From elementary reactions to evaluated chemical mechanisms for combustion models

Available online at www.sciencedirect.com

Proceedings of the

Combustion Institute

Proceedings of the Combustion Institute 32 (2009) 27–44

www.elsevier.com/locate/proci

From elementary reactions to evaluated chemical mechanisms for combustion models Michael J. Pilling * School of Chemistry, University of Leeds, Leeds LS2 9JT, UK

Abstract Methods of determining rate data for elementary reactions for combustion applications, using experimental and theoretical methods, are briefly reviewed. The approaches are illustrated by reference to recent research in three areas: (i) reactions of OH with C2H4 and C2H2, where theory, tuned by reference to experiment, has provided a substantial contribution to the determination of rate data for these complex reactions, over a wide range of temperatures; (ii) reactions between alkyl radicals and O2, where theory and experiment have been closely allied in discerning the details of mechanisms for small alkyl radicals; much remains to be done with larger radicals; (iii) reactions of methylene and the interactions between chemical reaction and the conversion of the singlet state into the triplet, where theory has played little part thus far. Comments are also made on the process of evaluating rate data for elementary reactions for incorporation in chemical mechanisms for use in combustion models. Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Reaction kinetics; Radicals; Chemical mechanisms

1. Introduction Combustion involves complex chemical mechanisms, which are made up of large numbers of elementary chemical reactions [1]. The features of the macroscopic combustion process – the rate at which heat is released, ignition characteristics, rates of production of pollutants—depend on the rates of and the interactions between the microscopic processes – the elementary reactions. Models require detailed, quantitative information on these reactions, particularly rate coefficients and product yields. The ordinary differential equations that describe the time dependence of chemical species concentrations in a combustion

*

Fax: +44 113 343 6401. E-mail address: [email protected]

model are based on a chemical mechanism, which is a list of the reactants and products in the elementary reactions that comprise the combustion process, together with associated rate coefficients and their dependence on temperature and, if appropriate, pressure. The components of the chemical mechanisms have been elucidated over many decades, and there is a general understanding of the types of reaction to include, although surprises continue to occur [2]. Determining the kinetics of the elementary reactions, the rate coefficients and the reaction products, continues to present both an experimental and a theoretical challenge. These properties are required under the combustion conditions, which may involve temperatures of thousands of degrees Kelvin and pressures of many bar; direct measurement in the laboratory is difficult under such conditions and some form of extrapolation is needed, often

1540-7489/$ - see front matter Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2008.08.003

28

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

involving theory. Some ‘elementary’ reactions are quite ‘complex’. The reaction between an alkyl radical, such as 1-butyl, with O2, which is central to many combustion processes, occurs via several short-lived intermediates to form several different sets of products whose relative yields depend sensitively on the temperature and pressure [3]. Although the general way in which these reactions occur has been understood for many years, a detailed and quantitative understanding only started a decade or so ago and is still in progress. Sections 2–4 briefly review the main experimental methods used to study elementary reactions, also on theoretical approaches. Sections 5–7 provide a number of examples drawn from personal interest. From a combustion perspective, the major application of chemical kinetic data on elementary reactions lies in their incorporation in chemical mechanisms for use in combustion models. Detailed mechanisms are developed ‘by hand’, using chemical knowledge and intuition [4–7] and through the use of expert systems [8–11], in which a large mechanism is generated computationally, using kinetic protocols. The practicality of using these detailed mechanisms in combustion models might then be enhanced through the use of reduction and lumping [12] or low dimensional manifold techniques [13]. For fuels such as H2 and CH4, the rate constants are derived explicitly from experimental and theoretical studies, and modellers and mechanism developers rely extensively on evaluations of available rate data. For more complex fuels, the mechanisms are larger and the elementary reactions are less well-studied—estimation, often based on group additivity or structure activity relations, is required. Some issues relating to the incorporation of kinetic data for elementary reactions in chemical mechanisms for use in combustion models, are discussed very briefly in Section 8. 2. Experimental methods for elementary reactions Two methods are widely employed in the study of elementary combustion reactions, laser flash potolysis (LFP) and shock tube (ST) techniques. The former is generally restricted to low temperatures (<1000 K), but has the advantage that multiple shot averaging techniques can be used, giving rise to high sensitivity in terms of the radical concentrations that can be measured. This means that secondary (radical + radical) reactions can be minimised so that the decay of the monitored radical is less affected by secondary reactions. The low temperature restriction, though, means that some form of extrapolation is needed for higher temperature applications. ST is essentially a single pulse method, so signal averaging is not feasible. Careful design has led to remarkable increases in sensitivity in recent years.

In LFP, radiation from a pulsed laser, usually operating in the UV, is used to photodissociate a precursor to form the radical under study [14]. An example is OH that can be formed, for example, from t-butylhydroperoxide [15]. Sometimes a combination of photolysis and reaction is used, for example in the formation of C2H5 from Cl + ethane, following pulsed photolysis of Cl2 to form Cl [16] (see Section 6). A wide range of detection techniques can be used with LFP, including laser induced fluorescence (LIF), [15] uv and ir absorption spectroscopy [17] and mass spectroscopy [18]. Absorption spectroscopy has been augmented over the last decade or so by cavity ring down and cavity enhanced spectroscopy in which the absorption signal is considerably enhanced by multiple reflections of selected single frequency laser radiation in an optical cavity [19]. In all cases, the signal/noise ratio is improved by repeating the experiment many times and then averaging the signal. Section 5–7 discuss applications using LIF and ir absorption spectroscopy. Shock tubes are used for higher temperatures and require high sensitivity detection methods because they are single shot methods, so that signal averaging cannot be used. A high pressure gas propagates through the reaction mixture and compressively heats it. For higher temperatures, the system is studied after the shock reflects from the end wall of the shock tube, passing back through the reaction mixture and heating it further. The radical under study is produced by pyrolysis of a precursor, on a timescale that is short compared with the reaction time. Srinivasan et al. [20] used the pyrolysis of methanol to form OH and studied its reaction with C2H2 and C2H4 over the temperature ranges 1509–2362 and 1463–1931 K, respectively. They used absorption spectroscopy at 308 nm, with an OH resonance lamp—a microwave discharge through water in Ar—as the light source; a multipass mirror system enabled them to work with single shot OH concentrations approaching those employed in multi-shot, signal averaged flash photolysis experiments. Oehlschlaeger et al. [21] studied H + benzyl over the temperature range 1256– 1667 K. They produced H from the pyrolysis of ethyl iodide and benzyl from toluene and monitored the benzyl by laser absorption at 266 nm. In both cases, it was necessary to take account of secondary reactions, using a model of the competing reactions. To demonstrate the validity of the methods, sensitivity analysis was used to show that the reactions under study made the major contribution to the radical signal decay. A wide range of other techniques have been used to determine rate constants, including the use flames and of flow and stirred reactors, under a wide range of configurations. Such systems are widely used to understand overall mechanisms of combustion and interactions between elementary

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

reactions, but, coupled with careful design and rate and sensitivity analysis, they also provide an excellent source of rate constant data, especially under realistic combustion conditions. 3. Electronic structure calculations There have been substantial improvements in recent years in calculations of potential energy surfaces for gas phase reactions of radicals and they now form a key element in the determination of rate coefficients for combustion reactions involving relatively small numbers of atoms [22]. Provided the appropriate level of theory is used, it is now feasible to calculate energies of transition states to an accuracy of 2–5 kJ mol1, and this is comparable with the accuracy of activation energies determined from experiments. These energy uncertainties affect the rate coefficient through the exponential term in the Arrhenius expression and, at this magnitude, introduce comparatively little error at temperatures of, say, 1000 K (5 kJ mol1 corresponds to a factor of 2 in the exponential term at 1000 K). For reactions with well-defined barriers, it is sufficient to apply transition state theory with a rigid rotor harmonic oscillator model for the reactants and the transition state. This requires information on the energy of the transition state and the geometries and vibrational frequencies of the reactants and transition state. For H atom transfer reactions, tunnelling may also be important. Many chemical mechanisms rely on estimates of rate constants—there have simply been too few experimental measurements, even for the combustion of modestly sized alkanes. Benson [23] made a major contribution through the development and application of the group additivity concept, in which both thermodynamics and kinetics were broken down into quantitative contributions from component groups in a molecule or in a reactive system. The approach depended on a degree of empiricism and on the use of experimental data. This is an application that it perfectly suited to electronic structure calculations, which can be tuned to available experimental data and then applied to a wide range of reactive systems. Examples of such applications include Senosiain et al. [24], who addressed the database for hydrocarbon bond dissociation energies, and Sumathi et al. [25,26], who have applied this approach to a range of reaction types, including H abstraction from alkanes by H and CH3. Some reactions, for example radical combinations, occur without a well-defined energy maximum. In such cases, the position of the transition state varies with the energy in the reacting system and it is necessary to use a variational model, which requires information on energies, geometries and vibrational frequencies along the

29

reaction coordinate. The calculation proceeds by determining the position of the minimum in the sum of states along the reaction coordinate. The minimum in the reaction flux, which determines the reaction rate, occurs at this position. Variational methods can be used to provide canonical rate constants as a function of temperature (k(T)), or microcanonical rate constants as a function of reaction energy (k(E)). In this case, it is necessary to include both anharmonicities and coupling between the modes of the combining radicals. The variable reaction coordinate transition state theory (VRC-TST) approach, developed by Klippenstein and co-workers, has been extensively used in this context [27–30]. Harding et al. [22] have recently reviewed ab initio methods for reactive potential energy surfaces and include a brief discussion of the methods available, and of results for a range of reactions of importance in combustion. The difficulties in generating reliable rate constants for radical + radical reactions, and the importance of using an appropriately high level of theory is illustrated by the CH3 + CH3 reaction, which is of central importance in combustion. The reaction is pressure dependent, and the quantity which can be directly compared with, for example, VRC-TST, is the high pressure limiting rate constant, k1(T). Master equation methods, discussed in the next section, are required to calculate the pressure dependence of the rate constant. A number of theoretical approaches have been used to calculate k1 for this reaction [22,31–35]. Figure 1 shows the results of an analysis by Harding et al. [22] which shows the range of values predicted by a

Fig. 1. High pressure limiting rate constants for CH3 + CH3 ? C2H6. Theoretical data are shown as full lines, obtained using different electronic structure methods, that are labelled on the right of the figure. Experimental results are shown as symbols: Hippler et al. [36] (d), Slagle et al. [37] (s), Walter et al. [38] (). (based on reference [22]).

