ARTICLE pubs.acs.org/JPCA
Measurements of the Absorption Line Strength of Hydroperoxyl Radical in the ν3 Band using a Continuous Wave Quantum Cascade Laser Yosuke Sakamoto† and Kenichi Tonokura*,‡ †
Department of Chemical System Engineering, Graduate School of Engineering, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan, ‡ Department of Environment Systems, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwanoha 5-1-5, Kashiwa, Chiba 277-8563, Japan
bS Supporting Information ABSTRACT: Mid-infrared absorption spectroscopy has been applied to the detection of the hydroperoxyl (HO2) radical in pulsed laser photolysis combined with a laser absorption kinetics reactor. Transitions of the ν3 vibrational band assigned to the OO stretch mode were probed with a thermoelectrically cooled, continuous wave mid-infrared distributed feedback quantum cascade laser (QCL). The HO2 radicals were generated with the photolysis of Cl2/CH3OH/O2 mixtures at 355 nm. The absorption cross section at each pressure was determined by three methods at 1065.203 cm1 for the F1, 131,13 r 141,14 transition in the ν3 band. From these values, the absolute absorption cross section at zero pressure was estimated. The relative line strengths of other absorptions in the feasible emitting frequency range of the QCL from 1061.17 to 1065.28 cm1 were also measured, and agreed with values reproduced from the HITRAN database. The ν3 band absorption strength was estimated from the analytically obtained absolute absorption cross section and the calculated relative intensity by spectrum simulation, to be 21.4 ( 4.2 km mol1, which shows an agreement with results of quantum chemical calculations.
1. INTRODUCTION The hydroperoxy radical (HO2) is important intermediate in both stratospheric and tropospheric chemistry.1 In the troposphere, the high reactivity of HO2 with NOx, itself, and alkylperoxy radicals, among others, keeps its concentration on the order of 107 molecules cm3.2 The main fate of HO2 in the troposphere is to react either with NO to produce a hydroxyl radical and nitrogen dioxide, or with itself to yield hydrogen peroxide. In the stratosphere, HO2 reacts with ozone or an oxygen atom to produce the hydroxyl radical, thus contributing to ozone loss processes. HO2 is also an important intermediate in combustion chemistry.3 Optical techniques have been widely used to monitor the HO2 radical directly in laboratory kinetic experiments. UV absorption spectroscopy has been the most commonly used method to detect the HO2 radical in the range 220230 nm, because of its strong cross sections (σ ≈ 1018 cm2 molecule1).4 However, the broad and structureless absorption of HO2 in this region due ~ 2A00 transition leads to overlaps ~ 2A00 r X to the predissociative B with the absorption of other species, such as hydrogen peroxide (σ ≈ 1019 cm2 molecule1), the main product of the HO2 selfreaction.4,5 Thus, the rovibrational absorption line is preferred for the detection of HO2 in experimental studies of such reaction systems. ~ 2A00 transition and the 2ν1 OH overtone ~ 2A0 r X The A transition of HO2, which occurs in the near-IR and has rovibronic r 2011 American Chemical Society
structure assigned to electronic transitions, have been widely examined.616 The line center absorption cross sections of the 2ν1 absorption have been determined to be on the order of 1019 cm2 molecule1 at several tens of Torr.6,7,1114 The ~ 2A00 band is on the same ~ 2A0 r X absorption cross-section of the A 14 order of magnitude as the 2ν1 band. Although the mid-IR spectroscopic technique provides highly selectivity and sensitive detection of HO2 due to the strong fundamental rovibronic absorption, spectroscopic studies of HO2 in the mid-IR region have been limited due to the lack of a practical light source.1725 There have been two experimental reports on the line strength of the ν3 vibrational band by Zahniser et al.23 and Buchanan et al.25 The estimated band strengths in these two reports are in good agreement, and the reported value by Zahniser et al. has been adopted by the HITRAN database.26 The band strength of the ν3 band of HO2 has also been estimated by theoretical calculations2731 showing a large discrepancy between experimental and theoretical values, in which the theoretical values were higher by a factor of about 26. Recently, distributed feedback quantum cascade lasers (QCLs) have gained wide use as a light source in mid-IR spectroscopy Received: August 4, 2011 Revised: December 9, 2011 Published: December 09, 2011 215
dx.doi.org/10.1021/jp207477n | J. Phys. Chem. A 2012, 116, 215–222
The Journal of Physical Chemistry A
ARTICLE
because of their narrow line width, single-mode operation, high output power, and thermoelectric-cooled operation. We previously reported a new experimental setup using mid-IR absorption spectroscopy to monitor the HO2 using a continuous wave (cw) QCL as a spectroscopic light source.32 In this study, we applied the mid-IR absorption spectroscopy using a QCL to measure the spectral line strength of the ν3 band of HO2. In addition, relative line strengths to that at 1065.203 cm1 for other absorptions were also measured and compared with the spectral simulation.
