Temperature-Dependent Branching Ratios of Deuterated Methoxy

Article pubs.acs.org/JPCA

Temperature-Dependent Branching Ratios of Deuterated Methoxy Radicals (CH2DO•) Reacting With O2 Hongyi Hu and Theodore S. Dibble* Chemistry Department, College of Environmental Science and Forestry, State University of New York, Syracuse, New York 13210, United States

Geoffrey S. Tyndall* and John J. Orlando Atmospheric Chemistry Division, National Center for Atmospheric Research, Boulder, Colorado 80305, United States S Supporting Information *

ABSTRACT: The methoxy radical is an intermediate in the atmospheric oxidation of methane, and the branching ratio (k1a/k1b) (CH2DO• + O2 → CHDO + HO2 (1a) and CH2DO• + O2 → CH2O + DO2 (1b)) strongly influences the HD/H2 ratio in the atmosphere, which is widely used to investigate the global cycling of molecular hydrogen. By using the FT-IR smog chamber technique, we measured the yields of CH2O and CHDO from the reaction at 250−333 K. Kinetic modeling was used to confirm the suppression of secondary chemistry. The resulting branching ratios are well fit by an Arrhenius expression: ln(k1a/k1b) = (416 ± 152)/T + (0.52 ± 0.53), which agrees with the room-temperature results reported in the only previous study. The present results will be used to test our theoretical understanding of the role of tunneling in the methoxy + O2 reaction, which is the prototype for the entire class of alkoxy + O2 reactions.

1. INTRODUCTION Methoxy radical is a key intermediate in atmospheric methane oxidation, one product of which is molecular hydrogen. Molecular hydrogen is the second most abundant trace gas in the atmosphere (after methane) with an average tropospheric mixing ratio of 0.5 ppm.1 Furthermore, hydrogen has been proposed as an alternative energy source since its combustion product is environmentally friendly. It would be valuable to be able to evaluate the global hydrogen budget so as to help understand the likely effects of future perturbations, such as an increasing hydrogen source due to its possible leakage during storage and transportation. The most recent study of the global hydrogen budget shows significant uncertainty, especially in the +30 sink (79−20 Tg/yr).2 One powerful way to constrain the uncertainty in the hydrogen budget is to apply isotopic analysis, which has been widely used for trace gases.3 Field measurements indicate that the deuterium content of hydrogen gas is enriched in the atmosphere relative to the seawater standard, especially in the stratosphere.1,4−6 By contrast, sources of hydrogen gas, such as fossil fuel burning and biomass burning, produce hydrogen gas with lower deuterium content than the seawater standard. Although the slower consumption of HD than H2 favors the accumulation of deuterium in the atmosphere, the extreme deuterium enrichment cannot be explained without significant deuterium enrichment during methane oxidation. Both measurement and modeling convincingly show that hydrogen © 2012 American Chemical Society

gas produced by the methane oxidation is dramatically deuterium enriched; however, the extent of this enrichment contains significant uncertainties.1,4,5,7 Scheme 1 shows the process of CH4 and CH3D oxidation. Three reactions contribute to the degree of deuterium Scheme 1. Simplified Oxidation Process of CH4 and CH3Da

a

Dashed arrows indicate minor paths. The reactions that do not produce molecular hydrogen (e.g., oxidation of formaldehyde by hydroxyl radical) are not shown.

enrichment of molecular hydrogen produced from CH3D: the initial methane oxidation by OH, formaldehyde photolysis, and reaction of deuterated methoxy radicals (CH2DO•) with O2. The isotope effects in the reaction of both OH and Cl with methane have been thoroughly studied by experiments and theoretical calculation, and branching ratios for these reactions Special Issue: A. R. Ravishankara Festschrift Received: December 9, 2011 Revised: February 28, 2012 Published: March 20, 2012 6295

dx.doi.org/10.1021/jp211873w | J. Phys. Chem. A 2012, 116, 6295−6302

The Journal of Physical Chemistry A

Article

with monodeuterated methane are available.8−11 The isotope effects in the formation of molecular hydrogen from formaldehyde photolysis have been studied experimentally under various temperature, pressure, and photolysis conditions.12−15 The reaction of CH2DO• with O2 produces either deuterated formaldehyde (reaction 1a) or regular formaldehyde (reaction 1b). The branching ratio of the reaction (i.e., k1a/k1b) determines the yield of deuterated formaldehyde and thus also influences the HD yield from CH3D oxidation. CH2DO • + O2 → CHDO + HO2