30

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

number of levels of theory. There are two major problems. The long range interaction between the two radicals, arising from dispersion forces, is an important determinant of k1, and is not included in all methods. Secondly, spin contamination effects become significant as the singlet and triplet states, deriving from the relative alignment of the spins on the two radicals, separate in energy as the C–C bond forms. Once again, this is treated better in some methods than in others. Figure 1 shows that the CASPT2 method, which accommodates both of these effects, shows excellent agreement with experiment [36–38]. Note the large underestimation of the values obtained with other theoretical methods, and also that all methods show a decrease in k1(T) as T increases. While k1 can be accurately and directly determined experimentally at low temperatures, the experimental values at the higher temperatures shown in Fig. 1 required extrapolation to the high pressure limit and the uncertainty in k1(T) increases as T increases. At these higher temperatures, VRC-TST using CASPT2 may be more accurate than experiment. Troe, Hippler and coworkers [35,39] have used very high pressures, typically up to 1000 bar, to help overcome this problem of the experimental determination of the high pressure limiting rate constant. In a recent application, this technique was applied to CH3 + O2, using pressures up to 1000 bar and temperatures up to 700 K [40]. The problem of interfering reactions in shock tube measurements was briefly referred to in the last section. Jasper et al. [41] examined the reactions contributing to the OH temporal profile in shock tube measurements of methanol dissociation. They found that a number of reactions of CH2 with other transient species were significant, and that the experimental database available in the literature contained too many disagreements for a satisfactory analysis. They carried out VRC-TST calculations, allowing them to make a choice between different experimental estimates, and, particularly, to determine the yields of different product channels. For 3CH2 + 3CH2, for example, which forms C2H2 + H2 or 2H, they showed that the atomic channel occurs with a yield of 80%. Experimental estimates vary widely [42–48]. 4. Master equation calculations As mentioned in the last section, the association of methyl radicals is pressure dependent, because of the competition between collisional stabilisation of the energised C2 H6 , formed from the reactants, and its re-dissociation. Dissociation and isomerisation reactions show a similar pressure dependence. In recent years, there has been increasing interest in reactions involving several

potential energy wells, some of which are connected by isomerisation, and several product channels, both those formed by dissociation from one or more potential well, and those formed by collisional stabilisation within one or more of the wells. This interest has derived both from experimental observations, and from the use of electronic structure calculations, that have considerably increased our knowledge and understanding of the often complex potential energy surfaces. The analysis of the kinetics of such reactions has been greatly aided by applications of master equation (ME) models [49–52]. The model is energy resolved and incorporates energy-dependent rate constants of dissociation, association and isomerisation and collisional energy transfer between the energy levels of each potential energy well. For reactions involving even only small molecules, there are far too many rovibrational levels for them to be treated explicitly and they are ‘bundled’ together in grains; each grain having a width, typically, of 0.5 kJ mol1. A rate equation is then set up for each grain. For a simple dissociation reaction, such as that of ethane, these take the form: X X dci ¼ k i ci  ½M j k ji ci þ ½M j k ij cj ðE1Þ dt where ci is the concentration of ethane in the ith grain, ki is the energy dependent rate coefficient for dissociation from grain i, kji is the rate constant for collisional energy transfer from grain i to grain j and M is the diluent gas. An exponential down model is used for the collisional energy transfer steps, in which it is assumed that the probability of transfer between grains falls off exponentially with the energy removed in the collision: k j;i ½M ¼ xP j;i P j;i ¼ Aj expððEi  Ej Þ=DEdown Þ; for Ei > Ej ðE2Þ Where x is the collision frequency, Ei is the energy of the ith grain and Aj is a normalization constant. DEdown is the average energy transferred in a downward direction in a single collision. Probabilities for collisional transfer of energy to the molecule are calculated from those removing energy by detailed balance: P i;j ¼

Ni P j;i expðbðEi  Ej ÞÞ; for Ei > Ej Nj ðE3Þ

so that, in the absence of reaction, an initially perturbed distribution approaches a Boltzmann distribution in the long time limit. Here, Ni is the number of states in the ith grain and b = 1/kBT, where kB is the Boltzmann constant. The whole set of coupled differential equations for all the grains can be expressed in matrix form:

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

dc ¼ Mc dt

ðE4Þ

where c is a vector of grain concentrations and M is a matrix containing the rate constant terms in equation (E1). Equation (E2) is solved by an eigenvalue analysis, which gives the eigenvalues, K, and associated eigenvectors, U, of M. The eigenvalues are all real and negative, showing that the system evolves in time as a sum of exponential decays: cðtÞ ¼ U expðKtÞU1 cðtÞ

ðE5Þ

where c(0) is the vector of initial grain concentrations. The eigenvalues of larger magnitude, corresponding to the faster exponential decays, relate to collisional relaxation. Miller and Klippenstein [51] have referred to these modes as the internalenergy relaxation eigenvalues (IERE). In most circumstances, this relaxation occurs on times which are small compared with the overall reaction time. For a simple dissociation, the eigenvalue of smallest magnitude, k1, corresponding to the slowest exponential decay, is equal in magnitude to the unimolecular rate coefficient for dissociation: k1 = kuni. Thus the pressure dependent unimolecular rate coefficient, the target of the master equation calculation, can be obtained from the eigenvalue analysis. The ME is readily extended to reactions involving association, isomerisation involving one or several potential energy wells and dissociation reactions to give one or several sets of products. The concentration vector c contains the grain populations for all of the potential wells. The association reaction is treated as a pseudo first order reaction, with the minority reactant, e.g., OH in the OH + C2H2 reaction, discussed below, included as a single element in c The products formed by dissociation may also be included in c, again as single elements, and the reverse rate constants, from the products to one or more isomers, included in M. If this is done, the system is conservative and there is a zero eigenvalue, corresponding to the establishment of equilibrium. Alternatively, these products can be treated as sinks and not incorporated in c, in which case there is no zero eigenvalue. The number of eigenvalues corresponds to the number of elements in c. The eigenvalues of largest magnitude relate to collisional relaxation, but there are now several eigenvalues relating to rate coefficients for chemical reactions; these have been termed the chemically significant eigenvalues (CSE) [53]. If the sink approach is used, the number of such eigenvalues is equal to the number of chemical species contained in the vector c, i.e., to the number of isomer wells plus the minority reactant. Generally speaking these eigenvalues are those of lowest magnitude, although at high tem-

31

peratures they may become comparable in magnitude to the numerically smallest relaxation eigenvalues. This leads to complications in the description of the kinetics of the reactions, and the usual rate constant description becomes inapplicable. This problem has been discussed extensively, e.g., by Tsang [54] and by Robertson et al. [52] for alkyl radical isomerisation and dissociation and by Miller and Klippenstein, for example for isomerisation in the C3H4 system [55]. When the separation between the IERE and CSE is significant, the rate constants can be properly defined and determined, but the relationship between the eigenvalues and the rate constants for individual reaction steps can be quite complex. The methodology has been discussed in detail by Klippenstein and Miller [51], following a much earlier approach by Bartis and Widom [56]. Blitz et al. [57] developed and applied a related technique to the H + SO2 reaction and investigated, in some detail, the decomposition of the eigenvalues, which show a complex dependence on T and p, into the component rate constants. A related and important issue is whether or not rate constants recovered from a master equation analyses satisfy detailed balance, i.e. is the ratio of rate constants for forward and reverse reactions equal to the equilibrium constant. This is a key issue in combustion, because forward and reverse rate constants, linked through detailed balance, are generally included in combustion models. Any deviations are likely to be small, except possibly for reactions of comparatively weakly bound species. The issue been discussed by Miller and Klippenstein [58]. 5. OH + C2H4 and C2H2 When OH reacts with a hydrocarbon containing a multiple carbon–carbon bond, reaction can occur by addition or by H abstraction. At low temperatures, the addition reaction dominates and for OH + C2Hn (n = 2, 4) the product is the adduct C2HnOH. At higher temperatures, the adduct can isomerise and also produce bimolecular products, and there is a sensitive competition between collisional stabilisation and isomer dissociation. At still higher T, direct abstraction can occur. Prior to the work of Srinivasan et al. [20], the bulk of the high temperature measurements for OH + C2H2 involved flame measurements, using, for example, OH absorption spectroscopy, coupled with numerical simulation to deduce the rate constant. At lower temperatures, Liu et al. [59] used pulse radiolysis + resonance absorption spectroscopy, while Smith et al. [60] used pulsed CO2 laser absorption to heat SF6 to 1100– 1300 K, where OH was formed by thermal dissociation of H2O2 and detected by LIF. These

