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A study of the low temperature autoignition of methyl esters
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Proceedings of the Combustion Institute 32 (2009) 239–246
Combustion Institute www.elsevier.com/locate/proci
A study of the low temperature autoignition of methyl esters K. HadjAli, M. Crochet, G. Vanhove, M. Ribaucour, R. Minetti * UMR CNRS 8522, Physico-Chimie des Processus de Combustion et de l’Atmosphe`re, Universite´ des Sciences et Technologies de Lille, 59655 Villeneuve d’Ascq Cedex, France
Abstract The autoignition of a series of C4 to C8 fatty acid methyl esters has been studied in a rapid compression machine in the low and intermediate temperature region (650–850 K) and at increasing pressures (4– 20 bar). Methyl hexanoate was selected for a full investigation of the autoignition phenomenology, including the identification and determination of the intermediate products of low temperature oxidation. The oxidation scheme and overall reactivity of methyl hexanoate has been examined and compared to the reactivity of C4 to C7 n-alkanes in the same experimental conditions to evaluate the impact of the ester function on the reactivity of the n-alkyl chain. The low temperature reactivity leading to the first stage of autoignition is similar to n-heptane. However, the negative temperature coefficient region is located at lower temperature than in the case of the n-alkanes of corresponding reactivity. An evaluation of the distribution of esteralkyl radicals R and esteralkylperoxy radicals ROO gives an insight into the main reaction pathways. Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Low temperature autoignition; Oxidation; Methyl esters; Fatty acid methyl esters (FAME)
1. Introduction The use of biofuels in compression–ignition engines is calling the attention of the combustion community, as the trend to manufacture biodiesel will probably increase. Particularly vegetable oils can be converted into fatty acid methyl esters, less viscous and still good fuels. These esters mixed to a conventional diesel fuel can be ignited by compression along with alkanes and other hydrocarbons. Experimental studies on the autoignition of esters [1–5] should allow drawing a meaningful comparison of the kinetic phenomenologies of
*
Corresponding author. Fax: +33 3 20 43 48 02. E-mail address: [email protected] (R. Minetti).
methyl esters and alkanes. As autoignition takes place at low temperatures, pyrolysis reactions are slow enough to be neglected and the driving reactions primarily involve fuel/oxygen interactions and the generation of oxygenated radicals. In diesel engines autoignition can be controlled by the timing of the fuel injection and there is no need for a deep understanding of the chemistry of methyl ester autoignition. However, for the application of new engine technologies to biofuels as the homogeneous charge compression ignition mode, the lack of understanding of low temperature oxidation mechanism of esters might be a significant deficiency for the autoignition timing control. The best known schemes of low temperature oxidation leading to autoignition are for alkanes [6]. The oxidation mechanism of alkenes is
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believed to follow the same scheme with some adaptations for resonance stabilised radicals and for addition reactions to the double bond [7]. Even the oxidation of dimethylether is believed to follow the same channels of reactions [8,9], although there are very few common structural features between dimethylether and alkanes. Starting from the well accepted low temperature scheme of oxidation of alkanes, for which a large amount of converging experimental data have been obtained, one can address the question of what the effect of the ester function will be on the overall reactivity of the molecule in the large range of temperature and pressure it undergoes during autoignition by compression. Many detailed low temperature oxidation and autoignition studies on alkanes have been performed with the rapid compression machine (RCM) at Lille. This paper describes a new database on methyl esters that can be directly compared to data on alkanes obtained in strictly equivalent conditions. For practical reasons, the initial temperature in the RCM limits the studies of homogeneous gas mixtures to esters lighter than the octanoic acid methyl ester. This, however, still permits the change in reactivity of alkanes induced by the methyl ester function to be identified. The phenomenology of autoignition of four methyl esters at high pressure below 1000 K has been investigated. This global study has given an overall idea of the behaviour of esters under rapid compression. The observations have been interpreted by a reaction scheme consistent with the results of chemical analysis of intermediate products and with the current theory of autoignition of alkanes [6]. A tentative modelling work for the application of esters in engines has been made in a valuable work [2] but, as the experimental data were scarce and referred mostly to rich mixtures and low pressures, the validation of the mechanism under compression–ignition engine conditions is uncertain. 2. Autoignition of methyl esters
and Pc were 600–850 K and 4–20 bar. Methyl esters were commercial samples of chromatographic quality (>99%) controlled by mass spectrometry before use. They were freed from dissolved air and vaporised before mix with the inert gas and oxygen. All initial gas mixtures were prepared in an enclosed space uniformly heated at 353 K and protected from light. The reaction of the gas mixture was followed by the pressure time profile generated by a Kistler 601A sensor and the detection of light emission behind a blue filter cen˚ . Figure 1 is a typical example tred around 4000 A of a pressure profile with a cool flame obtained with methyl hexanoate at Tc = 695 K. The first stage delay time is the time from EOC to the first pressure jump and light emission and the total delay time is taken from EOC to the final pressure jump and light emission. Sampling of the reacting mixtures was performed by means of an adiabatic expansion of the gas mixture, which froze the reactivity. The products of reaction were collected at 393 K, separated by gas chromatography and identified by a full interpretation of their electron impact mass spectra. The concentrations were obtained with a flame ionisation detector duly calibrated with known mixtures of compounds of the same family and atomic composition. Neon was used as an internal standard in the initial mixture and measured after reaction in order to express the concentration of products in percentage of carbon atoms. Samples of the gas mixture at EOC were analysed to ascertain the absence of significant reactions during the compression stroke. Five linear methyl esters of butanoic to octanoic acids were examined. Their reactivity under rapid compression was difficult to assess as no octane index of these compounds has been found. It was believed that the reactivity increases with the length of the alkyl chain but the effect of the ester function was unknown. The same is true for the intrinsic reactivity of the ester methyl group. As a very high reactivity was previously observed for dimethylether [12], one can surmise
The rapid compression machine and its analytical attachments have been described in detail in previous publications [10,11]. Its configuration was the same as that used before for studying alkanes. The initial cylinder temperature was 353 K. The compression ratio was fixed at 9.4. The temperature and pressure at the end of compression (EOC) were varied independently by changing the composition of the inert gases and the pressure P0 of the initial charge. All mixtures were stoichiometric and the dilution of oxygen was the same as in air. The pressure of the compressed charge Pc was measured at EOC. The temperature of the compressed gas mixture Tc was taken as reference temperature and calculated according to a core gas model. The range of Tc
Fig. 1. Pressure and light emission profiles during the compression of a stoichiometric mixture of methyl hexanoate and ‘‘air” to a core gas temperature of 695 K.
