8472
J. Phys. Chem. 1995,99, 8472-8476
Vibrational Energy Transfer and Quenching of OH A%+(v’=l) Measured at High Temperatures in a Shock Tube P. H.Paul Sandia National Laboratories, Livermore, Califomia 94551 Received: December 12, 1994; In Final Form: March 13, 1995@
Rate coefficients are reported for vibrational energy transfer and electronic quenching of OH A2F(v’=1) by N2, 0 2 , CO, C02, NO, Ar,Kr, and Xe. Rate coefficients for electronic quenching of O H A2X+(v’=0) by the same set of collision partners are also reported. The measurements were performed at high temperatures (1900 and 2300 K) behind reproducible shock waves. The cross sections for quenching in v’ = 1 were observed to be quite similar to the values found for quenching in v’ = 0. For all of the species studied, the cross sections were found to be independent of temperature from 1900 to 2300 K. However, all of the high-temperature cross sections were found to be smaller than the previously reported values for quenching and vibrational energy transfer at 300 K. The decrease in the cross sections with temperature was observed to be more pronounced for vibrational energy transfer than for electronic quenching.
Introduction For some years, collisional deactivation of excited electronic states of the hydroxyl radical has been an area of keen study.’ OH is important in the chemistry of the upper and tropospheric atmosphere and as an intermediate in hydrocarbon-air reactions. The spectroscopy of the OH A X system is well understood, and the excited state is readily accessible with common pulsed lasers. As such, OH is one of the most commonly addressed species for laser diagnostics of turbulent reacting flows, via single-point2 and planar3 laser-induced fluorescence (LIF) techniques. Corrections for collisional quenching and for vibrational energy transfer (VET) are required to be able to make quantitative linear LIF measurements. For OH A2X+(v’=O), the rate coefficients required to make such corrections have been measured at room temperature for a wide range of collision partners. Rate coefficients have been reported for a more limited set of collision partners at temperatures near 1200435and 2000 K.6 The available data are far more restricted for quenching and VET in OH A2Xf(v’=l) and these limited almost exclusively to measurements at 300 K. In this study, VET and electronic quenching of OH A2Z+(v’=l) at elevated temperatures (1900and 2300 K)are examined using LIF of shock-heated gases. The temperature range and the collision partners (N2,02, CO, C02, and NO) were selected because of their importance in making quantitative corrections to OH LIF measurements in combustion and aerothermodynamic systems. Studies of VET and electronic quenching by Ar, Kr, and Xe were also performed to provide an additional basis for model development.
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Experiment The measurements were performed using the shock tube facility and probe laser described p r e v i o ~ s l y .The ~ ~ ~laser was tuned to excited the Ql(5) transition in the OH A2Z+ X213 (1,O)system. A band-pass filter was used to isolate fluorescence in the spectral range of 285-295 nm, which is composed of most of the (1,O) band emission but which is contaminated with some (2,l)band emission? A second band-pass filter was used to isolate fluorescence in the spectral range of 307-310 nm, which is composed of a portion of the (0,O) band (portions of
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@Abstractpublished in Advance ACS Abstracts, May 1, 1995.