32

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

experimental data have recently been evaluated (see Section 8) [61]. Only an overall rate constant was recommended, with an uncertainty increasing from a factor of 3 at 1000 to 10 at 2000 K. The potential reaction channels were identified, but no channel yields provided, which presents difficulties to mechanism developers. A similar situation is found for OH + C2H4. The experimental techniques used are generally more direct, including laser flash photolysis, shock tubes and pulse radiolysis, but had not been extended to such high temperatures, before the work of Srinivasan et al. [20]. The evaluation again only recommends an overall rate constant, with an uncertainty of a factor of 3 over the range 650–1500 K [61,62]. The considerable advances made by combining electronic structure calculations of the potential energy surface and master equation have been exploited by Senosiain et al. [63,64] to provide a much more profound understanding and parameterisation of the rate constants for the possible product channels of these two reactions than has proved possible previously. For OH + C2H4, addition to form C2H4OH is the most important channel at temperatures up to 800 K and at 1 bar. Above this temperature, H abstraction takes over as the main channel producing C2H3 + H2O. Interestingly, the formation of vinyl alcohol, C2H3OH, +H becomes significant at these higher temperatures, accounting for 10% of the reaction products above 1500 K at a pressure of 1 bar. This reaction channel derives from initial addition, followed by dissociation over quite a high barrier. The reaction is more important than that forming acetaldehyde + H, which involves H atom migration in the initial adduct, CH2CH2OH, to form CH3CH2O, followed by dissociation to form H + the aldehyde. This reaction proceeds over lower energy barriers, but they are tighter than that leading to the alcohol. Formation of vinyl alcohol is not recognized in most combustion models, but has been observed recently by Taatjes et al. [65] in a range of low pressure fuels; simulations showed that the results of Senosiain et al. could successfully account for this observation. Figure 2 shows the calculated overall rate constants as a function of temperature, and compares them with some experimental results. The measurements of Tully [66,67] were particularly important, because they were used to tune the barrier height for the abstraction reaction. The accuracy of the calculations of the energies of the turning points on the surface (stable species and transition states) is 8 kJ mol1. The transition state energy was tuned by only 1.2 kJ mol1 to obtain the agreement shown in Fig. 2. A further important determinant of the overall behaviour of the reaction system is the high pressure limiting rate constant for the addition reaction to form C2H4OH, whose determination is discussed below.

Fig. 2. Arrhenius plot for the total reaction of OH with C2H4 at several pressures [64]. The lines denote the theoretical values, at a range of pressures. Experimental results are shown as symbols: Tully (N) [66,67]; Liu et al. [68] 1 atm Ar (M); Fulle et al. [39]: 1.1 atm He, (d), 15.2 atm He (j), 34.7 atm He () and 148.2 atm He (J).

Similar calculations were performed by Senosiain et al. for OH + C2H2 [63]. They showed that formation of the adduct C2H2OH is the most important channel at temperatures below 1200 K, when formation of H + ketene becomes the main channel up to temperatures of 2100 K. Above this temperature, the abstraction channel, forming H + C2H, takes over. The importance of addition decreases as the pressure falls, as for OH + C2H4. The details of the mechanism of the addition reactions, and the determination of rate constants as a function of T and p at the lower temperatures where it dominates, has also received considerable recent attention, and demonstrates a feature of reaction behaviour that is important for a number of reactions. The transition state leading from the reactants to the adduct, C2HnOH, is preceded by a van der Waals well, that affects the kinetics. A further interesting feature is that the transition state for OH + C2H4 lies below the energy of the reactants—it is known as a submerged transition state, while that for OH + C2H2 lies above the energy of the reactants. The latter property was used by Davey et al. [69] to study the C2H2  OH van der Waals complex experimentally, forming it in a supersonic expansion and probing it by infra red spectroscopy. They showed that the complex is T shaped, and obtained an upper limit for the well depth of 11.4 kJ mol1. They were unable to study C2H4  OH in the same way, because to reacts too rapidly over the submerged transition state to form the adduct C2H4OH. Greenwald et al. [69] examined OH + C2H4 in considerable detail. The used a variational method to calculate the high pressure limiting rate constant k1. As the reactants approach, they experience two transition states, which act, effectively, as bottlenecks, limiting the reactive flux. An outer transition state, TSo, lies at larger sepa-

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

rations than the van der Waals well, while the inner transition state, TSi lies between the van der Waals well and the adduct. At very low temperatures, TSo acts as the main bottleneck, and is the primary determinant of k1; in this regime, k1 increases strongly with decreasing T. At temperatures above 130 K, the inner transition state becomes more important and the negative T dependence becomes less marked. Greenwald et al. proposed a bi-exponential dependence: k1 = (4.93  1012 (T/298)2.488 exp(54.3 K/T) + 3.33  1012 (T/298)0.451 exp(59.2 K/T)) cm3 molecule1 s1. They compared their calculations with available experimental data, over the temperature range 100–600 K, and tuned their potential energy surface by reducing the energy of TSi by 4 kJ mol1. Senosiain et al. performed similar calculations for OH + C2H2 [63]; in this case, k1 increases with T, because TSi lies above the energy of the reactants, but, once again, a bi-exponential expression was needed to accommodate the variational effects. While these calculations were centred on explaining low T experimental data, they also provided important information for the higher temperature behaviour. Both association reactions have recently been studied experimentally, using laser flash photolysis at temperatures between 200 and 400 K [15,70], primarily to provide rate data for atmospheric applications. Under these conditions, the reactions are dominated by addition: OH þ C2 H4 þ M ! C2 H4 OH þ M

ð5:1aÞ

OH þ C2 H2 þ M ! C2 H2 OH þ M

ð5:1bÞ

Figure 3a and b shows the temperature and pressure dependence of the rate coefficients. In both cases, k1 is more closely approached under the experimental conditions at low T than at high T, because the higher thermal energy of the reactants gives the adduct more internal energy at higher temperatures, increasing its rate of dissociation so that higher pressures are required for stabilisation.

a

33

The most obvious qualitative difference between the two plots is that k1, increases with decreasing temperature for OH + C2H4, while it increases with increasing temperature for OH + C2H2. This behaviour is in agreement with the calculations of Greenwald et al. [69] and Senosiain et al. [63] and is related to the energy of TSi, submerged for the former and at a higher energy than the reactants for the latter. The experimental data for the two reactions were analysed using a master equation method [15,70]. The high pressure limiting rate constants were linked to the microcanonical rate constants for dissociation of the adduct, k(E), using an inverse Laplace transform method [71] that allows k(E) to be related to the Arrhenius parameters, A and Eact for the association reaction: k1,1 = A exp(Eact/RT). The data over the whole range of temperature and pressure were then fitted with these two parameters and the energy transfer parameter, hDEdowni, as variables. The ME calculations were repeated many times, with different parameter values and the best fit values determined as those providing the minimum value of v2, the squares of the differences between the calculated and experimental values at a particular T and p, summed over all experimental data points. These best fit ME data were then used to obtain an analytic form for k1b(T, p), using a modified Troe expression [72], which is shown in Fig. 3b as a set of smooth curves. The same procedure was adopted for OH + C2H4. While there is qualitative agreement between the directly determined experimental values for k1, and those derived from theory, there are significant differences. For example the experimental k1 for OH + C2H4 does not increase as rapidly with decreasing T as the values obtained theoretically while the experimental k1 for OH + C2H2 increases less rapidly with increasing T at higher temperatures. Given that the theoretical values were subject to some degree of tuning, by reference to earlier experiments, these differences can probably be resolved through retuning of the

b

Fig. 3. Bimolecular rate constants for (a) OH + C2H4 [15], (b) OH + C2H2 [70]. Also included in (b) are modified Troe fits [72] to the results of a the master equation fit to this dataset [70].

34

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

potential energy surface. The two approaches provide an interesting contrast. The master equation fitting to the data shown in Fig. 3a and b was achieved using a statistically robust method, which linked the data to a best fit high pressure limit through an inverse Laplace transform approach. The theoretical approach used a much more robust description of the complex potential energy surface and of its links to k1, but the comparison with experiment, that was used to tune the surface, was less statistically sound. An approach which combined these two approaches, and could be applied to all experimental data, with appropriate statistical weighting, would be of great value, but it would be computationally very demanding. 6. Oxidation of hydrocarbons: reactions of peroxy radicals The oxidation of hydrocarbons below 1000 K is central to autoignition [73,74]. Low temperature alkane oxidation occurs by the mechanism shown schematically in Fig. 4 [3]. The parent alkane, RH, reacts with a radical, usually OH, and loses a hydrogen atom to form an alkyl radical R. In general, R undergoes three types of reaction: addition of oxygen to form a peroxy radical (6.1), decomposition to an alkene, A1, and a smaller alkyl radical, R1 (6.2) or reaction with O2 to produce the conjugate alkene, A2 (with the same number of carbon atoms as the parent) and an HO2 radical (6.3). R þ O2  RO2 R ! R1 þ A1 R þ O2 ! A2 þ HO2

ð6:1Þ ð6:2Þ ð6:3Þ

There has been continuing discussion of the mechanism of formation of the conjugate alkene; it is now clear, as discussed below, that it occurs via the peroxy radical rather than via direct abstraction.

Fig. 4. Simplified outline mechanism for the low temperature oxidation of an alkane, RH. QOOH is an alkyl hydroperoxide radical, formed from RO2 by internal H atom transfer.