(1a)

CH2DO • + O2 → CH2O + DO2

(1b)

the synthesis,24 we conclude that CH2DONO in the experiment is 99.5% isotopically pure. CD3ONO was synthesized from CD3OH (Sigma-Aldrich, 99.8%). CD3ONO and CH3ONO could be distinguished via their sharp infrared spectral features at 915 cm−1 and 991 cm−1, respectively. A small impurity (3.6%) of CH3ONO was detected in the CD3ONO (probably carry-over from a previous synthesis). 2.2. Formaldehyde Reference Spectra. Integrated absorption cross-sections have been reported for all three isotopologues of formaldehyde (CH2O, CD2O, and CHDO) in the carbonyl stretch region.25 In order to obtain reference spectra of any one isotopologue, that species was generated in (or added to) the chamber, FTIR spectra obtained, and the concentration determined based on the reported band strengths. These spectra were then used as reference spectra to determine concentrations in the branching ratio experiments. Gaseous CH2O and CD2O were generated from normal and fully deuterated paraformaldehyde (Fluka), respectively. Reference spectra of CH2O were taken at each experimental temperature and were calibrated from the peak areas over the range 1660−1820 cm−1. Considering the uncertainty of the integrated peak area and the error of the absorption crosssection, the uncertainty (1σ) of the concentration of the reference spectrum is 3−4%. For CD2O, reference spectra were taken at 295, 319, and 336 K, and spectra were calibrated over 1620−1770 cm−1. The uncertainties of the concentration of the CD2O reference spectrum are 4−5%. Samples of CHDO were generated following Cl-initiated oxidation of CH2DOH. Cl2 (6.9 × 1014 molecule/cm3, Matheson Tri-Gas, 99.999%) gas was flushed into the chamber with CH2DOH (1.4 × 1015 molecule/cm3), O2 gas (6.5 × 1018 molecule/cm3, U.S. Welding, 99.999%), and buffer gas N2 (General Air, liquid nitrogen boil-off) to a total pressure of 700 ± 5 Torr. The reactions are shown below as reaction 2, 3a, and 3b. Infrared spectra were recorded before and after 30 min of photolysis. The product spectrum included CH2O, CHDO, HCl, DCl, and a small amount of HCOOH and DCOOH. The reference spectrum of CHDO is obtained by subtracting the spectra of CH2DOH (994 cm−1), HCOOH (1104 cm−1), CH2O (1745 cm−1), HNO3 (1325 cm−1), and DCOOH (1143 cm−1). The concentration of the reference spectrum was calibrated from the known integrated absorption cross-section (1640−1800 cm−1) and is estimated to have an uncertainty of 4.9%. Although temperature might change the shape of the spectrum, the room temperature spectrum of CHDO is used for all temperatures. The error caused by this approximation was estimated through an analysis of the 250 and 333 K spectra of CH2O using the 295 K reference spectrum; the resulting concentrations were off by no more than 3%.

Although a modeling study pointed out the sensitivity of the HD/H2 ratio to the isotopic branching ratio (k1a/k1b),16 only one previous experimental study addressed this topic, and only at room temperature.17 The goal of this work is to study the temperature-dependent branching ratios of reaction 1. The previous study found the branching ratio (k1a/k1b) to be 7.5 ± 0.8 at 295 K. It is expected that this branching ratio will be larger at lower temperature, due to zero-point energy effects and tunneling.18,19 Field and modeling studies indicate that the deuterium content of hydrogen produced by methane oxidation varies with latitude and, in the stratosphere, with altitude.1,4,5,16 Therefore, knowledge of the temperature-dependent branching ratio of the CH2DO• + O2 reaction is crucial in evaluating the isotopic composition of hydrogen gas produced by methane oxidation.