photolyzed with the third harmonics of a Nd:YAG laser at 355 nm (Continuum Surelite II). The photolysis laser was expanded using a beam expander and shaped with a circular orifice to 1.00 ( 0.05 cm diameter. The photolysis pulse energy was 49 ( 3 mJ pulse1 cm2 (experimental error of 5% and detector accuracy of 3%) as measured by a calibrated joule meter of 3% power accuracy (OPHIR, 10A-P). Typical initial reactant concentrations were [O2] = (0.21.3) 1018 molecules cm3 (used as a buffer gas), [He] = 3.9 1016, [Cl2] = 3.8 1015, [CH3OH] = 1.4 1015, and [1,4-c-C6H8] = 4.4 1014 molecules cm3. The concentrations of O2, He, and Cl2 were obtained from the total pressure and flow rates, CH3OH was directly measured, and 1,4-c-C6H8 was from the saturated vapor pressure and flow rate. Gas flows were regulated by four calibrated mass flow controllers (KOFLOC, models 3660 and 3650, accuracy of 99.999 95%). CH3OH and 1,4-c-C6H8 (Wako Co.) were introduced into the reaction cell by passing O2, or as diluted premixed gases stored in a 6 L canister coated with Silonite (Entech Instruments, Inc., Simi Valley, CA). Spectroscopic and kinetics experiments involving the photolysis laser were performed at a repetition of 2 Hz to ensure removal of the reacted mixture and replenishment of the gas sample between successive laser shots, as the retention time of sample gas was 0.25 s. A slow flow of O2 was introduced over the optical parts to protect probe and photolysis beam entrance windows from deposition of reaction products. Experiments were performed at room temperature (298 ( 3 K).
2. EXPERIMENTAL SECTION Mid-infrared absorption spectra of the ν3 band of the HO2 radical were measured using a pulse laser photolysis/cw direct absorption spectroscopy. Since the apparatus used in this study is described in detail elsewhere,32 herein will only be a brief outline. The mid-infrared probe beam at around 1065 cm1 was provided by a cw thermoelectrically cooled distributed feed-back QCL (LC0069, Hamamatsu Photonics K.K., Hamamatsu, Japan). The central laser wavelength can be selected by changing the device temperature between 30 and +35 °C with a Peltier driver (C10638-01, Hamamatsu Photonics K.K.). A laser driver (C10336, Hamamatsu Photonics K.K.) was used to operate the QCL. A Pyrex cell with an inner diameter of 21 mm with a length of 650 mm was used to measure the absorption spectra of the HO2 radical. Perforated quartz windows were attached to each side of the cell. Antireflection (AR) coated ZnSe windows were placed on the perforated quartz windows to allow the probe beam. The probe beam was focused on the center of the cell using an AR coated ZnSe lens with a 415 mm focal length. The optical path length of probe beam was 89 ( 1 cm, and the length of the overlap region between the photolysis and the probe beam was 40 ( 1 cm, both of which were directly measured. An off-axis parabolic mirror (25.4 mm diameter, 50.7 mm focal length) was used to collect the probe beam exiting the cell, which was focused through an interference filter (SPECTROGON, center wavelength 9400 nm, fwhm 220 nm) on a liquid nitrogen cooled HgCdTe detector (Kolmar Technologies, KLD-1-J1/DC/11). The detected photocurrent signal was averaged with a digital oscilloscope (Tektronix, TDS 520C) and transferred to a personal computer through a general purpose interface bus (USBGPIB, National Instruments). In the measurements of the absolute absorption cross section, HO2 was produced by the pulse photolysis of chlorine in the presence of CH3OH and oxygen. To measure the relative intensities, HO2 was prepared by the pulse photolysis of chlorine in the presence of 1,4-c-C6H8 and oxygen to avoid interfering absorptions from methanol. The following reaction sequence rapidly generates HO2: Cl2 þ hνð355nmÞ f 2Cl