The peroxy radical, RO2, can also undergo an internal hydrogen abstraction to form a hydroperoxide group (–OOH) and a new alkyl radical centre further along the carbon chain; the product is generally labelled QOOH: RO2 ! QOOH

ð6:4Þ

QOOH can cyclise, to form OH and a cyclic ether with ring sizes from 3 to 6 atoms. Other products, such as aldehydes, can also by formed, as coproducts of OH. The importance of the QOOH route increases as the size of the alkyl group increases; it is relatively unimportant for C2H5O2, which is one of the more fully investigated peroxy radicals. QOOH is an alkyl radical and can add another O2. Subsequent isomerisation of the peroxy radical so formed produces, through an unstable intermediate, a molecular (non-radical) hydroperoxide, R0 OOH, and an OH radical. R0 OOH is a degenerate branching agent and its dissociation leads to the formation of two radicals, one of which is OH. A hydroperoxide, ROOH can also be formed by H abstraction by RO2 from RH, and provides another route to branching. The termination steps which moderate or prevent this runaway are those early in the mechanism producing inert radicals, HO2 (reaction (3)) and small alkyl radicals (reaction (2)), such as CH3. The competition in the reactions of R and RO2, shown in Fig. 3, has the important consequence that branching is greatly favoured, and autoignition enhanced, when peroxy radical isomerisations are facile, since the route to branching involves two such reactions, while that to termination involves none. Isomerisation is easiest in long straight alkane chains and large n-alkanes autoignite under milder conditions than small or branched alkanes. Another significant and related feature of the mechanism is connected with the reversibility of the formation of RO2 (reaction (1)). As described above, the subsequent chemistry of RO2 radicals leads to branching while termination occurs through the alkyl radical R. At successively higher temperatures the equilibrium shifts to the left and the termination reactions through R are favoured over the branching reactions through RO2, so that the reaction gets slower. This results in a region of negative temperature coefficient [74] where the rate decreases as the temperature is raised. As discussed below, there are additional aspects of the reaction scheme that contribute to this region of negative temperature behaviour. All of these ideas were developed and tested through indirect experiments, especially by Walker and his co-workers [3]. In the last few years there have been several key experiments using laser flash photolysis by the Taatjes group [16,75–78] that, coupled with theory, have considerably enhanced our understanding of reactions of peroxy radicals.

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

The most detailed experimental studies of ethyl + O2, and of the product channels, have been made by Taatjes and co-workers [16,75]. They coupled laser flash photolysis to infra-red absorption spectroscopy to detect HO2 and to LIF to detect OH, producing C2H5 from Cl + C2H6, following photolysis of Cl2 or CFCl3 to form Cl. They measured the absolute yields of HO2 in reaction (3), calibrating the HO2 signal by replacing the C2H6 by CH3OH. The radical products of the Cl + CH3OH reaction (CH2OH, 85% yield and CH3O 15% yield at room temperature) both react with O2 to give HO2, which is thus formed in 100% yield in the Cl + CH3OH + O2 system. The OH LIF signal was calibrated by converting the HO2 from Cl + CH3OH + O2 to OH by reaction with NO. They showed that the major product is HO2, but that its time dependence is complex. At low temperatures (400 K) it is formed on a very short timescale from both C2H6 and CH3OH, by the R + O2 reaction and then decays on a much longer timescale primarily by HO2 + HO2. The yield of HO2 from C2H6 is much less than that from CH3OH, i.e. much less than unity—the majority of the R + O2 reaction involves formation of RO2. At higher temperatures (600 K), HO2 is again formed on a short timescale from C2H5 + O2, but the signal continues to rise as HO2 is generated on a longer timescale. The slower rise reflects HO2 formation from the dissociation of collisionally stabilised C2H5O2, with the faster component deriving from dissociation of C2 H5 O2 , formed directly from the alkyl radical + O2, without any collisional stabilisation taking place. The overall yield of HO2, from the slow and fast processes, increases with temperature and by 700 K is close to unity. These results are entirely compatible with earlier experimental results, but now provide much more detailed information on the time dependence of HO2 formation. Similar results were obtained for propane. The yield of OH, formed from QOOH, is much smaller than that of HO2 for both propane and ethane, reaching 1% at the highest temperature studied (700 K). All of these experiments are compatible with a model based on reactions 6.1 and 6.3, but with reaction 6.3 occurring via an energised peroxy radical rather than a direct abstraction as was at one time proposed. This reaction involves dissociation of the energised radical formed directly from C2H5 + O2, without collisional stabilisation to form C2H5O2. C2 H5 þ O2 ! ½C2 H5 O2  ! C2 H4 þ HO2

ð6:5Þ

where the square bracketed term has been included for clarity to indicate a species that is short lived and is not included in the set of reactions comprising a combustion mechanism. This reaction can be contrasted with the reaction sequence

35

involving collisional stabilisation and subsequent collisional activation of the peroxy radical. For the C2H5 + O2 system, this involves C2 H5 þ O2  C2 H5 O2 C2 H5 O2 ! C2 H4 þ HO2

ð6:6Þ ð6:7Þ

Both reactions 6.6 and 6.7 also proceed through C2 H5 O2 , but a key difference in this reaction sequence is that C2H5O2 is fully thermalised. The kinetic descriptions of these processes in a combustion model are different as are the competing elementary reactions. In the former case (reaction (6.5)), the reaction competes with other reactions of the alkyl radical, such as dissociation (reaction (6.1)), and is favoured by the regeneration of the alkyl radical from the peroxy radical (reaction (6.6)). In the latter case (reaction (6.7)), the reaction competes with other reactions of the peroxy radical, and especially with reverse dissociation to form the alkyl radical (reaction (6.6)). The reaction sequence has received considerable theoretical attention. Rienstra-Kiracofe et al. [79] used high level ab initio calculations to show that the lowest energy route for reaction (6.3) for R=C2H5 involves concerted elimination of HO2 from the ethyl peroxy radical, with a transition state slightly below the energy of reactants. They found that a mechanism involving the initial formation of an alkylhydroperoxy radical by H atom transfer, followed by CAO bond rupture to form CH3CHO + OH, has a significantly higher energy barrier, as do the dissociation of the alkylhydroperoxy radical to form oxirane + OH and the direct abstraction reaction. Figure 5 shows a potential energy surface obtained by Miller and co-workers [80,81], which illustrates the energetics of the reactions involving initial formation of the peroxy radical. Miller and co-workers [80,81] took the analysis further, using electronic structure calculations, coupled with a master equation model. They again found a low energy route from C2H5O2 to HO2, with the barrier below the energy of the reactants, C2H5 + O2, and higher channels with higher barriers to OH (Fig. 5). Miller and Klippenstein [81] restricted their master equation analysis to the reactants and the peroxy radical well, treating the HO2 channel as a sink and neglecting the very low probability OH channel, so that there are only two chemically significant eigenvalues. They compared their analysis with the experimental data obtained by Taatjes and co-workers [16] and showed that the reaction can be characterized by three different regimes. For T < 575 K reaction involves mainly formation of the peroxy radical (reaction (6.1)), with a small, instantaneous yield of HO2 that increases as the pressure decreases and as the temperature increases and derives from dissociation of C2 H5 O2 without stabilisation. In this temperature regime, the collisionally stabi-

36

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

Fig. 5. Potential energy surface for ethyl + O2. HO2 is formed in a concerted mechanism from C2H5O2, while there are two higher energy routes to OH, one of which involves isomerisation of C2H4OOH [83].

lised peroxy radical is stable on the experimental timescale of the C2H5 + O2 reaction and the eigenvalue related to reaction of the stabilised peroxy radical is very small in magnitude. The C2H4 + HO2 reaction route derives entirely from reaction from energized C2H5O2, formed from the reactants C2H5 + O2. It is termed an indirect reaction and is formally written as in reaction (6.3). The term indirect is used because the reactants and products are not connected by a single transition state, but by two transition states, one linking the reactants with C2H5O2, the other linking C2H5O2 and C2H4 + HO2. At intermediate temperatures (575 6 T/K 6 750) the system becomes more complex, because both the reverse (reaction (6.6)) and dissociation of thermalised C2H5O2 to form C2H4 + HO2 (reaction (6.7)) become significant; the chemical lifetimes of C2H5 and C2H5O2 are now becoming comparable. From the master equation viewpoint, the two eigenvalues of smallest magnitude, which relate to the overall chemical processes that are significant on the experimental timescale, become comparable in magnitude, in agreement with the observations of Taatjes et al. [16]. At still higher temperatures, T/K P 750, the system can once again be described by a single eigenvalue. In this regime, stabilisation of C2 H5 O2 is ineffective at all realizable pressures, and the sole products are C2H4 + HO2. The smallest eigenvalue now describes reaction (6.5) and a ‘zero pressure’ ME model provides an adequate description of the system at all realizable pressures. Reaction (6.5) now predominates and reaction (6.7) is unimportant. As discussed above, channels involving reaction (6.4) and its subsequent dissociation are comparatively ineffective in the ethane system, because

they involve transition states which are too high in energy to play a significant role. Products implying the involvement of QOOH have been observed extensively by Walker and co-workers [3] and this reaction is key to the formation of a range of oxygenated species (aldehydes and cyclic ethers) and is central to degenerate branching. The first direct observation of OH from QOOH was made by Hughes et al. [82,83]. They observed OH by LIF following reaction of the neopentyl (C(CH3)3CH2) radical with O2 in a laser flash photolysis system. The HO2 + alkene reaction is not feasible in this system, because there is no H on the carbon atom placed a to the radical centre. They used the observed growth in OH to determine the rate constant for the reaction: ðCðCH3 Þ3 CH2 Þ þ O2 ! OH þ 3; 3 dimethyloxetane

ð6:8Þ

which was presumed to proceed via the CCH2(CH3)3CH2OOH intermediate, with the H atom transfer reaction to form this intermediate from a stabilised peroxy radical as the rate determining step. They used this value to place relative rate data obtained by Walker and co-workers on an absolute basis. While the experimental basis of the work Hughes et al. is sound, the interpretation and the method of determining the rate constant for dissociation of the QOOH intermediate was subsequently shown to be incorrect. Hughes et al. had assumed that QOOH reacted sufficiently rapidly with O2 and by dissociation, that the reverse reaction to regenerate the peroxy radical, ie the reverse of reaction (6.4), could be neglected. This assumption was questioned by DeSain et al. [84]. Sun and Bozelli’s [85] calculations of the potential

