 -2	2.99 × 10 -2	3.65 × 10 -2	3.66 × 10 -2	3.53 × 10 -2
	CO 2	-	2.92 × 10 -4	5.02 × 10 -4	1.50 × 10 -3	1.81 × 10 -3	3.54 × 10 -3	4.61 × 10 -3	2.97 × 10 -3	5.59 × 10 -3	6.02 × 10 -3	5.51 × 10 -3	6.95 × 10 -3	7.65 × 10 -3	6.96 × 10 -3	1.14 × 10 -2	1.04 × 10 -2	9.28 × 10 -3
	CH 4	6.50 × 10 -5	6.41 × 10 -5	6.15 × 10 -4	6.70 × 10 -4	7.01 × 10 -4	1.57 × 10 -3	1.55 × 10 -3	1.40 × 10 -3	1.95 × 10 -3	2.03 × 10 -3	1.99 × 10 -3	2.05 × 10 -3	2.14 × 10 -3	2.11 × 10 -3	2.50 × 10 -3	2.44 × 10 -3	2.38 × 10 -3
	C 2 H 2	-	-	4.96 × 10 -7	6.71 × 10 -7	6.83 × 10 -7	3.31 × 10 -6	2.79 × 10 -6	3.45 × 10 -6	5.31 × 10 -6	5.00 × 10 -6	5.11 × 10 -6	6.02 × 10 -6	5.75 × 10 -6	6.17 × 10 -6	6.81 × 10 -6	6.56 × 10 -6	5.92 × 10 -6
	C 2 H 4	8.75 × 10 -5	8.09 × 10 -5	1.58 × 10 -3	1.71 × 10 -3	1.78 × 10 -3	3.53 × 10 -3	3.48 × 10 -3	3.20 × 10 -3	4.02 × 10 -3	4.13 × 10 -3	4.11 × 10 -3	4.02 × 10 -3	4.08 × 10 -3	4.02 × 10 -3	4.46 × 10 -3	4.36 × 10 -3	4.25 × 10 -3
	C 2 H 6	5.60 × 10 -7	7.81 × 10 -7	8.88 × 10 -6	1.04 × 10 -5	1.03 × 10 -5	2.05 × 10 -5	2.11 × 10 -5	1.82 × 10 -5	2.34 × 10 -5	2.44 × 10 -5	2.38 × 10 -5	2.18 × 10 -5	2.32 × 10 -5	2.25 × 10 -5	2.61 × 10 -5	2.44 × 10 -5	2.43 × 10 -5
	Methyl acrylate	7.66 × 10 -5	7.82 × 10 -5	8.67 × 10 -4	8.93 × 10 -4	9.12 × 10 -4	1.29 × 10 -3	1.30 × 10 -3	1.32 × 10 -3	1.31 × 10 -3	1.29 × 10 -3	1.30 × 10 -3	1.19 × 10 -3	1.18 × 10 -3	1.18 × 10 -3	1.19 × 10 -3	1.20 × 10 -3	1.09 × 10 -3
	Methyl crotonate	7.75 × 10 -5	7.61 × 10 -5	7.39 × 10 -4	7.68 × 10 -4	7.70 × 10 -4	8.81 × 10 -4	8.92 × 10 -4	9.03 × 10 -4	8.11 × 10 -4	7.87 × 10 -4	8.05 × 10 -4	7.10 × 10 -4	6.98 × 10 -4	7.23 × 10 -4	6.99 × 10 -4	7.03 × 10 -4	6.61 × 10 -4
	Methyl butanoate	1.94 × 10 -2	1.72 × 10 -2	1.50 × 10 -2	1.56 × 10 -2	1.51 × 10 -2	1.02 × 10 -2	1.04 × 10 -2	1.04 × 10 -2	8.14 × 10 -3	7.87 × 10 -3	8.06 × 10 -3	6.50 × 10 -3	6.42 × 10 -3	6.59 × 10 -3	5.83 × 10 -3	5.92 × 10 -3	5.56 × 10 -3
	φ = 1; X MB = 2%; X 02 = 13%; X He = 85%; T = 850 K
	O 2	9.77 × 10 -2	9.66 × 10 -2	8.41 × 10 -2	8.29 × 10 -2	8.84 × 10 -2	7.86 × 10 -2	7.37 × 10 -2	8.07 × 10 -2	7.51 × 10 -2	7.40 × 10 -2	8.50 × 10 -2	8.19 × 10 -2	8.51 × 10-2	7.24 × 10 -2	6.63 × 10 -2	6.20 × 10 -2	-
	CO	1.02 × 10 -2	1.09 × 10 -2	3.06 × 10 -2	2.92 × 10 -2	2.90 × 10 -2	3.64 × 10 -2	3.73 × 10 -2	3.78 × 10 -2	4.36 × 10 -2	4.06 × 10 -2	4.20 × 10 -2	4.09 × 10 -2	4.28 × 10 -2	4.45 × 10 -2	5.06 × 10 -2	5.11 × 10 -2	-
	CO 2	2.10 × 10 -3	2.19 × 10 -3	7.30 × 10 -3	8.41 × 10 -3	6.69 × 10 -3	1.07 × 10 -2	1.14 × 10 -2	1.01 × 10 -2	1.26 × 10 -2	1.18 × 10 -2	1.37 × 10 -2	1.21 × 10 -2	1.44 × 10 -2	1.39 × 10 -2	1.75 × 10 -2	1.99 × 10 -2	-

