14372
J. Phys. Chem. 1996, 100, 14372-14382
Kinetics of the Cross Reactions of CH3O2 and C2H5O2 Radicals with Selected Peroxy Radicals Eric Villenave and Robert Lesclaux* Laboratoire de Photophysique et Photochimie Mole´ culaire, UniVersite´ Bordeaux I, URA 348 CNRS, 33405 Talence Cedex, France ReceiVed: March 12, 1996; In Final Form: June 5, 1996X
The kinetics of the reactions of selected peroxy radicals (RO2) with CH3O2 and with C2H5O2 have been investigated using two techniques: excimer-laser photolysis and conventional flash photolysis, both coupled with UV absorption spectrometry. Radicals were generated either by photolysis of molecular chlorine in the presence of suitable hydrocarbons or by photolysis of the appropriate alkyl chloride. All such cross-reaction kinetics were investigated at 760 Torr total pressure and room temperature except for the reaction of the allylperoxy radical with CH3O2, for which the rate constant was determined between 291 and 423 K, resulting in the following rate expression: k15 ) (2.8 ( 0.7) × 10-13 exp[(515 ( 75)/T] cm3 molecule-1 s-1. Values of (2.0 ( 0.5) × 10-13, (1.5 ( 0.5) × 10-12, (9.0 ( 0.15) × 10-14, 280 nm) f 2Cl
(6)
Cl + RH f HCl + R
(7)
Cl + CH4 (C2H6) f HCl + CH3 (C2H5)
(8)
R + O2 + M f RO2 + M
(9)
CH3 (C2H5) + O2 + M f CH3O2 (C2H5O2) + M (10) followed by the corresponding self-reactions, cross reactions, and subsequent secondary reactions of peroxy and alkoxy radicals.
This method was used in the particular cases of benzylperoxy, cyclohexylperoxy, and acetylperoxy radicals. The concentration of molecular chlorine was measured by its absorption at 330 nm (σ ) 2.56 × 10-19 cm2 molecule-1)15 and maintained in the range 1.5 × 1016 to 4.5 × 1016 molecule cm-3. The concentrations of the precursor RH, methane (or ethane), and oxygen were chosen such that the conversion of chlorine atoms into radicals was very rapid (20 ms) and dominated all other loss processes of Cl atoms. In addition, relative concentrations of RH and CH4 (or C2H6) were such that comparable concentrations of RO2 and CH3O2 (or C2H5O2) were generated simultaneously. The total concentration of radicals was determined by producing CH3O2 alone using its well-known UV absorption cross sections.1,2 The relative concentrations of RO2 and CH3O2 (or C2H5O2) were determined from the relative concentrations of precursors and from the rate constants of their reactions with chlorine atoms. However, in the case of the acetylperoxy radical, relative concentrations could be determined by monitoring its typical absorption at 207 nm, while that of the methyl(or ethyl-) peroxy radical was monitored at 240 nm. The gas mixtures were prepared by diluting Cl2, RH, methane (or ethane), and oxygen into a large flow of nitrogen using calibrated flow controllers at a total pressure of 760 Torr. Under these experimental conditions, initial radical concentrations were in the range 1.5 × 1013 to 7.0 × 1013 molecule cm-3. The total flow rate was sufficiently high to ensure that the reaction mixture in the cell was completely replenished between each flash, thus preventing complications arising from reaction products. Laser-Flash Photolysis/UV Absorption Apparatus. The apparatus consisted of a cylindrical Pyrex reaction cell (80 cm in length) bearing a Suprasil-grade quartz window at each end. The cell could be heated to about 500 K.10 The beam of an excimer laser (Lambda Physik Model EMG 200) was directed lengthwise through the cell to photolyze the radical precursors. RO2 and CH3O2 (or C2H5O2) were generated by photolysis at 193 nm of the corresponding alkyl chloride, either RCl or CH3Cl, in the presence of CH4 (or C2H6) or RH, respectively:
RCl + hν (λ ) 193 nm) f R + Cl
(11)
Cl + CH4 (C2H6) f HCl + CH3 (C2H5)
(8)
followed by reactions 9 and 10. This method was used for the studies of the reactions of CH2dCHCH2O2 and CH2ClO2 with CH3O2 and of CH2dCHCH2O2 with C2H5O2. However, in studies of C2H5O2 and neo-C5H11O2 reactions, the rate of reaction of Cl atoms with the appropriate precursor RCl was too fast and could not be avoided completely, so the photolysis of CH3Cl was preferred to that of RCl.
