Photolytic measurement of the O+OH rate constant at 295 K

Robert Robertson, Gregory P. Smith *

Molecular Physics Laboratory, SRI International, 333 Ravenswood Avenue, Menlo Park, CA 94025-3493, USA

Received 12 February 2002; in final form 12 April 2002

Abstract

The photolysis of ozone in 40 Torr nitrogen with small amounts of water was used to measure the O+OH rate

constant at 295 K. A value of 3:17� 0:51ð1rÞ � 10�11 cm3=s was determined by kinetic modeling of OH decays

monitored by laser induced fluorescence, in agreement with current recommendations. � 2002 Published by Elsevier

Science B.V.

1. Introduction

Critical ozone photochemistry in the meso-sphere and upper stratosphere is largely controlledby simple reactions of odd hydrogen species, HOx.Recent, consistent observations by satellite andballoon provide OH concentration measurements;however, model results based on this chemistrysubstantially overpredict these values [1]. A cor-ollary model result is low ozone prediction.Among the most uncertain and sensitive reactions[2] are the difficult to measure radical–radicalprocesses OHþHO2 ! H2OþO2, OþHO2 !OHþO2, and OþOH ! HþO2. High powerlaser photolysis sources and diagnostics provideopportunities to remeasure these rate constants togreater accuracy, and we report here a new de-termination of the rate constant for O+OH atroom temperature.

The nature and importance of this ‘HOx di-lemma’ were recently highlighted in a Physics To-day article [3], drawing largely on the recentobservations of OH distributions from the latestMAHRSI mission and accompanying discussionof the problem [1]. Two MAHRSI missions pro-vide OH distributions through the mesosphere anddown to 40 km via limb measurements of solar-excited OH UV fluorescence, with accompanyinginfrared (IR) determinations of O3 [1,4]. In addi-tion, ground based microwave data on HO2 andO3 provide mesospheric concentrations [5], andballoon data on OH, HO2, O3, and H2O in theupper stratosphere give confirmation and conti-nuity at the stratopause [6]. Comparing results toour understanding of the photochemistry of theseregions by means of model predictions reveals thefollowing HOx dilemma discrepancies. OH isoverpredicted by models above 50 km by 30%.Mysteriously, OH is underpredicted somewhat at45 km, although the same photochemistry is op-erative. A small O3 (odd oxygen) deficit in modelresults may remain, and revisions to lower model

24 June 2002

Chemical Physics Letters 358 (2002) 157–162

www.elsevier.com/locate/cplett

* Corresponding author. Fax: +1-650-859-6196.

E-mail address: smith@mplvax.sri.com (G.P. Smith).

0009-2614/02/$ - see front matter � 2002 Published by Elsevier Science B.V.

PII: S0009-2614 (02 )00629-2

OH could help fix this problem [4]. Model resultsalso underpredict the observed levels of HO2 [6].Authors of these studies [1,6] attempt to removethe model discrepancies by proposing some rateconstant modifications: decreasing OþHO2 formore HO2 and odd oxygen, perhaps increasingO+OH also to shift OH to HO2 [6], and changingOHþHO2 up [1] or down [6] to control total HOx.New kinetics measurements can endorse or restrictsuch changes.

The literature rate constant results are shown inFig. 1. Three temperature-dependent studies of theO+OH rate constant [7–9] are used to derive theNASA JPL panel recommendation [10]. Consistentresults were also seen from another room tempera-ture study [11], and the recommended error bars are20–30%. However, a recent low-pressure dischargeLIF measurement reports a 30% higher value at298 K, and similar increases at lower temperature[12]. Although the NASA panel recommends a rateconstant of 3:3� 10�11 cm3=molecules=s, a secondcluster of measurements [13,14] suggests highervalues of 4:2� 10�11. The limited set of experimentsall deal with discharge flowmeasurements. Here wereport a photolytic determination to help clarify thisrate constant value.

2. Experiments

Our experimental approach employs the appa-ratus and photochemistry used by Marschall et al.

