On the collisional quenching of electronically excited OH, NH and CH in flames

Twenty-first Symposium(International) on Combustion/The Combustion Institute, 1986/pp. 1693-1702

ON THE COLLISIONAL QUENCHING OF ELECTRONICALLY EXCITED OH, N H A N D C H I N FLAMES NANCY L. GARLAND AND DAVID R. CROSLEY Chemical Physics Laboratory SRI International Menlo Park, California 94025

Relating emission intensities to molecular concentrations in laser-induced fluorescence measurements requires knowledge of collisional quenching rates in flame environments. We survey the current knowledge of quenching of electronically excited states of the radicals OH, NH and CH, as pertains to combustion studies. Considered are the dependence of the cross sections on collision partner, rotational level, and temperature. Using independently determined cross sections for OH, total quenching rates are estimated for hydrocarbon and ammonia flames described in the literature. We conclude that at present OH quenching can be estimated to within 30-50% in many cases, but only to within a factor of three for NH and CH.

1. Introduction Collisional quenching o f an electronically excited state of an atom or molecule determines the fluorescence q u a n t u m yield, needed to relate emission intensities to the concentration o f that excited state. In combustion studies, much interest in quenching is associated with the use of laser-induced fluorescence (LIF) to detect with high sensitivity a variety of reaction intermediates in combustion chemistry. T h e accuracy of such measurements depends on knowledge of the quenching rates; however, they have been m e a s u r e d for only a few radicals and collision partners, and then usually only at r o o m temperature. In this paper, we survey the current knowledge of quenching cross sections, pertinent to flame studies, for three important radical hydrides: OH, N H and CH. An important question arises from the t e m p e r a t u r e dependence o f quenching as d e t e r m i n e d recently in our laboratory for OH. A computational model based on attractive force interactions is used to describe O H quenching; we use it, together with data on major-species profiles taken from several flames r e p o r t e d in the literature, to consider the variation in quenching rates t h r o u g h those flames. For OH, quenching appears reasonably well understood for these purposes. Q u a n t u m yields for this radical can be estimated quite well for a variety o f flame environments, p e r h a p s within about +30%. T h e t e m p e r a t u r e d e p e n d e n c e of quen-

ching of NH a n d CH by most collision partners is not well e n o u g h known to make such estimates, a n d future experiments should address this problem.

2. Quantum yields in flame measurements. In LIF, 1 a laser excites a molecule to a particular q u a n t u m level (with vibrational, rotational, and total angular m o m e n t u m quantum numbers v', N ' a n d J ' , respectively) of some electronically excited state. T h e excited molecule then radiates to p r o d u c e the detected signal, with fluorescence intensity If. T h e desired quantity is the concentration of the absorbing g r o u n d state radical, Ng. It is related to If t h r o u g h the absorption coefficient, the laser power, and the fluorescence quantum yield ~f = A/(A+Q). A is the Einstein emission coefficient and Q is the quenching rate, both in s-I units (an additional nonradiative, noncollisional rate such as predissociation would a p p e a r in the denominator). ~ f gives the fraction o f excited molecules which emit photons. Q is needed to relate emission intensities to concentrations in other experiments besides LIF, such as electronically excited states produced directly via chemiluminescent reactions. Examples in flames are the CH + O2 reaction which produces A2]~+ O H , or the C2 + O H reaction yielding excited A2A CH molecules. Such emission can provide information on the combustion process if these production reac-