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

energy surface showed that the reverse isomerisation of QOOH to RO2 is faster than the forward reaction, so that equilibration, or near equilibration between these two species occurs under the conditions studied by Hughes et al., leading to a significant underestimation of the forward rate constant. The most recent investigation of this reaction system has been undertaken by Petway et al. [86]. They combined the experiment with a detailed analysis of the chemical mechanism, using the MIT reaction mechanism generator, and an extensive analysis of the sensitivity of the OH signal to the component reactions. They proposed that the formation of OH + 3,3-dimethyloxetane occurs via the energised states of the peroxy radical, without stabilisation into that well, as discussed above for HO2 formation from ethyl + O2 (reaction (6.5)). OH production in alkyl radical + O2 reactions requires elevated temperatures. By contrast, facile formation of OH has been observed even at room temperature in reactions of oxygenated radicals. CH3CO reacts with O2 to form the acetyl peroxy radical. At low pressures, though, OH formation has been implicated in kinetic measurements by Michael et al. [87] and by Tyndall et al. [88] and observed directly by LIF by Blitz et al. [89]. They ascribed their results to a mechanism involving reaction of CH3C(O)O2 to form CH2C(O)OOH, which then dissociates to form OH and the lactone cCH2C(O)O. Both of the transition states along this reaction route lie below the energy of the reactants CH3CO + O2. Here again, reaction takes place from the energised peroxy radical, formed from the acetyl + O2 reaction, without the intermediate involvement of the stabilised peroxy or hydroperoxy radicals. Indeed the OH yield decreases as the pressure increases, as stabilisation of the peroxy radical competes increasingly favourably with isomerisation. The channel leading to formation of HO2 + ketene has a transition state at much higher energies and is unimportant at low T. The ethyne  OH adduct formed at low T from the OH + C2H2 reaction (Section 5) reacts with O2 in the troposphere, but kinetic measurements demonstrated that the peroxy radical initially formed reacts rapidly to form (a) glyoxal + HCO and (b) formic acid + HCO, even at room temperature [90–92]. The proposed mechanism has been confirmed by ab initio calculations [93] showing that the peroxy radical, HOC2H2O2, isomerises rapidly via an H transfer reaction from the OH group to the peroxy group in channel (a) or forms a cyclic species with the O2 bridging across the double bond in channel (b). Both of these species dissociate rapidly, before collisional stabilisation can occur under atmospheric conditions. In stark contrast with the ethyl + O2 reaction, all the transition states leading from the peroxy radical to OH formation lie below the energy of even the peroxy radical, and

37

200 kJ mol1 below the energy of the reactants. Collisional stabilisation plays no role in either channel, because the isomerisation and dissociation rate constants are so rapid. The relative yields of the two channels, (a) and (b) above, are determined entirely by the initial reaction and whether O2 adds cis or trans to the OH group. Taatjes [75] recently commented that ‘‘the secondary chemistry of the QOOH species is one of the key unsolved questions in modeling ignition chemistry and low-temperature oxidation.” Recent experiments, based on observations of OH and HO2, have played a big role in unravelling some of this chemistry and in understanding some of the basic processes occurring on the complex potential energy surfaces that are involved. Further significant progress, through, depends on direct observation of the organic radicals, especially for the elucidation of the chemistry of QOOH. Taatjes outlined the great potential power of photoionisation mass spectrometry using the Advanced Light Source at the Lawrence Berkeley National Laboratory. Key targets are the isomerisation and dissociation of QOOH, together with its reaction with O2 and the steps leading to branching. These will undoubtedly be difficult to observe by direct methods. The complexity of the system means that, at observable QOOH concentrations, the total radical concentration will be large and the contribution of secondary reactions considerable—the use of detailed chemical kinetic models, of the sort employed by Petway et al. [87], will be essential. Electronic structure theory coupled with a master equation analysis will play a central role in understanding the reaction mechanisms, in helping to design and to interpret experiments and in extending this understanding to combustion conditions. There is also considerable interest in the complex chemistry following RO2 formation in atmospheric chemistry. Toluene is an important source of ground level ozone, which has serious effects on human health and on ecology. It reacts with OH mainly via addition to the ring. The adduct reacts with O2 to form a peroxy radical, but formation of the hydroperoxyl radical, the equivalent of QOOH, does not seem to be significant. Instead, the O2 bridges across the ring and this bicyclic compound goes on to react with another molecule of O2. Subsequent reactions lead to ring opening and formation of dicarbonyl compounds such as glyoxal. There is also some evidence that OH may be formed [93–96]. Unravelling this chemistry again presents challenges to both experiment and theory. 7. Excited electronic states: reactions of methylene Most reactions involve only reactants in their ground electronic states. Methylene, CH2, provides an interesting example of a system in which

38

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

excited state reactions are important. Its ground state is a relatively unreactive triplet, which we label 3CH2, while the much more reactive first excited state is a singlet, 1CH2. The energy separation is 38 kJ mol1 [97]. With closed shell molecules at room temperature, the difference in reactivity is 5–6 orders of magnitude [61,98– 101] CH2 is implicated in soot formation through its reaction with acetylene to form C3H3, which then reacts to form an aromatic ring [102–106]. An important process, from both fundamental and combustion perspectives, is the collisional conversion of the singlet into the triplet. This is induced efficiently by the inert gases [107–109], and also plays a significant role in reactions [61]. For example, the reaction of 1CH2 with C2H2, which leads to formation of C3H3 + H, also has a channel that converts the singlet into the triplet; the ratio of the reaction to deactivation rate constants is 4:1 at room temperature[110]. Deactivation of the singlet is important because it converts a highly reactive species into an unreactive one [61], and also because it provides a potential route for reaction of the triplet, by the reverse activation process to form the more reactive singlet state. The mechanism of conversion of the singlet to the triplet on collision with inert gases is termed collisionally induced intersystem crossing (CIISC); the rate constant increases with the mass of the inert gas atom and also with temperature. Some of the rotational states of the singlet and triplet lie very close in energy, leading to a perturbation. The perturbed states have both singlet and triplet character and are termed gateway states [111–114]. When the singlet is produced by reaction, the perturbed states with mixed singlet triplet character are also formed. Collisions with inert gas atoms, or, for example, with N2, transfer molecules in the gateway states into other rotational states of the triplet leading to a cascade of the rotational state populations down the energy levels of the triplet, until it is thermalised. They also transfer molecules from the unperturbed singlet rotational states into the now depopulated gateway states, providing a route for conversion of the singlet into the triplet. The rate constants for CIISC uniformly increase with temperature [115,116], behaviour attributed to increased access to mixed states at higher T, through the Boltzmann distribution [107,109]. Blitz et al. [117] studied the temperature dependence of the rate constant for 1CH2 + C2H2 reaction and showed that the rate constant decreases strongly with increasing T, over the temperature range 205–773 K: k = 3.0  1010 (T/298 K)0.9 cm3 molecule1 s1, with a decrease of a factor of 3.3 over the experimental range. As noted above, for interaction with C2H2, about 20% of collisions removing 1CH2 lead to deactivation. If the deactivation mechanism for acetylene is the same as that for the inert gases, with a rate constant that increases with increasing T, then, given

the decrease in the overall rate constant with T, the fractional reactive yield would decrease substantially with T and approach zero under the conditions appropriate to combustion. This problem has been addressed by Blitz et al. [118], by monitoring the H atom product for a number of reactions of 1CH2. With H2, the reactions: 1 1

CH2 þ H2 ! CH3 þ H 3

CH2 þ H2 ! CH2 þ H2

ð7:1aÞ ð7:1bÞ

occur, with kb/(ka + kb) = 0.15 at room temperature. [42,119] They generated 1CH2 by laser flash photolysis of ketene 308 nm and measured the time dependence of H, using vacuum UV laser induced fluorescence in three separate experiments: (i) In a large excess of hydrogen (10–60 Torr), where H was generated instantaneously, on the timescale of the experiment, by reaction 7.1a, and then decayed by diffusive loss from the experimental monitoring zone. (ii) In a large excess of hydrogen and a small concentration of NO (0.4 Torr). Under these conditions, the instantaneous rise was followed by a small subsequent rise in the OH signal, as the 3CH2 formed in reaction 7.1b reacted with NO to form H, with a channel efficiency of 0.9. (iii) In zero hydrogen, a large excess of He and 0.4 Torr NO. In this case, all of the 1CH2 was deactivated to the triplet, which subsequently reacted with NO to form H by reaction with NO. Figure 6 shows an example of the traces for these three experiments at 300 K. Analysis of the

Fig. 6. Time profiles for experiments (i), (ii), and (iii) in the determination of the yield of 3CH2 in the reaction of 1 CH2 with H2[118]: experiment (i) (s); experiment (ii) (j); experiment (iii) (D). The full lines represent the best fits to the data using a kinetic analysis of experiments (i)–(iii), with the initial (relative) yield of 1CH2, k7.1a/k7.1 and the rate constants for 3CH2 + NO and for diffusive loss of H as variable parameters. The traces were recorded at 20 Torr total pressure and at 295 K.