the R- and Q-branch bandheads) but is free of emission from other bands. The spectral band-pass of the filters were verified using a Cary spectrophotometer. The photomultiplier tubes used to record these signals were wired to use a limited number of dynodes to optimize the dynamic range. The signals were preamplified (lox gain) and were recorded on digital oscilloscopes (LeCroy 9450A). To verify the spectral response of the filtered detectors, fluorescence decays were recorded from the OH present in the products of a low-pressure microwave discharge in He seeded with a trace of water vapor. Under these conditions, there is essentially no vibrational energy transfer in the OH A2X+. Thus, the excitation to v’ = 0 or v’= 1 produces fluorescence almost exclusively from the laser-populated vibrational level. Selective excitation to each band and observation of the fluorescence from the other band indicated that the cross-talk was reduced to less than 0.3% of the peak, which is better than the signal resolution of the recording system. The base test gas mixture employed near equimolar quantities of H2 and N20 introduced at concentrations of less than 0.02% in high-purity argon. For these experiments, the Ar, Kr, Xe, and N2 were further purified by using a gas chromatography filter (Matheson 6404)designed to remove residual oxygen and water. Shock heating this gas mixture to near 1 atm of pressure and temperatures of 1900-2300 K produces OH with some water and nitrogen in a bath of argon. The quenching gases were added to this mixture at concentrations of a few percent. Gas mixtures were prepared in a Teflon-lined vessel by measuring the partial pressure of the various components with a capacitance manometer (MKS Baratron). After preparation and prior to use, the gas mixtures were allowed to stand for at least 15 h to ensure thorough mixing. Before each run, the test gases were allowed to flow through the driven section of the shock tube for at least 5 min to ensure passivation of the walls and, thus, a reliable composition of the mixture. The composition of the gas mixtures was designed to achieve an OH mole fraction near 0.0002% and to minimize the quenching contribution of the other reaction products. The composition of the test gas added to the mixture was set to achieve decay rate constants in the range of 5-20 ius-’. Dispersed fluorescence spectra recorded with a time-gated optical multichannel analyzer indicated that rotational thermalization occurs on a much faster time scale than that for
0022-3654/95/2099-8472$09.00/0 0 1995 American Chemical Society
Energy Transfer and Quenching of OH A2F(v’= 1)
J. Phys. Chem., Vol. 99, No. 21, 1995 8473
quenching or VET. Kienle et al.’O have reported steady-tostate and total rotational energy transfer (RET) rate coefficients for OH A2F(v’=l) in thermal collisions with a number of species as measured at 300 K. They find that the variation in the RET coefficients with collison partner is similar in character and magnitude with those previously reported for RET in OH A2Z+(v’=O). There are only a few studies of RET in OH A2Z+ at elevated temperatures, and the results are primarily limited to collisions with water. However, a comparison of the results of Jorg et al.” taken at 300 K with those of Lucht et a1.I2and Lee et al.I3 taken at temperatures near 1400 K suggests that the cross section for RET in OH A2Z+(v’=O) with water is roughly constant or possibly increases slowly with increasing temperature. Using the results of these studies and the reported values for VET in OH A2C+ as measured at 300 K,I4-l6 the estimated total RET in v’ = 1 or 0 and the total quenching plus VET rates for the test conditions are greater than 2 ns-I and of the order of 0.02 ns-I, respectively. The total RET rates are thus more than 50 times faster than the total electronic quenching and vibrational transfer rates at the experimental conditions. As such, the measured quenching and VET cross sections are taken to reasonably reflect thermal rotational distributions in v’ = 1 and v’ = 0.
Results Laser-induced fluorescence data from 147 high-temperature shock tube runs are employed in the data analysis. The data from each run are composed of a pair of fluorescence decays. To avoid interference from the laser pulse and the associated finite-rate excitation effects when fitting the data, the first 20 ns of the data record after the v’ = 1 fluorescence peak is not used (which corresponds to a delay of the order of 40 RET characteristic time scales). For each gas mixture and for each temperature, experimental decay traces are obtained 8- 10 times. Rate coefficients are determined for each set of decay traces, and the results are averaged. In the limit that the rotational thermalization rate is fast compared to the quenching and VET rates and for times well after the initial excitation transient, the normalized total densities in v’ = 1 and v’ = 0 can be modeled as an initial value problem of the form
