J. Phys. Chem. 1983, 87, 4966-4974
4966
Laser-Excited Fluorescence of the Hydroxyl Radical: Relaxation Coefficients at Atmospheric Pressure C. Y. Chan,’ R. J. O’Brlen, T. M. Hard, and T. B. Cook’ Chemistry Department and Environmental Sclences Doctoral Program, Portland State University, Portland, Oregon 9720 1 (Received: Aprli 25, 1983; In Final Form: June 30, 1983)
The energy-transfer processes of the hydroxyl radical in its A2Z+state have been studied at atmospheric pressure, a tenfold pressure increase over previous 300 K studies. Laser excitation produced the A(u’=l) state, and emission from A(u‘=O) was followed by the time-correlated photon-counting technique. Deconvolution of the energytransfer response function from the laser pulse shape allowed determination of the electronic and vibrational energy-transfer rate coefficients for argon, water, nitrogen, and oxygen. Some evidence for pressure dependence was found in quenching from A(u’=O) X with oxygen and water. A much stronger pressure dependence was found for the processes A(u’=l) A(u’=O) and for A(u’=l) X with oxygen as collision partner. These results indicate a major decrease in fluorescence efficiency for laser-excited fluorescence of HO at atmospheric pressure, relative to that calculated from low-pressure rate-constant measurements.
- -
Introduction The energy-transfer processes occurring in excited small molecules are of fundamental interest. These processes are commonly studied a t relatively low pressures, where the mechanism is usually controlled by bimolecular processes, and this has been the case in previous studies of the energy-transfer processes in the hydroxyl radical. However, a t higher pressures, the possibility of pseudotermolecular processes must be considered for instance, the formation of dimers, metastable complexes, or excimers. These processes, along with true termolecular processes, can give rise to an effective “collisional broadening” of a bimolecular rate coefficient, similar to collisional broadening of absorption lines. Attempts to measure ambient HO by pulsed laser-excited fluorescence (LEF)’p2 have been another motive for this undertaking. Due to the crucial importance of HO to our understanding of atmospheric chemistry, many such attempts have been made by using LEF and other metho d ~ . ~ The - ~ LEF technique involves exciting the HO radical with one of the rotation-vibronic lines in the X2rI(V”=O) A2Z+(u’=l) transitions near 282 nm and observing the A(u’=l) X(u”=l) transition near 314 nm or the A(u’=O) X(u”=O) transition near 309 nm. Since the fluorescence yield depends on the rates of electronic and vibrational relaxation by various ambient gases, accurate values of the rate constants allow calculation of the actual HO concentration from the measured fluorescence intensity. When all the possible energytransfer paths are taken into account, a description of the energy-transfer process becomes formidable. One solution to this problem is to summarize the energy-transfer processes with a three-level model and measure the effective energy-transfer rate coefficients pertaining to the model. Since many ambient HO measurements are made a t atmospheric pressure, it is appropriate to quantify the energy-transfer processes a t that pressure. Virtually all previous energy-transfer rate measurements have been made in the torr to millitorr range. Our experimental approach is designed to overcome the problem of short fluorescence lifetime and weak fluorescence signal due to the very fast quenching at atmospheric
- -
‘Present affiliation: Oak Ridge National Laboratory, Oak Ridge,
TN 37830.
-
pressure. The experiments follow the actual LEF procedure used by Davis et a1.2band Wang et a1.,2athat is, to excite HO with a pulsed laser near 282 nm and to monitor the fluorescence near 309 nm. The time-correlated or time-resolved photon-counting techniquelOJ1is used here to obtain the excitation and fluorescence waveforms. Since an inherent requirement of this technique is a low photon arrival rate, the technique is well-suited to measuring the weak and short HO fluorescence a t atmospheric pressure, even though it requires a long counting time to achieve a good signal-tonoise ratio with our present laser pulse rate.
Theory The kinetic processes involved in the LEF detection scheme are pictured in Figure 1. Since the repopulation of A(v’=l) states from the A(u’=O) states is not favored, kol may be ignored without jeopardizing the applicability of the result to the real situation. The energy-transfer processes are represented by eq 1-5. kF1
HO1
-+
HO
+ hvl
(1)
(1)We prefer to avoid the prevalent acronym LIF, for laser-induced fluorescence,because it may imply stimulated emission, a process which is simultaneous with the passage of the laser radiation through the sample. LEF is photochemically and photophysically more apt, since it allows energy transfer within the excited state and delayed spontaneous emission. (2){a) C. C.Wang, L. I. Davis, Jr., C. H. Wu, S. Japar, H. Niki, and B. Wemstock, Science, 189,797(1975). (b) D. D. Davis, W. Heaps, and T. McGee, Geophys. Res. Lett., 3, 331 (1976). (3) J. G. Anderson, Geophys. Res. Lett., 3, 165 (1976). (4)C. R. Burnett, Geophys. Res. Lett., 3 , 319 (1976). (5)D. Perner, D. H. Ehhalt, H. W. Patz, U. Platt, E. P. Roth, and A. Volz, Geophys. Res. Lett., 3, 466 (1976). (6)M. J. Campbell, J. C. Sheppard, and A. F. Au, Geophys. Res. Lett., 3, 175 (1979). (7)E. L. Baardsen and R. W. Terhune, Appl. Phys. Lett., 21, 209 (1972). (8)C.C. Wang, L. I. Davis, Jr., P. M. Selzer, and R. Munoz, J. Geophys. Res., 86,1181 (1981). (9)D.D. Davis, W. S. Heaps, D. Philen, M. Rodgers, T. McGee, A. Nelson, and A. J. Moriarty, Reu. Sci. Instrum. 50, 1501 (1979). (10)J. Yguerabide, Methods Enzymol., 26,498 (1972). (11)J. A. Irvin, T. I. Quickenden, and D. F. Sangster, Reu. Sci. Instrum., 52,191 (1981).
