Kinetic Analysis of the Gas-Phase Reactions of Methyl Vinyl Ketone with the OH Radical in the Presence of NO

Um mecanismo explícito para a reação do metil-vinil-cetona com radicais OH, numa mistura NOx -ar, foi simulado resolvendo as equações diferenciais ordinárias usando o método RungeKutta-4-semi-implícito. Os resultados simulados são consistentes com os dados experimentais publicados e o modelo explica as principais vias de reação para a oxidação do MVK com radicais OH na presença de NOx -ar. Usando uma análise dos autovetores e autovalores dos coeficientes de sensibilidade, para todas as espécies químicas envolvidas em diferentes tempos de reação, foi extraída informação cinética do sistema. Este método foi utilizado para reduzir o modelo cinético de forma objetiva. Foi utilizado, também, o método tradicional de análise de velocidade de produção (ROPA) para estudar a importância relativa das reações individuais. Usando a informação da análise de componente principal e da análise de velocidade de produção, foram identificadas as principais reações individuais.


Introduction
Methyl vinyl ketone is the simplest α,β-unsaturated ketone.It is produced, together with methacrolein, from the gas-phase reactions of isoprene with the OH radical in the presence of oxides of nitrogen (NOx) [1][2][3] and with O3 4,5 .The emissions of isoprene, which originate primarily from vegetation [6][7][8][9][10][11] , may dominate over anthropogenic nonmethane organic emissions on regional and global scales [12][13][14] .This potential environmental impact makes the inclusion of the isoprene atmospheric chemical reactions into airshed computer models necessary 15,16 , which in turn requires a quantitative understanding of the atmospheric chemistry of both methacrolein and methyl vinyl ketone.
In this work, the gas-phase reactions of methyl vinyl ketone (hereafter MVK, CH3COCH=CH2) with OH radicals in NOx-air systems are simulated and an eigenvalueeigenvector analysis of the linear sensitivity coefficients, called Principal Component Analysis 17 , is used to assess the relative importance of the elementary processes.
Reaction rate analysis for complex kinetic systems includes the solution of the kinetic differential equations, the study of the effects of parameter changes on the results and the exploration of important reaction pathways [17][18][19][20][21][22][23] .This information is important to decide which reactions should be included in an atmospheric photochemical mechanism and, also, which reactions should be experimentally studied.
Only one experimental study has been conducted for the MVK reaction with OH radicals 24 .The authors of this study measured and identified the products of MVK oxidation, obtaining directly quantitative yields for glycolaldehyde (HOCH2CHO), methylglyoxal (CH3COCHO) and formaldehyde (HCHO).They also discussed and recommended a mechanism to represent the MVK + OH chemistry.Nevertheless, to our knowledge, a sensitivity analysis of the mechanism has not been done up to now.
In this paper the initial conditions for the simulations were those of the laboratory smog chamber experiments of Tuazon and Atkinson 24 in order to compare the calculated and experimental results.

The chemical mechanism
As previously discussed 24 MVK reacts essentially with OH radicals by H-atom abstraction, with an overall rate constant of 18.80x10 -12 cm 3 molecule -1 s -1 at 298 K 25 .
The present chemical mechanism considers 28 species and 40 reactions and was proposed on the basis of reliable, previous models 26,27 and of the known MVK chemistry.Thermal rate constants were either taken from the literature [28][29][30][31] or estimated by comparison with similar compounds 32 .The photochemical reaction rates were estimated on the basis of the ethyl nitrite photodecomposition experimental data 24 .The chemical mechanism is listed in Table 1.

Methodology
The chemical process can be described by a system of kinetic differential equations, where c(t) is the n-vector of species concentrations with c(t = 0) = c 0 and k is the m-vector of kinetic parameters.Analytical solutions are not available for complex systems and a numerical solution is required.An important question in modeling studies is the effect of parameter change on the solution.In general, an alteration in the kinetic parameters from k 0 to k at time t1 causes a change in the solution of the system at a time t2 (with t2 > t1).The effect of the parameter change on the solution can be expressed through the first order local concentration sensitivity coefficients defined as The Sij coefficient is the linear approximation of concentration change of species i at the time t2 caused by the differential change of the parameter of reaction j at time t1 from value kj0 to kj.In this work the parameters are the photochemical coefficients and the thermal rate constants.
Sensitivity coefficients are normalized in order to eliminate their dependence on the dimensions of the kinetic model.The effect of a single parameter on a group of concentrations is demonstrated by the overall sensitivities which are the sum of the squares of the normalized sensitivities.A better description of parameter-concentration interdependence consists in the identification of the groups of parameters which have joint influence on a group of concentrations.This type of information is given by the principal component analysis of the normalized sensitivity matrix.The eigenvectors of the matrix S T S, where S is the array of sensitivity coefficients, identify parameter groups while the eigenvalues give information about the effectiveness of these parameter groups for the change of species concentrations.A parameter is considered important if it belongs to a large element of an eigenvector corresponding to a large eigenvalue.The methodology of numerical simulation, sensitivity and principal component analysis is fully discussed in the literature [33][34][35][36][37][38] .
An alternative method for the study of the reactions relevance is the rate of production analysis called ROPA 35,39 .Although the combination of species reduction and rate sensitivity analysis 36 seems to be a more effective way for this purpose, the rate of production analysis is a classic method for the identification of important reaction pathways.This methodology requires the calculation of the Pij matrix elements 40,41 , which show the contribution of reaction j to the rate of production of species i.The rate of production analysis is rather difficult to interpret in a correct way and must be analyzed together with principal component results.