2. EXPERIMENTAL METHODS 2.1. Experimental Chamber. The experiments involved the photolysis of deuterated methyl nitrite (CH2DONO) to produce deuterated methoxy radical (CH2DO•). Reaction of these radicals with oxygen produced either CH2O or CHDO, which were quantified by their infrared spectra. For some of the experiments, cyclohexane was added to scavenge OH radicals. Experiments were conducted between 250 and 333 K. The experiments were carried out at the National Center for Atmospheric Research (NCAR) using a 2 m long, 47 L chamber. The details of the apparatus have been reported elsewhere.20,21 An FT-IR spectrometer (BOMEM DA3.01) is used to measure the concentration changes in the chamber. The resolution of the spectra in the experiment was 1 cm−1, which is a good compromise between sensitivity and speed of analysis. The chamber is made of three layers of stainless steel. At both ends of the innermost layer sit Hanst-type optical mirrors, which enable the path of the light beam to reach 32.6 m. Heating/cooling fluid circulates in the middle layer; the outer layer is evacuated for insulation. The temperature of the apparatus can be controlled at 250−333 K. Thermocouples located around the chamber measure the temperature. The filtered output of a Xe-arc lamp located at one end of the chamber provided light between 235 and 400 nm to initiate the reaction by photolysis. As the photolytic precursor of CH2DO•, CH2DONO was synthesized and purified from CH2DOH (Cambridge Isotope Laboratories, Inc., > 98%) using the methods of Taylor et al.22 The chemical purity of the monodeuterated methyl nitrite was determined by FT-IR spectra, which excluded the presence of methanol. 13C{1H,2H} NMR spectroscopy of CH2DOH showed that the impurity of CH3OH is about 0.5%.23 Since the structure and isotopic content of the methyl group in the methanol is retained in its conversion to methyl nitrite during

hν

Cl2 ⎯→ ⎯ 2Cl

(2)

+O2

CH2DOH + Cl ⎯⎯⎯⎯⎯→ CHDO + HCl + HO2 +O2

CH2DOH + Cl ⎯⎯⎯⎯⎯→ CH2O + DCl + HO2

(3a) (3b)

2.3. Measuring the Branching Ratios (k 1a /k 1b ). CH2DONO (8 × 1014−1.7 × 1015 molecule/cm3) was flushed into the chamber with O2 (5.8−8.7 × 1018 molecule/cm3) and N2. The total pressure in the chamber was kept at 700 ± 5 Torr. 6296



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Table 1. CH2O Formation from Cyclohexane at 333 K at 333 K, CH3ONO impurity in CD3ONO (%)

3.6

Δ[CD2O] (1014 molecule/cm3)

Δ[CH2O] (1013 molecule/cm3)

Δ[cyclohexane] (1014 molecule/cm3)

Δ[CH2O] from cyclohexane (1012 molecule/cm3)

yield (CH2O) from cyclohexane (%)

1.56 1.75 2.24 2.56 1.22 1.38 1.78 2.44

1.19 1.71 2.37 2.81 1.19 1.35 1.63 2.17

1.04 1.49 1.91 2.42 0.62 0.83 1.08 1.35

6.33 10.81 15.61 18.86 7.53 8.58 9.90 12.92 average (±σ)

6.1 7.3 8.2 7.8 12.2 10.4 9.2 9.6 8.8 ± 1.9

3. RESULTS AND DISCUSSION 3.1. Determining CH2O Yields from Cyclohexane at 333, 320, and 295 K. According to Orlando et al., the products of the oxidation of cyclohexane were mainly cyclohexanone and formic acid at 273−296 K; formaldehyde formation was not observed.30 In the present work, under the same experimental condition (Cl-initiated reaction, 10 mTorr NO in the chamber), NO was consumed quickly, and CH2O formation was not observed. However, when the initial NO concentration was doubled (21 mTorr in the chamber), CH2O formation was found, with an average yield of 6%. In this case, the initial concentration of NO is the same as that of cyclohexane. Although Platz et al.31 did not observe CH2O formation in their experiment either, their initial concentration of NO is, at most, 23% of the concentration of cyclohexane. On the basis of this preliminary test, the presence of NO has a significant effect on the yield of formaldehyde. To simulate the condition of continuous NO release due to the photolysis of methyl nitrite in the branching ratio experiments, cyclohexane oxidation was carried out using CD3ONO as the source of both NO and hydroxyl radicals. The results from cyclohexane/CD3ONO experiments at 333 K are shown in Table 1. The amount of both CH2O and CD2O was quantified, and the amount of CH2O produced from cyclohexane was calculated by subtracting 3.6% of the CD2O production (to account for the CH3ONO impurity in the CD3ONO). The consumption of cyclohexane was also quantified to enable calculation of the molar yield of CH2O during the range of photolysis times. The yield does not show an obvious dependence on the photolysis time; therefore, the average yield was used to represent the CH2O yield at this temperature, which is (8.8 ± 1.9)% at 333 K. The results for 320 and 295 K are shown in the Supporting Information. At 320 K, the average yield of CH2O from cyclohexane is (5.5 ± 1.5)%, which is smaller than the yield at 333 K, while the average yield of CH2O at 295 K is (1.4 ± 0.4)%. In order to exclude the possibility that the CH2O signal is artificial, extra NO was put in the chamber. With extra NO, the CH2O yield increased significantly, while the consumption of cyclohexane remained as before. This confirmed that CH2O production came from the cyclohexane degradation process. Since the formation of CH2O depends on the concentration of NO, we inferred that the formation involves one or more conversions of peroxy radicals to alkoxy radicals via reaction with NO. One possible mechanism is shown in Scheme 2. At low temperatures, the reaction of cyclohexoxy radicals with O2 overwhelms the unimolecular decomposition and produces cyclohexanone as the major product. However, unimolecular