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that the methoxy function in methyl esters could be very reactive too. The present configuration of the RCM, which was the same as used for alkanes, limits the upper initial temperature to 353 K and the lower delay time range to 3 ms. The low volatility of methyl esters at 353 K ðP 353 Þ restricted the study of the gas phase oxidation to narrower ranges. Moreover, the relatively high thermal capacity of esters reduces the maximum temperature at EOC to Tc = 820 K when the nitrogen of ‘‘air” is fully replaced by the monatomic gas argon. Methyl butanoate (P 353 ¼ 48:2 kPa) was the most resistant species to autoignition. No reactivity was observed below Tc = 800 K and Pc = 15.7 bar. Above Tc = 800 K the autoignition occurred in one stage. Methyl pentanoate (P 353 ¼ 13:2 kPa) was more reactive with a limit below which autoignition no longer occurs observed at Tc = 670 K and Pc = 11.4 bar. At this temperature, the autoignition occurred in two stages with a clearly identified cool flame event. Methyl hexanoate (MHEX) was easier to study. Its volatility is not too low (P 353 ¼ 8:4 kPa) and its reactivity well within the range of the RCM capability. Its autoignition occurred in two stages between Tc = 625 and 780 K and in one stage above Tc = 780 K. After the first stage of reaction, the pressure was stable enough to perform sampling of the gas mixture in a relatively steady state of the mixture (Fig. 1). Therefore, it was selected for the chemical analysis of the inter mediates. Methyl heptanoate (P 353 ¼ 2:7 kPa) is much less volatile. It could only be studied at Tc = 800 K and Pc = 9.5 bar. In these conditions, autoignition occurred in two stages. The vapour pressure of methyl octanoate (P 353 ¼ 1:7 kPa) was too low to enable valid autoignition experiments. In order to compare the reactivities under compression of the four lower esters, from methyl butanoate to methyl heptanoate, autoignition delays were measured around Tc = 815 K with pressures increasing from Pc = 4–20 bar. The results are presented in Fig. 2. The total ignition delay times decreased as the length of the alkyl chain increased. The same tendency was observed for alkanes in the same conditions. Clearly the lower pressure at EOC below which autoignition no longer occurs decreases sharply as the length of the alkyl carbon chain increases. MHEX was of intermediate reactivity and its autoignition delays could be measured from Tc = 625–825 K and Pc = 5.2–16.7 bar. Figure 3 presents the first stage (Fig. 3a) and total autoignition delay times (Fig. 3b) of MHEX versus core gas temperatures. Both delay times decrease with an increase in pressure over the whole range of temperature. The total ignition delays show a well marked negative temperature dependence between Tc = 650 and 800 K, indicating that there is a region of temperature in which a
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Fig. 2. Autoignition delay times of fatty acid methyl esters around 815 ± 20 K at high pressures. Gas mixtures are stoichiometric with ‘‘air”. Methyl butanoate (crosses), methyl pentanoate (diamonds), methyl hexanoate (squares), and methyl heptanoate (circles).
Fig. 3. First stage (a) and second stage (b) autoignition delay times of methyl hexanoate for different initial charges (in bar): 0.40 (squares), 0.53 (circles), 0.67 (triangles), 0.93 (diamonds). All mixtures are stoichiometric in ‘‘air”.
competition between the low and intermediate temperature oxidation channels takes place, a feature that is common with long chain alkanes [13].
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Figure 4 shows a comparison of the first stage autoignition delay times (Fig. 4a) and the total autoignition delay times (Fig. 4b) of MHEX, nbutane, n-pentane and n-heptane for the same initial conditions of pressure, temperature, dilution and equivalence ratios. The overall phenomenology of autoignition of MHEX is qualitatively consistent with that of long chain n-alkanes. There are however two significant differences in detail. The first stage delay times of MHEX are very close to those of n-heptane. The delay times below Tc = 670 K are nearly the same and the lower temperature limits under which autoignition by compression does not occur are both at about Tc = 620 K. This is a rather surprising fact, taking into account that the maximum length of the alkyl chain is five carbons instead of seven for n-heptane and that autoignition delay times are very sensitive to the length of the carbon chain. n-Pentane with the same alkyl chain length as MHEX has longer first stage delay times and a temperature limit below which autoignition no longer occurs about 60 K higher. Not surprisingly, nbutane has still longer delay times and a higher limit. Clearly, the methylester function at the end of the n-alkyl chain has a promoting effect on the low temperature oxidation leading to the first stage of autoignition. A difference can also be seen in the temperature region of the negative temperature coefficient. The temperature from
Fig. 4. Comparison between first stage (a) and second stage (b) autoignition delay times of methyl hexanoate (circles), n-butane (squares), n-pentane (crosses), nheptane (diamonds). All mixtures are stoichiometric with ‘‘air” with a compressed charge of 138 mol.m3.
which the autoignition delay times do no more decrease is markedly lower for MHEX than for n-pentane and n-butane. 3. Intermediate products of methyl hexanoate and low temperature oxidation scheme Samples were withdrawn from the combustion chamber of the RCM and quenched after the first stage but before the second stage of autoignition. In this time of the delay, the pressure remains quite stable (Fig. 1), so that the small uncertainty of the sampling time is believed to be of less significance than in non-stationary periods of reaction. Figure 5 shows the chromatogram of the heavier products C4–C7 and Table 1 their name and selectivities of the species expressed in carbon atoms per 1000 carbon atoms of MHEX consumed. The lighter products appearing quickly in the chromatogram are not shown. They were acetic acid, propenal, 1-pentene, propanal, methyl acetate, butanone, butanal and butanone. Their origin is difficult to assess with certainty because of the numerous pathways that could be responsible for their formation. The consumption of initial MHEX amounts to about 50%. As the analytical technique was optimized for heavier products, our discussion will mainly concern the C4–C7 products. The identification of the various products was complicated because of some peaks overlapping and cis/trans isomerism of unsaturated esters. Another difficulty arose from a lack of reference spectra for epoxy compounds of methyl esters. Nevertheless, a careful inspection of the electron impact fragmentation spectra enabled to recognize the size and position of most of the O-heterocycles thanks to specific fragmentation paths: the molecular ions undergo transannular fragmentations leading to stable small molecules and an odd-electron fragment ion of even mass number. Fisher et al. have elaborated a detailed thermochemical model for the oxidation of methyl butanoate [2]. The low temperature oxidation scheme of their model has been based on the low temperature oxidation scheme of alkanes. We have applied the same scheme to MHEX. Many low temperature oxidation reactions have been supported by the nature of the oxidation products analyzed in the samples. Then the low temperature oxidation scheme has been used to throw light upon certain features of the autoignition phenomenology (Fig. 6). For convenience of the discussion, the carbon atoms of MHEX are numbered as follows: 5 6
O
3 4
2
7 O
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Fig. 5. Chromatogram of oxidation intermediates of a stoichiometric mixture of methyl hexanoate with ‘‘air” at 695 K. Sampling occurred 14.6 ms after the first stage of ignition and 7.8 ms before the second stage. The names of the products are in Table 1.