φ = 0.5; X MB = 2%; X 02 = 26%; X He = 72%; T = 800 K

  Methyl acrylate: C 4 H 6 O 2 ; methyl crotonate: C 5 H 8 O 2 ; methyl butanoate: C 5 H 10 O 2 . Each value in each column corresponds to a separate run.

																	1.32 × 10 -5	-
	C 2 H 4	4.27 × 10 -3	4.45 × 10 -3	7.77 × 10 -3	7.70 × 10 -3	7.66 × 10 -3	8.04 × 10 -3	7.99 × 10 -3	8.27 × 10 -3	8.44 × 10 -3	8.51 × 10 -3	7.93 × 10 -3	8.13 × 10 -3	8.42 × 10 -3	7.85 × 10 -3	8.31 × 10 -3	8.41 × 10 -3	-
	C 2 H 6	1.06 × 10 -4	1.44 × 10 -4	1.90 × 10 -4	1.90 × 10 -4	1.85 × 10 -4	1.76 × 10 -4	1.72 × 10 -4	1.80 × 10 -4	1.81 × 10 -4	1.90 × 10 -4	1.63 × 10 -4	1.75 × 10 -4	1.81 × 10 -4	1.60 × 10 -4	1.70 × 10 -4	1.76 × 10 -4	-
	Methyl acrylate	1.09 × 10 -3	1.07 × 10 -3	1.00 × 10 -3	1.09 × 10 -3	1.09 × 10 -3	8.05 × 10 -4	8.23 × 10 -4	-	7.23 × 10 -4	7.24 × 10 -4	7.37 × 10 -4	7.28 × 10 -4	7.18 × 10 -4	6.79 × 10 -4	4.92 × 10 -4	4.84 × 10 -4	3.85 × 10 -4
	Methyl crotonate	2.86 × 10 -4	2.75 × 10 -4	2.50 × 10 -4	2.50 × 10 -4	2.23 × 10 -4	1.71 × 10 -4	1.63 × 10 -4	1.45 × 10 -4	1.36 × 10 -4	1.40 × 10 -4	1.28 × 10 -4	1.42 × 10 -4	1.38 × 10 -4	1.34 × 10 -4	8.70 × 10 -5	8.51 × 10 -5	7.13 × 10 -5
	Methyl butanoate	1.12 × 10 -2	1.10 × 10 -2	6.53 × 10 -3	6.60 × 10 -3	5.86 × 10 -3	4.24 × 10 -3	4.13 × 10 -3	3.49 × 10 -3	3.47 × 10 -3	3.51 × 10 -3	3.56 × 10 -3	3.38 × 10 -3	3.32 × 10 -3	3.15 × 10 -3	2.06 × 10 -3	2.11 × 10 -3	1.74 × 10 -3

a Note:

Acknowledgements

This work has been supported by the "Région Lorraine" through the funding of the postdoc of M. Yahyaoui.