ð1Þ
Cl þ CH3 OH f CH2 OH þ HCl
ð2Þ
CH2 OH þ O2 f HCHO þ HO2
ð3Þ
3. RESULTS AND DISCUSSION 3.1. Determination of Absorption Cross Section of HO2 (σHO2) in the ν3 Band. The determination of the absorption cross
section of HO2 was done at an absorption line of F1 131,13 r 141,14 transition at 1065.203 cm1. Three methods were applied to quantify the HO2 concentration: (1) initial absorbance, (2) HO2 kinetics, and (3) comparison with the CH3OH absorption intensity. In the feasible frequency range of the QCL from 1061.17 to 1065.28 cm1, the broadened methanol absorption causes interference. The absorption line of HO2 in the ν3 band is split into F1 (J = N + 1/2) and F2 (J = N 1/2) spin components, where J is the total angular momentum and N is the rotational quantum number. The absorption spectra of the F1 and F2 lines interfere with each other.32 The neighboring absorption of F2, 131,13 r 141,14 transition at 1065.221 cm1 interferes with the absorption of F1 131,13 r141,14 transition at 1065.203 cm1. Thus, a correction of the absorption intensity attributed to the interference by CH3OH and HO2 was performed, the details of which are described in the Supporting Information (S.1 and S.2). 3.1.1. Determination of σHO2 from Initial Absorbance. The initial concentration of Cl produced by photolysis of Cl2 at 355 nm can be estimated from absorbed photolysis laser photon number
or Cl þ 1, 4-c-C6 H8 f c-C6 H7 þ HCl
ð4Þ
c-C6 H7 þ O2 f C6 H6 þ HO2
ð5Þ
½Cl0 ¼ 2½Cl2 0
Np σ Cl σL 2
ð6Þ
where NP is the laser photon number per pulse calculated from the laser pulse energy, σL is the laser beam cross section, σCl2 is the absorption cross section of Cl2 at 355 nm (1.60 1019 cm2 molecule1).34 [Cl2]0 is calculated from the flow rates and total pressure. The
The branching ratio of reactions 2, 3, and 5 is unity, while that of reaction 4 is 0.38 ( 0.03.33 The chlorine molecule was 216
dx.doi.org/10.1021/jp207477n |J. Phys. Chem. A 2012, 116, 215–222
The Journal of Physical Chemistry A
ARTICLE
Table 1. Reactions and Rate Constants Used in the Model Simulation at 17 Torr Total Pressure reaction
rate constant (298 K)a 11
ref
CH3OH + Cl f CH2OH + HCl
5.5 10
Cl f diffusion CH2OH + O2 f HO2 + CH2O
68 9.1 1012
this work 34
CH2OH + Cl2 f ClCH2OH + Cl
2.9 1011
38
CH2OH + Cl f CH2O + HCl
6.6 1010
39
CH2OH + CH2OH f products
1.5 1011
40
CH2OH f diffusion
73
this work
HO2 + HO2 f H2O2 + O2
1.8 1012
14
HO2 f diffusion
71
this work
HO2 + CH2OH f products HO2 + Cl f HCl + O2
6.0 1011 3.2 1011
41 34
9.1 1012
34
HO2 + Cl f OH + ClO
a 1
34
Figure 2. Absorption cross sections of HO2 at 1065.203 cm1 as a function of total pressure. The dashed, solid, and dotted lines are the fit using eq 9 to absorption cross sections obtained from the initial absorbance (1, green), the HO2 kinetics (9, red), and the ratio of absorption intensity to the CH3OH (2, blue), respectively.