Spectra were recorded before initiating photolysis and after each photolysis interval (3−10 min). The concentrations of CHDO and CH2O were obtained by comparing to the reference spectrum at 1640−1800 cm−1 and 1660−1820 cm−1, respectively. In addition to CHDO and CH2O, a large amount of CO was found in the product spectrum, which indicates the oxidation of formaldehyde by hydroxyl radicals (photolysis is too slow to contribute significantly). To minimize the concentration of hydroxyl radical, cyclohexane (Sigma-Aldrich, 99.9%, 1.4−2.8 × 1015 molecule/cm3) was added to the chamber (along with CH2DONO, O2 and N2), due to its relatively large rate constants for OH reaction. In the presence of cyclohexane, CO was not detected [less than 2 × 1013 molecule/cm3]. When cyclohexane was present at 295, 320, and 333 K, the amounts of cyclohexane consumption (1450 cm−1) were measured. Experiments were carried out three times in the presence of cyclohexane and twice in its absence. 2.4. Cyclohexane Oxidation at High Temperatures. A preliminary analysis of branching ratios at high temperatures suggested significant CH2O production was occurring from cyclohexane oxidation. In order to confirm and quantify CH2O production from cyclohexane, parallel experiments were done with CD3ONO instead of CH2DONO in the chamber. Separate experiments using UV absorption spectroscopy showed that the spectra of CD3ONO and CH3ONO were indistinguishable in the (near-UV) photolysis region. The quantum yield of the photolysis is unlikely to change with deuterium substitution because methyl nitrite dissociation occurs on ultrafast time scales.26 Thus, we assume that deuterium substitution does not affect the photolysis rate constants. CD3ONO (1.1−1.3 × 1015 molecule/cm3) was put in the chamber with oxygen gas and cyclohexane (1.4−2.8 × 1015 molecule/cm3), and reaction was initiated by photolysis. The production of CH2O was observed at 1660−1820 cm−1. In some experiments, a small amount of NO (3.5 × 1014 molecule/cm3) was added to the chamber. 2.5. Modeling. Kinetic models were built to observe the influence of reactions involving formaldehyde production/ consumption other than the title reaction, and the effect of cyclohexane on these reactions. The models were set up in Kintecus V4.35,27 including all reactions that play significant roles in the chamber. The rate constants of the input reactions are obtained from the IUPAC28 and JPL recommendations29 and the primary literature. The initial conditions of the models were set to match the experimental conditions. 6297



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Scheme 2. One Possible Mechanism of Cyclohexane Oxidation to Produce CH2Oa

a

Dashed arrows indicate the reactions competing with formaldehyde formation.