[15] to measure the O+OH(v ¼ 2) reaction andrelaxation rate constant. In a typical experimentconducted in 40 Torr nitrogen, metered portionsof the flow pick up 50 mTorr ozone from a trapand 100 mTorr water from a bubbler. The ozoneconcentration is determined in situ in the cell byabsorption of Hg penlamp radiation at 253 nm.An assumption that the water flow is at the satu-rated vapor pressure was confirmed by 185 nmabsorption in a separate long pass cell. A 0.133 cmdiameter cylinder of the cell gas is irradiated by thefocused (1.05 m f.l.) output of a 248 nm excimerlaser beam. A measurement of laser power while aknife edge is translated across the laser beamdemonstrates a uniform, top-hat intensity distri-bution. The excimer laser beam photolyzes almostall the ozone in its path, and while most of theO(1D) produced is quenched by nitrogen, a smallamount reacts with water forming OH reactant.After a variable delay time, a frequency-doubleddye laser system measures the OH by laser inducedfluorescence excitation of the A–X (1,0) Q13 line at282.24 nm. The coaxial concentric dye laser beamprobes the center 0.03 cm diameter portion of thephotolysis zone. The time decay of the OH in ex-cess O is largely determined by the target rateconstant, although some secondary processes willneed to be accounted for quantitatively throughkinetic modeling. Under the above conditions,½O > 20½OH.

The excimer laser power is sufficient to photo-dissociate nearly all of the ozone. By monitoringthe OH LIF signal level at minimal delay after theexcimer laser as a function of excimer power, wegenerated a saturation curve of ozone dissociationversus power. An exponential fit then suggests weobtained 98% ozone dissociation in the beam un-der typical operating fluence. The initial OH and Oconcentrations are then determined from the rel-ative rates of O(1D) reaction with the water in themixture versus quenching by the nitrogen, usingthe NASA rate constant recommendations [10]. Atthe typical gas flow and operating rate of 10 Hz,the entire photolysis cell gas sample is replacedevery three laser shots. Experiments conducted at5 Hz show no change in OH decay rate, whichindicates a fresh sample of ozone for each lasershot. Ozone concentrations are measured directly

Fig. 1. OþOH rate constants.

158 R. Robertson, G.P. Smith / Chemical Physics Letters 358 (2002) 157–162

with the excimer laser off by the in situ absorptionmonitor, which is 18.2 cm long and intersects thephotolysis laser column at 45�. Then the initial Oconcentrations are determined, assuming 98%photodissociation. Small depletions in the averagecell ozone can be detected while the excimer laser isfiring.

A simple pseudo-first order analysis of the OHdecay rates versus O atom concentration typicallyyields rate constant values 20% lower than theNASA recommendation, largely because second-ary processes must also be accounted for at allconcentrations investigated. (These complicationsare not readily apparent in the pseudo-first orderplot from a non-zero intercept or any curvature.)These additional processes include: the formationof OH(v ¼ 1 or 2) in the Oð1DÞ þH2O reaction,which is then collisionally relaxed to OH(v ¼ 0) byO, H2O, or N2 (or reacts with O); diffusion of Oand OH from the probed region and diffusion ofozone back in; and regeneration of OH by reactionof H atom product with ozone. We will accountfor such effects by including these kinetic processesin a model of each experimental OH(v ¼ 0) decay,and we minimize the size of the interferences byphotodissociating as large a fraction of the ozoneas possible, choosing favorable experimental gasconditions, probing the center area of the photo-dissociation zone, and selecting the most sensitiveand uncontaminated portion of the OH decay forthe determination (typically an exponential from80% to 20% of the OH peak). In addition, pres-sure, O atom (ozone), and OH (water) concen-trations were varied, as well as excimer photolysislaser focal volume and repetition rate, in the 62experimental OH decays recorded at 295 K. Theranges of conditions are listed in Table 1. Notrends of different rate constant values were ob-

served for these variables; variations were under20% and not systematic.

