Quantitative laser-induced fluorescence in oh transition probabilities and the influence of energy transfer

Eighteenth Symposium (International) on Combustion The Combustion Institute, 1981

Q U A N T I T A T I V E L A S E R - I N D U C E D F L U O R E S C E N C E I N O H "

T R A N S I T I O N P R O B A B I L I T I E S A N D T H E I N F L U E N C E O F E N E R G Y

T R A N S F E R

GREGORY P. SMITH AND DAVID R. CROSLEY

Department of Chemical Kinetics and Molecular Physics Laboratory SRI International, Menlo Park, California 94025

The technique of laser-induced fluorescence is used for measurements of the concentration and population distributions of the important OH molecule in flames. A quantitative analysis of the data obtained with this method requires accurate transition probabilities and knowledge of the influence of energy transfer on the observed signals. Recent experimental and theoretical studies of relative and absolute transition probabilities in the A--X system are discussed, leading to a recommendation of the value (1.10 • 0.03) • 10 ~ for the oscillator strength of the (0, 0) band. Experiments are described on excited state rotational population distributions within v' = 0, following single-level excitation of OH in the burnt gases of a methane-air flame. The distributions observed are not thermal but show a governance by detailed, state-to-state energy transfer. A simple interpretation indicates that the ratio of the quenching rate to the total rotational energy transfer rate increases with increasing rotational quantum number. Some implications of this energy transfer for quantitative measurement of both absolute concentrations and rotational temperatures are discussed.

Introduction

The past few years have seen the demonstration and development of several laser spectroscopic probe techniques for application to combustion systems. ~ Most prominent among these are laser-induced fluorescence (LIF), coherent anti-Stokes Raman scattering, spontaneous Raman scattering, and laser absorption. They all share a number of common attributes: sensitivity, molecular selectivity, spatial resolution (except for laser absorption, which is a line-of-sight method), temporal resolution, and a nonintrusive nature (assuming a low enough intensity or short enough pulse length such that laser-induced chemical reactions are insignifi- cant). The methods can be used to measure absolute concentrations of ground electronic states and population distributions among rotational and/or vibrational levels. From such distributions a temperature can be deduced if thermal equilibrium obtains; if not, then the distribution itself is of direct interest.

Specific features of each method dictate that there are conditions and species for which it is best suited. In general, the Raman probes are most useful for the measurement of majority species (fuel, oxidant,

principal exhaust gases and, in air flames, N 2), while LIF is the method of choice for the reactive interme- diates in the combustion chemical networks (often free radicals), which are present at low concentration. In this way, the different methods are comple- mentary, and the information desired as well as the conditions of a given experiment should dictate the method chosen. There is no doubt that the results obtained from these methods will in the future yield a new kind and quality of information which will greatly further our understanding of combustion.

There now exist about twenty known interme- diates in various combustion processes which have been observed using LIF in flow systems and/or in flames. Of these, the OH molecule has been the most extensively probed in flames, for a number of reasons. First, it is an important and ubiquitous participant in combustion chemistry. It is often present in flames in large enough concentrations (>0.1%) to yield high signal levels, and can be excited using efficient laser dyes. Second, its spectroscopic data base, both line poslhons'. 2 and transition probabilities, 3 is especially well characterized. Third, the existence of detailed state-to-state rotational energy transfer rates for the excited state, 4 plus the computational tractability afforded by its

1511

1512 COMBUSTION DIAGNOSTICS

small number of energy levels, have made it popular for computer models of the effects of collisions on LIF signals. '~ 7

This paper addresses some of the key pieces of information needed to obtain quantitative results from LIF measurements on OH in flames. First, recent results are reviewed, both experimental and theoretical, on relative and absolute transition probabilities in this molecule. Then experiments are described which probe the excited-state rotational relaxation following single-level excitation of OH, and the influence of this relaxation on measured signal levels is discussed. Finally, we conclude with some brief comments on the serious problem of accounting for collisional quenching in LIF, and the effects of rotational relaxation on the proposed solutions.