Christian Retoré

Type-theoretical natural language semantics: on the system F for meaning assembly

Roughly speaking, the compositional semantics analysis of natural language consists in mapping a sentence to a logical formula which depicts its meaning. To do so, a lexicon endow each word with a partial formula (a λ-term over the base type t for propositions and e for individuals), and the (binary) parse tree of the sentence specifies for each node which subtree is the function and which one is the argument. Hence a λ-term corresponding to the whole parse tree, and by reduction one obtains a λ-term of type t which corresponds to a formula of higher order logic. This classical process which uses Church's representation of formulae as simply typed λ-terms is the basis of the so-called Montague semantics, see e.g. [START_REF] Moot | The logic of categorial grammars: a deductive account of natural language syntax and semantics[END_REF]Chapter 3].

But it is more accurate to have many individual base types rather than just e. This way, the application of a predicate to an argument only happens when it makes sense. For instance sentences like "The chair barks." or "Their five is fast." are easily ruled out when there are several types for individuals by saying that "barks" and "fast" respectively require arguments of type "dog" and physical or animated object. Nevertheless, such a type system needs to incorporate some flexibility. Indeed, in the context of a football match, the second sentence makes sense, because "their five" may be understood as a player.

Accounts of these meaning transfers received a lot of attention since the 80's and some formal accounts were proposed in particular by Asher [START_REF] Asher | Lexical Meaning in context -a web of words[END_REF]. We also proposed an account using the system F of Girard (1971) [START_REF] Girard | The blind spot -lectures on logic[END_REF] and we studied the compositional properties of such a system in particular for quantifiers, plurals and generic elements, as well as the related lexical issues like meaning transfers, copredication, fictive motion,... see e.g. [START_REF] Bassac | Towards a Type-Theoretical Account of Lexical Semantics[END_REF][START_REF] Retoré | Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by "most[END_REF]. Our system works as follows: the lexicon provides each word with a main λ-term, the "usual one" which specifies the argument structure of the word, by using refined types (e.g. "sleeps: λx ani sleeps(x)" requires an animated subject). In addition, the lexicon may endow each word with a finite number of λ-terms (possibly none) that implement meaning transfers. For instance a "book" may be turned into a physical object φ or into an informational content I, by constants of respective types book → I and book → φ (sometimes the λ-terms are more complex than simple constants). That way a sentence like "This book is heavy but interesting." can be properly analysed. Some meaning transfers are declared to be rigid in the lexicon: rigidity prohibits the use of other meaning transfers thus we can block "* Liverpool defeated Chelsea and decided to build new docks." because the meaning transfer from a town to a football club is declared in the lexicon as rigid.

In such a setting it is very convenient to quantify over types, for instance quantifiers ∀, ∃ may be given a type Λα.(α →t)→ t It also allows a factorised treatment of conjunction: each time an object of type ξ can be viewed both as an object of type α (via an optional term f 0 : ξ → α) to which the property P applies and as an object of type β (via an optional term g 0 : ξ → β) to which the property Q applies, one can express that x enjoys P ∧ Q. This polymorphic "and" simply is: ΛαΛβλP α→t λQ β→t Λξλx ξ λf ξ→α λg ξ→β . (∧ t→t→t (P (f x))(Q (g x))). To sum up the logical system, we also have two layers but they slightly vary from the ones of Montague semantics. Our meta logic (a.k.a. glue logic) is system F with many base types t, e i (instead of simply typed λ-calculus with t, and e) Our logic for semantic representations is many-sorted higher-order logic (e i instead of a single sort e). For representing quantification, we actually prefer to use Hilbert's ǫ and τ -terms constructed with two constants ǫ, τ : Λα. (α → t) → α and one for generic elements [START_REF] Retoré | Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by "most[END_REF]. An important but rather easy property holds: if the constants define an n-order q-sorted logic, any (η-long) normal λ-term of type t does actually correspond to a formula of n-order q-sorted logic (possibly n = ω).