3. Results and analysis

A typical experimental data set and fit result isshown in Fig. 2. Modeling runs with various val-ues of the O+OH rate constant were performedwith the Sandia Chemkin code Senkin [16], usingthe HOx kinetics given by the NASA evaluation[10]. The OH vibrational states and collisional re-laxation are explicitly included up to v ¼ 8, and wehave assumed the reaction rate constant is inde-pendent of vibrational level. The OH product levelbranching for the Oð1DÞ þH2O and HþO3 re-actions are taken from [17] and [15,19]. OH vib-rational relaxation is mainly accomplished bycollisions with O atoms and water. For allOHðvÞ þO ! OHðv� lÞ þO, we use the differ-ence between the total loss rate constantof 4:6� 10�11 cm3=molecules=s measured byMarschall et al. [15] for OH(v ¼ 2) and the NASAv ¼ 0 reaction rate constant (i.e., 1:3� 10�11 forthe relaxation). Water values measured for v ¼ 1and 2 [20] have been scaled by v for higher levels,and upper limits recorded for nitrogen [18,21] wereused for relaxation by nitrogen (generally insig-nificant). Finally, an approximate model for dif-fusion of O, OH, and O3 was included by adding

Table 1

Range of experimental conditions

Variable Range Typical

Pressure (Torr) 10–86 41

Ozone (O atom) (mTorr) 28–93 55

Water (mTorr) 40–450 120

OH0 (ppm) 20–200 60

Photolysis diameter (cm) 0.13–0.26 0.133

Repetition rate (Hz) 5–10 10Fig. 2. OH decay: photolysis of 71 mTorr O3, 112 mTorr H2O,

40.5 Torr N2. Y-axis is from the model results.

R. Robertson, G.P. Smith / Chemical Physics Letters 358 (2002) 157–162 159

an exponential term for loss or gain, with timeconstants computed using the diffusion constantsin N2 from the Sandia transport code [22] and anapproximate distance of 0.052 cm, given by thedifference between the photolysis and probe laserradii. Table 2 lists the rate parameters in the modelto which the OH decay is sensitive, according tothe sensitivity analysis also provided by the Senkincode, discussed later.

For each experiment, a rate constant forO+OH was determined by first fitting the OHtime decay to a single exponential over a limitedtime range; for the run illustrated in Fig. 2, this isfrom 85% to 20% of the maximum OH signal,producing the solid line shown and a decay time of15:7 ls. (The early rise of the signal is less well fit,but data in the initial 5 ls is obscured by emissionfollowing the excimer laser pulse.) Model runs, asdescribed above, are computed to match this decayover its range by varying the rate constant – in thiscase giving k ¼ 3:18� 10�11 cm3=molecules=s. Theplot shows the result from using the similar NASAvalue of 3:29� 10�11. It is indistinguishable fromthe decay trace, and also describes the continuingOH decline out to much longer times. The dottedline shows an alternate calculation with a 40%faster rate constant, where we have also left 15% ofthe ozone undissociated to act as a source forsecondary regeneration of the OH reactant to slowthe decay. The data is clearly inconsistent with asignificantly faster (or slower) rate constant.

A completed analysis of 62 experiments showsno variation of the rate constant with experimentalvariables of pressure, ozone (thus O atom), or

water (thus OH) concentration – up to high levels.This is illustrated in Fig. 3, which displays thesedeterminations as a function of initial ozone con-centration, with separate symbols indicating runsat higher ð> 0:17 TorrÞ and lower ð< 0:05 TorrÞwater pressure, higher total pressure (80 Torr), andat twice the photolysis beam diameter. The com-plete experimental set yields a final rate constantvalue of 3:17� 0:28� 10�11 cm3=s ð1rÞ. Thisagrees with the NASA recommendation. However,our value depends on modeling the observed de-cay, and is somewhat influenced by other chosenrates. (For example, if one simply assumes a con-stant post-photolysis O concentration from thequenched fraction after 98% ozone photodissoci-ation, an O+OH rate constant 14% lower is de-rived, one more in the direction proposed by themodelers.) Thus we next examine the contribution

Table 2

Key rate parameters for the OH decay

Reaction k ð10�12 cm3=sÞ Source S(OH, 22 ls) S(OH decay)