Results and Discussions
The full mechanism and rate constants are presented in Table 1.The reduced mechanism was obtained after elimination of the non-important reactions (denoted by # in Table 1) on the basis of the principal component analysis described below.The rank of reactions ordered by overall sensitivities and rates is shown in Table 2.We calculated normalized sensitivities for all species at time points 1.9, 6.9, 11.9, 16.8, 21.8, 26.8, 33.8, 40.8 and 49.8 minutes.Eigenvalues of S T S and the corresponding eigenvectors are listed in Table 3.
In the conditions of the modeling, the main source of hydroxyl radicals is the reaction (5) (HO2 + NO → OH + NO2) which follows the photolysis of the ethyl nitrite   (CH3CH2ONO + hν → CH3CH2O + NO) and the oxidation of the CH3CH2O radicals (CH3CH2O + O2 → CH3CHO + HO2).Reaction (5) accounts for ca.92% of OH radical formed and the only significant sources of NO are the photodecomposition of ethyl nitrite (8%) and NO2 (91%), reactions ( 26) and (10), respectively.Since we had no data on photolysis light intensities during the experiments, the ethyl nitrite photodecomposition coefficient was estimated from experimental data (Fig. 1) and values, which gave consistent results for other photodecompositions, were used.The photolysis rates were also consistent with the value reported in the literature 42 for NO2 photodecomposition under the same experimental conditions.Also, photochemical reactions of other species, not including NO2 photodecomposition, are of negligible importance compared with other paths.As expected, the set of reactions (Table 1) accounts for the MVK photooxidation in good agreement with experimental data (Fig. 3).As presented in Figs. 2 and 4, simulated results for the formation of the main products, glycolaldehyde, methylglyoxal and formaldehyde, show a slight deviation mainly for longer times.
In the simulation conditions, formaldehyde is formed both from acetaldehyde, the initial product of ethyl nitrite photolysis, reaction (26), and by the sequence of reactions initiated by OH radical oxidation of MVK: The rate of production analysis shows that 63% of formaldehyde is formed through reaction ( 13), CH3O + (O2) → HCHO + HO2 and 37% through the reaction sequence ( 20), ( 21) and ( 22), which involve the reaction of CH3C(O)CH(OH)CH2O2 with NO.Under the modeling conditions, the secondary reactions of formaldehyde are of minor importance.As observed experimentally 24,42 , the formed formaldehyde reacts essentially with OH radicals which are in relatively high concentrations (calculated    values about 0.5-1.0x 10 7 molecule cm -3 ).Nevertheless, the rate of this reaction path is 5.1% of the total formation rate and, in comparison with OH radical reaction (11)  (HCHO + OH + (O2) → HO2 + CO + H2O), the photochemical decompositions ( 39) and (40) (HCHO + (2 O2) + hν → 2 HO2 + CO and HCHO + hν → H2 + CO) are of non-negligible importance (26%).
In the conditions of this simulation, the formation of acetaldehyde (Fig. 4) and peroxyacetyl nitrate (PAN) (Fig. 5) can be attributed to the photooxidation of ethyl nitrite 42 .The simulated results are in good agreement with experimental data only for peroxyacetyl nitrate.The main discrepancy between the experimental results and the model predictions is higher concentrations of calculated acetaldehyde.The reasons for this discrepancy are not well established, but may be associated to the large uncertainty in the related kinetic parameters.In comparison with OH radical reaction (CH3CHO + OH + (O2) → CH3CO3 + H2O), the acetaldehyde photochemical decompositions (CH3CHO + (2 O2) + hν → CH3O2 +HO2 +CO) are of non-negligible importance, as shown by the principal component analysis.
The 1 st and 2 nd principal components in Table 3 show that ethyl nitrite photodecomposition, reaction (26), oxidation of MVK, reaction (20), PAN chemistry, reactions ( 15) and ( 16), and OH/NO chemistry, reactions (3), ( 4) and ( 5), are strongly coupled and are the most influential reaction sequence in the mechanism.Thus, a small deviation in k20 or j26 should greatly affect the simulation results.
According to the magnitude of the eigenvalues and significant entries (≥ 0.20) of the corresponding eigenvector, the individual reactions may be classified in three groups: 1) Eigenvalues λ1 to λ22 are much larger than the remaining ones.Note that ∑  3)-( 10), ( 12)-( 16), ( 18), ( 20)-( 26), ( 29)-( 33), ( 36) and ( 37), forming the ''basic'' part of mechanism.According to Ψ1, the most influential reaction sequence is formed by ( 26), ( 20), ( 4), ( 16) and ( 15).This ''reaction kernel'' emphasizes that the largest effect is brought about by setting the parameters j26 and k20.Reactions ( 4), ( 15) and ( 16) largely affects the NO/NO2 ratio and the simulated results.Due to the coupling of the individual reactions, this ratio not only depends on the rate of reactions ( 20) and ( 26) but also on all the reactions involving NOx.Since j26 is an estimated parameter, some deviations of the simulated results may be attributed to it.An uncertainty analysis of this parameter shows that a change of 10% in j26 leads to a substantial change of all product concentrations (6.8% in glycoaldehyde 9.8% in methylglyoxal and 7.3% in formaldehyde).The inclusion of another minor path of reaction, such as the formation of alkylnitrates, might affect the NO/NOx ratios by a non-negligible amount.
As shown in Table 4, eliminating the last group of reactions causes small changes in concentrations and only the HCHO concentration shows a deviation greater than others (8.8%) because of the elimination of reaction (39).If this reaction is included in the reduced mechanism, this deviation decreases to 2.89%.However, additional elimination of steps ( 11), ( 12), ( 17), ( 38) and (40) (i.e.reactions of ''transitional'' importance) leads to large deviations (Table 4).That is, no further reduction of the mechanism is possible since all concentration changes should be small.
The rank of reactions by overall sensitivity (Table 2) suggests that reaction 39 may be eliminated.However, this   2), ( 19), ( 27), ( 28), ( 34), ( 35) and (39) (column A) and also steps ( 11), ( 12), ( 17), (38)  elimination leads to large deviations (e.g. at t = 49.9 min the deviation for HCHO is 8.8%).The rate reaction rank (Table 2) gives a different rank of reactions and is not an effective way of reducing a mechanism.Individual rates do not consider the interactions between reactions and may lead to incorrect conclusions about the relevance of individual reactions.Consequently, as previously shown the rate of production analysis is a good method for the exploration of the reaction pathways.