QQ22-3654/83/2Q07-4966$Ql.5O/Q 0 1983 American Chemical Society
The Journal of Physical Chemistry. Vol. 87, No. 24, 1983 4967
Laser-Excited Fluorescence of Hydroxyl
-+ +
HO1 M loss (2) k,O H 0 1 + M -+ HOo (3) kFO HOo HO + hvo (4) kQO HOo M 108s (5) Equations 1 and 4 show the spontaneous emissions with natural decay constants kF1 and kFo of the A(u'=l) and A(u'=O) states, respectively. Equations 2 and 5 represent quenching by inert species M into the lower electronic energy level. Equation 3 represents the overall effective relaxation from the A(u'=l) state into the A(u'=O) state through collisions with an inert species. We first consider excitation of the HO radical by a Dirac 6 function or an impulse function a t time t = 0. This impulse function produces [HO1loexcited hydroxyl radicals in the upper vibrational state A(u'=l). We denote the number of hydroxyl radicals at a subsequent time t in the u' = 1 state by [HO,] and in the u' = 0 state by [HO,]. Writing the appropriate differential equations and solving, we have [HO11 = [HOllo exp(-at) (6) kQ1
where
+ kQl[Ml + klO[MI b = kF0 + kQO[Ml
a = kF1
(8) (9) Lengel and Crosley12 and German13arrived a t similar equations giving the probability PJt) of a molecule being in a given vibrational state u. Since eq 6 and 7 are responses due to an impulse function, they are called impulse response functions. Since they are characteristic of the system, they are also called characteristic response functions. We are considering fluorescence a t 1 atm. The fluorescence lifetime will be too short for the laser to be regarded as an impulse function. We let f'(t) be the laser intensity profile, g be the response due to an impulse function, and h be the fluorescence output due to a laser of finite temporal width. If we assume that Beer's law holds, the concentration of excited HO1, [HO,], (initial concentration due to an impulse function at time 7 ) , is proportional to the concentration of ground-state hydroxyl, [HO], and the laser intensity, f ' ( 7 ) , a t time 7 . We define the input function f ( t ) = f'(t)u[HOl (10) where u is the absorption cross section of the HO radical and f'(t) is the laser flux a t time t. Essentially, f ( t ) is the instantaneous production rate of [HO,]. If we view the finite laser pulse as a succession of impulse functions spaced at intervals of T , then the output, h(t),due to an impulse function at 7 is defined for t > T (11) h(t) = f(7)g(t - 7 ) After t = 27, we have h ( t ) = f(7)g(t - 7 ) + f ( z r ) f ( t- 27) (12) Equation 12 has the term f(7)g(t - 7 ) , because after 27, the output is the sum of the response due to the impulse at 27 and whatever remains from the previous response at 7 . If we proceed in this manner, we get N
h(t) = C f ( n 7 ) g ( t- n7) n=O
(13)
(12) R. K. Lengel and D. R. Crosley, J.Chern. Phys., 64,3900 (1976). (13)K.R. German, J. Chern. Phys., 64, 4065 (1976).
Flgure 1. Model representing the energy transfers of excited hydroxyl radicals.
In the limit as the intervals between successive pulses approach zero, the summation can be replaced by an integration to become an exact solution h ( t ) = J >0 ( ~ ) g ( t - 7 ) d7
Equation 14 is the well-known convolution integral. It says that the fluorescence decay one measures at 309 nm with a laser pulse of finite temporal width is the convolution of the input function (the laser profile) and the response function g(t). Of course, the response function contains all the relevant rate coefficients. Although eq 14 is the exact way of denoting convolution, eq 13 is appropriate for data collected in discrete time intervals and processed by a digital computer. When we measure the integrated intensity, such as by photon counting, we are measuring the integrated area under the output function h(t):
Using a property of the Fourier-transformed convolution and setting the transformed frequency to zero, we can prove that
The important consequence of this separation of integrals is that the integrated fluorescence energy can be related to the laser intensity even at atmospheric pressure without requiring deconvolution. That is, the fluorescence yield expression applies a t all pressures. Combining eq 7 and 14, we can write the fluorescence decay at 309 nm as
(17) where a is the efficiency of the photon collection, filtering, and detection system. The fluorescence at 314 nm can also be written as
h ( t h = L'f(7)akFl exp[-a(t - 7)1 dT
(18)
The corresponding integrated fluorescence (I)at 309 and 314 nm can be shown, by eq 16, to be
Hence, eq 19 confirms the notion that the fluorescence energy a t 309 nm is proportional to klo and inversely proportional to the product of a and b at atmospheric pressure. Taking ItFl = kFO(ref 14) and assuming that the (14)K. Schofield, J. Phys. Chern. Ref. Data, 8,763 (1979).