Table 1 Intermediate products of low temperature oxidation of methyl hexanoate (Fig. 5) and selectivity (see text) in C per 1000 C consumed No.
Species
Selectivity
1 2 3 4 5 6 7 8 9–11 12 13 14 15 16–19 20
Methyl propenoate Methyl-3-butenoate Methyl-4-pentenoate 5-Butyl-1, 3-dioxolan-4-one Methyl-5-hexenoate Methyl-2-hexenoate Methyl hexanoate Methyl-4-hexenoate Methyl hexenoates Methyl-2-hexenoate Methyl-3, 5-epoxyhexanoate Methyl-2, 5-epoxyhexanoate Methyl-2, 4-epoxyhexanoate Methyl-i, i + 1-epoxyhexanoate Methyl-2, 3-epoxyhexanoate
200 43 6 25 8 Traces – Traces 54 16 11 43 29 Traces 23
The initiation reaction is between MHEX and molecular oxygen, RH þ O2 ¼ Ri þ HO2 , producing the first radicals. Then the main propagation reactions at low temperatures are H atom abstractions primarily by OH radicals: RH þ OH ¼ Ri þ H2 O. The second step is the addition of O2 to Ri yielding alkylperoxy radical RiOO: Ri þ O2 ¼ Ri OO Ri OO isomerizes through an internal H-atom transfer, which leads to a set of esterhydroperoxyalkyl radicals of formula Qj(OOH)i, in which Q is C6H12CO2, j indicates the radical site and i the site of the hydroperoxy function: Ri OO ¼ Qj ðOOHÞi . Qj(OOH)i either undergo unimolecular decompositions (reaction group I) or add O2 (reaction group II). Different types of decomposition (I) producing stable intermediate oxidation products occur according to the sites i and j. If i = j the stable product has a carbonyl function. Although this reaction may be of some importance for specific hydrocarbons,
it is not considered here because no corresponding product has been detected. If i is different from j, an O–O scission produces an oxygenated heterocycle QjOi of formula OC6H12CO2 by a cyclization reaction (type Ia). If i and j differ by one, a C–O scission gives a methyl hexenoate Qi, j of formula C5H9CO2CH3 (type Ib). If i and j differ by two, a C–C scission gives a lower unsaturated methyl ester together with an aldehyde (type Ic): (Ia) O–O scission when i – j: Qj(OOH)i = QjOi + OH (Ib) C–O scission when i ¼ j 1: Qj ðOOHÞi ¼ Qj; i þ HO2 (Ic) C–C scission when i = j ± 2: Qj(OOH)i = lower unsaturated methyl ester + aldehyde + OH The decompositions (Ia) are competitive to the decompositions (Ib) and (Ic). The reactions (II) produce a OOQj(OOH)i radical, which can isomerize further yielding a relatively stable oxohydroperoxide and an OH radical after the scission of the O–O bond in the hydroperoxy function: OOQj ðOOHÞi ¼ HOOQ0j Oi þ OH. When the decomposition temperature of the oxohydroperoxide is reached, it decomposes into three fragments: an OH radical, another radical and a lower molecule. This decomposition constitutes the low temperature branching step inducing the first stage of autoignition and the cool flame phenomenon, whereas the decomposition (Ia), (Ib), and (Ic) are propagation steps. 4. Distribution of selected radicals A theoretical distribution of Ri and RiOO radicals has been calculated in order to get an insight into the competition between the different pathways. The Ri radical distribution is deduced
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Fig. 6. Main pathways of low temperature oxidation of methyl hexanoate leading to detected products.
by assuming that they are mainly produced by H atom abstraction from MHEX by OH because OH is the most reactive radical at low temperature. The rate constant expressions recommended by Tully and Droege [14,15] for H atom abstraction by OH at primary, secondary, and tertiary sites for an alkane have been used. We have taken into account the bond dissociation energy (BDE) determined by El-Nahas et al. [16] for methyl butanoate to attribute the rate constant expression to the different sites of MHEX. By analogy with methyl butanoate structure we have considered the following BDE values for C–H bonds in methyl hexanoate: 101.2 kcal.mol1 for C6–H, 98.8 kcal.mol1 for C3to5–H, 99.0 kcal.mol1 for C7–H, and 94.3 kcal.mol1 for C2–H. The values for C6–H is typical of a primary C–H in alkanes, those for C3to5–H and C7–H are typical of a secondary C–H in alkanes [17]. The value for C2–H is similar to a tertiary C–H in an alkane. The BDE for a tertiary H atom in iso-butane (95.7 kcal.mol1 [18]) is indeed close to 94.3 kcal.mol1. Having recognized the similarity between the BDE of C–H in esters and alkanes, the rate constant expressions for H atom abstraction by OH radical from C–H in alkanes have been assigned to Ci–H abstraction in MHEX as follows: a tertiary C–H for i = 2, a primary C–H for i = 6 and a secondary C–H for i = 3–5 and 7. The corresponding rate constants have been calculated for 700 K, a temperature very near the temperature at the end of compression in the sampling conditions (Tc = 695 K). Table 2 lists their values and the Ri radical distribution. The weakest C–H bond leads to the most abundant
R2 . The strongest C–H bond leads to the less abundant R6 . The radical R7 is favoured over R3 , R4 , and R5 because three H atoms are available for its formation instead of two. The distribution of RiOO has been deduced from the distribution of Ri and the equilibrium constant of Ri þ O2 ¼ Ri OO . The thermochemical properties of Ri and RiOO have been estimated employing the THERM software [19], the equilibrium constants Kc and the distribution of RiOO calculated at 700 K and reported in Table 2. It can be seen that the formation of R2OO is thermodynamically unfavourable, whereas the formation of R7OO is favoured. Therefore R7OO is the most abundant radical followed by R3OO, R4OO, and R5OO, then R6OO, and finally R2OO. The competition between the different pathways may not be very marked, as the concentrations of RiOO are close to each other.