Transition Probabilities for OH

The search for the correct transition probabilities within the A 2y-+ - X2II, system of the OH molecule has been the topic of numerous investigations, both experimental and theoretical, over the last thirty years. Recent work, much of it involving LIF measurements together with computations, has cleared up many of the discrepancies existing in the earlier (pre-1975) literature. Nonetheless, several recent papers dealing with LIF measurements of OH in flames have used the older values. We discuss here the recent results in this area with the view of selecting the best relative (dependence on v and N) and absolute transition probabilities for this band system.

1. Relative Transition Probabilities

The electronic transition moment R~ (that is, the probability of occurrence of an electronic transition), varies markedly with internuclear distance r for the A--X system of OH. Together with the widely spaced energy levels and large centrifugal distortion in this light molecule, this produces a considerable variation with v and N of the electronic transition probability p(v' , N ' ; v", N"). (For A~E +, N repre- sents molecular rotation, J = N + 1/2.) These general facts have been known for some time, although until recently there have not existed conclusive experimental data on which to base the form of R.(r) and thus the values of p.

In 1975, 8 a series of measurements was made of the ratios of emission intensities to various v" levels, following laser excitation of single v ' , N ' levels of A2E +. These ratios were fitted to various assumed forms of R~(r), using Franck-Condon factors and r-centroids calculated from the well-known spectroscopic constants 2 of the two states�9 The best fit was produced by a transition moment linear in

internuclear distance:

R ( r ) cc (1 - 0.75r) (1)

(with r in A) as first suggested by Shuler. 9 In particular, Eq. (1) was clearly superior to the exponential form assumed for a widely used set of calculations. 1~ A critical examination s of previous experimental and theoretical studies confirmed these conclusions, which were further substantiated by a similar study on the OD molecule. H

The results of Refs. 8 and 11, for p values in different vibrational bands, in effect span a range of r from 0.58 to 1.31 A. The dependence of R~ on r and the variation in the Franck-Condon factors also lead to a dependence of p on the values of N ' and N" within a given vibrational band. However, the effective range of r covered by this N variation is small. Thus, the direct experimental evidence for the N-dependence of the O'S is not sensitive to the exact form of R(r ) , and constitutes a poor direct test of that form.

The approach 3 taken to establish the N-dependence of the p's was as follows. R~(r) was taken as in Eq. (1), well established by the sensitive (v', v") dependence, but modified at large r to tail asymptotically to zero (patterned after ab initio calculations12). The p(v', N ' ; v", N") were then calculated using wave functions obtained from RKR potential curves. An independent calculation of a similar type, ~3 though with a purely linear R,(r), has yielded results agreeing well with those of Ref. 3.

The results in either of these papers 3'13 should constitute the best available p ( v ' N ' ; v", N") for the A--X system; they use reliable wavefunctions

�9 . 8 , 1 1 and an R~(r) based on an exammahon of all the available data on vibrational bands. They agree also with recent direct experimental data 13-1" on the N-dependence of measured lifetimes. A comparison 3 indicates that the widely used results of Anketell and Learner 1~ are good to within - 10% for the variation of p with N, within a given band, but are considerably in error for the overall vibrational dependence.

A recent set of lifetime measurements 1" shows a smooth decrease of some 6% between N ' = 0 and 6, followed by an increase in the lifetime with further increase in N'. In addition, calculations are presented in Ref. 16 which, though apparently similar to those in Refs. 3 and 13, exhibit this same decrease. This constitutes a significant disagreement with the previous experimental 13.15 and computed 3' 13 dependence on N' , although there exists good agreement over the range N ' = 6 to 16. As discussed in more detail elsewhere, 17 the general forms of the OH wavefunctions and of R,.(r) indicate that only a monotonic increase in the lifetime with increasing N ' in the (0, 0) band should be found. This unre-

QUANTITATIVE LASER-INDUCED FLUORESCENCE IN OH 1513

solved discrepancy does not directly affect practical data for combustion diagnostics because the differences are only several percent; its significance is the indication that there remains something fundamentally incorrect in one 3't3"t5 or the other ~6 treatment.

2. Absolute Transition Probabilities

Most modern determinations of absolute transition probabilit ies have been made through measurements of radiative lifetimes at low pressures. This technique avoids the necessity of knowing the absolute OH concentration but requires corrections for collisional population and depopulat ion of the levels observed. Lifetime measurements and the corre- sponding oscillator strengths publ ished during the 1970s are collected in Table I.