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

traces allowed Blitz et al. to show that kb/ (ka + kb) falls from 0.15 at 300 K to zero at 500 K. The overall rate constant, (ka + kb), is essentially invariant with T, with a value of 1.0  1010 cm3 molecule1 s1 [120], showing that the rate constant for singlet to triplet deactivation, kb, decreases with temperature, in direct contrast with the rate constants for CIISC with the inert gases. This suggests that there is a different mechanism; the likely mechanism for H2 probably arises from the fact that the interaction between 1CH2 and H2 is strongly attractive—the reaction proceeds through the formation of a highly energised CH4, which dissociates rapidly to form CH3 + H. 3CH2, by contrast, has a repulsive interaction with H2—the activation energy for this reaction is large and positive. There is, therefore, probably an intersection of the reaction potential energy curves that permits facile crossing from the singlet curve to the triplet, with an associated formation of 3CH2. A quantitative description of this process, and of the origin of the negative temperature dependence for kb has not been developed and there is a clear need for theoretical contributions to the elucidation of the mechanism of singlet–triplet transfer in reactive systems. Blitz et al. [121] also studied the reaction of 1 CH2 with O2, once again probing the formation of H. They observed that H was formed on a comparatively long timescale, compatible with formation from 3CH2, which reacts with O2 about ten times more slowly than does the singlet. They argued that O2 exclusively deactivates 1CH2 to the triplet and obtained a yield of H from the reaction of 3CH2 with O2 of 0.8 ± 0.2. The reaction channels involved are: 3

CH2 þ O2 ! CO2 þ 2H

ð7:2aÞ

! CO þ OH þ H

ð7:2bÞ

More recently, Gannon has applied H atom detection to 1CH2 + C2H2, the reaction that started this series of investigations [121]. Once again, she found that the singlet triplet deactivation rate constant decreases with increasing T, with a yield for this channel at 200 K of 0.7, and of 0.1 and 0 at 300 and 500 K, respectively. The high value at low temperatures is particularly interesting, in terms of understanding the mechanism. That at 500 K clearly shows that the reactive channel dominates at temperatures of interest in combustion. Similar behaviour was observed for 1CH2 + C2H4. 8. The evaluation of rate data—progress towards reliable chemical mechanisms There are inherent uncertainties in kinetic measurements. Some are statistical and derive from

39

random errors associated, for example, with noise in the signal. Other sources are systematic, deriving, for example, from secondary reactions that affect the signal whose form is then not solely due to the single reaction under study. More accurate measurements can be made by increasing the sensitivity of the detection technique, so that it is possible to work at lower reactant radical concentrations and hence reduce the impact of secondary reactions. It is also possible to build a model of the competing reactions, and make allowances for them in deriving the rate coefficient for the reaction under study; the work of Petway et al. [87] on neopentyl + O2 provides an example of such an approach, using an automatic mechanism generator, while that of Jasper et al. [41] shows the power of electronic structure calculations, coupled with transition state theory, to provide rate constants for such a mechanism, where the experimental database is inadequate. Even so, there are often significant discrepancies between rate coefficients derived using different methods and/ or from different laboratories. This problem has led to the establishment of groups of experts who evaluate the available rate data [61]. The group examines the methods that have been used to measure specific reactions, and, on the basis of the data and their assessment of the experimental method, they make a reasoned recommendation of the rate coefficient expression over a specific range of temperature and, if appropriate, pressure. They also recommend an uncertainty range for the rate coefficient parameters. The resulting tabulations provide an essential resource for modellers and those constructing chemical mechanisms. The assessments also provide a means of identifying reactions in need of further study. The traditional approach to evaluation was developed by Baulch in the 1960s [122]. It was initially conducted through staff at the University of Leeds, but was then extended to include international experts. The aim was to assemble and document all of the experimental measurements of specific reactions of importance in combustion and to evaluate them: to compare them both quantitatively and qualitatively – the latter involving a subjective assessment of the quality of a measurement and the likelihood that the resulting rate constant is accurate within its quoted range of uncertainty. The final stage is the recommendation of a rate constant expression, including the dependence of the rate constant on temperature and, if appropriate, pressure, together with an assessment of the uncertainty associated with the recommended expression. The published versions of the evaluations have been widely used in the construction of mechanisms for combustion models and are extensively cited. Related approaches were developed by Cohen and Westberg [123] and by Hampson and Garvin [124], the latter at the then National Bureau of Standards in Wash-

40

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

ington, that led to the recommendations initiated by Tsang and Hampson [125] and later to the unevaluated tabulations in the NIST database [126]. Two series of evaluations continue in atmospheric chemistry, through the NASA [127] and IUPAC panels [128]. The community owes Don Baulch a great debt of gratitude for his pioneering efforts. The approach adopted has stood the test of time well, although there are two clear deficiencies that can now be identified, although the approach adopted was entirely appropriate for much of the period over which the evaluations were conducted: 1. The first of these was the decision just to use just experimental data. While this was justifiable until relatively recently, because theoretical rate constants were not sufficiently accurate, it is no longer tenable. Theory plays an increasing role and under some circumstances, especially for reactions involving radical reactions where the radicals are difficult to observe or to generate cleanly, theory is often the better approach, or it can be used to select and refine the more reliable experimental studies. Theory also often fulfils the essential step of providing a robust method of extrapolation to combustion conditions for reactions studied experimentally over only a limited range of T and p. Increasingly publications on rate constant determinations include both theory and experiment. It is frequently necessary to ‘tune’ electronic structure calculations using experimental data, usually by optimising the energy of a transition state within the accepted uncertainty limits of the method used. It is also worth stating that care needs to be used in applying theoretical methods to radical reactions, and that an appropriately high level of theory is employed. 2. The evaluations include an estimate of the uncertainty in a rate constant or in a channel yield. These are purely subjective estimates, designed to indicate which rate constants are quite well defined and which need further work. They are not based on a strict statistical analysis of the available data, but often rely, instead, on the consensus shown by the different investigations. The quality of a given experimental approach is assessed and the data used selectively in the recommendation on that basis. So an approach based on a weighted fit to all the available data, and of the associated standard deviation, is not deemed appropriate. Increasingly, though, modellers need to assess the uncertainty of a model prediction, e.g., through a Monte Carlo analysis, [129,130] or in model optimisation [6]. To do this they need the uncertainties in the model components, including the rate constants; all that is available is the set of subjective uncertainties pro-

vided with the recommended rate data. An approach is needed that combines the expert nature of the evaluation process with a more objective, and probably less conservative, method of assessing uncertainty. One method that has been used to generate practical mechanisms is to optimise the model by tuning all of the rate data together through comparisons with target data, e.g. observations of species concentrations in flames or flow reactors. This approach, which was adopted by Frenklach and co-workers in GRI-Mech [6,131], still relies on the definition of an acceptable tuning range for a rate parameter, which is taken as the uncertainty in the evaluation. Frenklach [132] has argued that optimisation is an essential process, not only in the generation of a practical mechanism that forms part of a range of predictive combustion models, but also in the assessment of rate data and the identification of parameters that are inconsistent with experimental target datasets. He contends that not to use target datasets to tune and assess rate parameters is to neglect a significant component of the available information. Thermodynamic data are an essential element of kinetic evaluations, because of the need to calculate the rate constant for the reverse process and to assess the likelihood of a specific channel contributing to a reaction on purely energetic grounds. Thermodynamic data are also evaluated, e.g., by the IUPAC panel, chaired until recently by Tibor Berces and now by Branko Ruscic [133]. There are strong links between the two types of dataset, for example because rate data have played a role in the determination of enthalpies of formation of radicals. Ruscic and co-workers have taken the interlinkages between thermodynamic and rate and other data used for determining enthalpies of formation to a higher level through global multiset data optimization in the generation of the Active Thermodynamic Tables [134]. The wider implications for chemical mechanisms within combustion models was discussed at length by Frenklach [132] in his paper Transforming data into knowledge—Process informatics for combustion chemistry, at the 31st Symposium. He presented a vision for the future of predictive combustion models through what he termed Process Informatics which ‘‘relies on three major components: proper organization of scientific data, availability of scientific tools for analysis and processing of these data, and engagement of the entire scientific community in the data collection and analysis.” With colleagues, Frenklach has established PrIMe, the Process Informatics Model, that is starting to implement this vision. It is based on a Depository, to which data providers submit their results on complex combustion

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

systems and on elementary reactions. In addition there are two sets of Tools. One set enables the collection, transfer, organization, display, curation, and mining of the data, the other provides the scientific and numerical tools required to convert the data into optimized models. Through these facilities, Frenklach see the community acting together to generate single accepted mechanisms, populated with evaluated and optimized rate data that can be used not only in predictive models but also as a means of identifying the areas in which the community can best spend its effort in the determination of new rate data for elementary reactions, through a combination, as appropriate, of theory and experiment, and new data for complex combustion systems. This identification would also be able to specify the accuracy needed in the results returned from such new investigations. The PrIMe experiment has started and its success in engaging the community is being put to the test [135]. There are a number of questions that remain to be answered, including the roles of publications and peer review, that have been central to the traditional evaluation process, the roles of publishers and of personal and institutional datasets, and the ownership of the data. The sociological aspects present problems as challenging as the scientific ones. The solution or solutions extend well beyond combustion to the chemistry of the earth’s and other planetary atmospheres, to interstellar chemistry and to metabolic pathways, to name but a few. There is no doubt that, whichever way we go, we will need to change our approach to collaboration, but that is clearly changing already. 9. Conclusions Rate data for elementary reactions are essential elements of combustion models. Direct methods of measuring rate data, both rate constants and channel yields, have improved substantially over recent years, with the development of new and the improvement of old detection techniques. Even more dramatic advances have been made in theoretical methods, both in electronic structure methods for calculating potential energy surfaces, and in methods for calculating rate data from those surfaces, using variants of transition state theory and, where necessary, master equation calculations. The most significant advances have been made where theory and experiment are combined. This conclusion was illustrated by reference to three combustion kinetic problems: (i) The reactions between OH and C2H2 and C2H4 proceed by complex mechanisms involving both addition and H abstraction. The addition reactions can lead to a range

41

of products, especially at higher temperatures. The abstraction reactions are favoured by high temperatures. The experimental database on the overall rate constant as a function of T and p is substantial, but reliable information of product channels is much less firmly based. Theory has been used for both reactions, using selective experiments for tuning the potential energy surface where necessary, to give a complete set of rate parameters for use in combustion models. (ii) A close collaboration between theory and experiment has led to a substantial increase in our understanding of key reactions occurring when alkyl radicals react with oxygen to form peroxy radicals. Important insights have been derived for small alkyl radicals and an improved understanding is beginning to develop for larger alkyl radicals. Further progress is needed, though, for the types of radicals that are important in automotive fuels. (iii) Reactions of methylene, which are important, for example, in soot formation, are reasonably well characterised experimentally, at least at low T. Other than in providing a basic framework for these reactions, theory has so far played little role in developing our detailed understanding. This is an area where new theoretical input is required. From a combustion perspective, rate data only become of value when they are used in chemical mechanisms incorporated in combustion models. This process is also undergoing a revolution, related both to the developments in experiment and theory and in the potential of collaborative activities across the community. These developments will almost certainly change the way in which our research is conducted and developments made. Just exactly what changes will occur and how they will be implemented is not yet clear.