Table 2 Rate constants k of H atom abstractions in s1 and equilibrium constants Kc of Ri þ O2 ¼ Ri OO in mol1.cm3 i
RiH + OH (1012 k)
Ri (%)
Ri þ O2 (104 Kc)
RiOO (%)
2 3 4 5 6 7
3.09 1.83 1.83 1.83 9.63 2.74
25.2 14.9 14.9 14.9 7.8 22.3
2.48 9.46 9.46 9.46 1.47 9.46
7.7 17.3 17.3 17.3 14.2 26.0
Distribution of Ri and RiOO at 700 K.
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The chemical analysis of the major oxidation products can give information about the Qj(OOH)i radicals distribution. All the detected heavy products that are seen on the chromatogram (Fig. 5 and Table 1) can be formed by decomposition reactions (I): products (4) and (13)–(20) by the type (Ia), products (5)–(12) by the type (Ib), and products (1), (2), and (3) by the type (Ic). Figure 6 shows the reactions leading to the major oxidation products from the Qj(OOH)i radicals. It is noteworthy that the major products are formed either by the abstraction of the relatively labile C2–H bond and isomerization by the internal transfer of less labile 3, 4, 5, 7 hydrogen atoms or by the initial attack on less labile 3, 4, 5, 7 hydrogens and isomerization by the internal transfer of the C2–H labile hydrogen. The only stable product formed by a reaction of the C7–H bond either by Q7(OOH)2 or Q2(OOH)7 is product (4). 5. Discussion and conclusions Figure 4 shows that the cool flame delay times decrease in the order n-butane, n-pentane, n-heptane. MHEX exhibits identical cool flame delay times as n-heptane. According to the oxidation scheme of alkanes, the cool flame is triggered by the decomposition of oxohydroperoxides HOOQO, which are degenerate branching agents [20]. Hence, the cool flame delay time depends on the rate of the reaction sequence: Ri þO2 ¼ Ri OO ; Ri OO ¼ Qj ðOOHÞi ; Qj ðOOHÞi þ O2 ¼ OOQj ðOOHÞi ; OOQj ðOOHÞi ¼ HOOQ0 O þ OH. The rate limiting steps are those involving the internal H atom transfer. They are also most sensitive to the fuel structure. Those with a six-centre transition state are kinetically favoured due to rather low ring strain energy and a rather high A-factor [21] as confirmed quantitatively using Curran’s values for iso-octane [22]. By counting the possible ROO and OOQOOH isomerizations involving a six-centres transition state, we can compare the rate of production of oxohydroperoxides. The higher this number, the higher the rate of production of oxohydroperoxides, and the shorter the cool flame delay times. For the series n-butane, n-pentane, n-heptane, and MHEX, these numbers are respectively 4, 6, 12, and 12. The number increases with the length of the alkane chain and is identical for n-heptane and MHEX, in agreement with the observation of the order of cool flame events. The position of the negative temperature coefficient region depends largely on the competition between the net production of OH by scheme (II) with other R consuming reactions. The resulting balance is very sensitive to the temperature and pressure and can only be predicted by a detailed mechanism with realistic channels and rate constant expressions. This work adds
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new autoignition data to recent methyl ester oxidation studies [23–25] valuable to the building up and validation of such detailed mechanisms in the low and intermediate temperature regions. Acknowledgment This work is a part of the project BIOKIN supported by the ‘‘Agence de l’Environnement et de la Maıˆtrise de l’Energie”, the ‘‘Institut Francßais du Pe´trole”, Total, and PSA Peugeot-Citroe¨n. References [1] P. Dagaut, S. Gaı¨l, M. Sahasrabudhe, Proc. Combust. Inst. 31 (2) (2007) 2955–2961. [2] E.M. Fisher, W.J. Pitz, H.J. Curran, C.K. Westbrook, Proc. Combust. Inst. 28 (2000) 1579–1586. [3] S. Gaı¨l, M.J. Thomson, S.M. Sarathy, et al., Proc. Combust. Inst. 31 (2007) 305–311. [4] J.P. Szybist, A.L. Boehman, D.C. Haworth, H. Koga, Combust. Flame 149 (2007) 112–128. [5] W.K. Metcalfe, S. Dooley, H.J. Curran, J.M. Simmie, A.M. El-Nahas, M.V. Navarro, J. Phys. Chem. A 111 (2007) 4001–4014. [6] R.W. Walker, C. Morley, in: M.J. Pilling (Ed.), Comprehensive Chemical Kinetics, vol. 35, Elsevier, New York, 1997, p. 1. [7] G. Vanhove, M. Ribaucour, R. Minetti, Proc. Combust. Inst. 30 (2005) 1065–1072. [8] H.J. Curran, S.L. Fischer, F.L. Dryer, Int. J. Chem. Kinet. 32 (2000) 741–759. [9] P. Dagaut, J. Luche, M. Cathonnet, Combust. Sci. Technol. 165 (2001) 61–84. [10] M. Ribaucour, R. Minetti, M. Carlier, L.R. Sochet, J. Chim. Phys. 89 (1992) 2127–2152. [11] R. Minetti, M. Carlier, M. Ribaucour, E. Therssen, L.R. Sochet, Combust. Flame 102 (1995) 298– 309. [12] K. HadjAli, G. Vanhove, M. Ribaucour, V. Carre´, R. Minetti, 21st International Colloquium of the Dynamics of Explosions and Reactive Systems, Poitiers, France, 2007. [13] R. Minetti, M. Ribaucour, M. Carlier, L.R. Sochet, Combust. Sci. Technol. 113–114 (1996) 179–192. [14] F.P. Tully, J.E. Goldsmith, A.T. Droege, J. Phys. Chem. 90 (1986) 5932–5937. [15] A.T. Droege, F.P. Tully, J. Phys. Chem. 90 (1986) 1949–1954. [16] A.M. El-Nahas, M.V. Navarro, J.M. Simmie, et al., J. Phys. Chem. A 111 (2007) 3727–3739. [17] Y.R. Luo, Handbook of Bond Dissociation Energies in Organic Compounds, CRC Press, Boca Raton, FL, 2003. [18] W. Tsang, in: J.A. Martinho Simoes, A. Greenberg, J.F. Liebman (Eds.), Energetics of Organic Free Radicals, vol. 4, Blackie, New York, 1996. [19] E.R. Ritter, J. Chem. Inf. Comput. Sci. 31 (1991) 400–408. [20] C.K. Westbrook, Proc. Combust. Inst. 28 (2000) 1563–1577. [21] M. Ribaucour, R. Minetti, L.R. Sochet, H.J. Curran, W.J. Pitz, C.K. Westbrook, Proc. Combust. Inst. 28 (2000) 1671–1678.