We preferred system F to modern type theories (MTT) used by Luo [START_REF] Luo | Contextual analysis of word meanings in type-theoretical semantics[END_REF] or to the categorical logic of Asher [START_REF] Asher | Lexical Meaning in context -a web of words[END_REF] because of its formal simplicity and absence of variants -as the terms are issued from the lexicon by means of syntactic rules, F terms with a problematic complexity are avoided. There are two properties of Luo's approach [START_REF] Luo | Contextual analysis of word meanings in type-theoretical semantics[END_REF] that would be welcome: a proper notion of subtyping, mathematically safe and linguistically relevant, and predefined inductive types with specific reduction rules. Subtyping is most welcome in particular to represent ontological inclusion (a "human being" is an "animal", thus predicates that apply to "animals" also apply to "human beings"). Coercive subtyping as developed by Luo and Soloviev [START_REF] Soloviev | Coercion completion and conservativity in coercive subtyping[END_REF] sounds promising for F (and other notions as well [START_REF] Longo | Coherence and transitivity of subtyping as entailment[END_REF]). The key property of coercive subtyping is that there is at most one subtyping map between any two complex types, provided that there is at most one subtyping map between any two base types. Predefined types, inductive types would be most welcome in our setting, e.g. integers as in Gödel's system T and finite sets of α-objects. Of course, F can encode such types, but such encodings are far from natural. Reduction in such a setting is related to the work of Soloviev and Chemouil [START_REF] Soloviev | Some Algebraic Structures in Lambda-Calculus with Inductive Types[END_REF] The key point is to show that normalisation and confluence are preserved and that there is no constant-free and closed term of a false type. We shall also illustrate the linguistic relevance of these extensions, which are already included in Moot's semantical and semantical parser for French. [START_REF] Moot | Wide-coverage French syntax and semantics using Grail[END_REF]

Funded by ANR projects Loci and Polymnie.


Jérémie Stagnara

Francine Garnache Ottou

Fanny Angelot

Guillaume Mourey

Estelle Seilles

Sabéha Biichlé

Philippe Saas

Evelyne Racadot

Correlation between platelet-derived microparticle

enumeration by flow cytometry and phospholipid-dependent procoagulant activity in microparticles: the centrifugation step matters!

Correlation between platelet-derived microparticle enumeration by flow cytometry and phospholipid-dependent procoagulant activity in microparticles: the centrifugation step matters! J r mie Stagnara

, Evelyne Racadot

Dear Sirs

The interest in circulating microparticles (MP) shown by the scientific community is increasing. These MP emitted from membranes by activated or apoptotic blood cells have been considered for a long time merely as cell debris without biological activities. However, " "

MP are now considered as critical effectors involved in numerous biological processes (e.g., coagulation, angiogenesis, immunomodulation) (1 5).

-Two major complementary approaches on the boundary between cellular hematology and haemostasis are used to monitor circulating MP in clinical settings: a quantitative and descriptive approach which uses flow cytometry and a qualitative/function alone assessing MP biological activities, involving phospholipid-dependent procoagulant activities in MP. This is explored using haemostasis techniques such as fluorometry or chronometry. Few studies have compared both approaches [START_REF] Connor | The majority of circulating platelet-derived microparticles fail to bind annexin V, lack phospholipid-dependent procoagulant activity and demonstrate greater expression of glycoprotein Ib[END_REF]. Here, we report a correlation between platelet-derived

MP (PMP) enumeration by cytometry and assessment of their procoagulant activity by fluorometry (thrombin generation TG

[ ] measurement) and chronometry assays (factor X FX activity). Two different centrifugation protocols were compared.