CH3Cl + hν (λ ) 193 nm) f CH3 + Cl
(12)
Cl + RH f HCl + R
(7)
followed by reactions 9 and 10. Note that in both methods, equal concentrations of RO2 and CH3O2 were generated, thus providing the best conditions for investigating the cross-reaction kinetics. The detection system was the same as described above for the argon-lamp flash photolysis apparatus. Concentrations of precursors were adjusted so that the absorption of the laser beam at 193 nm was always in the range 20-40%. Larger absorptions would have resulted in unsuitable longitudinal radical concentration gradients and associated complications.10 Radical concentrations were typically monitored at 235 nm, which corresponds to the maximum of the UV absorption
14374 J. Phys. Chem., Vol. 100, No. 34, 1996
Villenave and Lesclaux
spectrum of most peroxy radicals. In addition to the radical absorption, two other effects had to be taken into account, which resulted in an additional absorption signal at this wavelength: (i) a slight decrease in the transmission of optical elements (dichroic mirrors and windows) when impinged upon by the 193 nm laser pulse, resulting in an almost constant transient absorption of about 0.5-1%; (ii) the formation of ozone due to the photolysis of oxygen at 193 nm:
O2 + hν (193 nm) f 2O(3P)
(13)
O(3P) + O2 + M f O3 + M
(14)
The amount of ozone formed in the system was generally on the order of (2-5) × 1012 molecule cm-3, i.e., an order of magnitude lower than the total initial radical concentration. Such a concentration was too low to perturb significantly the reaction system. Other possible reactions of oxygen atoms leading to the formation of radical species were also negligible under our experimental conditions. To prevent too high a concentration of ozone being formed and to ensure a stochiometric conversion of radicals (R and CH3 (or C2H5)) into peroxy radicals, the concentrations of oxygen had to be adjusted within a fairly narrow range (typically from 2.5 × 1017 to 7.0 × 1017 molecule cm-3). The combination of both the above effects resulted in a slightly decreasing transient signal, which generally represented 20-30% of the total initial absorption. It was calibrated before and after each experiment in the absence of any radical precursor and taken into account in simulations as previously described.10 It was confirmed before each experiment that the conditions were appropriate and the technique viable by photolyzing CH3Cl in concentrations that gave roughly the same fractional absorption of the laser beam as above (in the presence of methane and oxygen) to generate CH3O2 radicals alone. The rate constant for the CH3O2 self-reaction was then measured and verified to compare favorably with the well-known value reported in the literature.1,2 The laser was operated at repetition rates of 0.25-0.40 Hz to ensure that the gas mixture was replenished between each pulse. A typical experiment required between 80 and 160 laser shots to obtain a satisfactory signal-to-noise ratio. Gas mixtures were introduced via a glass vacuum line using calibrated gas-flow controllers. Liquid radical precursors, such as CH2dCHCH2Cl, c-C6H12, CH2Cl2, CH3CHO, or C6H5CH3, were introduced into the gas mixture by passing a slow flow of nitrogen through a bubbler containing the appropriate precursor cooled in a water-ice bath. Oxygen, nitrogen, synthetic air, methane (AGA Gaz spe´ciaux, >99.995%), ethane (AGA Gaz spe´ciaux, 99.4%), chlorine (AGA Gaz spe´ciaux, 5% in nitrogen, >99.9%), chloromethane (L’Air Liquide, >99.5%), chloroethane (Aldrich, 99.7%), dichloromethane (Aldrich, 99.9%), allyl chloride (Aldrich, 99%), acetaldehyde (Aldrich, 99%), toluene (Aldrich, 99.5%), neopentane (ARGO int.Ltd., 99.0%), and cyclohexane (SDS, 99.5%) were all used without further purification. Synthetic air was employed as the main carrier gas in flash photolysis experiments. However, nitrogen was used instead in laser-flash photolysis experiments in which oxygen had to be limited to low concentrations to minimize the previously discussed formation of ozone. Data Analysis. A typical decay trace is shown in Figure 1 for the case of the reaction of CH2dCHCH2O2 (allylperoxy) with CH3O2. Decay traces were analyzed by numerical integration of a set of differential equations that took into account the
Figure 1. Experimental decay trace recorded at 235 nm and best-fit simulation (solid line) for the cross reaction of CH2dCHCH2O2 with CH3O2 at room temperature. Dashed line represents simulations with k15 changed by (40%.