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Proceedings of the Combustion Institute 32 (2009) 239–246
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A study of the low temperature autoignition of methyl esters K. HadjAli, M. Crochet, G. Vanhove, M. Ribaucour, R. Minetti * UMR CNRS 8522, Physico-Chimie des Processus de Combustion et de l’Atmosphe`re, Universite´ des Sciences et Technologies de Lille, 59655 Villeneuve d’Ascq Cedex, France
Abstract The autoignition of a series of C4 to C8 fatty acid methyl esters has been studied in a rapid compression machine in the low and intermediate temperature region (650–850 K) and at increasing pressures (4– 20 bar). Methyl hexanoate was selected for a full investigation of the autoignition phenomenology, including the identification and determination of the intermediate products of low temperature oxidation. The oxidation scheme and overall reactivity of methyl hexanoate has been examined and compared to the reactivity of C4 to C7 n-alkanes in the same experimental conditions to evaluate the impact of the ester function on the reactivity of the n-alkyl chain. The low temperature reactivity leading to the first stage of autoignition is similar to n-heptane. However, the negative temperature coefficient region is located at lower temperature than in the case of the n-alkanes of corresponding reactivity. An evaluation of the distribution of esteralkyl radicals R and esteralkylperoxy radicals ROO gives an insight into the main reaction pathways. Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Low temperature autoignition; Oxidation; Methyl esters; Fatty acid methyl esters (FAME)
1. Introduction The use of biofuels in compression–ignition engines is calling the attention of the combustion community, as the trend to manufacture biodiesel will probably increase. Particularly vegetable oils can be converted into fatty acid methyl esters, less viscous and still good fuels. These esters mixed to a conventional diesel fuel can be ignited by compression along with alkanes and other hydrocarbons. Experimental studies on the autoignition of esters [1–5] should allow drawing a meaningful comparison of the kinetic phenomenologies of
*
Corresponding author. Fax: +33 3 20 43 48 02. E-mail address: [email protected] (R. Minetti).
methyl esters and alkanes. As autoignition takes place at low temperatures, pyrolysis reactions are slow enough to be neglected and the driving reactions primarily involve fuel/oxygen interactions and the generation of oxygenated radicals. In diesel engines autoignition can be controlled by the timing of the fuel injection and there is no need for a deep understanding of the chemistry of methyl ester autoignition. However, for the application of new engine technologies to biofuels as the homogeneous charge compression ignition mode, the lack of understanding of low temperature oxidation mechanism of esters might be a significant deficiency for the autoignition timing control. The best known schemes of low temperature oxidation leading to autoignition are for alkanes [6]. The oxidation mechanism of alkenes is
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believed to follow the same scheme with some adaptations for resonance stabilised radicals and for addition reactions to the double bond [7]. Even the oxidation of dimethylether is believed to follow the same channels of reactions [8,9], although there are very few common structural features between dimethylether and alkanes. Starting from the well accepted low temperature scheme of oxidation of alkanes, for which a large amount of converging experimental data have been obtained, one can address the question of what the effect of the ester function will be on the overall reactivity of the molecule in the large range of temperature and pressure it undergoes during autoignition by compression. Many detailed low temperature oxidation and autoignition studies on alkanes have been performed with the rapid compression machine (RCM) at Lille. This paper describes a new database on methyl esters that can be directly compared to data on alkanes obtained in strictly equivalent conditions. For practical reasons, the initial temperature in the RCM limits the studies of homogeneous gas mixtures to esters lighter than the octanoic acid methyl ester. This, however, still permits the change in reactivity of alkanes induced by the methyl ester function to be identified. The phenomenology of autoignition of four methyl esters at high pressure below 1000 K has been investigated. This global study has given an overall idea of the behaviour of esters under rapid compression. The observations have been interpreted by a reaction scheme consistent with the results of chemical analysis of intermediate products and with the current theory of autoignition of alkanes [6]. A tentative modelling work for the application of esters in engines has been made in a valuable work [2] but, as the experimental data were scarce and referred mostly to rich mixtures and low pressures, the validation of the mechanism under compression–ignition engine conditions is uncertain. 2. Autoignition of methyl esters
and Pc were 600–850 K and 4–20 bar. Methyl esters were commercial samples of chromatographic quality (>99%) controlled by mass spectrometry before use. They were freed from dissolved air and vaporised before mix with the inert gas and oxygen. All initial gas mixtures were prepared in an enclosed space uniformly heated at 353 K and protected from light. The reaction of the gas mixture was followed by the pressure time profile generated by a Kistler 601A sensor and the detection of light emission behind a blue filter cen˚ . Figure 1 is a typical example tred around 4000 A of a pressure profile with a cool flame obtained with methyl hexanoate at Tc = 695 K. The first stage delay time is the time from EOC to the first pressure jump and light emission and the total delay time is taken from EOC to the final pressure jump and light emission. Sampling of the reacting mixtures was performed by means of an adiabatic expansion of the gas mixture, which froze the reactivity. The products of reaction were collected at 393 K, separated by gas chromatography and identified by a full interpretation of their electron impact mass spectra. The concentrations were obtained with a flame ionisation detector duly calibrated with known mixtures of compounds of the same family and atomic composition. Neon was used as an internal standard in the initial mixture and measured after reaction in order to express the concentration of products in percentage of carbon atoms. Samples of the gas mixture at EOC were analysed to ascertain the absence of significant reactions during the compression stroke. Five linear methyl esters of butanoic to octanoic acids were examined. Their reactivity under rapid compression was difficult to assess as no octane index of these compounds has been found. It was believed that the reactivity increases with the length of the alkyl chain but the effect of the ester function was unknown. The same is true for the intrinsic reactivity of the ester methyl group. As a very high reactivity was previously observed for dimethylether [12], one can surmise
The rapid compression machine and its analytical attachments have been described in detail in previous publications [10,11]. Its configuration was the same as that used before for studying alkanes. The initial cylinder temperature was 353 K. The compression ratio was fixed at 9.4. The temperature and pressure at the end of compression (EOC) were varied independently by changing the composition of the inert gases and the pressure P0 of the initial charge. All mixtures were stoichiometric and the dilution of oxygen was the same as in air. The pressure of the compressed charge Pc was measured at EOC. The temperature of the compressed gas mixture Tc was taken as reference temperature and calculated according to a core gas model. The range of Tc
Fig. 1. Pressure and light emission profiles during the compression of a stoichiometric mixture of methyl hexanoate and ‘‘air” to a core gas temperature of 695 K.