The results cluster into two sets of values, near 0.7 and 0.8 t~sec, with quoted error bars from each set of measurements which do not span the gap. The Hanle effect value z~ of 0.58 I~sec depends critically on an assumption about relative hyperfine contributions, as discussed in Ref. 15, and may be consistent with the 0.7 txsec set. I t is not immediately clear, however, which set is correct, since collisional effects can either lengthen or shorten the apparent measured lifetime. Quenching collisions produce a x(apparent) < r(actual). On the other hand, the time

dependence of the population of a level populated by rotational energy transfer and depopulated by quenching and fluorescence is the sum of increasing and decreasing exponentials. Under certain conditions, fitting the shape to a single exponential can cause r(apparent) > r(actual). Thus, there exists no obvious choice between the two sets on the basis of lifetime value alone.

Population of a single initial level (through laser pumping as opposed to discharge excitation) and operation at low pressures avoids both types of collisional complications. Of the results in Table I, all the 0.7 Ixsec results except one ~9 are from experiments involving single-level excitation. The result of Ref. 23 is consistent with the 0.7 ~sec set, according to a reanalysis. ~3 Of the 0.8 Ixsec values, all but one ~4 come from experiments involving multilevel excitation. The 0.8 txsec result of Ref. 24 using LIF was obtained at a total pressure of - 1 torr Ar, where - 3 rotational transfer collisions occur per radiative lifetime. 4

The two sets of LIF measurements ~a.~5 exhibiting excellent agreement at 0.687 ~sec were, on the other hand, carried out at extremely low total pressures. German ~'~ worked at pressures <10 3 torr while Dimpfl 's experiments ~2 were all done at pressures <10 -5 torr. 27 At these pressures, collisional effects should be totally negligible according to known cross sections: if all of German's total pressure were

TABLE I OH (v' = 0) lifetime measurements in the 1970s

Author (year) Lifetime

Method "% (Ixsec)

Oscillator strength

foo • 10 a Reference

Smith (1970) deZafra, Marshall and Metcalf

(1971) Elmergreen and Smith (1972) German, Rergeman, Weinstock,

and Zare (1973) Sutherland and Anderson (1973) Becker and Haaks (1973) Brophy, Silver, and Kinsey

(1974) Becker, Haaks, and Tatarczyk

(1974) Hogan and Davis (1974) German (1975) Rrzozowski, Erman, and Lyyra

(1978) Dimpfl and Kinsey (1979) Anderson (1979)

phase shift 0.85 • 0.13

Hanle effect 0.660 • 0.022 phase shift 0.80 _+ 0.08

Hanle effect 0.58 • 0.05 pulsed discharge 0.79 • 0.02 pulsed discharge 0.83 + 0.08

LIF 0.788 + 0.013

LIF 0.82 + 0.04 LIF 0.72 • 0.03 LIF 0.688 _+ 0.021

pulsed discharge 0.77 + 0.02 LIF 0.686 + 0.014 pulsed discharge 0.73 + 0.02

8.9 _+ 1.4

11.5 _+ 0.4 9.5 + 0.9

13.1 +_ 1.1 9.6 • 0.2 9.1 • 0.2

9.6 • 0.2

9.2 • 0.5 10.5 • 0.4 11 .0 + 0.3

9.8 • 0.3 11.0 _+ 0.2 10.4 • 0.3

18

19 20

21 14 ~ 22

23 h

24 25 15

16 13 26

~Reanalyzed in Ref. 26. bReanalyzed in Ref. 13.


either H or H~O, each of which has a large quenching rate, there would be <1% shortening of the lifetime due to collisions.

For these reasons (although without finding specific fault with any of the other measurements listed in Table I), we favor the LIF lifetime results of References 13 and 15, and recommend the value of (1.10 + 0.03) • 10 -3 as the oscillator strength for the (0, 0) band of OH. Values as a function of J, and for other vibrational bands, can be deduced from this value, and the computed results of Refer- ences 3, 8, and 13.

Finally, we note that the two most recent direct measurements of the absorption coefficient for the (0, 0) band have used an equilibrium mixture of OH in hot H20. One, ~8 with a continuum source dispersed through a monochromator, yielded f = (0.95 + 0.19) x 10-3; while the other 29 employed a cw laser as the source, obtaining f = (1.13 + 0.01) • 10-3 for the rotationless level, and a N-dependence consistent with the calculated values over the range N ' = 3 to 10.