complete reaction mechanism and simulated by adjusting selected parameters (rate constant and initial concentration) using nonlinear least-squares fitting. As an example, the reaction mechanism is detailed in the particular case of the CH2dCHCH2O2 + CH3O2 reaction in Table 1. For all the RO2 radicals investigated, the corresponding mechanism included the following reactions: self and cross reactions of RO2 and CH3O2 (or C2H5O2), including the terminating and nonterminating channels; the reactions of alkoxy radicals, i.e., reaction with O2 (forming HO2) and/or decomposition; the reactions of RO2 and CH3O2 (or C2H5O2) with HO2, assumed to produce the corresponding hydroperoxides; the reactions of peroxy radicals produced by the decomposition of the alkoxy radicals; the self-reaction of HO2. In addition to the UV absorption of peroxy radicals and HO2, the absorption of all products (carbonyls, H2O2, and hydroperoxides) was included in simulations of decay traces despite their small contribution (Figure 1). Where UV absorption spectra were unavailable, the spectra of structurally similar compounds were used instead, and the unknown absorption cross sections used in simulations were assumed to be identical with those known for this surrogate. A particular concern with these experiments was the sensitivity of the system to the various parameters used in simulations. It should be pointed out that the experimental conditions were such that the kinetic simulations were particularly sensitive to the rate constant of the fastest RO2 + RO2 reaction and to that of the RO2 + CH3O2 (or C2H5O2) reaction, provided the latter was not too small (generally not less than a factor of about 5 smaller than the highest RO2 + RO2 reaction rate constant). This was the case for most reactions investigated in this work, except for the benzyl peroxy radical, for which only an upper limit of the cross-reaction rate constant could be determined. The uncertainty of the rate constants of cross reactions is strongly dependent on the parameters used in simulations and on the knowledge of the reaction mechanism. This is the main reason that has led us to study RO2 radicals whose self-reaction had already been investigated in detail. Results Studies of the cross reactions of the CH2dCHCH2O2, C2H5O2, neo-C5H11O2, c-C6H11O2, C6H5CH2O2, CH2ClO2, and CH3C(O)O2 radicals with CH3O2 and of the CH2dCHCH2O2, neoC5H11O2, c-C6H11O2, and CH3C(O)O2 radicals with C2H5O2 are reported below. The reaction of the allylperoxy radical CH2dCHCH2O2 with CH3O2 has been selected as a typical case for a detailed presentation of the results and for a study of the temperature dependence of the rate constant. The results for other reactions are only briefly reported, since experiments and
CH3O2 and C2H5O2
J. Phys. Chem., Vol. 100, No. 34, 1996 14375
TABLE 1: Reaction Mechanism Used in Simulations of the CH2dCHCH2O2 + CH3O2 Cross Reaction reaction CH2dCHCH2Cl + hν f CH2dCHCH2 + Cl CH4 + Cl f CH3 + HCl CH2dCHCH2 + O2 + M f CH2dCHCH2O2 + M CH3 + O2 + M f CH3O2 + M CH2dCHCH2O2 + CH3O2 f CH2dCHCH2O + CH3O + O2 CH2dCHCH2O2 + CH3O2 f CH2dCHCH2OH + CH2O + O2 CH2dCHCH2O2 + CH3O2 f CH2dCHCHO + CH3OH + O2 CH2dCHCH2O2 + CH2dCHCH2O2 f 2CH2dCHCH2O + O2 CH2dCHCH2O2 + CH2dCHCH2O2 f CH2dCHCH2OH + CH2dCHCHO + O2 CH3O2 + CH3O2 f 2CH3O + O2 CH3O2 + CH3O2 f CH3OH + CH2O + O2 CH3O + O2 f HO2 + CH2O CH2dCHCH2O + O2 f HO2 + CH2dCHCHO CH2dCHCH2O2 + HO2 f CH2dCHCH2OOH + O2 CH3O2 + HO2 f CH3OOH + O2 HO2 + HO2 f H2O2 + O2 aUnits
}
rate constanta (298 K)
ref
1.0 × 10-13 6.0 × 10-13 1.21 × 10-12
16 17 16
1.7 × 10-12
this work
10-13
4.3 × 2.7 × 10-13 1.22 × 10-13 2.48 × 10-13 2.0 × 10-15 2.0 × 10-15 b 1.0 × 10-11 5.8 × 10-12 3.0 × 10-12
10, 18 10, 18 1, 2 1, 2 16 10 1, 2 1, 2
of cm3 molecule-1 s-1. bAssumed equal to methyl analogue.