Acknowledgments I am grateful to my colleagues at Leeds, and especially to Mark Blitz, David Glowacki, Kevin Hughes, Struan Robertson, and Paul Seakins for their many contributions to our work together on reactions kinetics. EPSRC and NERC are acknowledged for funding. References [1] J.F. Griffiths, J.A. Barnard, Flame and Combustion, third ed., Blackie, London, 1995.

42

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

[2] C.A. Taatjes, N. Hansen, J.A. Miller, et al., J. Phys. Chem. A 110 (2006) 3254–3260. [3] R.W. Walker, C. Morley, in: M.J. Pilling (Ed.), Low-Temperature Combustion and Autoignition, Elsevier, Amsterdam, The Netherlands, 1997, p. 1. [4] A.A. Konnov, Combust. Flame 152 (2008) 507– 528. [5] W.J. Pitz, C.V. Naik, T. Ni. Mhaolduin, et al., Proc. Combust. Inst. 31 (2006) 267–275. [6] M. Frenklach, M. Goldenberg, N. Moriarty, et al., Proc. Int. Gas Res. Conf. 5 (1998) 329–336. [7] K.J. Hughes, T. Turanyi, A.R. Clague, M.J. Pilling, Int. J. Chem. Kinet. 33 (9) (2001) 513–538. [8] G. Moreac, E.S. Blurock, F. Mauss, Combust. Sci. Technol. 178 (2006) 2025–2038. [9] S. Touchard, R. Fournet, P.A. Glaude, et al., Proc. Combust. Inst. 30 (2004) 1073–1081. [10] R.G. Susnow, A.M. Dean, W.H. Green, P. Peczak, L.F. Broadfelt, J. Phys. Chem. A 101 (1997) 3731– 3740. [11] Y. Muharam, J. Warnatz, Phys. Chem. Chem. Phys. 9 (31) (2007) 4218–4229. [12] H. Huang, M. Fairweather, J.F. Griffiths, A.S. Tomlin, R.B. Brad, Proc. Combust. Inst. 30 (1) (2005) 1309–1316. [13] V. Bykov, U. Maas, Combust. Theory Model. 11 (6) (2007) 839–862. [14] S.H. Robertson, P.W. Seakins, M.J. Pilling, in: M.J. Pilling (Ed.), Low-Temperature Combustion and Autoignition, Elsevier, Amsterdam, The Netherlands, 1997, p. 125. [15] P.A. Cleary, M.T.B. Romero, M.A. Blitz, et al., Phys. Chem. Chem. Phys. 48 (2006) 5633–5642. [16] P. Clifford, J.T. Farrell, J.D. DeSain, C.A. Taatjes, J. Phys. Chem. A 104 (2000) 11549–11560. [17] H. Qian, D. Turton, P.W. Seakins, M.J. Pilling, Chem. Phys. Lett. 322 (2000) 57–64. [18] J. Eskola, R.S. Timonen, Phys. Chem. Chem. Phys. 5 (2003) 2557–2561. [19] S. Brown, A.R. Ravishankara, H. Stark, J. Phys. Chem. A 104 (2000) 7044–7052. [20] K. Srinivasan, M.-C. Suz, J.V. Michael, Phys. Chem. Chem. Phys. 9 (2007) 4155–4163. [21] M.A. Oehlschlaeger, D.F. Davidson, R.K. Hanson, J. Phys. Chem. A 110 (2006) 9867–9873. [22] L.B. Harding, S.J. Klippenstein, A.W. Jasper, Phys. Chem. Chem. Phys. 9 (2007) 4055–4070. [23] S.W. Benson, Thermochemical Kinetics, second ed., Wiley, New York, 1976. [24] J.P. Senosiain, J.H. Han, C.B. Musgrave, D.M. Golden, Faraday Discuss. 119 (2001) 173–189. [25] R. Sumathi, H.-H. Carstensen, W.H. Green Jr., J. Phys. Chem. A 105 (2002) 6910–6925. [26] R. Sumathi, H.-H. Carstensen, W.H. Green Jr., J. Phys. Chem. A 106 (2002) 5474–5489. [27] S.J. Klippenstein, J. Phys. Chem. 98 (1994) 11459– 11464. [28] Y. Georgievskii, S.J. Klippenstein, J. Chem. Phys. 118 (2003) 5442–5455. [29] Y. Georgievskii, S.J. Klippenstein, J. Phys. Chem. A 107 (2003) 9776–9781. [30] L.B. Harding, Y. Georgievskii, S.J. Klippenstein, J. Phys. Chem. A 109 (2005) 4646–4656. [31] M. Evleth, E. Kassab, Chem. Phys. Lett. 131 (1986) 475–482. [32] K.V. Darvesh, R.J. Boyd, P.D. Pacey, J. Phys. Chem. 93 (1989) 4772–4779.

[33] S.H. Robertson, D.M. Wardlaw, D.M. Hirst, J. Chem. Phys. 99 (1993) 7748–7761. [34] M. Naroznij, J. Chem. Soc. Faraday Trans. 94 (1998) 2531. [35] S.J. Klippenstein, L.B. Harding, J. Phys. Chem. A 103 (1999) 9388–9398. [36] H. Hippler, K. Luther, A.R. Ravishankara, J. Troe, Z. Phys. Chem. Neue Folge 142 (1984) 1–12. [37] I.R. Slagle, D. Gutman, J.W. Davies, M. Pilling, J. Phys. Chem. 92 (1988) 2455–2462. [38] D. Walter, H.-H. Grotheer, J.W. Davis, M. Pilling, A.F. Wagner, Proc. Combust. Inst. 23 (1990) 107–114. [39] D. Fulle, H.F. Hamann, H. Hippler, C.P. Jansch, Ber. Bunsen-Ges. Phys. Chem. 101 (1997) 1433–1442. [40] R.X. Fernandes, K. Luther, J. Troe, J. Phys. Chem. A 110 (13) (2006) 4442–4449. [41] A.W. Jasper, S.J. Klippenstein, L.B. Harding, J. Phys. Chem. A 111 (2007) 8699–8707. [42] W. Braun, A.M. Bass, M.J. Pilling, J. Chem. Phys. 52 (1970) 5131–5143. [43] H.H. Carstensen, Dissertation, Max-Planck-Institut fu¨r Stro¨mungsforschung, Go¨ttingen, 1995. [44] P. Frank, T. Just, Proc. Int. Symp. Shock Tubes Waves 14 (1984) 706. [45] P. Frank, K.A. Bhaskaran, T. Just, J. Phys. Chem. 90 (1986) 2226–2231. [46] S. Bauerle, M. Klatt, H.G. Wagner, Ber. BunsenGes. Phys. Chem. 99 (1995) 870. [47] H.M. Frey, R. Walsh, J. Phys. Chem. 89 (1995) 2445–2446. [48] R. Becerra, C.E. Canosa-Mas, H.M. Frey, R. Walsh, J. Chem. Soc. Faraday Trans. 283 (1987) 435–448. [49] R.G. Gilbert, S.C. Smith, Theory of Unimolecular and Recombination Reactions, Blackwell Scientific Publications, Oxford, 1990. [50] K.A. Holbrook, M.J. Pilling, S.H. Robertson, Unimolecular Reactions, Wiley, London, 1996. [51] S.J. Klippenstein, J.A. Miller, J. Phys. Chem. A106 (2002) 9267–9277. [52] S.H. Robertson, M.J. Pilling, L.C. Jitariu, I.H. Hillier, Phys. Chem. Chem. Phys. 9 (2007) 4085– 4097. [53] J.A. Miller, Faraday Discuss. 119 (2001) 461–475. [54] W. Tsang, V. Bedanov, M.R. Zachariah, Ber. Bunsen-Ges. Phys. Chem. 101 (1997) 491–499. [55] J.A. Miller, J.A. Miller, S.J. Klippenstein, J. Phys. Chem. A 107 (2003) 2680–2692. [56] J.T. Bartis, B. Widom, J. Chem. Phys. 60 (1974) 3474–3482. [57] M.A. Blitz, K.J. Hughes, M.J. Pilling, S.H. Robertson, J. Phys. Chem. A 110 (2006) 2996–3009. [58] J.A. Miller, S.J. Klippenstein, J. Phys. Chem. A 110 (2006) 10528–10544. [59] A. Liu, W.A. Mulac, C.D. Jonah, J. Phys. Chem. 92 (1988) 5942–5945. [60] P. Smith, P.W. Fairchild, D.R. Crossley, J. Chem. Phys. 81 (1984) 2667–2677. [61] D.L. Baulch, C.T. Bowman, C.J. Cobos, R.A. Cox, T. Just, J.A. Kerr, et al., J. Phys. Chem. Ref. Data 34 (2005) 757–1397. [62] D.L. Baulch, C.J. Cobos, R.A. Cox, E. Esser, P. Franck, Th. Just, J.A. Kerr, M.J. Pilling, J. Troe, R.W. Walker, J. Warnatz, J. Phys. Chem. Ref. Data 21 (1992) 411–734. [63] J.P. Senosiain, S.J. Klippenstein, J.A. Miller, J. Phys. Chem. A 109 (2005) 6045–6055.