3. Optical Depth Considerations

If the OH is present in relatively large amount and there exists a considerable path length through the flame, then an appreciable amount of the incident laser radiation and /or the fluorescence can be ab- sorbed while passing through the flame; that is, the flame is optically thick. This problem has been treated in detail due to its effect on excited state rotational temperatures as determined by conven- tional emission spectroscopy; see, for example, the discussion in Ref. 30.

The effect of extensive absorption of the laser radiation on OH LIF signals has been studied for a CH4/air f lameJ ~ The use of a burner designed to present a small path length through the flame 32 is one way to circumvent the problem. Alternatively, transitions having a low value of the product of transition probability times ground state level population can be used. In general, the sensitivity of LIF permits adequate signal levels for weaker absorptions well below those at which these problems arise. For example, excitation in the (1, 1) band was used to obtain rotational temperatures from a CH4/N20 flame under conditions in which significant absorption occurred in (0, 0). 33

In a first approximation it is usually considered that self-absorption of the fluorescence only causes constant attenuation for a constant pathlength, but this is not strictly true. As described below, the upper state population distribution varies with the rotational level pumped by the laser, i.e., it does not relax to a thermal distribution before radiating. Because of this, the degree of self-absorption can vary as well, and rotational temperature plots can be affected. Also, such attenuation will, of course,

not be the same if different spatial regions of the flame are probed. Observing weaker, high v", fluorescence bands can solve this problem.

While these potential complications due to optical thickness can easily be avoided, they should be taken into account at the time of experiment design, and checks made under operating conditions to confirm their absence.

Rotational Energy Transfer in OH in Flames

The most probable fate in a flame for an OH molecule, excited into a specific level by a laser of low intensity, is collisional removal from that level. For v ' = 0, these collisions can be of two kinds: quenching (with rate Q) back to the ground state, and rotational energy transfer within v ' = 0 (RET, with total rate R out of a given level). Upward vibrational transfer to v ' = 1 occurs much less frequently, 34 and wilt be ignored here. If Q >> R, then little or no RET occurs, and the pumped level contains all of the upper state population produced by the laser excitation. If R >> Q, then considerable RET occurs, tending toward rotational thermalization within v ' = O.

Available quenching and RET rate constants for collisions of OH with some gases found in flames suggest that R is usually a few times Q, so that neither limit would apply. A pre-laser-era experiment 3'~ using atomic line single-level excitation of OH in both low-pressure and atmospheric pressure flames has shown this to be the case. Two other investigations 3~'37 concurrent with this study have also found non-Boltzmann distributions in the excited state. Thus the detailed state-to-state dependence of the R and Q will dictate the form of the rotational distribution. A variation in this distribution with

TABLE II OH(A2E § v ' = 0) rotational level dependence of

the ratio of quenching to RET rates

Pumped Pump line" level (N') Energy b Q / R

QI1, 1' F,(1), F2(1 ) 35 0.11 P12 c F~(1) 35 0.10 P~2 ~ F~(1) 35 0.11 R~4 F~(5) 510 0.17 R24 F2(5 ) 510 0.21 Rt9 F~(10) 1840 0.25 R29 F2(10 ) 1840 0.28 R 214 F 2 (15) 3950 0.32

~Notation of Ref. 2. bin em -l above F~(0) in v ' = 0, from Ref. 2. ~Two separate rHns.


EXCITE F2(10}

2 (0.0) BANO FLUORESCENCE

A

p22,2 Qt 6 S 4 3 2 ?

EXCITE F1(1)

FIG. 1. A portion of the fluorescence spectra obtained upon exciting two different rotational levels, illustrating the differences in the rotational distributions. Top: excitation of N ' = 10, J ' = 19/2; Bottom: excitation of N ' = 1, J ' = 3/2.

the quantum number of the pumped level will produce a variation in the emission spectrum and, for finite bandpass detection, in the observed emission intensity per pumped molecule.

We here describe experiments investigating the state-to-state dependence of the Rs under flame conditions, so as to assess the influence of the distributions on observed signal levels. We find that these distributions can be qualitatively understood using state-to-state RET rates of the same general form as found in a low-temperature study. 4 Simple models of the observed distributions are also used to illustrate the influence of RET on apparent rotational temperatures from LIF excitation scans.