reactions (k1a/k1b) will equal the observed product branching ratio ([CHDO]/[CH2O]), provided that CHDO and CH2O are only produced from reactions 1a and 1b, respectively, and provided that side reactions do not alter the observed product branching ratio. In such a case, the slope of the plot of CHDO concentration vs CH2O concentration would equal the branching ratio. Such a plot was constructed for each temperature, combining data from multiple experiments into each plot. The slope of each plot was obtained by linear regression, the uncertainty of which is reported as one standard deviation (1σ). As an example, the plot of [CHDO]/[CH2O] at 250 K in the presence of cyclohexane is shown in Figure 1, in which the slope is 9.2 ± 0.2. The slopes of the plots for experiments both without and with cyclohexane at 250−333 K are listed in Table 2. For the experiments with cyclohexane at 295, 320, and 333 K, the concentration of CH2O has been

decomposition is the major fate of cyclohexoxy radicals at high temperatures, which finally leads to the CH2O through the competition between isomerization and decomposition of the alkoxy radical labeled AO2 in Scheme 2. The decomposition channel forming CH2O probably has a higher activation energy than the competing isomerization; therefore, higher temperature might be expected to favor the production of CH2O via the decomposition reaction. It is worth noting that the reaction of peroxy radicals with HO2 is competing with the peroxy-toalkoxy conversion. At high NO concentrations, the peroxy-toalkoxy conversion dominates, and CH2O production is enhanced. 3.2. Branching Ratio Experiments. The concentrations of CHDO and CH2O were measured with an average uncertainty of 5% and 10%, respectively. Accounting for the uncertainties of concentrations in the reference spectra, the overall uncertainties in the determination of the concentration of CHDO and CH2O are 7.1% and 10.8%, respectively. The other products that were detected are methyl nitrate (CH2DONO2), formic acid (HCOOH and DCOOH), and CO (only detected in the absence of cyclohexane). Typical concentrations of the products at the end of photolysis were 1014 molecule/cm3 for CHDO, 1013 molecule/cm3 for CH2O, methyl nitrate, and HCOOH, respectively, and 1014 molecule/cm3 for CO (only in the absence of cyclohexane). The concentration of DCOOH was not quantified due to the lack of a reference spectrum, but modeling suggests a concentration roughly three times that of HCOOH. The concentration of methyl nitrite (CH2DONO) was also quantified, and all the detectable products (CHDO, CH2O, HCOOH, DCOOH, and CO) together account for 60−70% of methyl nitrite loss after one hours’ photolysis. We are unable to quantify HOCH2OOH and its isotopologues. While formaldehyde can be lost to surfaces, evidence suggests this is minor: 2 × 1014 molecule/cm3 CH2O in air subjected to 81 min of photolysis over a total time of 104 min exhibited only 6% loss. However, the missing carbon balance does not affect the result of the branching ratio experiments since reactions 1a and 1b share the same reactants. The branching ratio of the two

Figure 1. Result of branching ratio experiments at 250 K in the presence of cyclohexane, with the concentration of CHDO (unit, 1013 molecule/cm3) plotted vs the concentration of CH2O (unit, 1013 molecule/cm3). The linear regression shows the slope of the line to be 9.2 ± 0.2. 6298



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Table 2. Product Branching Ratio between CHDO and CH2O Determined from the Linear Regressions of the Plots of [CHDO] vs [CH2O] in the Absence and Presence of Cyclohexanea T (K) 250 265 278 295 320 333 a

slope without cyclohexane (CH) (1σ) 8.6 7.8 7.5 7.1 6.3 5.2

± ± ± ± ± ±

At 295, 320, correction for with overall formaldehyde column.

0.2 0.1 0.1 0.2 0.1 0.1

slope with CH before correction (1σ)

slope with CH after correction (1σ)

± ± ± ± ± ±

N/A N/A N/A 7.2 ± 0.3 6.4 ± 0.1 5.7 ± 0.1

9.2 7.8 7.3 6.7 4.9 3.8

0.2 0.1 0.1 0.3 0.1 0.1

branching ratio with overall uncertainties (1σ) 9.2 7.8 7.3 7.2 6.4 5.7

± ± ± ± ± ±

1.2 1.0 0.9 0.9 0.8 0.7

and 333 K, the slopes are listed both before and after CH2O from cyclohexane (CH). The branching ratios uncertainties (dominated by the uncertainties in concentration measurements) are listed in the last

