2924
J . Phys. Chem. 1984, 88, 2924-2925
TABLE I: Comparison of Relative Fluorescence Signal Strengths
Chan et al,” Germanb this work 420 42 380 18 15 (kl5%)
z309(N2)/z309(02)
1309(N2)/1309(90%0 2 + 10% N , )
20% 0, + 13 torr of H 2 0 )
42
2.0
2.0 (413%)
51.5
2.5c
2.5 (413%)
“Reference 5 . bThe values in German’s work6 are those predicted by using the lowest k level reported. CCalculatedby using k ( H 2 0 ) values of Chan et aL5
of atmospheric pressure and temperature, using the notation presented by Chan et alSs Thus, the fluorescence quantum efficiency for the system A(v’=O)
-
X(u”=O)
is given by kFoklOIMl
Yo = (kFo
+ kQo[Ml)(kQl[Ml + klO[M1 + kFI)
for A(v’=l) Y1 =
-
School of Geophysical Sciences Georgia Institute of Technology Atlanta, Georgia 30332
X(v’=l)
+ klO[Ml
where kFIand kFo are the rates for spontaneous emission from A(u’=l) and A(u’=O), respectively; and kQl,k,+, and klorepresent quenching of the OH radical by molecule M involving A(u’=l) X(v”=O,l, ...), A(u’=O) X(v”=O,l, ...), and A(v’=l) A(v’=O), respectively. In Table I we have listed calculated relative fluorescence signal X(v”=O) strengths, based on the values of Yo for the A(u’=O) transition. These ratios are based on Yo(N2)/Yo(M)using the relaxation coefficients of Chan et al.5 and Germana6 In this evaluation we have assumed kFo = kFI = 1.4 X lo6 s-l while neglecting effects of fluorescence terms such as A(v’=l) X( ~ 0 and ) A(u’=O) X(u”=l). Also shown in Table I are two fluorescence efficiency ratios measured in our laboratory. From Table I, it can be seen that our measured relative signal are in excellent agreement with those strengths, 13w(N2)/13w(M), predicted by German’s relaxation coefficients and differ from those of Chan et aL5by a factor of 21. The disagreement between the results of German6 and Chan et ale5also can be seen by comparing X(u”=O), 13@, to those the relative signal strengths for A(u’=O) X(v”=l), Z314 as predicted by for A(v’=l)
-
D. D. Davis* J. D. Bradshaw M. 0. Rodgers
Received: February 7, 1984
kF~
kFl + kQl[Ml
1309/1314 ratio of 5.5 using the Chan et ale5rate constants. If we assume that no buffer gas was used, the calculated ratio would be 3.07. In this context, while Chan et aL5 have noted the disagreements with other investigators as related to kal[02] and klo[0,], it would appear equally significant to us that the latter authors also have quite different values for kQa[N,] and kl0[N2]. In this case, the values of Chan et al. are low when compared to other reported values. We have noticed that the largest discrepancies in the relaxation rates of Chan et aL5,as compared with other investigators, occur for the collision partners N, and 02.For these gases, measurements of the relaxation rate coefficients were carried out under conditions where very short quenching fluorescence lifetimes had to be measured. It would appear, therefore, that their signal/ background ratios were typically much lower for N2 and 0, than for Ar and H20. Unfortunately, details about the nonresonance fluorescence background levels and necessary temporal corrections are not given by Chan et al. We can only suggest that erroneous deconvolutions might exist for the case of low signal/background ratios, especially when the background nonresonant fluorescence may be quenched by the same collisional partners as used to quench OH. Registry No. Hydroxyl radical, 3352-57-6.