[ ]

The study population consists of 40 platelet donors. Samples were taken at the French Blood Agency (EFS Bourgogne-Franche-Comté , Besan on, France) after signature of the informed consent (Approval from the local research ethics committee, CCP Est II, Besan on).

ç ç

After a venepuncture without a tourniquet as proposed [START_REF] Yuana | Pre-analytical and analytical issues in the analysis of blood microparticles[END_REF], samples were collected after the elimination of the first millimeters, which are rich in tissue factor (TF) [START_REF] Yuana | Pre-analytical and analytical issues in the analysis of blood microparticles[END_REF], in Vacutainer tubes (Becton-Dickinson, Le Pont de Claix, France) containing Citrate-Theophylline-Adenosine-Dipyridamole (CTAD) anticoagulant, in order to limit platelet activation [START_REF] Yuana | Pre-analytical and analytical issues in the analysis of blood microparticles[END_REF] and therefore the in vitro non-specific MP production. Samples were centrifuged (less than an hour after venepuncture). The 40 samples were centrifuged in order to obtain platelet-poor plasma (PPP) with the following centrifugation protocol: 1500 for 15 minutes, decantation and then 13000 for the two centrifugation protocols (number of platelets before centrifugation: 121 000 to 234 000/ L; number of platelets obtained after μ centrifugation: 6 32/ L using protocol 1 6 21/ L using protocol 2). All the samples were frozen and stored at 80 C in 1.5ml

- μ # vs - μ # - °polypropylene
microtubes (TreffLab, Degersheim Switzerland) and thawed quickly at 37 C for 5 minutes before analysis.

°The later generation NAVIOS cytometer (Beckman Coulter, Miami, FL) was used together with Megamix beads (Biocytex, ™ Marseille, France) to define a standard-sized area and Flow-Set fluorosphere beads (Beckmann Coulter) to enumerate PMP as we ™ previously described [START_REF] Pelletier | Increased levels of circulating endothelial-derived microparticles and small-size platelet-derived microparticles in psoriasis[END_REF]. Inter-, intra-assay coefficient of variations (CV), lower limits of detection and raw cytometry data are given in [START_REF] Pelletier | Increased levels of circulating endothelial-derived microparticles and small-size platelet-derived microparticles in psoriasis[END_REF] for protocol 1. To compare the data obtained by cytometry with haemostasis techniques, PMP were assessed by triple staining using # Annexin V (a phosphatidylserine ligand) and two monoclonal antibodies directed against platelets (CD31 and CD41). We assessed externalized phosphatidylserines in PMP, since phospholipid-dependent procoagulant activitiesare limited to the PMP subsets exposing phosphatidylserines [START_REF] Connor | The majority of circulating platelet-derived microparticles fail to bind annexin V, lack phospholipid-dependent procoagulant activity and demonstrate greater expression of glycoprotein Ib[END_REF].

Thrombin generation (TG) was measured by means of Calibrated Automated Thrombography (CAT, chronometric method) (Diagnostica Stago, Asni res-sur-Seine, France) using the platelet-rich plasma (PRP) Reagent (containing only of 1 pMTF). The aim of è this reagent is to assess procoagulant phospholipid-dependent activities of MP and the thrombin peak (assessed by C parameter) is the max critical parameter.

The chronometric method used was the STA Procoag PPL (Diagnostica Stago) performed on the STA-Revolution (STA-R )

® ® ®
instrument (Diagnostica Stago). This method explores phospholipid-dependent procoagulant activity component of MP and is not sensitive to the TF [START_REF] Connor | Detection of the procoagulant activity of microparticle-associated phosphatidylserine using XACT[END_REF]. After an incubation (120 seconds,37 C) of PPP with a reagent consisting of procoagulant phospholipid-depleted human °plasma, activated FX and calcium were added and clotting time was measured using the STA-R instrument.