1693

1694

COMBUSTION DIAGNOSTICS

tions are well e n o u g h u n d e r s t o o d within the context of the pertinent flame chemistry. T h e radiative rates o f O H , N H and CH, are 1.4, 2.3 and 1.8 x 106 s -1, respectively. T h e quenching rates 2 in an atmospheric pressure flame are - l0 s to 109 s -x, so that a typical ~ f is of the o r d e r of 0.1 to 1%. Consequently, its value must be known to quantitatively relate If to Ng; the error in Ng is directly proportional to the uncertainty in Q when Q>>A. T h e r e are several ways to deal with quenching in LIF and chemiluminescent measurements: direct measurement, the use o f saturated fluorescence, and calculation of Q using independently determined cross sections, U n d e r certain conditions, Q can be directly measured in a flame environment. If the total n u m b e r density is low enough, the rate of decay o f the excited state following pulsed laser excitation furnishes Q. This method has been applied to O H 3'4 in low pressure flames o f propane/oxygen, a n d to CH in low pressure methane 5 and acetylene 6 flames. However, at pressures greater than about 100 Torr, the excited state population decays in times less than 10 ns, and the rate can be measured only using picosecond excitation. Although this has been applied to O H at atmospheric pressure 7, the laser and detection hardware is quite cumbersome for routine use. A n o t h e r a p p r o a c h designed to circumvent the problem of quenching in LIF is saturated fluorescence s, in which a high laser power density causes the major removal rate of the excited state to be stimulated emission, not quenching. Although saturated LIF has attracuve aspects, it is not applicable or necessarily easily interpretable u n d e r all circumstances. O u r considerations o f quenching will be directed toward L I F in the linear intensity regime, although the results can be used in interpreting results o f saturated LIF experiments as well. We can calculate Q using independently d e t e r m i n e d cross sections for each collider gas present in the flame environment. For each collider one needs its n u m b e r density n, which could be measured by Raman scattering or mass spectrometric detection. Also required is its rate constant kQ o r the cross section tyQ, related by the mean velocity o:

kQ = OCtQ

(1)

(however, for the radicals considered here, the existence of a d e p e n d e n c e of aQ on both collision energy a n d rotational level means that

this relationship must be a p p r o a c h e d carefully, as discussed below). T h e n

Q = Ei kQ~i.

(2)

T h e actual composition o f the collisional environment at the location o f the LIF measurement can be difficult to determine. This can be true even in stable flames, due to problems in precise definition of the volume p r o b e d by the laser. Recently, there has been much interest in detection o f radicals in turbulent flames, especially two-dimensional L I F imaging 9. In such flames, it is impossible to characterize the instantaneous local coUisional environment at the same time as the laser pulse. A way is needed to relate Q to observables such as the t e m p e r a t u r e T, to d e t e r m i n e ~f. L I F can also be used to identify species not previously considered within the flame chemistry. Only semiquantitative detection of some intermediate may be valuable in shaping concepts about flame chemistry. In such cases, it will likely be necessary to estimate quenching rate constants to obtain a measure of the concentration. For example, in our laboratory, 1~ NS was detected in CH4]O2 flames seeded with NH3 a n d H2S. Rate constants for quenching of the C2~ + state excited in that e x p e r i m e n t are not known, but estimates were m a d e considering analogous states in NS, NO and PO.

3. Quenching rate constants in diatomic hydrides. T h r e e important radicals found in flames are OH, N H and CH, and each can be detected using LIF with readily available lasers. OH, the most important reactive molecular radical in flame systems, has been the subject of the vast majority of flame L I F studies. N H is likely a key intermediate in NOx production from fuel nitrogen and in the p r o m p t - N O mechanism. CH is easily detected in hydrocarbon flames, although its role in the chemistry is unknown. However, its concentration may perhaps track those of the chemically i m p o r t a n t CH2 and CHs radicals, which are much h a r d e r to detect optically. Additionally, the CH + N2 reaction has been suggested as a part of p r o m p t - N O formation. Recently, a series o f quenching measurements of these three radicals has been undertaken in o u r laboratories. We summarize here those results p e r t i n e n t to the understanding and estimating quenching rates in flames. We