Oð1DÞ þH2O ! 2OHðvÞ 200. 10 1.024 0.054

Oð1DÞ þN2 ! OþN2 26.05 10 )1.024 )0.054OþOHðv ¼ 0Þ ! O2 þH 32. fit )1.272 )0.918OþOHðv > 0Þ ! O2 þH 32. ¼ kðv ¼ 0Þ )0.152 )0.127OHðvÞ þO ! OHðv� lÞ þO 13. 16 0.044 )0.012OHðvÞ þH2O ! OHðv� 1Þ þH2O 13:3 � v 18 0.084 )0.020HþO3 ! OHðvÞ þO2 28.92 10 0.001 0.006

O ! transport loss 2300/s Calc. 0.034 0.051

OH ! transport loss 2200/s Calc. )0.048 )0.037Transport in ! O3 ½O30 � 1000=s Calc. 0.0003 0.0024

Fig. 3. Rate constant results for OþOH as a function of initial

ozone partial pressure.

160 R. Robertson, G.P. Smith / Chemical Physics Letters 358 (2002) 157–162

of these other processes to the rate constant un-certainty using sensitivity analysis.

The sensitivity coefficients computed by theSenkin code are SijðtÞ ¼ dCi=Ci=dkj=kj ¼ d lnCi=d ln kj, and give the relative change in concentra-tion (OH) for a relative variation in a rate con-stant. Since these are logarithmic quantities, thesensitivity of a decay rate, which comes from aconcentration ratio, can simply be determinedfrom a difference in sensitivity versus time. Sincethe reaction rate kr½O ¼ 1=s is given by dðlnCOHÞ=dt, if we pick the times t2 and t1 at the end and startof the fit decay, the rate sensitivity is given byfSjðt1Þ � Sjðt2Þgs=ft2 � t1g. This decay sensitivityas well as sensitivity coefficients for OH concen-tration at 20 ls are given in Table 2 for the run ofFig. 2. The O+OH sensitivity is near unity, butthere is a forecast 8% shortfall in a rate constantsimply computed from the OH decay rate by1=sOBS½O.

Note first that while OH is very sensitive to theratio of rates for Oð1DÞ reaction versus quenching,its decay is not. This is mostly because the Oconcentration is only slightly diminished by in-creasing the minority reactive branch. Since thisrate ratio is well determined, only a few percentuncertainty in our rate constant could derive fromthis source. We also see very small negative OHdecay sensitivities to vibrational relaxation fromhigher levels of OH. While these rates are poorlyknown, even tripling them would only decreasethis experiment’s rate constant by 6%. Third, therate constant determination is sensitive to thetransport rates, although if one assumes errors inthis treatment are systematic and thus in one di-rection, the overall transport sensitivity is only 2%and the net uncertainty again is small. (We do notethat the tail of OH at long times is sensitive to thetransport and relaxation rates, as well as thefraction of dissociated ozone, and the extent of agood model fit there helps validate the model.)

The only other significant OH decay sensitivitycomes from the contribution of the O+OH(v ¼1; 2) reaction rate, which we assumed equal to thatfor v ¼ 0. To the extent that the larger measuredOH(v ¼ 2) disappearance rate (and v ¼ 1, vidainfra) is reaction not relaxation, it in part getsmeasured by the OH(v ¼ 0) decay and the real

O+OH(v ¼ 0) rate constant is slower. But eventhe full 40% difference will only depress the derivedrate constant by 4% according to the sensitivityanalysis.

The largest model uncertainty contribution tothe rate constant determination derives from thefraction of O3 dissociation, which directly influ-ences the O concentration as well as the amount ofOH regeneration. Modeling the same experimentwith 95% dissociation lowers the rate constant by4%. Altering the model water concentration 10%only produces a 0.2% change.

Adding in quadrature the uncertainty contri-butions of 9% from statistics, 8% from kinetics, 4%from ozone dissociation, and 10% from ozoneconcentration, we estimate a rate constant errorbar ð1� rÞ of 16%. The O+OH rate constantdetermined at 295 K is 3:17� 0:51� 10�11 cm3=s,in agreement with the NASA evaluation of previ-ous experimental results, lower than the recent lowpressure discharge determination [12], and fasterthan the proposed atmospheric model modifica-tion. We plan next to examine lower temperaturesrelevant to the upper atmosphere.