s for unimolecular reactions and cm molecule1 s1 for bimolecular reactions. 3
Table 2. Summary of the Absorption Cross Sections for the F1, 131,13 r 141,14 Transition of HO2 at Each Total Pressurea absorption cross sections/1018 cm2 molecule1
a
absorption of HO2 is measured in absorbance form, which obeys Beer’s law ΔI ð7Þ ¼ σHO2 ½HO2 l A ¼ ln 1 I0 where I0 is the probe laser intensity without HO2 absorption, ΔI is the differential HO2 absorption intensity, and l is the optical path length. Then, σHO2 can be determined from eq 8. AHO2 , 0 AHO2 ðmaxÞ ¼ 2αðNp =σL Þ½Cl2 0 σ355 ½HO2 0 l Cl2
HO2
CH3OH absorption
absorbance
kinetics
cross section
7
1.87 ( 0.19
1.87 ( 0.12
1.73 ( 0.09
10
1.57 ( 0.16
1.49 ( 0.12
1.49 ( 0.07
13 17
1.23 ( 0.12 1.19 ( 0.12
1.18 ( 0.08 1.28 ( 0.11
1.11 ( 0.08 1.06 ( 0.04
20
1.00 ( 0.10
1.06 ( 0.09
0.91 ( 0.04
25
0.89 ( 0.09
0.94 ( 0.08
0.85 ( 0.03
30
0.81 ( 0.08
0.95 ( 0.08
0.74 ( 0.04
35
0.62 ( 0.06
0.74 ( 0.06
0.64 ( 0.03
40
0.58 ( 0.06
0.64 ( 0.05
0.51 ( 0.03
The errors indicate 1σ.
The α is conversion factor of Cl to HO2, which is not unity because Cl is consumed via reactions with CH2OH and HO2 and diffusion out of the detection area, and was calculated by kinetic simulation for each set of conditions. The reactions used for the simulation are summarized in Table 1. Diffusion rates were determined in this study, the details of which are described in Section 3.1.2. A typical time profile of HO2 produced from the reaction of CH2OH + O2 at 20 Torr is shown in Figure 1. Sensitivity analysis shows that the main reactions contributing to the rise of HO2 are reactions 2 and 3, and the contributions of self-reactions and diffusion are negligible in the range of ∼0.1 ms. Thus, AHO2(max) can be regarded as AHO2,0. Figure 2 shows σHO2 obtained from AHO2(max), which were corrected for the overlap of neighbor absorption of the F2, 131,13 r 141,14 transition (details are in Section S.2). The values were summarized in Table 2 as a function of total pressure. Error bars include measurement deviation and errors of the photolysis/probe laser overlap length, photolysis laser cross section, estimation of concentration, and photolysis laser power. The dependence of the peak absorption cross sections on the total pressure can be represented by eq 9 derived from analytical solution of the Voigt function35
Figure 1. Upper panel: the simulated HO2 rise (solid line) and Cl decay (dashed line) profile, and the observed absorbance of HO2 (open circle) at 20 Torr total pressure. The simulation conditions were [Cl]0 = 1.37 1014, [Cl2]0 = 3.8 1015, [CH3OH]0 = 1.4 1015, and [O2] = 6.1 1017 molecules cm3. Lower panel: the sensitivity of the reactions: CH3OH + Cl (solid line), CH2OH + O2 (dashed line), HO2 + HO2 (dotted line), and HO2 + Cl (shortened dashed line).
σHO2 ¼
initial total pressure/Torr
ð8Þ
Here AHO2 (max) is the maximum value for HO2 absorbance after photolysis corrected for the methanol absorbance (details are in Section S.1). The methanol absorbance refers to the absorbance change by methanol loss via reaction 2 in this paper.
Z σ 2 ¼ pffiffiffi expðy2 Þ σD π 217
∞ y
expð t 2 Þ dt
ð9Þ
dx.doi.org/10.1021/jp207477n |J. Phys. Chem. A 2012, 116, 215–222
The Journal of Physical Chemistry A
ARTICLE
where σ is the absorption cross section at each pressure, σD is the Doppler absorption cross section at zero total pressure, and y is the normalized pressure broadening parameter given by wL pffiffiffiffiffiffiffi ln 2 ð10Þ y¼ wD
Table 3. Summary of the Diffusion Rate Coefficients of CH3OHa
where wL is the Lorentz width of half-width at half-maximum (HWHM) which is the sum of all broadening effect by itself and other species and wD is the Doppler width (HWHM) wL ¼
∑i γi 760i p
ð11Þ
rffiffiffiffiffi T 7 v0 wD ¼ 3:581 10 M
a
ð15Þ
71.7 ( 0.7
20
48.9 ( 0.7
25
30.0 ( 0.6
30
28.0 ( 0.7
35
11.9 ( 0.6
40
7.4 ( 0.7
The errors indicate 1σ.