corrected for CH2O production from cyclohexane. The concentrations of CHDO vs CH2O and vs the corrected CH2O are shown in Figure 2 for temperatures of 295 and 333 K. Omitting the correction for the extra CH2O produced from cyclohexane would lead to an underestimate of the slope, especially at higher temperatures. Table 2 explicitly indicates the effect of this correction on the observed concentration ratio. Assuming that the uncertainties in the formaldehyde reference spectra and in the concentration measurements are independent, an overall uncertainty of 13% is assigned to the branching ratio at each temperature. 3.3. Data Analysis and Kinetic Modeling. As stated previously, the observed product ratio, [CHDO]/[CH2O], equals the rate constant branching ratio k1a/k1b only if other reactions involving CHDO/CH2 O do not change the concentration ratios of these two species. Scheme 3 shows all significant gas-phase sources and sinks of CHDO and CH2O in these experiments, in which the title reactions and two other reactions produce CHDO and CH2O, while three reactions consume CHDO and CH2O. Kinetic models were built to study the effect of these reactions on the observed formaldehyde concentration ratios. The complete model is presented in the Supporting Information, and only the major issues are discussed here. Recall that the experiments were unable to achieve a mass balance, which means that if the photolysis rate constant of methyl nitrite is chosen to match the measured rate of loss, modeled formaldehyde concentrations would be significantly larger than the observed concentrations. Therefore, the photolysis rate constant of methyl nitrite was adjusted to enable a match to the formaldehyde concentrations for one experiment at 295 K and applied to models at all temperatures. The side reactions that produce CHDO/CH2O are the reactions of OH with CH2DONO2 and with CH2DONO. OH + CH2DONO → H2O + CHDO + NO

(4a)

OH + CH2DONO → HDO + CH2O + NO

(4b)

OH + CH2DONO2 → H2O + CHDO + NO2

(5a)

OH + CH2DONO2 → HDO + CH2O + NO2

(5b)

Figure 2. Result of branching ratio experiments at 295 K (a) and 333 K (b) in the presence of cyclohexane, with the concentration of CHDO (unit, 1013 molecule/cm3) plotted vs the concentration of CH2O (unit, 1013 molecule/cm3). The red open dots represent the raw experimental results, while the black filled squares represent the results after the correction for CH2O production from cyclohexane oxidation. The linear regressions of the corrected results suggest the slopes of the lines to be 7.2 ± 0.3 at 295 K and 5.7 ± 0.1 at 333 K.

Scheme 3. Reactions Resulting in Formaldehyde Production or Consumption

rate constant for the OH + CH2DONO2 reaction can be estimated from the temperature-dependent rate constants for the OH + CH3ONO2 and OH + CD3ONO2 reactions.32 As a consequence, the pre-exponential factor for reaction 5a is taken as two-thirds that of the pre-exponential factor for the OH + CH3ONO2 reaction, and the activation energy for the two reactions is assumed to be the same. Similarly, the preexponential factor for reaction 5b is one-third of the preexponential factor for the OH + CD3ONO2 reaction, and the activation energy is the same. By the same logic, the rate

Assuming that the three hydrogen/deuterium atoms in the methyl group influence the rate constant independently, the 6299



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constant of reaction 4a was assumed to be two-thirds of the rate constant of the OH + CH3ONO reaction at 298 K, and the temperature dependence of reaction 4a was ignored due to the lack of data.33 No data is available to estimate the rate constant for reaction 4b. We discuss the inference of the branching ratio for the OH + CH2DONO reaction in the Supporting Information. Formaldehyde is consumed in reactions with OH and HO2/ DO2 radicals and by photolysis. The temperature-dependent rate constant for the OH + CH2O reaction28 and the rate constant for the OH + CHDO reaction at room temperature34 are known. We treat the two hydrogen atoms in CH2O independently; therefore, the pre-exponential factor for OH + CHDO → H2O + CDO

(6a)

is taken as half of that for OH + CH2O → H2O + CHO, while the activation energy is the same. By assuming the same preexponential factor holds for the rate constant of OH + CHDO → HDO + CHO