Chan et ai. CRYSTAL
Nd-YAG
DYE
C L L T C R MONOCHROMATOR
c
Le ClOV
QVT ANALYZER
I e
-@
Dl S P LAY
MICROCOMPUTER r
TTY
Equation 21 allows one to measure klo relative to b by taking the ratio of the integrated fluorescence at 309 nm to that at 314 nm. The components of a and b depend on the constituents of the gaseous medium, which in turn is prepared according to the rate constants desired for measurement. For example, when the medium consists of argon and water vapor only, and ignoring the fluorescence term, the term a is kQIHpOIHZOl + k10H20[H!201+ kQlAr[Arl + k l O A r [ A r l (22) If we differentiate a with respect to [HzO]at constant total pressure, we have a
Thus a graph of a vs. [H,O] has a slope given by eq 23 and an intercept of ( k g l + ~ ~klOAr)[Ar].The term b is (24) b = kQOHpO[HZOl + kQOAr[Arl Differentiating a t constant total pressure, we get
The intercept is kgok[Ar]. Thus measuring a and b as a function of water concentration will reveal the desired rate constants. A similar procedure can be used with varying Nz/Oz mixtures a t constant water concentration.
Experimental Section The experimental setup is illustrated in Figure 2. HO radicals were generated by 185-nm photolysis of water at atmospheric pressure with two mercury lamps (BHK, Inc. OZ4T5) within the fluorescence cell, parallel to the laser beam. The 7-11s half-width laser pulses at 282 nm were obtained from a frequency-doubled Rh6G dye laser pumped by a frequency-doubled Nd:YAG laser. The 282-nm pulses had a half-width of about 0.5 cm-’ and were tuned to the Ql(l,l’) absorption line of HO. Fluorescence in the detection zone was collected by a silica lens, and unwanted Rayleigh and Raman scattering were filtered by cellulose triacetate film and a 2.8-nm bandpass 0.25-m monochromator. The fluorescence signal was detected by an RCA 8575 photomultiplier attached to an ORTEC 270 constant-
fraction discriminator adjusted according to the manufacturer’s manual. The discriminator output was passed to the stop input of a LeCroy QVT3001 multichannel analyzer used in its time-measurement mode. The start input for each laser pulse or measurement cycle was generated by a reverse-biased photodiode (Motorola MRD 500) looking a t a portion of the undoubled 564-nm output of the frequency-doubling crystal. At each measurement cycle, the MCA stored the time between start and stop inputs. After many cycles, the MCA had accumulated a profile of fluorescence vs. time in the nanosecond range. In at least 90% of the cycles, no photon was counted. In each experiment the total number of cycles was used in the Coates algorithm15 to correct the fluorescence waveform for statistical distortion, since the MCA detected only the first count in any cycle. The waveform accumulated in the MCA could be displayed on an oscilloscope or read out, on command, into a Rockwell AIM-65 microcomputer through an interface adaptor. The final result was stored on cassette tape and analyzed either with a Tektronix 4051 desktop graphic microcomputer or with a Honeywell 66/40 computer. The resolution of the MCA was set to 0.1 or 0.4 ns per channel depending on the fluorescence decay rate. The HO fluorescence cell was made of aluminum, roughened on the inside and black-anodized to reduce reflections. Openings, sealed off by removable lids, were made so that the inside could be reached for optical alignments. To reduce the background from the two mercury lamps, both lamps were masked off leaving only two slots exposed parallel to and facing the laser excitation zone. Tygon tubing was used to deliver the gas mixtures into the cell. The water content of the gas was monitored before it entered the cell by either an EG&G 911 Dew-all or a General Eastern 1100DP dew-point hygrometer. Gas flow into the 1-L cell volume was maintained at about 200 cm3 min-’. Attenuation of signal to the desired level was achieved by putting masks with holes of various sizes in front of the quartz window of the fluorescence cell. The laser profile was measured by the same procedure, using either the nitrogen Raman scattering at 302 nm or the Rayleigh scattering a t 282 nm. For all the measurements, photoelectron arrival rate was maintained at around 0.05 per laser pulse whenever the signal was strong enough. The ideal way to carry out the experiments would be to rapidly alternate observations of the laser profile and the fluorescence profile to minimize the effect of time drift of the detection system. In reality, practical experimental difficulties necessitated measurement of the laser profile a t the beginning and the end of each fluorescence experiment. The sum of all measured laser profiles was taken as the input function. Finally, since the theory assumes that the system response is linear, radiative saturation was avoided by maintaining the laser power low and the laser beam diameter adequately large.