-
-
-
Reply to Comments on “Laser-Excited Fluorescence of the Hydroxyl Radical: Relaxatlon Coefficients at Atmospherlc Pressure” by C. Y. Chan, R. J. O’Brlen, 1.M. Hard, and 1.B. Cook
-
Sir: We thank Drs. Wang and Davis et al. for their comments regarding our paper.’ The issues they raise deal mainly with the fluorescence yield of HO excited at 282 nm in air at atmospheric pressure and with the temporal resolution of the experimental system used to determine the quenching rates. Although the fluorescence yield of HO was not our prime interest in undertaking the work in question, this quantity is important. Our point in deriving a fluorescence yield from our measurements was to stress the uncertainty which our results threw on this quantity. This was probably ill-advised, however, in that it utilized a three-level model on which we cast doubt. Because of the interest in the fluorescence yield, we have obtained it directly at 6 torr. Our photon-counting apparatus has been temporarily dismantled; these measurements were made in a low-pressure flow Assuming detection efficiencies and laser pump parameters to be tube in which room air was excited by an electric discharge upconstant, under conditions involving 1 atm of dry air, one calculates stream from the observation region, producing HO concentrations Z309/1314 = 1.3 based on the relaxation rates reported by Chan sufficient to yield several hundred detected fluorescence photons et aLs By comparison, using German’s6 relaxation rates, the from each laser pulse. The amplified photocurrent was displayed calculated value is 2.8. The latter value is close to that measured on a 400-mHz oscilloscope, and about 300 successive traces were in our lab of 2.5 (f2O%)’ and to that measured earlier by Selzer superimposed photographically by time exposure. Photographs and Wangs of 2.3. On a related point, we find it unclear how the reported 1309/13,4of the scattered laser waveform and the H O fluorescence and off-resonance background waveforms at 309 and 314 nm were ratio for nitrogen (4.4) is consistent with the quenching rate digitized manually. The first-order decay rates, a and 6 , were constants reported by Chan et aL5 It appears that the gas mixture measured by the deconvolution procedure outlined in our paper,l used for the Z309/1314 measurement consisted of 5 torr of N2 and using eq 17 and 18. 0.01 torr of H 2 0 (p 4970) with an undisclosed concentration of Utilizing the relationship y309 = (Z309/13,4)Y314 or Y309 = buffer gas (probably Ar). If we assume that an argon buffer gas (Z309/Z314)(kfl/a314), we calculate the 6-torr fluorescent yield at was employed at a total pressure of 1 atm, we calculate an expected 309 nm to be -0.03 as compared to 0.07 calculated from German’s2 rate coefficients for air at 50% RH. We note that this
-
-
-
(7) This value was estimated from our comparing fluorescence levels from 50- and 100-Abandpass filters and those from a system having no bandpass filter. (8) P. M. Selzer and C. C. Wang, J. Chem. Phys., 71, 3786 (1979).
0022-3654/84/2088-2924$01.50/0
(1) C. Y . Chan, R. J. OBrien, T. M. Hard, and T. B. Cook, J . Phys. Chem., 87, 4966 (1983).
0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 13, 1984 2925
Comments 600
510 480
420
360 ! I
c
300 240 180
r
1
1
1
1 t 1 1
0
20
40
60
80
100 120 140
160 180 200
CHANNEL NUMBER Figure 1. H O fluorescence in nitrogen: X indicates the measured net
fluorescence waveform; the solid line is the fluorescence predicted by German’s rate coefficients via convolution with our laser waveform; the points are the measured off-resonance background in N,, amplified for clarity. Resolution is 0.2 ns per channel. calculation does not rely on the three-level model, only requiring that the 3 14-nm decay is accurately characterized. In a related experiment, we have determined the Z309/Z314 intensity ratio in 02/0.5%H 2 0 at a pressure of 3.6 torr to be 0.36 0.18, as compared to 0.22 as predicted by German’s3 rate constants. These intensity ratios were determined by gated charge integration (from -150 to +850 ns with respect to the onset of scattering) with off-resonance background subtraction. Unfortunately, the large uncertainty in our result renders the experiment less than conclusive concerning unusual behavior in the presence of oxygen. Dr. Wang mentions the inconsistency between eq 21 and the experimental data reported in Figure 10. This inconsistency was the intended point of our statement “the measured intensity ratio varies in this region in a way that is inconsistent with pseudofirst-order kinetics”. The experimental observations reported by Davis et al. of Z30,(N2)/Z309(N2+02) at two widely differing O2concentrations, and of 1309(air)/Z314(air), provide strong (though not conclusive) evidence that the low-pressure rate coefficients of German remain valid at atmospheric pressure. As Drs. Davis et al. correctly mentioned, it was necessary to subtract the off-resonance background from the waveforms before deconvolution. We were aware (as we stated) that our nitrogen a value was lower by about a factor of 2 than German’s value2 measured at much lower pressure. Also, we were aware that an increase in this value (the intercept in Figure 8a) would bring the oxygen a value into better agreement with German’s value for oxygen. Davis et al. correctly point out that improper background subtraction could lead to errors in the rate constants derived from
*
(2) K. R. German, J . Chem. Phys., 64, 4065 (1976). (3) R. N. Bracewell, “The Fourier Transform and Its Applications”, McGraw-Hill, New York, 1978.