(6b)

we can estimate the activation energy for the OH + CHDO reaction from the room-temperature rate constant. Another sink of formaldehyde is the reaction with HO2 radicals, which occurs via the addition to form HOCH2O2 radicals,28,35 and for which isotopic effects should be minor. The concentrations of HOCH2O2 radicals and its isotopologues are significantly lower than the concentration of HO2 radicals; therefore, the reactions of HOCH2O2 with itself (or its isotopologues) are negligible. The concentration of cyclohexyl peroxy is comparable to that of HO2. However, the rate constant of cyclohexyl peroxy with other organic peroxy radicals (RO2)36 is 2−3 orders of magnitude smaller than the rate constant of HO2 with RO2. Therefore, RO2 + RO2 reactions were omitted from the model. The rate constants and the isotopic branching ratios of RO2 + HO2 reactions are estimated based on the limited experimental results and statistical branching ratios (see Supporting Information). The last channel to consume formaldehyde is photolysis. The photolysis rate constant of CH2O was estimated by scaling from that of methyl nitrite in the same ratio as in ref 17. Combining this value with the isotope effect of formaldehyde photolysis reported by Röckmann et al.14 enables calculation of the photolysis rate constant of CHDO. For our modeling, we initially assumed that the product branching ratio ([CHDO]/[CH2O]) obtained in the presence of cyclohexane, shown in the last column of Table 2, equals the rate constant branching ratio k1a/k1b. With this assumption, the modeled product branching ratio in the presence of cyclohexane matches the experimental data very well. An example is shown in Figure 3a at 278 K in which the fitted slope for the experimental result (in black) is 7.28 ± 0.10, while the fitted slope for the modeling result (in red) is 7.31 ± 0.01. At all temperatures, the modeled product branching ratio deviated from the measured product yield ratio by no more than 1%. Furthermore, the model and experiment agree well on the time history of CHDO and CH2O, as Figure 3b shows at 278 K. These results offer significant support to our assumption that the product branching ratio [CHDO]/[CH2O] obtained in the presence of cyclohexane equals the rate constant branching ratio k1a/k1b. Figure 4 illustrates the relative importance of various sources and sinks of the two isotopologues of formaldehyde in the presence of cyclohexane as a function of time at 278 K. The y axis in Figure 4 is the ratio of CHDO or CH2O produced or

Figure 3. Comparison of experimental and modeled results in one case at 278 K in the presence of cyclohexane: (a) the comparison of the formaldehyde branching ratio ([CHDO]/[CH2O]) and (b) the comparison of the time history of formaldehyde formation. The unit of the concentration is 1013 molecule/cm3. The initial CH2DONO concentration, O2 concentration, and cyclohexane concentrations in this case were 1.29 × 1015, 6.94 × 1018, and 2.76 × 1015 molecule/cm3, respectively. In panel a, the fitted slope for the experimental result (black line) is 7.28 ± 0.10, while the fitted slope for the modeling result (red dash) is 7.31 ± 0.01.

removed by various reactions relative to that produced in reaction 1a or reaction 1b, respectively. The formaldehyde + hydroperoxy radical reactions are reversible, and the value of

Figure 4. Ratio of CHDO or CH2O produced or removed by various reactions relative to that produced in reaction 1a or reaction 1b, respectively, in the presence of cyclohexane at 278 K. 6300



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of H atoms to D atoms in CH2DO•. Previous theoretical studies indicated that tunneling plays a dominant18,19 role in the title reaction near room temperature. If this were the case, one would expect the Arrhenius plot of the branching ratio in Figure 5 to curve upward from linear at low temperature. The present data do not exhibit significant curvature, but the uncertainty in our results does not allow the present results to be used as an argument against significant tunneling. 3.5. Atmospheric Application. The branching ratio obtained in our experiments can be used to evaluate the deuterium enrichment during methane oxidation. The deuterium content in a species is quantified in delta notation:

the ratio plotted in Figure 4 refers to the net extent of reaction (extent of forward reaction minus extent of reverse reaction). As stated above, the mechanism of this reaction implies that isotope effects will be minor, so this reaction has negligible effects on the observed product yield ratio. The modeling results demonstrated that in the presence of cyclohexane, the reaction of OH/OD with CH2DONO, the reaction of OH/OD with CH2O (CHDO), the reaction of OH/OD with CH2DONO2, and the photolysis of CH2O (CHDO) all have small impacts on the [CHDO]/ [CH2O] ratio. This finding validates our initial assumption, stated above, that the observed product branching ratio between CHDO and CH2O in the presence of cyclohexane (corrected, if necessary, for CH2O production from cyclohexane) nearly equals the branching ratio of the CH2DO• + O2 reaction. In the absence of cyclohexane, the reactions of OH/OD with methyl nitrite and formaldehyde are expected to be very significant. Our modeling, presented in the Supporting Information, confirms that expectation. The model can match both the product yield ratio and the time history of CHDO and CH2O concentration, provided the rate constant k4b is varied within physically reasonable bounds to enable a consistent fit. To recapitulate, our model matches the experimental formaldehyde isotope ratio and time history of formaldehyde in the presence of cyclohexane. This fact strongly supports the assumption that the product concentration ratios obtained in the presence of cyclohexane is nearly equal to the rate constant branching ratio k1a/k1b. The effect of side reactions are negligible compared with the uncertainties in the product branching ratios (listed in the last column of Table 2). 3.4. Temperature Dependence of k1a/k1b. The values of k1a/k1b, from the last column of Table 2, are plotted in Arrhenius form in Figure 5. The data is well fit by the Arrhenius