1. Experimental

A slightly lean (0 = 0.86) methane-air flame burning on a water-cooled 0.5-in. cylindrical burner packed with small wires is probed in the burnt gas region using a Chromatix CMX-4 flashlamp-pumped dye laser. From an excitation scan, taking into account the influence of RET as discussed below, the temperature is -1900 K. Tests confirm operation under optically thin conditions and at laser levels below optical saturation. A 3/4-m spectrometer with typically a 0.4 A bandpass is used to scan the fluorescence, and a second spectrometer is used to monitor the constantly drifting laser power to permit normalization. A boxcar integrator is used for signal processing.

The levels pumped are listed in Table II. By choice of the exciting transition, we pump only one of the two spin components (the F~ level with J = N + 1 /2 or the F 2 with J = N - 1/2), except for one of the runs for N ' = 1.

A portion of the fluorescence spectra obtained upon pumping two different levels is shown in Figure 1. In each case, the pumped level contains a higher population than any other individual level, although RET has clearly taken place. Moreover, the spectra show clearly that the actual population

distribution depends markedly on the level pumped. The population in levels several rotational quanta from the pumped level is the consequence of both multiple quantum (AN > 1) RET, and of multiple collisions. As will be seen below, the OH molecule undergoes between 3 and 10 collisions on the average before being quenched, depending on N'.

One feature which recurs throughout is illustrated in Figure 2, which shows the spectra obtained upon pumping in turn each of the fine-structure levels of a single rotational level. The OH molecules transfer preferentially into the same spin component as originally excited, that is, F, ---* F, and F~ --* F~ transfer is more probable than F~ *-* Fz, even for changes of several rotational quanta.

Those lines which were well enough resolved to provide single-level information (typically ~40 in each run) were converted to populations. Contribu- tions from satellite lines were ignored, but these significantly affect only the two or three lowest levels.

2. Results

(a) Population Distributions The population distribution obtained upon

pumping the F~(10) level is shown in Figure 3, plotted in a Boltzmann fashion. It exhibits features common to all runs: upward transfer produces a thermal-like distribution, although with an effective temperature which increases with increasing N ' ; downward transfer is described by a statistical distribution, with little or no energy dependence; F, ---* F~ or F 2 ~ F~ transfer is favored over F~ F 2 by an average factor of 1.7 for )ANI -< 3; excess

EXCITE F1(5)

P2 1~1 101 9[ 81 71 P, "1 lo[ 91 8]

TA-330523-10

FIG. 2. The P-branch region in fluorescence obtained upon pumping different spin components of the same rotational level. For a given N', P~(P2) branches are stronger when the F~ (Fz) component is pumped.


I I I

A

-%

Z

A

A z~

-2

0 A

-4 - O -

R19

0 1000 2000 3000

E(cm -1 ) TA-330522-146

Fro. 3. A plot, in Boltzmann form, of the population distr ibution observed upon pumping the F, (10) level. Triangles, F, levels; circles, F z levels. The general features of the distributions described in the text can be discerned here. The line, drawn simply for reference, corresponds to a Boltzmann distribution at 2100 K in the excited state.

population exists in the pumped level and nearby ones of the same spin component.

These distr ibutions are generally what would be expected from a consideration of the low-temperature, state-to-state RET cross sections for collisions with N 2.4 Two computational models 6'7 of the excited state rotational relaxation utilize an information- theoretic form 3s of these cross sections constructed for extrapolation to high temperatures. Each yields predictions in good qualitative agreement with these experimental distributions, al though in particular, the observed propensity for spin component con- servation is larger than the models suggest. Clearly, detailed state-to-state RET rates must be used to understand the rotational population distributions following single-level excitation of OH in flames.