Data Analysis Figure 3 shows the HO fluorescence profiles in argon at several water concentrations. The fluorescence decay rate decreases with decreasing water concentration. Typical results of HO fluorescence in both the argon/water and the nitrogen/oxygen/water cases are summarized in Figures 4-6. Each curve represents the cumulative data collected for one gas mixture. The data are corrected according to the Coates algorithm15 and smoothed by a five-point running average. The laser profiles are shown (15)P.B. Coates, J. Phys. E l , 878 (1968).
The Journal of Physical Chemistry, Vol. 87, No. 24, 1983
Laser-Excited Fluorescence of Hydroxyl
700
4969
r
560
490 420 I-
3
350 280 210 140
70 IIME(ns)
0
Flgure 3. Fluorescence waveforms of HO in argonlwater at 1 atm and water concentration indicated by the dew point for each curve: (X) laser profile; ( 0 ) fluorescence. The graph shows that the waveform broadens as the concentration of water decreases.
400 450
i X
300 270
n 240
X
.
X
250 -
x
200
.
n
150
-
x
100.
,"
20
40
60
80 100 120 140 160 180 200 CHANNEL NUMBER
Flgure 5. Fluorescence of HO in nitrogen (dew point -16.0 "C): ( 0 ) fluorescence; (solid llne) least-squares fit of eq 17. Time scale is 0.2 ns per channel.
%I
X
350
0
i 1
210
X
300
5
180
i
150
120
X
90
60 50
90
0 0
32
64
96
128 160 192 CHANNEL NUHBER
224
256
Flgure 4. Fluorescence decay of HO in argonlwater (dew point -16.0 "C): (X) kser profile; ( 0 ) fluorescence; (solid line) least-squares fit of eq 17. Time scale is 0.4 ns per channel.
to illustrate the differences between the laser profiles and the fluorescence profiles. The solid lines are the fits of the following expressions (based on eq 13 and 17) to these data points found by a two-parameter, least-squares, simplex search:16J7 (area of fluorescence) X a X b X (step size) m= (26) (area of laser) N f(n7) h ( t ) = m C -(exp[-a(t - n7)] - exp[-b(t - n7)I) n = b-a ~
(16) J. A. Nelder and R. Mead, Comput. J., 5, 308 (1965). (17) L. C. W. Dixon, *Nonlinear Optimization", Crane, Russak and Co., New York, 1972.
0 96 128 160 192 224 256 CHANNEL NUMBER Flgure 6. Fluorescence of HO in nltrogen/5% oxygen (dew point -16.0 "C): ( 0 ) fluorescence; (solid llne) least-squares fA of eq 17. Time scale is 0.1 ns per channel.
0
32
64
In a few cases where a significant portion of the tail area of the waveform was not captured, the parameter m was made an independent variable in a three-parameter simplex search. From eq 23 and 25, we expect that a and b are linear functions of water, or of the oxygen concentration. Figure 7 shows graphically the linear least-squares fits to the a's and b's of argonlwater as a function of the water concentration. Figure 8 shows a similar plot of a's and b's of nitrogen/oxygen/water as a function of the oxygen concentration. Due to the nature of the characteristic response function (eq 7), a and b are experimentally indistinguishable in the 309-nm emission waveform, and the tail of the waveform
The Journal of Physical Chemistry, Vol. 87,
4970
No. 24, 1983
Chan et ai. l.OE*IO r
,, ,, /
, ,, ’ 0
I
Lr )
(I
t 0
0 2 .OE+ I7
0
WATER CONCENTRATION
4.0Et17
7 6,OE-t7
S.OE+I7
OXYGEN CONCENTRATION
I .OE+18
I .5E+l8
( m o I ecu I e cme3>
( m o i ecu I e cm-3>
B.OE*B
6.OE-8 n
c
I
3 4 . OETB
-0
0
0
Z,OE*l7
4.E-17
5 .Or+ 17
I .at18
1.5E+18
6.OE-17
OXYGEN CONCENTRATION (molecule cm WATER CONCENTRATION
C m o I ecu i e cm-3>
Flgure 7. Linear least-squares fit to a ’ s arid b’s in argon as a function of water concentration.
is dominated by the term with the smallest exponent. This creates the problem of labeling the two values obtained by the simplex search. The problem in the argonjwater case can be broken into two parts. One is how to gather the results into two groups. The other problem is how to label the two groups. In Figure 7 a value from each gas mixture is assigned to a group in such a way that the resulting group forms a straight line when plotted against water concentration. While there remains some uncertainty in the grouping of the coefficients where they are nearly equal, the separation is unambiguous at low water concentration. After grouping, the next step is to identify which group is a and which group is b. Note that a denotes the deactivation of the u’ = 1 state. The identification procedure requires measuring the integrated fluorescence intensity at 309 and 314 nm in heliumjwater and argonlwater. Equation 21 becomes I(309) k,o~,[HeI -- ~IOH~O[H@] (28) 1(314) kQOH20[H20] + kQOHe[Hel Since helium is relatively ineffective in removing electronic
-3
Flgure 8. Linear least-squares fit to a ’ s and b ’ s in nitrogen as a function of oxygen concentration at constant humidity.
and vibrational energy, at high enough water concentration we expect
This assumption was checked by measuring the ratio at various water concentrations in helium at 1 atm. The result is shown in Figure 9. The solid line is the fit of eq 28 to the measured points. The result shows that above the dew point (17 “C) the ratio does approach the limit of klOHzOjkw~0With this ratio and the 1(309)/1(314)ratio in argonjwater, we can identify the a and b in Figure 7 . We find that quenching by water of u’ = 0 is faster than the combined quenching and vibrational relaxation of u’ = 1.