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that the methoxy function in methyl esters could be very reactive too. The present configuration of the RCM, which was the same as used for alkanes, limits the upper initial temperature to 353 K and the lower delay time range to 3 ms. The low volatility of methyl esters at 353 K ðP 353 Þ restricted the study of the gas phase oxidation to narrower ranges. Moreover, the relatively high thermal capacity of esters reduces the maximum temperature at EOC to Tc = 820 K when the nitrogen of ‘‘air” is fully replaced by the monatomic gas argon. Methyl butanoate (P 353 ¼ 48:2 kPa) was the most resistant species to autoignition. No reactivity was observed below Tc = 800 K and Pc = 15.7 bar. Above Tc = 800 K the autoignition occurred in one stage. Methyl pentanoate (P 353 ¼ 13:2 kPa) was more reactive with a limit below which autoignition no longer occurs observed at Tc = 670 K and Pc = 11.4 bar. At this temperature, the autoignition occurred in two stages with a clearly identified cool flame event. Methyl hexanoate (MHEX) was easier to study. Its volatility is not too low (P 353 ¼ 8:4 kPa) and its reactivity well within the range of the RCM capability. Its autoignition occurred in two stages between Tc = 625 and 780 K and in one stage above Tc = 780 K. After the first stage of reaction, the pressure was stable enough to perform sampling of the gas mixture in a relatively steady state of the mixture (Fig. 1). Therefore, it was selected for the chemical analysis of the inter mediates. Methyl heptanoate (P 353 ¼ 2:7 kPa) is much less volatile. It could only be studied at Tc = 800 K and Pc = 9.5 bar. In these conditions, autoignition occurred in two stages. The vapour pressure of methyl octanoate (P 353 ¼ 1:7 kPa) was too low to enable valid autoignition experiments. In order to compare the reactivities under compression of the four lower esters, from methyl butanoate to methyl heptanoate, autoignition delays were measured around Tc = 815 K with pressures increasing from Pc = 4–20 bar. The results are presented in Fig. 2. The total ignition delay times decreased as the length of the alkyl chain increased. The same tendency was observed for alkanes in the same conditions. Clearly the lower pressure at EOC below which autoignition no longer occurs decreases sharply as the length of the alkyl carbon chain increases. MHEX was of intermediate reactivity and its autoignition delays could be measured from Tc = 625–825 K and Pc = 5.2–16.7 bar. Figure 3 presents the first stage (Fig. 3a) and total autoignition delay times (Fig. 3b) of MHEX versus core gas temperatures. Both delay times decrease with an increase in pressure over the whole range of temperature. The total ignition delays show a well marked negative temperature dependence between Tc = 650 and 800 K, indicating that there is a region of temperature in which a
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Fig. 2. Autoignition delay times of fatty acid methyl esters around 815 ± 20 K at high pressures. Gas mixtures are stoichiometric with ‘‘air”. Methyl butanoate (crosses), methyl pentanoate (diamonds), methyl hexanoate (squares), and methyl heptanoate (circles).
Fig. 3. First stage (a) and second stage (b) autoignition delay times of methyl hexanoate for different initial charges (in bar): 0.40 (squares), 0.53 (circles), 0.67 (triangles), 0.93 (diamonds). All mixtures are stoichiometric in ‘‘air”.
competition between the low and intermediate temperature oxidation channels takes place, a feature that is common with long chain alkanes [13].
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Figure 4 shows a comparison of the first stage autoignition delay times (Fig. 4a) and the total autoignition delay times (Fig. 4b) of MHEX, nbutane, n-pentane and n-heptane for the same initial conditions of pressure, temperature, dilution and equivalence ratios. The overall phenomenology of autoignition of MHEX is qualitatively consistent with that of long chain n-alkanes. There are however two significant differences in detail. The first stage delay times of MHEX are very close to those of n-heptane. The delay times below Tc = 670 K are nearly the same and the lower temperature limits under which autoignition by compression does not occur are both at about Tc = 620 K. This is a rather surprising fact, taking into account that the maximum length of the alkyl chain is five carbons instead of seven for n-heptane and that autoignition delay times are very sensitive to the length of the carbon chain. n-Pentane with the same alkyl chain length as MHEX has longer first stage delay times and a temperature limit below which autoignition no longer occurs about 60 K higher. Not surprisingly, nbutane has still longer delay times and a higher limit. Clearly, the methylester function at the end of the n-alkyl chain has a promoting effect on the low temperature oxidation leading to the first stage of autoignition. A difference can also be seen in the temperature region of the negative temperature coefficient. The temperature from
Fig. 4. Comparison between first stage (a) and second stage (b) autoignition delay times of methyl hexanoate (circles), n-butane (squares), n-pentane (crosses), nheptane (diamonds). All mixtures are stoichiometric with ‘‘air” with a compressed charge of 138 mol.m3.
which the autoignition delay times do no more decrease is markedly lower for MHEX than for n-pentane and n-butane. 3. Intermediate products of methyl hexanoate and low temperature oxidation scheme Samples were withdrawn from the combustion chamber of the RCM and quenched after the first stage but before the second stage of autoignition. In this time of the delay, the pressure remains quite stable (Fig. 1), so that the small uncertainty of the sampling time is believed to be of less significance than in non-stationary periods of reaction. Figure 5 shows the chromatogram of the heavier products C4–C7 and Table 1 their name and selectivities of the species expressed in carbon atoms per 1000 carbon atoms of MHEX consumed. The lighter products appearing quickly in the chromatogram are not shown. They were acetic acid, propenal, 1-pentene, propanal, methyl acetate, butanone, butanal and butanone. Their origin is difficult to assess with certainty because of the numerous pathways that could be responsible for their formation. The consumption of initial MHEX amounts to about 50%. As the analytical technique was optimized for heavier products, our discussion will mainly concern the C4–C7 products. The identification of the various products was complicated because of some peaks overlapping and cis/trans isomerism of unsaturated esters. Another difficulty arose from a lack of reference spectra for epoxy compounds of methyl esters. Nevertheless, a careful inspection of the electron impact fragmentation spectra enabled to recognize the size and position of most of the O-heterocycles thanks to specific fragmentation paths: the molecular ions undergo transannular fragmentations leading to stable small molecules and an odd-electron fragment ion of even mass number. Fisher et al. have elaborated a detailed thermochemical model for the oxidation of methyl butanoate [2]. The low temperature oxidation scheme of their model has been based on the low temperature oxidation scheme of alkanes. We have applied the same scheme to MHEX. Many low temperature oxidation reactions have been supported by the nature of the oxidation products analyzed in the samples. Then the low temperature oxidation scheme has been used to throw light upon certain features of the autoignition phenomenology (Fig. 6). For convenience of the discussion, the carbon atoms of MHEX are numbered as follows: 5 6
O
3 4
2
7 O
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Fig. 5. Chromatogram of oxidation intermediates of a stoichiometric mixture of methyl hexanoate with ‘‘air” at 695 K. Sampling occurred 14.6 ms after the first stage of ignition and 7.8 ms before the second stage. The names of the products are in Table 1.