®

Correlation analyses were performed by Spearman s rank correlation analysis. The inter-technique correlation curves obtained are

'
shown in Figure 1.The strong correlations obtained between the 3 techniques demonstrate that with a good control of the pre-analytic variables, MP monitoring can be evaluated by two different approaches. An increase in the PMP numbers quantified by cytometry demonstrates an increase in procoagulant activity measured by haemostasis techniques (characterized by an increase in the C of TG max measurement and by shortening clotting time measured using the STA Procoag PPL method).

® Furthermore, we observed that with a more intense centrifugation protocol (protocol 2), the number and procoagulant activity of the # PMPs were reduced and that for lower values (< 2000 MP/ l, clotting time > 70 sec, C < 60 nM) correlations between techniques were μ max not as good (Figure 1B). Today, we cannot explain such observation. The advantages of cytometry are the detection of lineage markers which are useful in determining the cellular origin of MPs, but the complexity in detecting MPs < 0.5 m in a standardized manner is μ currently its main limitation. The advantages of haemostasis techniques are their low cost and the fact that they can be carried out quickly, and therefore easy to perform in routine practice. These techniques assess a functional parameter and do not rely on size determination, unlike cytometry.

In conclusion, a statistically significant correlation exists between the three approaches used to analyze phospholipid-dependent procoagulant activities in MPs by two distinct haemostasis methods and enumeration of circulating PMP expressing phosphatidylserines.

Each method exhibits advantages and restrictions. One may suggest that the most automated method ( , the STA Procoag PPL ) can be i.e.

® used as first-line method to monitor MP. Moreover, our data support that the less intense centrifugation protocol (protocol 1) gives a # better correlation between the different methods. Further studies are urgently needed to confirm these observations.

Acknowledgements:

This work is supported by a grant from the Etablissement Fran ais du Sang (French Blood Agency depending from the French Ministry of ç Health, APR 2011, grant 2011-11 to PS).

#

We would like to thank Frances Mary Sheppard and Sarah Odrion for editorial assistance.

Footnotes:

: The authors reported no potential conflicts of interest.

2 g g minutes (centrifugation protocol 1 ,#

 1 Ref.8). The last 20 samples collected were also centrifuged at the same time with the following # protocol: 2500 for 15 minutes, decantation and then 2500 for 15 minutes again (centrifugation protocol 2, according to International g gSociety on Thrombosis and Haemostasis ISTH recommendations). Residual platelet removal assessed by cytometry was similar between[ ]

Conflict of interest

The correlation between the enumeration of PMP assessed by cytometry and phospholipid-dependent procoagulant activity assessed by haemostasis methods A-The study was performed in 40 healthy donors and samples were centrifuged according to protocol 1. A1-Comparison of the respectively. Intra-and inter-assay CV s for cytometry using protocol 2 are 7.8 and 9.4 , respectively compared with 6.7 and 5.7 using

protocol 1 [START_REF] Yuana | Pre-analytical and analytical issues in the analysis of blood microparticles[END_REF]. -


Eric Toussirot

Marie Bossert

Georges Herbein

Philippe Saas

Primary Sjögren's syndrome occurring after influenza A H1N1 vaccine administration

Correspondence to the article by Tabache F. et al "Acute polyarthritis after influenza A (H1N1 immunization", Joint Bone Spine, 2011, doi:10.1016/j.jbs.2011.02.007:

Primary Sjögren's syndrome occurring after influenza A H1N1 vaccine administration

Éric Toussirot [START_REF] Tabache | Acute polyarthritis after influenza A (H1N1 immunization[END_REF][START_REF] Balofsky | The new H1N1 and HPV vaccines and old fears[END_REF][START_REF] Agmon-Levin | Vaccines and autoimmunity[END_REF] , Marie Bossert 4 , Georges Herbein [START_REF] Agmon-Levin | Vaccines and autoimmunity[END_REF][START_REF] Shoenfeld | ASIA -Autoimmune /inflammatory syndrome induced by adjuvants[END_REF] , Philippe Saas 2,,6, 7,8 The patient was treated by hydroxychloroquine giving progressive improvement of arthralgia, but she had still mild and persistent symptoms.