The identification of a and b in the nitrogenjoxygenj water experiments is straightforward. The 1(309)/1(314) ratio was measured in nitrogen at 5 torr with about 0.01 torr of water vapor, giving k l O N z j k ~ > N z1. Therefore klONl + kQINz> kQONz, and a > b for nitrogen. The Same result holds for oxygen at pressures above a few torr. Here the intensity ratio measurements used a flowing mixture of
The Journal of Physical Chemistry, Vol. 87, No. 24, 1983 4971
Laser-Excited Fluorescence of Hydroxyl
TABLE I: Electronic and Vibrational Relaxation Rate Coefficientsa for HO A 2 z + 1 0 1 2 ( k g ,+ k l o )
1012kgo
(0.61 i 0.76) 6.4 2 1.2
argon nitrogen water oxygen
5.9 i 1.3 9 O i 24 487 i 96 2600 i 1 5 0 0
770i 60 260 i 40
~~
1(309)/1(314)
101*k,,
10IZkg,
1.99i 0.25 4.41 i 0.886 0.50 i 0.07 0.50 i 0.1gc
3.5 i 1.6 5 0 i 12 330 i 60 140 i 56
40 i 27 160 i. 110 2460 i 1 5 0 0
2.3
i
~
2.1
Units of molecule-' cm3 s - l For comparison, 4.3 i 0.6 was reported by Lengel and Crosley and 5.0 i 0.7 can be derived from German's reported coefficients, For comparison, 0.13 i 0.02can be derived from German's reported coefficients.
c'8
I
0
I
I
1
2
WATER CONCENTRATION
3
4
5
(mo i ecu I e cm-3)
Flgure 9. Ratio of time-integrated fluorescence intensity at 309 nm to that at 314 nm as a function of water concentration in helium at atmospheric pressure. Solid line Is a least-squares fit of eq 26 to the experimental data.
30% 02,70% Ar, and 0.5% HzO,at total pressures ranging from 0.4 to 200 torr. The results in Figure 10 show a pronounced pressure dependence. The intensity ratio for oxygen as partner in Table I is the average of these measurements in the range between 20 and 200 torr. These N2and O2ratio measurements were done in a different cell from that used to measure a and b, but eq 21 still applies. Alternatively, unambiguous measurements of a could be obtained with 282-nm excitation and 314-nm detection, and of b with both excitation and detection near 309 nm. Due to competing demands on our laser system, time for such experiments has not been available.
Discussion The final results are tabulated in Table I. Due to propagation of error, calculation of kQl from measured values of a and intensity ratios results in large uncertainty. Nevertheless, the large uncertainty associated with kQl does not affect the calculated fluorescence efficiency, Y3,which depends on (kQ1 + klo), k,,, and k1o:
The discrete convolution (eq 13) is only an approximation. Its departure from the exact solution was estimated with simulations. The closed form of eq 14 was evaluated with chosen values of a and b and a y function as the input function. Discrete intensities with various step sizes were then obtained from this exact output function. The simplex program was then used to recover values of a and b from the stepped waveform. Results indicated that, with practical step sizes, the errors were no more than 1%. Effects of random counting noise on the accuracy were also estimated by similar simulations with noise amplitudes in
0
4.OE+18
PRESSURE
8 .OE+18
Cmo I ecu I e ~ r n - ~ )
Flgure 10. 1(309)/1(314) intensity ratios in 30% 0,/70% Ar/0.5% H,O as a function of total pressure. The solid and dotted curves are described in text. The small inserted figure is an enlargement of the same curve below 10 torr. The rectangle indicated by the arrow in the inserted figure indicates the pressure region investigated by German.
both laser and fluorescence waveforms equal to the square roots of the channel counts. Results indicated that errors less than 3% were introduced by noise under normal experimental conditions. The instrumental uncertainties arise from two general sources: the inherent timing uncertainty and the long-term drift of the detection system. The inherent uncertainty refers to the uncertainty in the timing circuit of the MCA, the transit-time fluctuations in the photomultiplier, and the jitters in the start and the stop pulses. The uncertainty of the triggering diode and the timing circuit in the MCA was estimated to be about 0.2 ns. The most serious problem was the change in the response characters of the detection system due to factors such as changes in the room temperature. Due to the low repetition rate of the laser system, each experiment took several days to complete. The total timing error was estimated by measuring the laser profile repeatedly during a period of 12 days. The misalignment of the recorded profiles was found to be about 0.3 ns. This 0.3-ns uncertainty in timing introduced error in a and b ranging from 1% to 3070, with the largest relative errors for the largest values of a and b. These errors are consistent with the uncertainties in a and b obtained from the real experimental data by the following procedure. In Figures 7 and 8, the central points at each gas composition are averages of several experiments, each with its own two-parameter search, and the standard deviations are shown as vertical error bars. These deviations were then used to weight the linear least-squares fit of the central points with varying gas composition. The calculated probable errors in slope and intercept thus include the uncertainties associated with each datum. These probable errors are added to the best-fit slope and intercept to give the upper dashed line in Figures 7 and 8, and
4972
The Journal of Physical Chemistry, Vol. 87,
No. 24, 1983
Chan et al.