COLLISIONAL QUENCHING OF ELECTRONICALLY EXCITED SPECIES also consider the results o f other investigations p e r f o r m e d with sufficient internal-state resolution that comparison is possible. Pertinent numerical values are given in Table I for O H and Table II for N H and CH. (Other literature values for O H may be found in Refs. 2 and 12.) Many aspects of q u e n c h i n g o f O H in the A2~ +, v ' = 0 state have been studied including the collision ~ a r t n e r d e p e n d e n c e at room t e m p e r a t u r e l l ' l " and at elevated temperatureq3A4, the rotational level d e p e n d e n c e at r o o m t e m p e r a t u r e 11'~2, and the te m p e r a t u r e d e p e n d e n c e for several colliders 15'16. Quenching rate constants have been measured at elevated temjaerature for the v ' = 0 levels ofA3IIi N H a7 and A ~A CH as using a laser pyrolysis/laser fluorescence (LP/LF) method. In all cases, the rate constants were d e t e r m i n e d f r o m the dependence o f the decay rate o f the electronically excited species on the pressure o f the added quenchers, using a fast transient digitizer. Several interesting and i m p o r ta n t features have e m e r g e d from these studies. T h e first is the rotational level d e p e n d e n c e o f kQ found for O H at r o o m temperature. First noticed for H2 and N2 by McDermid and Laudenslager 19, this p h e n o m e n o n occurs to a greater or lesser degree for all 19 of the collision partners discussed in Ref. 12. T h e cross section CrQ(N) may be represented as tTQ = ~Q(N=0) exp [ - aN(N+ 1)]

(3)

where a is a constant for each collider. Because the rotational population distribution shifts to

1695

higher N at higher temperature, this rotational level d e p e n d e n c e of the q u e n c h i n g causes a decrease with T in the q u en ch i n g cross section averaged over N. However, note that the N - d e p e n d e n c e has been measured only at room temperature, and no information exists concerning its t em p er at u r e dependence. Second, the large cross sections (typically I 0 100 ~2) are strong evidence that attractive forces play a major role in O H quenching. A calculation involving dipole and quadrupole moments, ionization potentials and polarizabilities of O H and the collision partners, with no adjustable parameters, showed a reasonable correlation with experimental values in many cases. This description will be used below for the calculation o f ~Q. This third aspect concerns the temperature d e p e n d e n c e o f CrQ. A collisional event governed by attractive forces has a velocity-dependent cross section decreasing with increasing collisional energy. Averaged over velocity, it will then decrease with increasing t em p er at u r e (in addition to the T-dependence due to rotational averaging.) Comparison o f results at room t e m p e r a t u r e 12 and high t e m p e r a t u r e 13'14 shows that the d r o p in O'Q for O H is universal. This is readily understood in terms o f the attractive force interactions, and the calculated temperature d e p e n d e n c e o f the cross sections agrees reasonably with experiment. T h e q u e n c h i n g o f O H by large hydrocarbons is clearly governed by attractive forces but does not c o n f o r m to the multipole model. T h e cross

TABLE I Experimental OH Quenching Cross Sections, As ll00K b

300K a QUENCHER Ns Os H20 Hs COs CO NsO NH3 CH4 NO CsHs C~H4

CsH6

Ref 12. 3.2 20.6 90 10 57 45 60 94 32 46 86 89 79

-+ 0.8 - 1.1 - 3 -+ 1 -+ 3 -+ 2 - 1 -+ 3 -+ 1 -+ 1 - 2 + 2 "4- 2

a) Values for N=2 chosen or interpolated b) Thermally-averaged cross sections c) Ref. 16

Ref. 19 3.2 + 0.4 14.5 -+ 0.8 61.2 -+ 1.4

Ref. 13 0.68 -+ 0.16 11 -+ 3 26 -+ 3

--

10

---

13 + 3 20 30 39 -+ 7 15 -+ 5 26 -+ 4 ----

--

---

-----

+

3

Ref. 14 0.63 -+ 0.10 10.3 -+ 1.2 5.4 16.3 20.3 21.6 42 14.9

-+ 0.7 - 2.0 -+ 2.4 -+ 2.6 - 5c + 2.1

44.2 -+ 5.4 45.6 -+ 5.9 29.2 -+ 3.9

COMBUSTION DIAGNOSTICS

1696

TABLE II Experimental CH and NH Quenching Cross Sections, ,~z CH Ref. 18 1400K

NH Ref. 21 300K

Ref. 17 1400K

Ref. 20 300K

QUENCHER

(,~2)