Vaccine has been associated to the development of autoimmune diseases for a long time (2,3) and the vaccination causality is mainly suspected by the temporal relationship between these two events. Different mechanisms may explain these autoimmune phenomena: molecular mimicry, epitope spreading, polyclonal activation and bystander activation (3). Our patient had positive antinuclear antibodies and this may be explained by a quick response of the immune system to the vaccine.

Alternatively, she could have had these antibodies before the vaccination due to a dormant autoimmune disease and the injected vaccine had revealed the disease. We did not detect the presence of influenza A H1N1 RNA in the labial tissue using PCR method, leading to the conclusion that there was no direct viral presence within the salivary glands. Since the Pandemrix ® adjuvant vaccine did not contain viral genetic particles, we can hypothesize that vaccine antigens could activate the immune system, and immune cells secondarily traffick to the glands, leading to the clinical symptoms of sicca syndrome. Our patient had a predisposing genetic background (DRB1* 03, *15) for the development of SS (4). Thus, the vaccine (viral particles and/or the adjuvant or both) (5) may have played a role as a triggering event in this patient with a genetic background for SS. Chronic autoimmune phenomena following vaccine administration (such as influenza A H1N1 vaccine) are important to report in order to better understand the responsibility of this vaccine. However, these cases are infrequent and a coincidental event cannot be ruled out.

1 -

 1 University hospital de Besançon, department of rheumatology, 25000 Besançon, France 2-University hospital de Besançon,CIC Biotherapy-506, 25000 Besançon, France. 3-UPRES EA 4266 « Pathogens and Inflammation», University of Franche-Comté, 25000 Besançon, France 4-Department of Rheumatology, Centre Hospitalier, 25200 Montbeliard, France 5-University hospital de Besançon, department of Virology, 25000 Besançon France 6-INSERM UMR645, 1 Bd A Fleming, 25020 Besançon cedex, France 7-Université de Franche-Comté, UMR645, IFR133 25020 Besançon cedex, France 8-EFS Bourgogne Franche-Comté, Plateforme de Bio-monitoring, 25020 Besançon cedex, France. Corresponding author:Éric Toussirot, department of rheumatology, university hospital Jean Minjoz, 25000 Besançon, France etoussirot@chu-besancon.fr Word count : 500 We read with interest the paper published by Tabacheet al, reporting a case of acute and transient polyarthritis following influenza A H1H1 vaccination (1). We report here a case of persistent autoimmune disease that developed after the same vaccination. The patient was a 30-year-old Caucasian woman without medical history. Due to the national H1N1 vaccination program in France, she received one dose of Pandemrix ® in December 2009. Seven days later, she presented with arthralgia of shoulders, knees, ankles, wrists and fingers. In March 2010, she still had polyarthralgia and reported symptoms of dry mouth and dry eyes. At physical examination, there were tender joints but no joint swelling. Laboratory investigations showed an erythrocyte sedimentation rate of 24 mm/h, normal C-reactive protein level, positive rheumatoid factors (224 UI/L, nephelometry), positive antinuclear antibodies (1/640, Hep-2 cells), positive antibodies to SSA (211 UI, ELISA), negative anti-citrullinated peptides antibodies, negative SSB and anti-double stranded DNA antibodies. The HLA class II genotyping was: DRB1* 03, *15, DQB1*02, *06. Results from serologic tests for parvovirus B19, Lyme disease, hepatitis B and C virus, human immunodeficiency virus, cytomegalovirus and influenza A and B virus were negative. Shirmer's test was altered and a lip biopsy showed the presence of lymphocytic infiltrates in the salivary glands. A RT-PCR was also performed on the salivary gland tissue and failed to detect the presence of the influenza A/H1N1 virus.