data analysis were conducted in a similar way. Only the particular features of each of the other cross reactions are emphasized. For most systems investigated, the reaction mechanism is known, or at least can be reasonably assumed from the known mechanism of the RO2 and CH3O2 (or C2H5O2) self-reactions. The main uncertainty is the branching ratio for the terminating and nonterminating channels of the cross reaction RO2 + CH3O2 (or C2H5O2) (1-Rc and Rc, respectively), which have not been determined. For RO2 + CH3O2, the possible reaction channels are
RO2 + CH3O2 f RO + CH3O + O2 f ROH + CH2O + O2 f R-HO + CH3OH + O2
(Rc) (1-Rc)
(16) Cl + CH4 f HCl + CH3 10-13
molecule-1
(8)
s-1
at 298 with k8 ) 1.0 × The principal possible secondary reaction for chlorine atoms was the reaction with allyl chloride: cm3
K.16
(15a)
(15c)
The kinetics of the reaction of the allylperoxy radical with CH3O2 were investigated simultaneously as part of a study of the CH2dCHCH2O2 radical self-reaction and of its reaction with HO2.10 The radicals were generated by laser photolysis of allyl chloride at 193 nm in the presence of excess methane and oxygen. The determination of k15 was carried out at six
(17)
with k7 ) 1.87 × 10-10 cm3 molecule-1 s-1 at 298 K.19 Thus, the loss of chlorine atoms through reaction 17 was never larger than 10%. The allyl chloride concentration was controlled in the cell by its absorption at 193 nm. Cross sections of allyl chloride have been measured using a UV CARY 2000 spectrophotometer, and the value obtained was σ ) (5.4 ( 0.5) × 10-18 cm2 molecule-1 at 193 nm. The concentration was maintained in the range 3.2 × 1014 to 10.2 × 1014 molecule cm-3 (0.01-0.03 Torr) so that the absorption of the laser beam was limited to less than 30%, thus ensuring relatively small concentration gradients along the cell. The photolysis produced peroxy radical concentrations between 0.9 × 1013 and 7.0 × 1013 molecule cm-3 for a laser pulse energy varying between 5 and 30 mJ cm-2. The stochiometric conversion of radicals into peroxy radicals was ensured by adding an excess of oxygen:
CH2dCHCH2 + O2 + M f CH2dCHCH2O2 + M -13
f CH2dCHCH2OH + CH2O + O2 (15b) f CH2dCHCHO + CH3OH + O2
CH2dCHCH2Cl + hν (λ ) 193 nm) f CH2dCHCH2 + Cl
Cl + CH2dCHCH2Cl f products
where R-HO is a carbonyl compound (aldehyde, ketone, or acid). Following Madronich et al.,3 we have found it reasonable to assume that, in all systems, Rc can be taken as the arithmetic average of the R values that have been determined for the corresponding self-reactions (where R is the ratio of the rate constant for the alkoxy channel to the total self-reaction rate constant). There is no particular chemical property that can be put forward to justify this assumption, but it should normally minimize the errors due to the use of an erroneous value of Rc. It should also be emphasized that for most systems, the branching ratios for the individual self-reactions are close to each other and, therefore, it is reasonable to assume that the branching ratio for the cross reaction has a similar value. The uncertainty introduced by this assumption is discussed below for each individual system. Reactions of the Allylperoxy Radical with CH3O2 and C2H5O2. The following reaction channels are expected for the reaction with CH3O2:
CH2dCHCH2O2 + CH3O2 f CH2dCHCH2O + CH3O + O2
temperatures between 291 and 423 K at 760 Torr and monitored at 235 nm, which corresponds to the maximum of both the allylperoxy and methylperoxy spectra.1,2,18 The decay time was always 200 ms, which was the most appropriate for kinetic analysis. The concentration of methane was high enough ((2.2-3.6) × 1018 molecule cm-3) to ensure that all chlorine atoms were stochiometrically converted into methyl radicals:
with k18 ) 6 × 10
-1 -1
3
cm molecule
s
CH3 + O2 + M f CH3O2 + M -12
with k10 ) 1.8 × 10
3
(18)
at 760 Torr 17 (10)
-1 -1
cm molecule
s
at 760 Torr 15
The low allyl-O2 bond dissociation energy17 means that there exists the possibility that reaction 18 becomes equilibrated at the highest temperatures explored in this study. As a consequence, experiments had to be limited to about 420 K where the concentration ratio [CH2dCHCH2O2]/[CH2dCHCH2] was equal to or greater than 50 for the highest oxygen concentrations
14376 J. Phys. Chem., Vol. 100, No. 34, 1996
Villenave and Lesclaux TABLE 4: Sensitivity Parameters Sija for the Rate Constant of the CH2dCHCH2O2 + CH3O2 Cross Reaction ai σ(CH2dCHCH2O2) σ(CH3O2) k(CH3O2 + HO2) k(CH2dCHCH2O2 + HO2) k(CH3O2 + CH3O2) k(CH2dCHCH2O2 + CH2dCHCH2O2) Rc
Figure 2. Arrhenius plot for the rate constant k15 of the cross reaction of CH2dCHCH2O2 with CH3O2.