(~2)

(~e)

(~)

CO H~

8.5 --- 1.0 3.6 --- 0.4

6.1 +- 0.4 0.5 +-- 0.1

6.9 --- 0.8 4.5 - 0.5

2.8 • 0.4 5.5 -+ 0.7 1.3 • 0.2 -2.2 + 0.3 22.5 • 3.0

1.9 • 0.1 0.6 • 0.1 -2.1 • 0.1 ---

4.7 -+ 0.6 2.8 • 0.3 < 0.1 7.8 • 1,5 1.9 • 0.2 26 --+ 3

6.4 2.9 4.4 4.3

O~ N20 N~ CH4 COs NH~ NO C2H2 C2H4 C~H6

-----

12.4 22 23 12.7

- 0.5 --- 1 • 1 • 0.6

-* 0.5 - 0.3 a +- 0.4 b + 0.4

< 0.006 8 • 1.5 1.2 + 0.2 b 44 -+ 5.6 a 69 -+ 5.6 b 17 -+ 1.1

a) High N' distribution b) Relaxed, low N' distribution

sections are v e r y large, typically 100]k 2 at r o o m t e m p e r a t u r e 12 a n d d r o p with increasing temperatureS4; they are h o w e v e r larger t h a n the c o m p l e x f o r m a t i o n cross section described below. Several values are listed in T a b l e I. Cross sections for q u e n c h i n g NH(A~IIi, v' = -18 0) 17 and CH(A 2 A, v r =0) were- - m e a s u r e d only at elevated t e m p e r a t u r e in the L P / L F a p p a r a tus. I n each case, the cross section for the p o l a r collider NH~ is large. H o w e v e r , the o t h e r colliders studied d o not show the same d e g r e e o f correlation with calculated aQ as did O H . T h e s e e x p e r i m e n t s w e r e p e r f o r m e d on a rotationally a v e r a g e d distribution and f u r n i s h e d no i n f o r m a t i o n on possible N - d e p e n d e n c e . N o m e a s u r e m e n t s h a v e e v e r b e e n m a d e for q u e n c h i n g o f e i t h e r C H or N H by H 2 0 at any t e m p e r a t u r e , a m a j o r gap in o u r k n o w l e d g e for c o m b u s t i o n p u r p o s e s . For these two radicals, the d e p e n d e n c e o f r on t e m p e r a t u r e is n o t clear. We c o m p a r e d o u r high t e m p e r a t u r e L I F - d e c a y d e t e r m i n a t i o n s with m e a s u r e m e n t s m a d e on N H 2~ a n d C H 21 at r o o m t e m p e r a t u r e . I n those e x p e r i m e n t s , the radicals w e r e p r o d u c e d directly in the e m i t t i n g state following dissociation o f p a r e n t comp o u n d s such as NH~ a n d acetone. T h e nascent v',J' distribution was not thermal. H e l i u m was used to rotationally relax the C H radicals a n d