The initial condition is taken to be Nl(0) = c and No(0) = 1 c, where 0 5 c 5 1. Equations l a and Ib are solved analytically by Laplace transformation to give
N, = C,, exp(-at)
+ D, exp(-Pt)
(2)
where the subscript refers to v’ = 0 or 1. The pairs of experimentally measured decays are simultaneously fit to eq 2, which yields six coefficients: C,, D,,a, and p. Two of these coefficients are eliminated, specifically D,, by normalizing the fits to match the initial conditions which introduces c as a measured parameter. The upward VET rate coefficient can be written in terms of the downward rate by invoking detailed balance; thus, let
a = vo*/v,o =fB(v’=l,T)?IfB(v’=o’T)
(3)
which is purely a function of the measured temperature. Here,
f~ is the Boltzmann population fraction. From the analytical solution to eqs l a and lb, we have
CdC,=z(l/a- l/(l+c~+z-cz))+l/a
(4)
which is solved for the nondimensional parameter z , given by
z
(Q, - Qo + A I - Ao)/Vio
(5)
From the analytical solution to eqs l a and lb, we also have
d p = Y
1 +2a+2z+a2+z’+ l+a+z+vaz
(6)
which is solved for the nondimensional parameter v, given by Y
V,d(Qo + A,)
(7)
The experimental data are thus transformed to a fit in four coefficients (Le., c, z, v, and a) and the known parameter a. From the analytical solution to eqs l a and lb, we have
which is solved for Qo given the known value of TO = 690 ns.I7 Equation 7 is then used to determine a value for Vlo, and eq 5 is used to determine a value for Ql given the known value of T I = 736 ns.I7 Here the data reduction makes use of the observation that the spontaneous emission rates do not change appreciably as a function of rotational level for rotational levels less than approximately 15.18 The experimentally determined collisional rates, Qo, Ql, and V I O can , be related to the cross sections 00, 01, and 010, respectively, via
Q = no (“OH) C Xp[J’ + m()H/mpl
112
op
(9)
P
Here no is the total number density, (VOH) E ( 8 k T / 7 ~ m o ~ )and ”~, the summation is over all collision partners, p, present at a mole fraction, xp. In the data reduction, this summation is extended to all collision partners having a nonnegligible contribution to the rates. The data were analyzed using a multiplex regression over all of the experimental runs. The initial guess for the data reduction was made by assuming olP= ooPand o1oP= bpup. Here the constant b, was taken from the 300 K data where known or taken to be b, = 0.1 and 1.0 for polar and nonpolar quenchers of OH, respectively, and b, = 4 for weak quenchers of OH (Le., Ar or N2). The initial guess for oop was made using the values predicted by a harpoon m0de1.I~ The data reduction procedure is in general well conditioned if the v’ = 0 signal maximum is part of the data record. For values of z of order zero, the v’ = 0 fluorescence peak occurs at a delay of
to,max= ln(1
+ v(1 + a ) ) / ( l+ a)vQo
(10)
from the v’ = 1 fluorescence peak. For each gas mixture, an initial run was performed assuming a value of Y = 0.6 as a basis to determine the amount of gas mixture to be added to the argon. The data from this run were then reduced to obtain a better estimate for Y,and the total amount of mixture added to the argon was adjusted to try to achieve a value of to,max near 50 ns and thus to achieve a well-conditioned data record for fitting. This mixture was then held fixed for all of the runs used to acquire quenching and VET data. In most cases, only a small adjustment was required (e.g., for Y = 0.05 or 8, the mixture would be set to achieve a value of Qo = 5 or 20 ps-l, respectively).
Paul
8474 J. Phys. Chem., Vol. 99, No. 21, 1995 TABLE 1: Cross Sections for VET and Electronic Quenching of OH A2C+(v’=1,O)” cross sections, A 2 ~~~
2300 f 50 K
1900 f 50 K
co11id er Ar
co
coz Kr N2 NO 0 2
Xe a
00
‘0.05 13.1 f 1.6 12.2 f 1.5 1.07 f 0.12 0.52 f 0.1 1 27.1 f 1.5 7.05 f 1.6 9.10 f 1.4
01
‘0.08 10.4 f 2.0 12.9 f 1.8 1.87 f 0.19 0.58 f 0.16 28.2 f 1.9 7.93 f 1.4 9.52 f 2.1
010
00
01
010
10.22 3.81 f 0.56 8.4 f 0.91 4.33 f 0.73 3.60 f 0.37 3.02 f 0.61 0.88 f 0.26 10.1 f 1.4
10.05 13.7 f 1.8 12.5 f 1.4 1.12 f 0.15 0.56 f 0.17 29.0 f 1.7 7.43 f 1.1 9.02 f 1.3
‘0.07 11.1 f 2.0 12.1 f 1.9 1.92 f 0.23 0.61 f 0.22 29.3 f 2.5 8.01 f 1.9 9.31 f 1.8
‘0.18 4.12 f 0.67 9.3 f 1.1 4.20 f 0.88 3.41 f 0.46 2.47 f 0.55 0.83 f 0.29 11.3 f 2.1
The quoted errors reflect the 2 standard deviation statistical error estimates.