TABLE 2: Absorption Cross Sections at 235 nm (1018σ/cm2 molecule-1)
d
T/K
HO2a
CH3O2a
CH2dCHCH2O2b
H2O2c
291 310 333 373 403 423
1.79 1.80 1.81 1.82 1.84 1.85
4.60 4.56 4.51 4.40 4.32 4.27
6.17 6.17d 6.17d 6.17d 6.17d 6.17d
0.15 0.15d 0.15d 0.15d 0.15d 0.15d
aTaken from ref 20. bTaken from ref 18. cTaken from ref 21. Assumed independent of temperature.
TABLE 3: Experimental Values of the Rate Constant for the CH2dCHCH2O2 + CH3O2 Reaction T/K
no. of determinations
k15a/10-12 cm3 molecule-1 s-1
291 310 333 373 403 423
15 2 2 2 2 2
1.71 ( 0.20 1.22 ( 0.15 1.00 ( 0.20 1.23 ( 0.15 1.10 ( 0.10 0.91 ( 0.09
aErrors
are based only on experimental scatter. See text for details.
that could be used without producing significant ozone concentrations, i.e., ∼7 × 1017 molecule cm-3. Figure 1 shows a typical decay trace obtained at room temperature along with the results of numerical simulations (smooth lines). All the parameters used in simulations were well established in the literature and are presented in Tables 1 and 2, with the exception of the branching ratio Rc ) k15a/k15. As mentioned above, Rc was taken as the average of the selfreaction branching ratios, i.e., R(CH3O2) ) 0.33,1,2 R(CH2dCHCH2O2) ) 0.61,18 giving Rc ) 0.47 at room temperature and assumed to increase with temperature (up to 0.66 at 420 K), assuming a temperature dependence similar to that of R(CH3O2).1,2 The average optimized values of k15 obtained are presented as a function of temperature in Table 3. Figure 2 shows the variation of k15 with temperature in Arrhenius form, yielding the following rate expression:
k15 ) (2.8 ( 0.7) × 10-13 × exp[(515 ( 75)/T] cm3 molecule-1 s-1 (T ) 291-423 K) and where the quoted uncertainties represent statistical errors (1σ) alone. Although the rate constant k15 was extracted from a relatively complex chemical system, it was essential to quantify its sensitivity to the parameters used for analysis, and a systematic analysis of propagation of errors was thus carried out as described previously.13 Artificial decay traces were generated with the same rate constants, initial radical concentrations, and
∆ai/ai %
∆k15/k15 %
Sij
(15 (10 (15 (25 (10 (20 (30
(8 (9 (2 (2 (2 (5 (8
0.53 0.90 -0.13 -0.08 -0.20 -0.25 -0.27
a Sij ) (∆k/k)/(∆ai/ai), where ai refers to the analysis parameter. Fractional change in k15 is given by the fractional change in the analysis parameter multiplied by the appropriate sensitivity coefficient.
absorption cross sections employed in the analysis (see Tables 1-3). They were analyzed in the same manner as the experimental traces except for varying the most important analysis parameters of those in Tables 1-3 by 10-30% (depending on the uncertainty on the parameter) and noting the change in the value of the cross-reaction rate constant returned by the data analysis program. The results for the allylperoxy radical are presented in Table 4. It is clear that the cross-reaction rate constant is particularly sensitive in this case to σ(CH2dCHCH2O2), σ(CH3O2), the branching ratio Rc, and, to a lesser extent, the corresponding self-reaction rate constants. Allowing for errors of approximately 15% in σ(CH2dCHCH2O2) and 10% in σ(CH3O2) resulted in a variation of 8% and 9%, respectively, in k15(CH2dCHCH2O2 + CH3O2). This relative sensitivity can be explained by the fact that most of the experiments were performed at 235 nm, a wavelength that corresponds to the maximum of the UV absorption of the allyland methylperoxy radicals and where the signal-to-noise ratio was maximum. Hence, the error in σ(HO2) has less influence on the shape of the decay traces, since it absorbs more at lower wavelengths.1,2 Reasonable variations of 15% in the rate constant of the reaction of CH3O2 with HO2 and of 25% in that of the corresponding reaction of CH2dCHCH2O2 result respectively in only