(b) The Ratio Q/R As noted earlier, the ratio Q / R forms a simple

measure of the degree of thermalization of the excited state prior to emission. A very simple interpretation of our data permits us to extract a value for this

quantity. Consider that RET, at a rate R, transfers molecules from the initially excited level e into all other levels o. Levels o are then quenched at a rate Q, which is much faster than the radiative rate at 1 atm. Transfer back into e is ignored. A steady-state approximation is applied to N o , the total population of the other levels:

d N o - - = O = R N - Q N , , (2)

dt

yielding N~/N o = Q/R. The value No is obtained from the populations

for each level, using interpolation from the observed distributions when necessary. The results for various initially excited levels e are listed in Table II, and are plotted in Figure 4 as a function of rotational quantum number. The error bars are nominal 20% estimates of the accuracy of our data. Also included in the figure are the results for Q / R from Carring- ton's atomic line excitation 35 (with his error bars), and the values from our similar analysis of published data of Chan and Daily, 3~ and of the predicted population distribution of one of the computer models. 6

Even given the simplifications needed to deduce Q / R from our data, the dependence of this quantity on N ' is clear. The low-temperature, bimolecular collision results show no variation of R 4 or Q39 over the range N ' = 0 to 6 for the collision partners Hz, N z, 0 2, or Ar. On this basis, the magnitude of the change seen in Figure 4 is unanticipated. In our flame, most of the RET is probably caused

0.6

0.4

0.2

I I I

~

l I F I 0 5 10 15

N' JA-330532-2

FIc. 4. A plot of Q/R, obtained as described in the text, versus rotational quantum number N'. Circles: present results with estimated error bars. The three runs for N' = 1 and two each for N' = 5 and 10 are slightly separated for clarity. Square: result of Carrington, Ref. 35. Triangle: our analysis of Chan and Daily data, Ref. 36. Diamond: value obtained from populations predicted by a computer model, Ref. 6.


by N~, whereas the major responsibility for quenching is likely shared between N 2 and H~O. These data thus raise the question of an N ' dependence of the H~O quench rate. Because the quantity Q / R is used in the models ~-7 of the response of OH to laser excitation, its direct measurement for O H - - H 2 0 collisions would be desirable.

3. Effects on Rotational Temperature Determinations

It can be seen directly from Figure 1 that detection using a finite bandpass in nearly any region of the spectra illustrated will result in a different intensity of emission per excited molecule for these two levels. This can produce a systematic error in the absolute concentration or the Boltzmann plot from which a rotational temperature is derived, even if a relatively wide bandpass is used for detection. In general, a finite bandpass, centered near the intense emission in the (0, 0) band, will discriminate against the P and Q lines emitted by levels of high N'. RET causes these levels to have a greater portion of the population when a level with high N ' is pumped. Thus, the ground-state populations of high N" will appear anomalously low. The temperatures derived from Boltzmann plots can in turn be sensitive to these populations on the tail of the distribution.

To illustrate the effects this can have, we constructed a computer model of the distributions, numerically expressing the general features described above, and in accord with our fluorescence measurements exemplified by Figure 3. Thus, for each initially excited level, the relative amount of fluorescence D, detected for a defined bandpass and center wavelength could be calculated. The fluorescence signal S~ obtained upon pumping some ground state level with population N~ is then:

S~ = cB,:, D~.N~ (3)

where c is a constant, and B is the transition probability for the absorption line connecting e and g.

Figure 5 exhibits the deviation from the Boltz- mann plot predicted by the model for a particular excitation scan. It demonstrates that the combination of state-specific RET and finite bandpass detection can lead to systematic errors in an apparent Boltz- mann plot. We emphasize that our model is constructed mainly for illustrative purposes; more information (particularly the temperature dependence) on RET is necessary before this approach can be used to calculate precise temperature corrections for LIF experiments in general.

We made several excitation scans to verify, these concepts. For wide bandpass detection (30 A), the data yield low apparent temperatures, as predicted

in Figure 5, and the highest rotational levels appear significantly under-populated. For narrow bandpass detection (6 A), differences in apparent populations occur at different center wavelengths. These differences are less systematic, and often give the appearance of excessive data scatter.