δD = ((D/H)sample /((D/H)VSMOW − 1)) × 1000 (8)

where VSMOW stands for the isotopic standard: Vienna Standard Mean Ocean Water. Our analysis follows Feilberg et al.12 and assumes a simplified mechanism for methane oxidation in the atmosphere with radicals, formaldehyde, and molecular hydrogen at steady state in a 0-D box. Updated rate constants for this calculation are listed in the Supporting Information. Starting with δD(CH4) in the troposphere of −86‰, the calculation indicates that δD(H2) arising solely from methane +17 +15 oxidation would be 232−23 ‰ at 295 K and 306−19 ‰ at 250 K (the cited uncertainty only considers that arising from the uncertainty in the branching ratio for the title reaction). If the value of the branching ratio of the title reaction was assumed independent of temperature and the value at 295 K was used, +17 the computed value of δD(H2) at 250 K would be 271−22 ‰. While 250 K is the lowest temperature achieved in our experiments, one can consider the effects of lower temperature by extrapolating the Arrhenius expression (eq 7) for the branching ratio of the title reaction. At 200 K, this extrapolation yields a branching ratio of 13.4, and δD(H2) can be estimated to be 410‰, which is much larger than the δD(H2) value (330‰) estimated with the branching ratio at room temperature (7.2). While this extrapolation may carry large uncertainties, it illustrates that the temperature dependence leads to larger extents of deuterium enrichment in the stratosphere than in the troposphere. The experimental branching ratio determined herein can be further applied in chemical transport models to study in more detail the deuterium composition of hydrogen gas and its global budget.

4. CONCLUSIONS The temperature-dependent branching ratio for the title reaction has been determined over the range 250−333 K. Results agree well with the single previous determination at 295 K,17 and an Arrhenius expression provides an excellent fit to the present results. The quality of this fit does not support a dominant role for tunneling in the room-temperature rate constant, contrary to the theoretical results of Setokuchi and Sato18 and Bofill et al.19 The temperature dependence of the branching ratio is significant, which indicates the importance of considering this temperature dependence in modeling the isotopic fractionation of molecular hydrogen in the atmosphere.

Figure 5. Natural logarithm of the branching ratio vs the reciprocal of the temperature. The red open circle is the result from Nilsson et al.17

form without significant curvature, albeit over a limited temperature range. A linear regression of the data provides the following Arrhenius expression for the branching ratio (±1 σ): ln(k1a /k1b) = (416 ± 152)/T + (0.52 ± 0.53)

(7)

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The result suggests that R1b (abstraction of D from CH2DO) has an activation energy that is (3.5 ± 1.3) kJ/mol higher than R1a (abstraction of H), and the ratio of the pre-exponential factors (A1a/A1b) is (1.7 ± 0.9). This ratio is expected to be close to 2.0 since it will be dominated by the statistical 2:1 ratio

ASSOCIATED CONTENT

S Supporting Information *

Tables of data on CH2O formation from cyclohexane subsequent to CD3ONO photolysis at 295 and 320 K; 6301



Article

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complete kinetic model of the branching ratio experiment with references and notes, description of the construction and results of this model in the absence of cyclohexane; updated rate constants for computing δD(H2) in a 0-D box model. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Fax: 315-470-6856. E-mail: [email protected] (T.S.D.); [email protected] (G.S.T.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

H.H. and T.S.D. gratefully acknowledge support from the National Science Foundation under grant ATG-0937626. The National Center for Atmospheric Research is sponsored by the National Science Foundation.

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Temperature-Dependent Branching Ratios of Deuterated Methoxy

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