TABLE 2: Rate Coefficients for VET and Electronic Quenching of OH A2C+(v’=l,0P rate coeff, lo-” cm3/s 1900 f 50 K
2300 f 50 K
collider
ko
ki
kio
ko
ki
kio
Ar
‘0.092 25.6 & 3.1 22.1 f 2.7 1.81 f 0.20 1.01 f 0.22 52.2 f 2.9 13.4 f 3.0 14.9 f 2.3
10.147 20.3 3.9 23.4 f 3.3 3.16 f 0.32 1.13 f 0.31 54.3 i 3.7 15.1 f 2.7 15.6 f 3.4
‘0.404 7.4 f 1.1 15.9 f 1.6 7.31 1.24 7.02 i 0.72 5.82 1.18 1.68 f 0.50 16.5 f 2.3
co.101 29.4 f 3.9 24.9 f 2.8 2.08 i 0.28 1.20 0.37 61.4 f 3.6 15.6 f 2.3 16.2 f 2.3
10.141 23.8 f 4.3 24.1 f 3.8 3.56 f 0.43 1.31 f 0.47 62.0 f 5.3 16.8 f 4.0 16.7 f 3.2
10.364 8.2 f 1.3 18.5 f 2.2 7.80 f 1.63 7.32 f 0.99 5.23 f 1.16 1.74 f 0.61 20.3 f 3.8
co
coz Kr
N2 NO 0 2
Xe
*
* *
*
The quoted errors reflect the 2 standard deviation statistical error estimates. The measured cross sections and the corresponding rate coefficients are summarized in Table 1 and Table 2,respectively. The data in these tables are quoted with 2 standard deviation experimental error limits. The data analysis provides a measure of the rates for electronic quenching in v’ = 0, the values of which are also given in Tables 1 and 2. The error bars on the measured temperatures are estimated to be f 5 0 K. Estimates for the systematic errors are discussed below. In this study, reactive shocks are employed to produce OH at high temperatures and pressures. Some of the minor products of the reaction are known quenchers of OH. The particular quenching species added to the mixture may also participate in the reactions. The behavior of the system was modeled using the chemical kinetics code CHEMKKN20as modified to include the effects of shock propagation.21 In combination with a chemical kinetics mechanism, this code was used to simulate the incident shocks to predict temperatures, pressures, and species concentrations as a function of time. The particular chemical mechanisms used here were taken from Miller and Bowman.** In the data analysis, values for the quenching and VET cross sections of the minor constituents had to be fixed, a priori, for the temperature range of 1900-2300 K. Here the same values were taken for crop as used in the previous study by our group of quenching in v‘ = 0.6 Specifically, values of 00, = 14, 10, 28, 4.5, 23.5, and 22.5 A2 for quenching by H, 0, OH, H2, HzO, and N20, respectively. For the minor species, the same set of values was assumed for alp. The cross sections for VET by the minor constituents were taken to be alop = b,uop. Again the constant b, was set according to the reported roomtemperature values available or set according to the classification scheme proposed by Copeland et ~ 1 Specifically, . ~ ~ the value
choices for the initial guess, and (iii) different choices for the cross sections of the minor constituents. As before, it was found that the predicted systematic errors are within the observed statistical errors in the measurements except for the case of quenching and VET with Ar. It was only possible to establish upper limits for the cross sections for Ar because the rates were found to be sufficiently sensitive to the choice of the minor species cross sections. In the prior work, it was established that the systematic error incurred in preparing the gas mixtures, in the contaminate history, and in the day-to-day cycling of the facility was of the order of f5% in the measured cross sections. The time-integrated spectra recorded with an optical multichannel analyzed indicated some emission from OH A2Z(v’ = 2). At the highest temperature studied here (2300 K), the spectra indicated that less than 2% of the population in OH A2Z was in v’ = 2. In the time-resolved decay measurements, the detection bandwidth for the v’ = 1 channel included a fraction of the (2,l)band emission. The system was modeled by adding a rate equation for v’ = 2 to eqs l a and lb. In the previous work on quenching in v’ = 0, it was found that little or no bias was introduced due to VET with v’ = 1. Similarly here, the modeling indicated that the systematic error introduced by VET with v’ = 2 was less than 1% in the measured cross sections at 2300 K. The effect will be smaller in the cross sections measured at a temperature of 1900 K. Discussion