1065:180 A1065:203 ðtÞ CH3 OH ðtÞ ¼ RAS A
ð19Þ
Figure 2 shows the determined σHO2 from the HO2 decay profile as a function of total pressures, which are corrected for the overlap with the neighboring absorption from the F2, 131,13 r 141,14 transition (details are in Section S.2), and a fitting line by eq 9. The values were summarized in Table 2 as a function of total pressures. The error bars include the error from measurement deviation and the fitting, kself, l, and kdiff (see Table 3). The main source of error in the estimation of σHO2 is the error of kself. The absolute absorption cross section estimated by fitting was to be (3.1 ( 0.1) 1018 cm2 molecule1 (1σ). Considering the fitting uncertainty (6%) originated from error of γO2, and
At the short reaction times, exp(kdifft) can be approximated by 1 + kdifft. Then, eq 16 is modified to the following equation in absorbance form σHO2 ½HO2 0 l 1 þ ðkdiff þ 2kself ½HO2 0 Þt
17
where σCH3OH is the absorption cross section of CH3OH at 1065.180 cm1, l is the length of photolysis/probe laser overlap region, and RD is the ratio of the beam cross section of photolysis laser to that of the reaction cell (0.227). The obtained kdiff values are shown in Table 3. No dependence of kdiff on the initial Cl2 concentration was observed. The HO2 decay profiles, corrected for the absorption of CH3OH, were analyzed by least-squares fitting of eq 17. Figure 3 shows an example of HO2 decay corrected for CH3OH and a fitting line by eq 17. The CH3OH decay profile at 1065.203 cm1 was reproduced from the CH3OH decay at 1065.180 cm1 using the absorption ratios, RAS (details in Section S.1). Figure 3 also shows a reproduced CH3OH time profile.
The time profile of [HO2] can be found by integration of eq 15 ! 1 2kself 2kself 1 ¼ þ þ expðkdiff tÞ ð16Þ kdiff kdiff ½HO2 t ½HO2 0
AðtÞ ¼ σHO2 ½HO2 t l ¼
143.1 ( 1.6 113.6 ( 1.6
ð18Þ
ð13Þ
ð14Þ
d½HO2 ¼ 2kself ½HO2 t 2 þ kdiff ½HO2 t dt
272.6 ( 4.1
10 13
AðtÞ ¼ σCH3 OH Δ½CH3 OH0 lfRD þ ð1 RD Þexpð kdiff tÞg
Approximating the diffusion loss process as a first order reaction, HO2 loss rate can be written as following equation
7
7 Torr, 10 Torr, 13 Torr, and others, respectively. Then, from these two parameters, σHO2 can be determined using the values of kdiff and kself. The kself value of (1.75 ( 0.25) 1012 cm3 molecules1 s1 at 298 K14 was used, which includes the interference from CH3OH and shows no pressure dependence in the range 030 Torr. The kdiff of HO2 was estimated by measuring the kdiff of CH3OH and correcting it by the root of the molar weight. The kdiff of CH3OH was directly determined by measuring the absorbance time profile at 1065.180 cm1, where CH3OH peak is present, which is affected by the removal of CH3OH from probe region by reaction 2 and by the subsequent inflow of CH3OH to the probe region. Approximating the diffusion loss process as a first order reaction, and taking into account the base validation by CH3OH mixing, the observed decay can be written in absorbance form as the following expression
and secondarily to the diffusion loss from the probe region HO2 f diffusion
kdiff/s1
ð12Þ
where γi is the broadening coefficient by the species i, pi is the partial pressure in Torr of the species i, M is the molecular weight in atomic unit, and v0 is the frequency of spectrum peak center in cm1. The partial pressure other than O2, almost of which was He, was controlled to be 1.2 Torr. In this work, the total pressure was approximately treated as O2 partial pressure. Figure 2 also shows the fitting line for σHO2 by eq 9. Absolute absorption cross section of HO2 was obtained as fitting parameter to be (3.0 ( 0.1) 1018 cm2 molecule1 (1σ). Considering the fitting uncertainty (6%) originated from error of γO2, and propagating the error of absorption cross sections at each pressure (10%, see Table 2), the final value was to be (3.0 ( 0.4) 1018 cm2 molecule1 (1σ). 3.1.2. Determination of σHO2 from HO2 Kinetics. Under the present experimental system, HO2 decay is mainly attributed to its self-reaction HO2 þ HO2 f H2 O2 þ O2
total pressure/Torr
ð17Þ
and σHO2[HO2]0l and (kdiff + 2kself[HO2]0) are obtained as fitting parameters. In the fitting procedure, the time ranges of 0 to 1.5 ms, to 3 ms, to 4 ms, and 5 ms were used for a total pressure of 218
dx.doi.org/10.1021/jp207477n |J. Phys. Chem. A 2012, 116, 215–222
The Journal of Physical Chemistry A
ARTICLE
Figure 5. Absorption cross sections of CH3OH at 1065.180 cm1 as a function of total pressure. The dashed line shows the reproduced absorption cross section from the HITRAN values.26
Figure 3. Typical HO2 decay profile at 17 Torr total pressure with [O2] = 5.1 1017, [CH3OH]0 = 1.4 1015, and [Cl2]0 = 3.8 1015 molecules cm3 corrected for CH3OH (blue line). The pink line shows a fitting line for the corrected HO2 decay. The green line shows the reproduced CH3OH decay from that at 1065.180 cm1. The red line shows the HO2 decay without correction.