TABLE 11: Rate Coefficientsa for HO A2C+ ref
remarks
35 31 27 26 38 18 19 32 1 3' 36' 30 2 5' this work
flame temperature electron beam excitation molecular resonance lamp photolysis of water photolysis of water photolysis of water photolysis of water laser, 282-nm excitation laser, 282-nm excitation laser, 282-nm excitation laser, 282-nm excitation laser, 308-nm excitation laser, 282-nm excitation
35 13' 36' 42 this work
laser, laser, laser, laser, laser,
Ar
H2O
2
dry airb
300
204
100 130 260
43 70 57
120 150 183
14
123
50
140
68
N2
0
10'2kgo
1 0.34
0.6
950 530 270 500 700 290 450
390 570 770
180
12 5 10
30 57 6.4
1012k,,
1012kgl 13 this work
282-nm excitation 282-nm excitation 282-nm excitation 282-nm excitation 282-nm excitation
1.3 2.9 3.5
180 330
laser, 282-nm excitation laser, 282-nm excitation
30 157 55 2.3 160 40 2460 524 shown for N , and 0,. ' The quoted values are for the Units of molecule-' cm3 s - ' . Calculated from the values . lowest rotational level studied: several levels were studied. ~~~
subtracted to give the lower one. The uncertainties in a and b quoted in Table I are the same slope or intercept errors after propagation through the appropriate calculation for each gas species. Table 11, which includes studies published since Schofield's review,14 compares the results of this work with previous studies. Our known sources of error are photon noise (including that due to background subtraction), drift in the timing system, and possible drift in the laser pulse width. Possible errors in previous studies include (1) misidentification of the coefficients in the difference of exponentials (eq 7) in the case of water (kg1 + klo < kgo) and (2) neglect of the contribution of unmeasured water contamination, particularly at low total pressure, leading to the overestimation of kQofor nitrogen. In order to compare our high-pressure rate measurements with the literature values in the context of the pressures under which they were measured, we present the literature rate constants and our measured values graphically in Figure 11. The abscissa gives the total pressure under which each measurement was carried out. The ordinate is the reported rate constant times the pressure a t which it was determined (in almost all cases this quantity, rather than the rate constant itself, is experimentally determined). The straight line in each subfigure has a slope of one (pseudo-first-order quenching) and an intercept equal to our measured rate constant. This graphical comparison is made for k ~ , for , which ample literature values are available. In the case of argon and nitrogen, the interpretation of the graphs is straightforward, for other than a minor amount of water, each was the only gas present. Thus the range of literature values is shown by the vertical distance of each point from a line with unit slope on the log/log scale. For water and oxygen, our measurements were made in a gas mixture with nitrogen at a total pressure of l atm. Considering first the argon experiment, Figure lla, the range of scatter is quite large, possibly because argon is an ineffective quencher and is prone to interference by other gases present (water, NO, or NOz)used to generate hydroxyl. This would be the case particularly at lower argon pressures. Our datum agrees well with the low pressure values and there is no evidence,
Flgure 11. Plot of log ( k Q o [ M ]against ) log [MI. The straight line has slope equal to 1 and intercept equal to log (koa) measured in our experiments. The numbered points are as follows: 1, ref 14; 2, ref 26; 3, ref 18; 4, ref 19; 5, ref 27; 6, ref 28; 7, ref 13; 8, ref 14; 9, ref 29; 10, ref 30; 11, thls work; 12, ref 40; 13, ref 41; 14, ref 35.