There have been a number of room-temperature studies of VET and quenching in OH A2Z+(v’=1) by the simple diatomics and by the lighter noble g a s e ~ . ’ ~ - ’ ’ ,Of ~ ~these, Lengel and Crosley16 have studied the problem in considerable detail, observing that the rates for VET are a very strong function of ofbP=1,1,0.1,1.7,0.1,and0.7forH,O,OH,H~,H~O,and rotational level. They found no evidence to support isoenergetic N20, respectively. transfer mechanisms as well as no evidence for atom-exchange The same suite of sensitivity tests used in the prior study6 reactions (e.g., OH A2Z+ D2 OD A2Z+ HD). Copeland were employed here to estimate the systematic error in the et aLz3have expanded the room-temperature data base reporting measurements. These include reduction of the data under the rates for VET and quenching in OH A2Z+(v’=1) by CF4, C&, assumptions of ( i ) different chemical mechanisms, (ii) different
+
-
+
J. Phys. Chem., Vol. 99, No. 21, 1995 8475
Energy Transfer and Quenching of OH A2Z+(v’=1) CO2, H20, NH3, N2, N20, and sF6. They observe that the variation with collision partner tends to fall into three categories: (i) the strongly polar species have large cross sections for quenching and relatively small cross sections for VET; (ii) species like CH4, C02, and N20 have reasonably large cross sections for both quenching and VET; and (iii) species like CF4, N2, and SF6 have large cross sections for VET but are inefficient at quenching. They also observe that the species-specific cross sections for quenching in v‘ = 1 tend to be equal to or slightly greater than those for quenching in vf = 0. This observation is confirmed in the rates reported by Cleveland and W i e ~ e n f e l d ~ ~ for quenching of OH A2Z+(vf=0,1)by water at 300 K. Cattolica and Mataga26reported cross sections of 32 & 2.5 and 10 f 3 A2 for quenching of OH A2Z+(v’=l,N ’ 4 ) at 1048 K by water and H atoms, respectively. Their measurements were performed in the products of a low-pressure H2-02 flame as diluted in Ar. They observed no measurable (0,O) band fluorescence, from which they concluded that the VET cross section due to water was very small. A number of other studies of total quenching and VET in OH A2Z+(v’=l) have been performed in flames. Smith and Crosley2’ performed low- and high-resolution LIF emission scans from OH in a slightly lean atmospheric pressure CH4air flame (measured temperature of 2200 K). They employed these data to infer a total value of 010 % 0.5800 for excitation to OH A2Z+(v’=1,N’=5). Combining this value with previously reported measurements for quenching in v’ = O6.I9 and assuming that all of the VET is due to N2 provide an upper limit of 010 < 8.800 or 010 < 4.8 A2 for N2 at 2200 K. Kollner et al.2s have reported the results of a study using time-resolved OH LIF measurements performed in atmospheric pressure premixed flames. They employed a picosecond excitation source and recorded the temporal decays with a streak camera. For the postflame gases of a stoichiometric CH4-air flame (estimated temperature of 2100 K), they report characteristic total fluorescence lifetimes of 1.85 f 0.12 ns following excitation to OH A2Z+(v’=O,N”=5) and 1.78 & 0.18 ns following excitation to OH A2Z(v’=1,N ’4).For this same flame condition, they also provide a measurement of 010 0.60~. The observed decays in the total fluorescence were subsequently characterized as ~ingle-exponential.~~ This behavior would be expected (using the solution to eqs l a and l b above) if OIO OI x 00 or if
+
which are mutually exclusive conditions. Given the value of 010 % 0.6u0, these conditions would require 01 0.400 or 01 % 00, respectively. The evidence for the latter condition is more favorable since the ratio for quenching in vf = 1 by water alone to total quenching in vf = 0 appears to require 01 > 0.7500 for the flames. More recently, Steffens30 has been reported the results of a study of quenching and VET in OH A2Z+(vf=0,1) for the temperature range of 196-300 K and for the collision partners N2,02, and C02. The results of Steffens are in good agreement with previous measurements at room temperature and confirm the general trend that the magnitude of the cross sections decreases with increasing temperature. The results given in Tables 1 and 2 indicate that the collisionpartner-specific cross sections for electronic quenching in v’ = 1 at high temperatures are near equal or slightly greater than those for v’ = 0 with the particular exceptions of quenching by Kr and CO. For Kr, the cross sections for quenching in v’ =
TABLE 3: Cross Sections for Electronic Quenching of OH AZZ+(v’=O). 00%
1900 f 50 K collider ____
Ar CO C02 Kr NZ NO 0 2
Xe
this work ~~
ref 6
A2 2300 f 50 K this work
ref 6
~
x0.05 ‘0.057