Table 5. CH3OH Absorption Cross Sections at 1065.180 cm1 at Each Total Pressurea
Table 4. Summary of the Ratios of Absorbance of HO2 at 1065.203 cm1 to That of CH3OH at 1065.180 cm1a
absorption cross section/1018 cm2 molecule1
7
1.43 ( 0.06
RA
10
1.23 ( 0.04
7
1.085 ( 0.032
10
1.087 ( 0.037
13 17
1.03 ( 0.07 0.97 ( 0.03
13
0.969 ( 0.020
20
0.84 ( 0.03
0.985 ( 0.024
25
0.79 ( 0.02
0.987 ( 0.026
30
0.68 ( 0.03
0.980 ( 0.031
35
0.60 ( 0.02
1.000 ( 0.035
40
0.50 ( 0.03
total pressure/Torr
17 20 25 30 35 40 a
total pressure/Torr
a
0.996 ( 0.033 0.952 ( 0.037
The errors indicate 1σ.
The errors indicate 1σ.
Table 6. Summary of Absolute Absorption Cross Sections of HO2 at 1065.203 cm1a absolute absorption cross section/1018 cm2 molecule1
method
a
initial absorbance
3.0 ( 0.4
HO2 kinetics
3.1 ( 0.3
CH3OH absorption cross section recommendation value
2.8 ( 0.3 3.0 ( 0.5
The errors indicate 1σ.
cross section of HO2 can be estimated by comparison of the loss of CH3OH with the generation of HO2. Figure 4. Example spectrum of the CH3OH/Cl2/O2 system at 7 Torr total pressure. The peaks on the left and the right are CH3OH and HO2, respectively.
σ HO2 ¼ RA
A1065:203 ½CH3 OH ½CH3 OH 2 σ CH3 OH ¼ HO σCH3 OH ½HO2 ½HO2 A1065:180 CH3 OH
ð20Þ propagating the error of absorption cross sections at each pressure (8%, see Table 2), the final value was to be (3.1 ( 0.3) 1018 cm2 molecule1 (1σ). 3.1.3. Determination of σHO2 from Comparison with the CH3OH Absorption Intensity. Since the absorption line of CH3OH presents at 1065.180 cm1 near that of HO2 at 1065.203 cm1 in the CH3OH/Cl2/O2 system, the absorption
Here AHO2 is the absorbance of HO2 corrected for CH3OH, and RA is the ratio of averaged absorbance from 0.1 to 0.3 ms of HO2 at 1065.203 cm1 to that of CH3OH at 1065.180 cm1, which was obtained by measuring the spectra and is summarized in Table 4. The ratio of [CH3OH] to [HO2] at 0.2 ms was calculated to be 1.12 by kinetic simulation for each set of 219
dx.doi.org/10.1021/jp207477n |J. Phys. Chem. A 2012, 116, 215–222
The Journal of Physical Chemistry A
ARTICLE
Figure 6. the HO2 relative intensity spectrum to the absorption intensity of 1065.203 cm1 at 13 Torr. The solid line shows experimental data. The red line shows simulated spectrum from the parameters of HITRAN.26.