convolution. In light of these comments, we have reexamined our nitrogen data of Figure 5 . We reproduce those data in Figure 1 here and include the results of convolving German’s a and b values with our laser excitation function. The difference in the two waveforms is apparent, and no reasonable variation in our subtractive background could bring these two waveforms into congruence. Davis et al. did discover a computational error in our paper. For nitrogen, the integrated intensity ratio Z309/Z314 was measured at a total pressure of 5 torr (no buffer gas) and was correctly reported as 4.4 in Table I. This result agrees within the experimental uncertainty with that of German2measured at lower pressures, A subsequent error in our calculation of klONz and kQlN2led to the inconsistency noted for Nz. Dr. Wang comments that the temporal resolution of the excitation and detection instrument used by us was insufficient to measure the reported decay rates. He refers specifically to the determination of first-order quenching rates with constants on the order of 5 ns-I. As a matter of principle, eq 17 or 18 of ref 1 is an exact description of the fluorescence output waveform and it does not place any constraints upon the excitation function. It should be noted that the laser function we measured is the convolution of the true laser waveform with that of the detection system. If both the laser function and the output waveform are measured with adequate signal-to-noiseratio and adequate digital resolution, then the response function of the molecular sample can be retrieved by deconvolution. Thus it is noise and the resolution of the multichannel analyzer which limit the achievable temporal resolution in our experiments. According to sampling theory3 a single exponential decay of lifetime 0.2 ns can be measured with a sampling interval of 0.1 ns (the Nyquist interval). This subject was treated by simulations in our paper. To further demonstrate the systematic error at this limit, we have convolved a r function (having the same fwhm as the observed laser waveform) with the difference-of-exponentials response using a = 5 ns-’ and b = 0.5 ns-], and digitized the resultant waveform with a resolution of 0.1 ns. Deconvolution revealed a 10% systematic underestimate of a and negligible error in b. By comparison, in analog signal processing a 1:2 ratio of detector to detected risetimes gives 12% error. The 3% error reported for the simulation in our paper used a = 2 and b = 0.5 ns-I. Thus, in the absence of noise, the resolution of the detection electronics is adequate for the reported measurements. Other sources of systematic error were also discussed in our paper. Lacking a quantitative theoretical treatment of the signal-tonoise requirement, we evaluated it in two days as we described.’ First, the above r excitation function was used to generate an exact signal waveform. Then N 1 / 2noise was added to discrete values of each waveform at 0.1 ns intervals, and the waveforms were deconvolved to obtain values for the two rate parameters, a and b, as above. Second, random errors in our reported results were evaluated by deconvolving subsets of the real experimental data at each gas composition. Since these errors were larger than the other errors discussed, they were represented by the error bars shown in Figures 7 and 8, and, to that extent, the largest measured rates were “inaccurate”. Thus, the instrument and the observation times were adequate to determine the reported lifetimes, subject to the stated’ uncertainties. Registry No. Hydroxyl radical, 3352-57-6.
-
Department of Chemistry Portland State University Portland, Oregon 97207 Received: March 22, 1984
C.Y. Chan*
R. J. O’Brien T. M. Hard