Acknowledgements

This work was supported by the NASA Iono-spheric Thermospheric and Mesospheric PhysicsProgram, Grant NAG5-8123. The authors thanktheir colleagues Drs. J. Marschall and R.A. Co-peland for advice and discussions regarding theexperimental protocol.

References

[1] R.R. Conway, M.E. Summers, M.H. Stevens, J.G. Cardon,

P. Preusse, D. Offermann, Geophys. Res. Lett. 27 (2000)

2613.

[2] G.P. Smith, M.K. Dubey, D.E. Kinnison, P.S. Connell, J.

Phys. Chem. 105 (2001) 1449.

[3] C. Day, Phys. Today (2000) 17.

[4] M.E. Summers, R.R. Conway, D.E. Siskind, M.H. Ste-

vens, D. Offermann, M. Riuese, P. Preusse, D.F. Strobel,

J.M. Russell III, Science 277 (1997) 1967.

[5] B.J. Sandor, R.T. Clancy, J. Geophys. Res. 103 (1998)

13337.

R. Robertson, G.P. Smith / Chemical Physics Letters 358 (2002) 157–162 161

[6] K.W. Jucks, D.G. Johnson, K.V. Chance, W.A. Traub, J.J.

Margitan, G.B. Osterman, R.J. Salawitch, Y. Sasano,

Geophys. Res. Lett. 25 (1998) 3935.

[7] A.A. Westenberg, N. de Haas, J.M. Roscoe, J. Phys.

Chem. 74 (1970) 3431.

[8] R.S. Lewis, R.T. Watson, J. Phys. Chem. 84 (1980) 3495.

[9] M.J. Howard, I.W.M. Smith, J. Chem. Soc. Faraday

Trans. II 77 (1981) 997.

[10] W.B. DeMore, S.P. Sander, D.M. Golden, R.F. Hampson,

M.J. Kurylo, C.J. Howard, A.R. Ravishankara, C.E.

Kolb, M.J. Molina, Chemical Kinetics and Photochemical

Data for Use in Stratospheric Modeling – Evaluation 12,

JPL Publication 97-04; Jet Propulsion Laboratory, Cali-

fornia Institute of Technology, Pasadena, CA, 1997.

[11] W.H. Brune, J.J. Schwab, J.G. Anderson, J. Phys. Chem.

87 (1983) 4503.

[12] I.W.M. Smith, D.W.A. Stewart, J. Chem. Soc. Faraday

Trans. 90 (1994) 3221.

[13] J.E. Breen, G.P. Glass, J. Chem. Phys. 52 (1970)

1082.

[14] I.M. Campbell, B.J. Handy, Chem. Phys. Lett. 47 (1977)

475.

[15] J. Marschall, K.S. Kalogerakos, R.A. Copeland, Labora-

tory measurements of OHðv ¼ 2Þ collisional deactivation

by oxygen atoms, American Geophysical Union Spring

2001 meeting, paper SA31A-21.

[16] A.E. Lutz, R.J. Kee, J.A. Miller, SENKIN: A Fortran

Program for Predicting Homogeneous Gas Phase Chemical

Kinetics with Sensitivity Analysis, Sandia National Labo-

ratories, Report SAND87-8248, 1987.

[17] K.-H. Gericke, F.J. Comes, R.D. Levine, J. Chem. Phys.

74 (1981) 6106.

[18] K. Knutsen, M.J. Dyer, R.A. Copeland, J. Chem. Phys.

104 (1996) 5798.

[19] H. Ohoyama, T. Kasai, Y. Yoshimura, H. Kimura, K.

Kuwata, Chem. Phys. Lett. 118 (1985) 263.

[20] G.A. Raiche, J.B. Jeffries, K.J. Rensberger, D.R. Crosley,

J. Chem. Phys. 92 (1990) 7258.

[21] M.J. Dyer, K. Knutsen, R.A. Copeland, J. Chem. Phys.

107 (1997) 7809.

[22] R.J. Kee, J. Warnatz, J.A. Miller, A Fortran Computer

Code Package for the Evaluation of Gas Phase Viscosities,

Conductivities, and Diffusion Coefficients, Sandia National

Laboratories, Report SAND83-8209, 1983.

162 R. Robertson, G.P. Smith / Chemical Physics Letters 358 (2002) 157–162