Table 7. Relative Absorption Intensities to the Absorption at 1065.203 cm1 at 13 Torr Total Pressure relative
relative a
wavenumber intensity
a
Table 8. Summary of the Absorption Band Strength of HO2 in the ν3 Band method
a
HITRAN wavenumber intensity
HITRAN
Sband/km mol1
ref
laser photolysis
21.4 ( 4.2
this work
1061.291
0.203(17)
0.170
1064.179
0.492(27)
0.445
discharge flow
7.8 ( 1.9
23
1061.659 1061.903
0.532(76) 0.976(44)
0.425 0.932
1064.216 1064.452
0.202(29) 1.070(42)
0.171 1.090
flash lamp photolysis B3LYP/aug-cc-pVQZ
6.7 26.5
25 this work
1061.913
1.084(31)
0.987
1064.464
1.043(48)
1.060
CCSD(T)/TZ2PF
31.7
29
1061.945
0.789(29)
0.780
1064.469
0.977(34)
1.006
CCSD/aug-cc-pVTZ
32.2
31
1062.090
0.737(48)
0.738
1064.631
0.847(95)
0.844
BP/TZVPD
16.8
30
1062.102
0.695(46)
0.684
1064.639
0.785(54)
0.766
1062.165
0.677(51)
0.684
1064.696
0.788(41)
0.739
1062.171
0.674(46)
0.720
1064.710
0.742(30)
0.690
1062.236 1062.393
0.664(57) 1.064(100)
0.619 1.181
1064.768 1064.910
0.742(17) 1.137(86)
0.671 1.254
1062.395
1.093(78)
1.222
1064.913
1.219(136)
1.305
1062.700
0.895(25)
0.918
1065.203
1.000
1.000
1062.716
0.856(33)
0.861
1065.221
0.931(17)
0.926
1063.806
0.205(41)
0.183
estimation error of the absorption cross section of methanol (see Table 5). The absolute absorption cross section was estimated by fitting to be (2.8 ( 0.1) 1018 cm2 molecule1 (1σ). Considering the fitting uncertainty (7%) originated from error of γO2, and propagating the error of absorption cross sections at each pressure (5%, see Table 2), the final value of (2.8 ( 0.3) 1018 cm2 molecule1 was determined (1σ), and summarized in Table 6 with the values from other methods. Taking the results of three different methods into account, the recommended value was to be (3.0 ( 0.5) 1018 cm2 molecule1, which is an averaged value of three methods, and its error was determined to cover all range of three methods. 3.2. Absorption Spectrum and Band Strength of the HO2 ν3 Band. The absorption spectrum of HO2 was measured over the range 1061.171065.28 cm1 at 13 Torr total pressure in the 1,4-c-C6H8 system. Over 7000 points were measured. Each data point was the average of 20 laser shots at the mean absorbance between 0.1 and 0.3 ms after photolysis with a repetition rate of 2 Hz. The wavelength was calibrated with CH3OH and HO2 peaks. Figure 6 shows the HO2 absorption spectrum at 13 Torr between 1061.17 and 1065.29 cm1. Table 7 summarizes the comparison between the measured relative intensities and those reproduced with use of the parameters listed in HITRAN.26 The measured relative peak intensities are in good agreement with those reproduced from HITRAN.26 The line strength can be calculated from the absolute absorption cross section as follows:
Numbers in parentheses represent the deviation (1σ) in last digits.
conditions. An example spectrum of HO2 and CH3OH at a total pressure of 7 Torr averaged between 0.1 to 0.3 ms is shown in Figure 4. σCH3OH at 1065.180 cm1 was directly determined by measuring the absorbance of the premixed CH3OH/O2 sample of the concentration range from 0.8 to 1.9 1015 molecules cm3, the range through which the contribution from self-broadening is negligible. The obtained σCH3OH at 1065.180 cm1 is shown in Figure 5 and summarized in Table 5 as a function of total pressure and shows the close agreement with the values calculated with integrated absorption cross section and air broadening coefficient recommended in the HITRAN database.26 Error (1σ) included the experimental deviation, the estimation error of the optical path length, and methanol sample concentration. The determined σHO2 values, which are corrected for the overlap with the neighboring F2, 131,13 r 141,14 transition (as described in Section S.2), and the fitting line from eq 9, are shown in Figure 2. The values were summarized in Table 2. The error bars include measurement deviation of RA (see Table 4) and
Z Sline ¼ 220
σ dv ¼ σD
a h
ð21Þ
dx.doi.org/10.1021/jp207477n |J. Phys. Chem. A 2012, 116, 215–222
The Journal of Physical Chemistry A
ARTICLE
Table 9. Summary of the HO2 Geometry and Frequencies frequency/cm1
geometrya level of theory b
a
Sband/km mol1
R(OO)
R(OH)
θ(OOH)
ν3
ν2
ν1
ν3
ν2
ν1
B3LYP/aug-cc-pVQZ
1.325
0.975
105.55
1166
1435
3598
26.5
39.8
24.7
CCSD(T)/TZ2PFc
1.333
0.977
104.20
1138
1439
3696
31.7
39.8
36.9
CCSD/aug-cc-pVTZd
1.321
0.966
104.63
1183
1473
3655
32.2
41.9
36.2
BP/TZVPDe
1.347
0.995
104.8
1118
1377
3391
16.8
33.8
11.8
experimental
1.331f
0.971f
104.29f
1098g
1392g
3436h
R/Å, θ/deg. b This work. c Ref 29. d Ref 31. e Ref 30. f Ref 42. g Ref 36. h Ref 43.