given the large scatter, of any nonlinear pressure dependence of the quenching rates. Our value for nitrogen (Figure l l b ) is lower than most of the reported values for intermediate pressures, but is in good agreement with a few. Given the large scatter, no conclusion about reaction order can be drawn, but certainly an order higher than unity appears unlikely. There is far less scatter in the values for water, Figure l l c , and slight upward curvature may be real, indicating a contribution from higher-order processes. Finally, there are relatively fewer quenching rate constants for oxygen, but the scatter is minimal and
Laser-Excited Fluorescence of Hydroxyl
The Journal of Physical Chemistry, Vol. 87, No. 24, 1983
the upward curvature is significant. Although no conclusive statement should be made about the pressure dependence of kQofrom comparison of separate experiments at different pressures, the results indicate the value of a single experiment covering this whole range of pressures, so that systematic errors would be reduced. The largest disagreement between the present results and those of German13is for O2 Both studies obtain klF, from meausurement of ,k and the fluorescence intensity ratio 1(309)/1(314). There is about a factor of 4 difference between our 1(309)/1(314), observed above 20 torr, as shown in Figure 10, and the smaller ratio implied by German’s values of kloo and ky obtained at much lower pressures. The solid fine is ased on eq 21, our ratio measured above 20 torr, our high-pressure measurement of kQo,and the literature value for kFO. The dotted line is calculated with German’s values for oxygen and our rate constant for water. It is evident that the rate constants for oxygen reported by German cannot account for our measured intensity ratios. The small inserted figure is an enlargement of the same curve below 10 torr. The measured intensity ratio varies in this region in a way that is inconsistent with pseudo-first-order kinetics. Moreover, our observed value for a is several times higher than that calculated from the values of k1002and kQ10 reported by German. Our value is about 4 times the hard-sphere collision rate (6 X cm3 SI). Recognizing that the average time interval between photon excitation and the first collision is half the average interval between collisions, we note that the observed rate is within experimental uncertainty of twice the collision rate. Electronic quenching rate constants higher than the collision rate have been reported for NO, whose states are similar to those of H0.20 We have considered the possible effect of ozone interference, which has been a major concern of the LEF r n e t h ~ d . ~ l Our - ~ ~ computer simulations show that this source of spurious HO fluorescence can only decrease the apparent values of (k1o + kQJ and kQ0. One reasonable explanation for the observed high value of kQlo2is resonant energy transfer: HO(A22+(u=1)) 02(X3X;(u=O)) HO(X2n(u=O)) + 0,(A3z,+(~=O))
+
-
--
The energy of the rotationless transition37 O,(X(u=O) A(u=O)) is about 400 cm-’ below that of HO(X(u=O) A(v=l)), and about 2600 cm-’ above HO(X(u=O) A(u=O)). Since the high-pressure kQl exceeds observed39rotational relaxation rates in HO(A), it seems likely that the resonant quenching process connects the pumped HO(A(u=l,K=O)) level directly with a high rotational level of O,(A(u=O)). In contrast, in HO(A(u=O)), levels below K = 12 cannot interact resonantly with 02,and thus k,
Flgure 12. Linear least-squares fit to the literature values, kq,,,[N2] In Figure l l b as a function of their corresponding experimental pressures. The solid lines are the uncertaintiesobtained without the present experimental value and the broken lines are the smaller uncertainties obtained by including it.
HO(A(U=l))
+ O~(X(U=O))
-+
HO(A(u=O)) + 0 2 ( X ( ~ = 2 ) ) but unlike the electronic quenching of HO(A(u=l)),this reaction requires a small net input of rotational or translational energy in the reactants. A similar V V exchange with the second harmonic of the water bending vibration may account for the large klo we observe with water as partner. Lengel and CrosleyZ9found no evidence for resonant V V transfer in comparing H2 with D2 as HO collision partners, but the latter species offer fewer coincidences with HO A than does O2 with its more closely spaced rotational levels. A thorough investigation of the O2 case would include HO rotational relaxation rates, which depend both on HO rotational levels and on the collision partner.29 Our high-pressure experimental results are examined in another context in Figure 12. Since the actual HO fluorescence efficiency depends on the rates rather than the rate constants, it is reasonable to compare the rates rather than the rate constants. Figure 12 is a linear plot of the same points as in Figure lob, emphasizing the difference in pressure at which the rates have been measured. This graphical procedure is the one normally em-
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-
~
~~~
(25)I. S.McDermid and J. B. Laudenslager,J.Chem. Phys., 76,1824 (1982). (26)M. Kaneko, Y. Mori, and I. Tanaka, J. Chem. Phys., 48, 4468 (1968). (27)M. A. A. Clyne and S. Down, J. Chem. Soc., Faraday Trans. 2, 70,253 (1974). (28)R. K. Lengel and D. R. Crosley, Chem. Phys. Lett., 32,261 (1975). (29)R. K. Lengel and D. R. Crosley, J. Chem. Phys., 68,5309(1978). (30)P.M.Selzer and C. C. Wang, J. Chem. Phys., 71,3786 (1979). (31)T.I. Quickenden,J. A. Irvin, and D. F. Sangster, J.Chem. Phys., 69,4395 (1978). (32)P. Hogan and D. D. Davis, J. Chem. Phys., 62,4575 (1975). (33)T. M. Hard, R. J. O’Brien,T. B. Cook, and G. A. Tsongas, Appl. Opt., 18,3216 (1979). (34)T. M.Hard, R. J. O’Brien, and T. B. Cook, J. Appl. Phys., 51, 3459 (1980). (35)H.P.Hooymayers and C. Th.J. Alkemade, J. Quant. Spectrosc. Radiat. Transfer, 7,(1967). (36)R. K. Lengel and D. R. Crosley, Chem. Phys. Lett., 32,261(1975). (37)P.H.Krupenie, J.Phys. Chem. Ref. Data, 1, 423 (1972). (38)I. P.Vinogradov and F. I. Vilesov, Opt. Spectrosc., 40,32(1976). (39)R. K. Lengel and D. R. Crosley, J. Chem. Phys., 67,2085(1977). (40)B. G.Bunnett and F. W. Dalby, J. Chem. Phys., 40,1414(1964). (41)T. Carrington, J. Chem. Phys., 41,2021 (1964).