Table 1 Intermediate products of low temperature oxidation of methyl hexanoate (Fig. 5) and selectivity (see text) in C per 1000 C consumed No.
Species
Selectivity
1 2 3 4 5 6 7 8 9–11 12 13 14 15 16–19 20
Methyl propenoate Methyl-3-butenoate Methyl-4-pentenoate 5-Butyl-1, 3-dioxolan-4-one Methyl-5-hexenoate Methyl-2-hexenoate Methyl hexanoate Methyl-4-hexenoate Methyl hexenoates Methyl-2-hexenoate Methyl-3, 5-epoxyhexanoate Methyl-2, 5-epoxyhexanoate Methyl-2, 4-epoxyhexanoate Methyl-i, i + 1-epoxyhexanoate Methyl-2, 3-epoxyhexanoate
200 43 6 25 8 Traces – Traces 54 16 11 43 29 Traces 23
The initiation reaction is between MHEX and molecular oxygen, RH þ O2 ¼ Ri þ HO2 , producing the first radicals. Then the main propagation reactions at low temperatures are H atom abstractions primarily by OH radicals: RH þ OH ¼ Ri þ H2 O. The second step is the addition of O2 to Ri yielding alkylperoxy radical RiOO: Ri þ O2 ¼ Ri OO Ri OO isomerizes through an internal H-atom transfer, which leads to a set of esterhydroperoxyalkyl radicals of formula Qj(OOH)i, in which Q is C6H12CO2, j indicates the radical site and i the site of the hydroperoxy function: Ri OO ¼ Qj ðOOHÞi . Qj(OOH)i either undergo unimolecular decompositions (reaction group I) or add O2 (reaction group II). Different types of decomposition (I) producing stable intermediate oxidation products occur according to the sites i and j. If i = j the stable product has a carbonyl function. Although this reaction may be of some importance for specific hydrocarbons,
it is not considered here because no corresponding product has been detected. If i is different from j, an O–O scission produces an oxygenated heterocycle QjOi of formula OC6H12CO2 by a cyclization reaction (type Ia). If i and j differ by one, a C–O scission gives a methyl hexenoate Qi, j of formula C5H9CO2CH3 (type Ib). If i and j differ by two, a C–C scission gives a lower unsaturated methyl ester together with an aldehyde (type Ic): (Ia) O–O scission when i – j: Qj(OOH)i = QjOi + OH (Ib) C–O scission when i ¼ j 1: Qj ðOOHÞi ¼ Qj; i þ HO2 (Ic) C–C scission when i = j ± 2: Qj(OOH)i = lower unsaturated methyl ester + aldehyde + OH The decompositions (Ia) are competitive to the decompositions (Ib) and (Ic). The reactions (II) produce a OOQj(OOH)i radical, which can isomerize further yielding a relatively stable oxohydroperoxide and an OH radical after the scission of the O–O bond in the hydroperoxy function: OOQj ðOOHÞi ¼ HOOQ0j Oi þ OH. When the decomposition temperature of the oxohydroperoxide is reached, it decomposes into three fragments: an OH radical, another radical and a lower molecule. This decomposition constitutes the low temperature branching step inducing the first stage of autoignition and the cool flame phenomenon, whereas the decomposition (Ia), (Ib), and (Ic) are propagation steps. 4. Distribution of selected radicals A theoretical distribution of Ri and RiOO radicals has been calculated in order to get an insight into the competition between the different pathways. The Ri radical distribution is deduced
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Fig. 6. Main pathways of low temperature oxidation of methyl hexanoate leading to detected products.
by assuming that they are mainly produced by H atom abstraction from MHEX by OH because OH is the most reactive radical at low temperature. The rate constant expressions recommended by Tully and Droege [14,15] for H atom abstraction by OH at primary, secondary, and tertiary sites for an alkane have been used. We have taken into account the bond dissociation energy (BDE) determined by El-Nahas et al. [16] for methyl butanoate to attribute the rate constant expression to the different sites of MHEX. By analogy with methyl butanoate structure we have considered the following BDE values for C–H bonds in methyl hexanoate: 101.2 kcal.mol1 for C6–H, 98.8 kcal.mol1 for C3to5–H, 99.0 kcal.mol1 for C7–H, and 94.3 kcal.mol1 for C2–H. The values for C6–H is typical of a primary C–H in alkanes, those for C3to5–H and C7–H are typical of a secondary C–H in alkanes [17]. The value for C2–H is similar to a tertiary C–H in an alkane. The BDE for a tertiary H atom in iso-butane (95.7 kcal.mol1 [18]) is indeed close to 94.3 kcal.mol1. Having recognized the similarity between the BDE of C–H in esters and alkanes, the rate constant expressions for H atom abstraction by OH radical from C–H in alkanes have been assigned to Ci–H abstraction in MHEX as follows: a tertiary C–H for i = 2, a primary C–H for i = 6 and a secondary C–H for i = 3–5 and 7. The corresponding rate constants have been calculated for 700 K, a temperature very near the temperature at the end of compression in the sampling conditions (Tc = 695 K). Table 2 lists their values and the Ri radical distribution. The weakest C–H bond leads to the most abundant
R2 . The strongest C–H bond leads to the less abundant R6 . The radical R7 is favoured over R3 , R4 , and R5 because three H atoms are available for its formation instead of two. The distribution of RiOO has been deduced from the distribution of Ri and the equilibrium constant of Ri þ O2 ¼ Ri OO . The thermochemical properties of Ri and RiOO have been estimated employing the THERM software [19], the equilibrium constants Kc and the distribution of RiOO calculated at 700 K and reported in Table 2. It can be seen that the formation of R2OO is thermodynamically unfavourable, whereas the formation of R7OO is favoured. Therefore R7OO is the most abundant radical followed by R3OO, R4OO, and R5OO, then R6OO, and finally R2OO. The competition between the different pathways may not be very marked, as the concentrations of RiOO are close to each other.