Here a/h = 2.43 103 cm1 is the area to height ratio of the Doppler absorption line profile at zero pressure. The band strength is the summation of the line strength for all rotational transitions Sband ¼
∑
Sline ¼ Sline ðF, 131, 13 r 141, 14 Þ
ka, kc, F
∑
16.8 km mol1 with BP/TZVPD,30 and 32.2 km mol1 with CCSD/aug-cc-pVTZ level of theory,31 respectively. In this study, we performed the frequency analysis with B3LYP/aug-cc-pVQZ level of theory, resulting in the value of 26.5 km mol1. The calculated ν3 absorption band strengths are also summarized in Tables 8, and the HO2 geometry and frequencies are in Table 9. Our experimental value of 21.4 ( 4.2 km mol1 is in fair agreement with those theoretical values based on the quantum chemical calculation. It is noteworthy that the band strength determined in the present work includes the systematic error because the absolute absorption cross section at zero pressure was estimated from the absorption cross sections at higher pressures.
RI
ka, kc, F
ð22Þ where RI is the relative intensity to the F1, 131,13 r 141,14 transition. The summation of the relative intensity of 4.9 102 was estimated in our temperature condition from the reproduced spectrum with molecular parameters of HO2 radical reported by Nelson and Zahniser36 using the PGOPHER software.37 Since the HO2 radical is a near symmetric prolate top with k = 0.993, the effects of a small asymmetry on the transition intensity are very small. Therefore, we calculated relative rovibrational intensities using the symmetric top H€onlLondon factors and no other factors. Nelson and Zahniser calculated the relative intensities of HO2 ν3 band with the H€onlLondon factors and showed an agreement with experimental relative intensities within 10% error.36 Our calculation is essentially the same with Nelson and Zahniser. Considering the uncertainty of the relative intensities of 10%, the ν3 band strength was estimated from our recommendation for absolute absorption cross section to be 21.4 ( 4.2 km mol1. The band strength is represented by the following equation24 Sband ¼
2π2 ν jμj2 3ε0 hcQvib
4. CONCLUSION A QCL as mid-IR laser source has been used to determine the absolute absorption cross section of HO2 ν3 band. The absolute absorption cross sections of the F1, 131,13r141,14 transition at 1065.203 cm1 were estimated by three methods. These three estimated values are in good agreement with each other. The absorption spectrum of HO2 ν3 band was also measured from 1061.17 to 1065.28 cm1. The measured spectrum features show an agreement with that reproduced from the reported molecular parameters. The determined absorption cross section was converted to the ν3 absorption band strength to be 21.4 ( 4.2 km mol1, in agreement with results of the frequency analysis of quantum chemical calculations.
ð23Þ
where ε0 is the vacuum permittivity, h is the Planck’s constant, c is the velocity of light, ν is the wavenumber at band center, Qvib is the vibrational partition function, and |μ| is the vibrational transition dipole moment. For the ν3 band with 1097.625 cm1, eq 23 gives |μ| = 0.088 ( 0.009 D. There are two previous experimental studies reporting the band strength of the HO2 ν3 band, as summarized in Table 8. Buchanan et al.25 reported the value of 6.7 km mol1 using the single mode diode laser combined with the flash lamp photolysis. Zahniser et al.23 reported 7.8 ( 1.9 km mol1 using the multimode diode laser with monochromator in the discharge flow system. The previously reported values are small compared to our value of 21.4 ( 4.2 km mol1. The value by Buchanan et al.25 was measured with the low signal-to-noise ratio (S/N) of