[Addendum. Since submission of this manu- script, we have obtained quantitative verification of these effects of RET on the excitation scan rotational temperature T a . A scan is first made using a wideband (250A) filter in front of the photomulti- plier to avoid any effects due to RET. This yielded a T R = 1910 + 40 K. Detection using the spectometer set at the Q2-head with a 13.5A bandpass produced in apparent T R = 1180 + 70 K. When the apparent populations from this latter run are corrected for

4

3

~- 2

t t 1

I I I 0 1000 2000 3000

E (crn -1 ) JA-330532-1

FIG. 5. An example of the influence of the BET on a rotational temperature plot, from the model calculations. The actual ground state populations are given by a Roltzmann distribution at 1800 K, indicated by the straight line. The cricles show the apparent populations of the ground state levels (plotted versus energy), i.e., a plot of ln(S/gB) from Eq. (3). This gives an apparent temperature of 1400 K. The detection parameters for this plot are a 30 /~ wide bandpass centered at 3090 A, and an excitation scan through the R-branch sequence. A similar plot is obtained for the same bandpass and a center wavelength of 3070 A.


the effects of RET using equation (3) and the values of D e obtained independently from the rotational distributions, the result is 1810 + 140 K, in agreement with the wide bandpass run. A paper 4~ de- scribing these results is in preparation.]

We conclude that the use of LIF excitation scans for temperature determinations must be approached with care. Preferably, a wide bandpass and two or more center wavelengths should be used (this may conflict with requirements of species selectivity, however). Lower weighting should be placed on the populations of high N" levels in a Boltzmann plot. Finally, we note that excitation to v ' = 1 and observation of (0, 0) band fluorescence presents similar problems, due to the variation in the OH vibrational transfer rate with rotational l eve lY '4~

4. Implications for Optically-Saturated LIF

At present, the chief barrier to the application of LIF for a quantitative measurement of absolute concentrations is the need to account for collisional quenching. The fraction of excited molecules which radiate (under conditions of low laser intensity) is A/Q, where A is the radiative rate, and this ratio must be known to relate signal levels to concentrations.

It is encouraging that recent direct lifetime measurements 4~ of laser-excited OH in a low-pressure propane-oxygen flame indicate 4~ that Q is not a sensitive function of the conditions of that flame. However, it remains a difficult quantity to estimate from bimolecular collision data, which usually exist for much lower temperatures than found in flames. One approach 44 to this problem is operation under conditions such that the effective Q is the sum of quenching plus vibrational and rotational energy transfer, coupled to a calibration downstream in the flame where the probed species exists under chemical equilibrium conditions. This requires knowledge of the temperature dependence of the effective Q (assumed to scale as T ~/2 in Ref. 44) and observable signal levels at a point where equilibrium concentrations can be confidently calculated, but is an attractive solution and likely useful for OH.

The method which has received the most attention is that of optical saturation of the transition, 45 which has been applied to a number of atoms and molecules in flames, including OH. 37 The laser intensity is increased to a power level where the rate of stimulat- ed emission becomes comparable to Q. For a simple two-level system, the degree of departure from lin- earity of the fluorescence signal as a function of laser power can be used to determine Q. Molecules, having internal energy levels, obey forms of a two- level model only in the limits Q / R > > 1 or Q / R < < 1. 6 The present results show that neither limit applies and a more complex analysis will be re- quired. Combined with the results of the modeling

study 6 incorporating internal energy levels in both electronic states (although not an N' dependent R/Q), we conclude that optically saturated LIF in OH can be used to obtain absolute concentrations to within perhaps a factor of three. The uncertainty arises principally from lack of knowledge of ground state energy transfer rates.

5. Summary

The present results demonstrate that state-specific RET produces rotational distributions in OH which vary with the level pumped by the laser. Particularly evident state-specific phenomena are the propensity for maintaining a spin component even after transfer by several rotational quanta, and the increase in the ratio Q / R with increasing N'. The RET can produce significant effects on the determination of rotational temperatures, and the values of the ratio R / Q indicate that simplified models are inadequate to describe optically saturated LIF.

Acknowledgment

This research was supported by internal research and development funds of SRI International. The computer used for the excitation scan modelling was furnished under Grant PHY 76-11436 from The National Science Foundation.