Conclusions
The mechanism of Table 1 is quite successful in reproducing chamber data for the oxidation of MVK by OH radicals.The rate of production analysis gives useful information in determining the main reaction pathways.
Rate of production results in combination with principal component analysis show that reaction are strongly coupled and confirm that the most influential reactions paths are the ethyl nitrite photolysis, the MVK oxidation and the chemistry of NOx, PAN and OH radical.On the basis of the calculated eigenvalues, the mechanism can be reduced to 33 reactions.No further reduction is possible since all concentration changes should be small.Certainly, the conclusions taken from the eigenvalue-eigenvector analysis are only valid for the rather narrow range of conditions of the smog chamber experiments.However, the information seems useful for identifying a minimal reaction set and for assessing the relationships and dependencies among the parameters.
Since reactions ( 21) -( 25) form the basic part of the mechanism, the estimation of their rate constants may lead to a considerable uncertainty in the simulated results.Thus, further experiments with this system, in order to study those reaction paths, would be important for the improvement of atmospheric photochemical mechanisms.

Figure 2 .
Figure 2. Simulated and experimental data for the main products of the gas-phase reactions of MVK with the OH radical in the presence of NOx as a function of reaction time.

Figure 1 .
Figure 1.Simulated and experimental data for the ethyl nitrite photodecomposition as a function of reaction time.

Figure 4 .
Figure 4. Simulated and experimental data for aldehyde concentrations as a function of reaction time.

Figure 3 .
Figure 3. Simulated and experimental data for the oxidation of the MVK as a function of reaction time.

Figure 5 .
Figure 5. Simulated and experimental data for the peroxyacetyl nitrate (PAN) concentrations as a function of reaction time.

Table 1 .
Chemical Mechanism for Gas-Phase Reactions of MVK with the OH Radical in the Presence of NOx.

Table 2 .
Rank of Reactions by Overall Sensitivity and Rates.