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44 [64] J.P. Senosiain, S.J. Klippenstein, J.A. Miller, J. Phys. Chem. A 110 (2006) 6960–6970. [65] C.A. Taatjes, S.J. Klippenstein, N. Hansen, J.A. Miller, T.A. Cool, J. Wang, M.E. Law, P.R. Westmoreland, Phys. Chem. Chem. Phys. 7 (2005) 806–813. [66] F.P. Tully, Chem. Phys. Lett. 96 (1983) 148–153. [67] F.P. Tully, Chem. Phys. Lett. 143 (1988) 510–514. [68] A.D. Liu, W.A. Mulac, C.D. Jonah, J. Phys. Chem. 92 (1988) 3828–3833. [69] E.E. Greenwald, S.W. North, Y. Georgievskii, S.J. Klippenstein, J. Phys. Chem. A 109 (2005) 6031–6044. [70] K.W. McKee, M.A. Blitz, P.A. Cleary, D.R. Glowacki, M.J. Pilling, P.W. Seakins, J. Phys. Chem. A 111 (2007) 4043–4055. [71] J.W. Davies, N.J.B. Green, M.J. Pilling, Chem. Phys. Lett. 126 (1986) 373–379. [72] J. Troe, J. Phys. Chem. 83 (1979) 114–126. [73] D. Bradley, C. Morley, in: M.J. Pilling (Ed.), LowTemperature Combustion and Autoignition, Elsevier, Amsterdam, The Netherlands, 1997, p. 661. [74] J.F. Griffiths, C. Mohamed, in: M.J. Pilling (Ed.), Low-Temperature Combustion and Autoignition, Elsevier, Amsterdam, The Netherlands, 1997, p. 545. [75] C.A. Taatjes, J. Phys. Chem. A 110 (2006) 4299– 4312. [76] J.D. DeSain, E.P. Clifford, C.A. Taatjes, J. Phys. Chem. A 105 (2001) 3205–3213. [77] J.D. DeSain, C.A. Taatjes, J. Phys. Chem. A 105 (2001) 6646–6654. [78] J.D. DeSain, C.A. Taatjes, J.A. Miller, S.J. Klippenstein, D.K. Hahn, Faraday Discuss. 119 (2001) 101–120. [79] J.C. Rienstra-Kiracofe, W.D. Allen, H.F. Schaefer, J. Phys. Chem. A 104 (2000) 9823–9840. [80] J.A. Miller, S.J. Klippenstein, S.H. Robertson, Proc. Combust. Inst. 28 (2000) 1479–1486. [81] J.A. Miller, S.J. Klippenstein, Int. J. Chem. Kinet. 33 (2001) 654–668. [82] K.J. Hughes, P.D. Lightfoot, M.J. Pilling, Chem. Phys. Lett. 191 (1992) 581–586. [83] K.J. Hughes, P.A. Halford-Maw, P.D. Lightfoot, T. Turanyi, M.J. Pilling, Proc. Combust. Inst. 24 (1992) 645–652. [84] J.D. DeSain, S.J. Klippenstein, C.A. Taatjes, Phys. Chem. Chem. Phys. 5 (2003) 1584–1592. [85] H. Sun, J.W. Bozzelli, J. Phys. Chem. A108 (2004) 1694–1711. [86] S.V. Petway, H. Ismail, W.H. Green, E.G. Estupinan, L.E. Jusinski, C.A. Taatjes, J. Phys. Chem. A111 (2007) 3891–3900. [87] J.V. Michael, D.G. Keil, R.B. Klemm, J. Chem. Phys. 83 (1985) 1630–1636. [88] G.S. Tyndall, J.J. Orlando, T.J. Wallington, M.D. Hurley, Int. J. Chem. Kinet. 29 (1997). [89] M.A. Blitz, D.E. Heard, M.J. Pilling, Chem. Phys. Lett. 235 (2002) 374–379. [90] S. Hatakeyama, N. Washida, H. Akimoto, J. Phys. Chem. 90 (1986) 173–178. [91] W.P.L. Carter, D. Luo, I.L. Malkina, Investigation of the Atmospheric Ozone Formation Potential of Acetylene. Center for Environmental Research and Technology, Riverside, California, 1997. [92] Z.Y. Zhang, J. Peeters, in: G. Restelli, G. Angeletti (Eds.), Proceedings Fifth European Symposium on

43

Physico-Chemical Behaviour of Atmospheric Pollutants, Kluwer Academic Publishers, Dordrecht, 1990, p. 377. [93] D.R.Glowacki, Ph.D. Thesis, University of Leeds, 2008. [94] S. Raoult, M.T. Rayez, J.-C. Rayez, R. Lesclaux, Phys. Chem. Chem. Phys. 6 (2004) 2245–2253. [95] B. Bohn, C. Zetzsch, Phys. Chem. Chem. Phys. 1 (1999) 5097–5107. [96] C. Bloss, V. Wagner, M.E. Jenkin, R. Volkamer, W.J. Bloss, J.D. Lee, Atmos. Chem. Phys. 5 (2005) 641–664. [97] P. Jensen, P.R. Bunker, J. Chem. Phys. 89 (1988) 1327–1332. [98] W. Kirmse, Carbene Chemistry, second ed., Academic, New York, 1971. [99] H. Okabe, Photochemistry of Small Molecules, John Wiley & Sons, New York, 1978. [100] R. Becerra, C.E. Canosa-Mas, H.M. Frey, et al., J. Chem. Soc. Faraday Trans. 2 83 (1987) 435–448. [101] C.E. Canosa-Mas, H.M. Frey, R. Walsh, J. Chem. Soc. Faraday Trans. 2 81 (1985) 283–300. [102] C.H. Wu, R.D. Kern, J. Phys. Chem. 91 (1987) 6291–6296. [103] R.D. Kern, H.J. Sing, C.H. Wu, Int. J. Chem. Kinet. 20 (1988) 731–747. [104] U. Alkemade, K.H.Z. Homann, Z. Phys. Chem. (Munich) 161 (1989) 19–34. [105] R.D. Kern, H. Chen, J.H. Kiefer, P.S. Mudipalli, Combust. Flame 100 (1995) 177–184. [106] C.E. Canosa-Mas, M. Ellis, H.M. Frey, R. Walsh, Int. J. Chem. Kinet. 16 (1984) 1103–1110. [107] G. Hancock, M.R. Heal, J. Phys. Chem. 96 (1992) 10316–10322. [108] O. Langford, H. Petek, C.B. Moore, J. Chem. Phys. 78 (1983) 6650–6659. [109] U. Bley, F. Temps, H.G. Wagner, Ber. BunsenGes. Phys. Chem. 96 (1992) 1043–1048. [110] W. Hack, M. Koch, H.Gg. Wagner, A. Wilms, Ber. Bunsen-Ges. Phys. Chem. 92 (1988) 674–678. [111] K.F. Freed, Adv. Chem. Phys. 47 (1981) 291–336. [112] U. Bley, M. Koch, F. Temps, Ber. Bunsen-Ges. Phys. Chem. 93 (1989) 833–841. [113] K.F. Freed, J. Chem. Phys. 64 (1976) 1604–1611. [114] W.M. Gelbart, K.F. Freed, Chem. Phys. Lett. 37 (1976) 47–50. [115] R. Wagener, Z. Naturforsch. 45a (1990) 649–656. [116] F. Hayes, W.D. Lawrence, W.S. Staker, K.D. King, J. Phys. Chem. 100 (1996) 11314–11318. [117] M.A. Blitz, M.S. Beasley, M.J. Pilling, S.H. Robinson, Phys. Chem. Chem. Phys. 2 (2000) 805–812. [118] M.A. Blitz, N. Choi, P.W. Seakins, M.J. Pilling, Proc. Combust. Inst. 30 (2005) 927–933. [119] M.A. Blitz, M.J. Pilling, P.W. Seakins, Phys. Chem. Chem. Phys. 3 (2001) 2241–2244. [120] K.L.Gannon, Ph.D. Thesis, University of Leeds, 2007. [121] M.A. Blitz, K.W. McKee, M.J. Pilling, P.W. Seakins, Chem. Phys. Lett. 372 (2003) 295–299. [122] D.L. Baulch, in: M.J. Pilling (Ed.), Low-Temperature Combustion and Autoignition, Elsevier, Amsterdam, The Netherlands, 1997, p. 235. [123] N. Cohen, K. Westberg, J. Phys. Chem. 83 (1979) 46–50. [124] R.F. Hampson, D. Garvin, J. Phys. Chem. 81 (1977) 2317–2319. [125] W. Tsang, R.F. Hampson, J. Phys. Chem. Ref. Data 15 (1986) 1087–1279.

44

M.J. Pilling / Proceedings of the Combustion Institute 32 (2009) 27–44

[126] Availbale at: . [127] Available at: . [128] Available at: . [129] I. Gy. Zsely, J. Zador, T. Turanyi, Proc. Combust. Inst. 30 (2005) 1273–1281. [130] J. Zador, I.G. Zsely, T. Turanyi, M. Ratto, S. Tarantola, A. Saltelli, J. Phys. Chem. A 109 (2005) 9795–9807.

[131] Available at: . [132] M. Frenklach, Proc. Combust. Inst. 31 (2007) 125– 140. [133] B. Ruscic, J.E. Boggs, A. Burcat, A.G. Czasar, J. Demaison, R. Janoschek, J. Phys. Chem. Ref. Data 34 (2005) 573–656. [134] B. Ruscic, R.E. Pinzon, M.L. Morton, G.V. Laszewski, S.J. Bittner, S.G. Nijsure, J. Phys. Chem. 108 (2004) 9979–9997. [135] Available at: .