REFERENCES

1. CROSLEY, D. R., Ed., "Laser Probes for Combus- tion Chemistry," Amer. Chem. Soc., Symp. Series 134, 1980.

2. DIEKE, G. H., AND CROSSWHITE, H. M., J. Quant. Speet. Rad. Transfer 2, 97 (1962).

3. CHIDSEY, I. L., AND CROSLEY, D. R., J. Quant. Spect. Rad. Transfer ,?,3, 187 (1980).

4. LENGEL, R. K., AND CROSLEY, D. R., J. Chem. Phys. 67, 2085 (1977).

5. LOCHT, R. P., AND LAURENDEAU, N. M., Appl. Opt. 18, 856 (1979).

6. KOTLAR, A. J., GELB, A., AND CROSLEY, D. R., in Ref. 1.

7. CHAN, C., AND DAmY, J. W., Appl. Opt., 19, 1357 (1980).

8. CROSLEY, D. R., AND LENGEL, R. K., J. Quant. Spect. Rad. Transfer 15, 579 (1975).

9. SHULER, K. E., J. Chem. Phys. 18, 1221 (1950). 1O. LEARNER, R. C. M., AND ANKETELL, J., Proc. Roy.

Soc. A301, 355 (1967). i1. CROSLEY, D. R., AND LENCEL, R. K., J. Quant.

Spect. Rad. Transfer 17, 59 (1977). 12. HENNEKER, W. H., AND Poexm, H. E., J. Chem.

Phys. 54, 1763 (1971). 13. DIMPFL, W. L., AND KINSEY, J. L., Quant. Speet.

Rad. Transfer 21, 233 (1979).

QUANTITATIVE LASER-INDUCED

14. SUTHERLAND, R. A., AND ANDERSON, R. A., J. Chem. Phys. 58, 1226 (1973).

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Scripta 17, 507 (1978). 17. CROSLEY, D. R., J. Quant. Spect. Rad. Transfer,

in preparation. 18. SMITH, W. H., J. Chem. Phys. 53, 792 (1970). 19. DE ZAVRA, R. L., MARSHALL, A., AND METCALr,

H., Phys. Rev. A3, 1557 (1971). 20. ELMERGREEN, B. G., AND SMITh, W. H., Astrophys.

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M., AND ZARE, R. N., J. Chem. Phys. 58, 4304 (1973).

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FLUORESCENCE IN OH 1519

31. CATrOUCA, R. J., Paper 78-18, Western States Meeting of the Combustion Institute, Boulder, Colorado, April 1978.

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COMMENTS

K. Brezinsky, Princeton University, USA. Your work on transition probabilities and quenching processes has been very important for work on determining OH radical concentrations. In view of the amount of time and effort involved in obtaining the pertinent values for OH, how would you evaluate the near future prospects of using laser induced fluorescence for measuring concentrations of other diatomic radicals as well as polyatomic radicals?

Author's Reply. Such an evaluation really depends on the quality of the information you seek. If you will settle for nothing less than absolute concentrations to within ten percent for any collision environment, then the prospects now are bleak even for OH and hopeless for anything else. If, however, you pose questions which can be addressed by relative profiles through a laminar flame, or ratios of concentrations to within a factor of two or three,

the situation is much better. For example, last winter we made a fluorescence measurement of the ratio of the concentration of NH to that of OH in a C H J N 2 0 flame. Using the gross assumption that Q / A was the same for each species, the ratio was found to be about 0.04. This is important information even with that assumption, because it tells us that breakage of the N--N bond in the N20 has occurred and that nitrogen-containing molecules participate significantly in the flame chemistry. Thus this simple experiment and analysis sets the entire tone for an initial model of that chemistry.

Thus with a number of well-chosen experiments on other diatomics, to sort out transition probabilities and measure a few representative collision rates with the major flame gases, we should be able to obtain very useful information. OH has received a lot of attention, and merits even some more, due to its special role as the primary radical species in so many

I520 COMBUSTION DIAGNOSTICS

flames and its use for thermometric purposes. As the radicals get larger, the problems increase

rapidly due to the much higher energy level density. First, transition probabilities are more complex, due to the existence of perturbations and frequent multi- component decay mechanisms. Second, collisions spread the population over the much larger number of accessible states, reducing sensitivity and exacer- bating the finite-bandwidth-detection problem. At the present time, even rudimentary knowledge is lacking for nearly all polyatomics. Even so, there

may well be situations in which the mere detection of some given species at an order-of-magnitude level of accuracy will provide very useful information. It is important to try to design hypotheses which can be tested within the capabilities of the techniques available; if higher accuracy appears especially desirable in a given case, then the supporting spectroscopic research on transition probabilities and collision effects can be focussed on the appro- priate species.

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Quantitative laser-induced fluorescence in oh transition probabilities and the influence of energy transfer