J. Phys. Chem. 1983, 87, 4974-4978
4974
ployed in extracting rate coefficients from pressure-dependent measurements of pseudo-first-order rates. Using a linear least-squares fit to the literature values, the uncertainty of the rate becomes large as we extrapolate to atmospheric pressure. The inclusion of our experimental value in the least-squares fit narrows the uncertainty at atmospheric pressure considerably. From the rate constants for major air constituents in Table 11, we calculate the effective rate coefficients for dry air in the last column. This can then be used to estimate the fluorescence efficiency, Y3,of the three-level system at atmospheric pressure. German13has obtained Y3= (9.4 for dry air and Y3 = (7.4 f 0.7) X f 0.6) X for moist air a t 50% relative humidity, based upon his lowpressure measurements. From the rate coefficients measured here, we obtain Y3 = (1.1f 0.6) X for dry air and (1.0 f 0.5) X for moist air (1% water). Considering the uncertainty in Y3,we feel that present ambient HO fluorescence instruments require calibration methods that are independent of fluorescence efficiency. We agree with McDermid and LaudenslagerZ5that twolevel LEF incurs less uncertainty due to fluorescence efficiency. Moreover, the two-level fluorescence efficiency (Yz = kFO/(kFO kQo[M])is about 8 times as high as Y3 based on our values of kQo in dry air and moist air (15% HzO). Even then, accurate measurements of kQpunder ambient conditions are useful, particularly for lidar instruments where independent calibration is difficult. In any case, reliable measurements of the rate constants are required for instrument design and evaluation. For example, the present results extend the pressure range over which gas e x p a n ~ i o n ,can ~ ~ 'be ~ ~used to reduce backgrounds and interferences without major losses of response to ambient hydroxyl radical. Conclusion This study shows that useful relaxation rate coefficients
+
(42) D.K.Killinger, C. C. Wang, and M. Hanabusa, Phys. Reu. A, 13, 2145 (1976).
for LEF of atmospheric species can be extracted from atmospheric-pressure fluorescence waveforms, using pulsed laser excitation, time-correlated photon counting, and deconvolution from the laser waveform. Our results indicate that this approach is preferable to reliance on lowpressure measurements. Greater accuracy can be achieved with a higher laser pulse repetition rate, two or three parallel time-resolved photon-detection channels, shorter laser pulses, and sample pressures spanning the region from 1 atm to the low pressures used in most of the previous studies. Since we have conclusively demonstrated that there is pressure dependence in at least one process, extension of this study to higher and lower pressures is called for. In examining our observation of non-pseudo-first-order relaxation of HO(A) by oxygen, we note that, at atmospheric pressure, classical termolecular collisions cannot account for rates approaching the bimolecular collision rate. Instead, the third body may influence one or more product paths of a metastable complex which otherwise reverts to the reactants. The latter model can be made to fit the intensity ratio data in Figure 10, and, if valid, it would change the molecular coefficients derived in Table I from the observed a and b for oxygen as partner. Further study of the hydroxyl-oxygen system is desirable, and is planned. Acknowledgment. This work was supported, in part, by NSF Atmospheric Chemistry Program Grant ATM 8003312, U S . EPA Office of Research and Development Grant R807733, and the Portland State University Research and publication Committee. Although the research described in this article was funded in part by the U S . EPA, it has not been subjected to the Agency's required peer and administrative review and therefore does not necessarily reflect the view of the Agency and no official endorsement should be inferred. Registry No. Ar, 7440-37-1; HO, 3352-57-6; HzO, 7732-18-5; NO, 7727-37-9; 02,7782-44-7.
Enrichment of Na', Mn2+, Fe3+, and Cu2+ at Water Surfaces Covered by Artificial Multilayer Films Jens Thomsen GKSS-Forschungszentrum, Geesthacht, West Germany (Received:June 5, 198 1; I n Final Form: March 8, 1983)
A surface sampler is introduced by which the enrichment of cations at film-coveredwater surfaces can be measured under laboratory conditions. Experiments were performed with aqueous solutions of Na+, Mn2+,Fe3+,and Cu2+covered by artificial multilayer films of hexadecylsulfonic acid. The enrichment due to counterion
attachment to the surfactant molecules of the film was described by empirical equations of adsorption, which could be fitted to the experimental data. The sequence of enrichment obtained from the calculated adsorption constants is Fe3+ > Cu2+> Mn2+> Na+. Introduction The Gibbs adsorption of organic surfactants at the air/water interface of electrolyte solutions gives rise to a surface fractionation of dissolved ions due to counterion attachment to the surfactant charge groups. Several methods can be applied to measure the ion adsorption on charged monolayers. The influence of dissolved ions on the surface properties of a film-covered solution, such as surface tension, pressure, or potential, provides an indirect 0022-3654/83/2087-4974$0 1.50/0
method. Using one of the models developed to account for this influence,l ion concentrations as functions of depth and surface site binding constants can be obtained. Direct approaches to determine the ion content of monolayers are radiotracer methods which measure the concentration of adsorbed ions by a counting device over the water surface,2r3or the chemical analysis of the film after it has been (1)R. 0.James, Colloids Surf.,2,201 (1981).
0 1983 American Chemical Society