Table 2 Rate constants k of H atom abstractions in s1 and equilibrium constants Kc of Ri þ O2 ¼ Ri OO in mol1.cm3 i
RiH + OH (1012 k)
Ri (%)
Ri þ O2 (104 Kc)
RiOO (%)
2 3 4 5 6 7
3.09 1.83 1.83 1.83 9.63 2.74
25.2 14.9 14.9 14.9 7.8 22.3
2.48 9.46 9.46 9.46 1.47 9.46
7.7 17.3 17.3 17.3 14.2 26.0
Distribution of Ri and RiOO at 700 K.
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The chemical analysis of the major oxidation products can give information about the Qj(OOH)i radicals distribution. All the detected heavy products that are seen on the chromatogram (Fig. 5 and Table 1) can be formed by decomposition reactions (I): products (4) and (13)–(20) by the type (Ia), products (5)–(12) by the type (Ib), and products (1), (2), and (3) by the type (Ic). Figure 6 shows the reactions leading to the major oxidation products from the Qj(OOH)i radicals. It is noteworthy that the major products are formed either by the abstraction of the relatively labile C2–H bond and isomerization by the internal transfer of less labile 3, 4, 5, 7 hydrogen atoms or by the initial attack on less labile 3, 4, 5, 7 hydrogens and isomerization by the internal transfer of the C2–H labile hydrogen. The only stable product formed by a reaction of the C7–H bond either by Q7(OOH)2 or Q2(OOH)7 is product (4). 5. Discussion and conclusions Figure 4 shows that the cool flame delay times decrease in the order n-butane, n-pentane, n-heptane. MHEX exhibits identical cool flame delay times as n-heptane. According to the oxidation scheme of alkanes, the cool flame is triggered by the decomposition of oxohydroperoxides HOOQO, which are degenerate branching agents [20]. Hence, the cool flame delay time depends on the rate of the reaction sequence: Ri þO2 ¼ Ri OO ; Ri OO ¼ Qj ðOOHÞi ; Qj ðOOHÞi þ O2 ¼ OOQj ðOOHÞi ; OOQj ðOOHÞi ¼ HOOQ0 O þ OH. The rate limiting steps are those involving the internal H atom transfer. They are also most sensitive to the fuel structure. Those with a six-centre transition state are kinetically favoured due to rather low ring strain energy and a rather high A-factor [21] as confirmed quantitatively using Curran’s values for iso-octane [22]. By counting the possible ROO and OOQOOH isomerizations involving a six-centres transition state, we can compare the rate of production of oxohydroperoxides. The higher this number, the higher the rate of production of oxohydroperoxides, and the shorter the cool flame delay times. For the series n-butane, n-pentane, n-heptane, and MHEX, these numbers are respectively 4, 6, 12, and 12. The number increases with the length of the alkane chain and is identical for n-heptane and MHEX, in agreement with the observation of the order of cool flame events. The position of the negative temperature coefficient region depends largely on the competition between the net production of OH by scheme (II) with other R consuming reactions. The resulting balance is very sensitive to the temperature and pressure and can only be predicted by a detailed mechanism with realistic channels and rate constant expressions. This work adds
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new autoignition data to recent methyl ester oxidation studies [23–25] valuable to the building up and validation of such detailed mechanisms in the low and intermediate temperature regions. Acknowledgment This work is a part of the project BIOKIN supported by the ‘‘Agence de l’Environnement et de la Maıˆtrise de l’Energie”, the ‘‘Institut Francßais du Pe´trole”, Total, and PSA Peugeot-Citroe¨n. References [1] P. Dagaut, S. Gaı¨l, M. Sahasrabudhe, Proc. Combust. Inst. 31 (2) (2007) 2955–2961. [2] E.M. Fisher, W.J. Pitz, H.J. Curran, C.K. Westbrook, Proc. Combust. Inst. 28 (2000) 1579–1586. [3] S. Gaı¨l, M.J. Thomson, S.M. Sarathy, et al., Proc. Combust. Inst. 31 (2007) 305–311. [4] J.P. Szybist, A.L. Boehman, D.C. Haworth, H. Koga, Combust. Flame 149 (2007) 112–128. [5] W.K. Metcalfe, S. Dooley, H.J. Curran, J.M. Simmie, A.M. El-Nahas, M.V. Navarro, J. Phys. Chem. A 111 (2007) 4001–4014. [6] R.W. Walker, C. Morley, in: M.J. Pilling (Ed.), Comprehensive Chemical Kinetics, vol. 35, Elsevier, New York, 1997, p. 1. [7] G. Vanhove, M. Ribaucour, R. Minetti, Proc. Combust. Inst. 30 (2005) 1065–1072. [8] H.J. Curran, S.L. Fischer, F.L. Dryer, Int. J. Chem. Kinet. 32 (2000) 741–759. [9] P. Dagaut, J. Luche, M. Cathonnet, Combust. Sci. Technol. 165 (2001) 61–84. [10] M. Ribaucour, R. Minetti, M. Carlier, L.R. Sochet, J. Chim. Phys. 89 (1992) 2127–2152. [11] R. Minetti, M. Carlier, M. Ribaucour, E. Therssen, L.R. Sochet, Combust. Flame 102 (1995) 298– 309. [12] K. HadjAli, G. Vanhove, M. Ribaucour, V. Carre´, R. Minetti, 21st International Colloquium of the Dynamics of Explosions and Reactive Systems, Poitiers, France, 2007. [13] R. Minetti, M. Ribaucour, M. Carlier, L.R. Sochet, Combust. Sci. Technol. 113–114 (1996) 179–192. [14] F.P. Tully, J.E. Goldsmith, A.T. Droege, J. Phys. Chem. 90 (1986) 5932–5937. [15] A.T. Droege, F.P. Tully, J. Phys. Chem. 90 (1986) 1949–1954. [16] A.M. El-Nahas, M.V. Navarro, J.M. Simmie, et al., J. Phys. Chem. A 111 (2007) 3727–3739. [17] Y.R. Luo, Handbook of Bond Dissociation Energies in Organic Compounds, CRC Press, Boca Raton, FL, 2003. [18] W. Tsang, in: J.A. Martinho Simoes, A. Greenberg, J.F. Liebman (Eds.), Energetics of Organic Free Radicals, vol. 4, Blackie, New York, 1996. [19] E.R. Ritter, J. Chem. Inf. Comput. Sci. 31 (1991) 400–408. [20] C.K. Westbrook, Proc. Combust. Inst. 28 (2000) 1563–1577. [21] M. Ribaucour, R. Minetti, L.R. Sochet, H.J. Curran, W.J. Pitz, C.K. Westbrook, Proc. Combust. Inst. 28 (2000) 1671–1678.
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