N~ was used as a r e l a x e r in some N H experiments. For N H , GrQ d e c r e a s e d with N for the colliders N H s a n d H2. T h e q u e n c h i n g o f C H and N H is very d i f f e r e n t f r o m O H (see T a b l e II). ~Q for N H - N H 3 collisions, g o v e r n e d by attractive forces as i n d i c a t e d by its large size, does decrease as T increases. H o w e v e r , t h e r e is no decrease at e l e v a t e d t e m p e r a t u r e for q u e n c h ing of N H by H 2 a n d CO2 w h e n one c o m p a r e s the results o f Refs. 17 and 20. For CH, a c o m p a r i s o n b e t w e e n the values f r o m Refs. 18 and 21 can be m a d e for f o u r colliders. For each q u e n c h e r , the cross section is significantly h i g h e r at the h i g h e r t e m p e r a t u r e . T h i s indicates some kind o f b a r r i e r to the q u e n c h i n g , a b e h a v i o r quite unlike that o f O H . N2, a n i m p o r t a n t collider in air-based flames, behaves quite peculiarly c o m p a r e d to the o t h e r q u e n c h e r s c o n s i d e r e d here. I n the case o f O H , its cross section is m u c h smaller t h a n calculated with the m o d e l a n d it decreases sharply with t e m p e r a t u r e (7,~ 2 at 230K to 0.7,~ 2 at 1100K); this result has b e e n i n t e r p r e t e d 15 as d u e to e n h a n c e d state m i x i n g in the longer-lived collisions at lower t e m p e r a t u r e . N2 was f o u n d 2~ to q u e n c h N H p o o r l y (CrQ < 0.01~2), but it q u e n c h e s C H m o r e efficiently t h a n O H , with a cross section is o f 1.3,~ 2 at 1400K.

COLLISIONAL QUENCHING OF ELECTRONICALLY EXCITED SPECIES

1697

TABLE llI Calculated OH Quenching Cross Sections, ~2 QUENCHER

500K

1000K

1500K

2000K

68 7.2 32 1.8 14 62 40 24 28 37

41 4.5 20 0.8 8.9 38 23 17 16 20

30 3.2 14 0.5 6.5 28 16 13 11 14

23 2.4 11 0.3 4.9 21 11 9.8 7.7 9.6

NHs H2 NO N~ O~ H20 N20 CH4

CO COs

4. Calculated O H q u e n c h i n g cross sections at elevated temperature

To estimate quenching rates a n d thus quantum yields in flame environments, one must know the t e m p e r a t u r e d e p e n d e n c e of crQ. Only for O H does sufficient information exist for such considerations. For the purpose of considering quenching in flames, both the collision p a r t n e r and t e m p e r a t u r e d e p e n d e n c e of the ~Q can be fundamentally u n d e r s t o o d on the basis of attractive forces. We will describe the calculation o f T-dependent cross sections using such a picture; further details can be f o u n d in Refs. 12 and 13. A simple one-dimensional potential, used to describe O H - q u e n c h e r collision complex formation, x5 is f o r m e d from multipole attractive terms and a repulsive centifugal barrier. A complex formation cross section ~r~fis calculated using this potential and averaged over collision energy. T h e complex dissociates with probability P to leaving the O H in the ground state. Then OrQ,calc =

P~4

(4)

P should vary with collider species; it is near 0.5 for many molecules i m p o r t a n t in flames except N 2. We use the P obtained by comparing the calculated cr4 with the experimental ~Q measured at room temperature. An average is then taken over the rotational distribution, using the cross section d e p e n d e n c e on rotational level expressed in Eq. (3), with the multipole calculation and Eq. (4) furnishing ~Q(N=0). T h e a values were d e t e r m i n e d from a fit of the room t e m p e r a t u r e CyQ(N). T h e a values are likely t e m p e r a t u r e d e p e n d e n t , but there exist no experimental data bearing on the question and it is ignored here. T e m p e r a t u r e - d e p e n d e n t cross sections for

2500K 18 1.8 8.5 0.2 3.8 17 8.4 7.7 5.7 7.1

O H were calculated in this way, and are listed in Table III. These form a consistent set of O'Q all c o m p u t e d in the same way. Given the lack of knowledge o f the t e m p e r a t u r e d e p e n d e n c e of a and P, this appears preferable to separate fits to the two experimental values (room and elevated temperature) available for each collider. (For nitrogen, the multipole model underestimates by a factor o f six the experimentally d e t e r m i n e d t e m p e r a t u r e dependence, so O'Q (N2) was simply a p p r o x i m a t e d to reflect smoothly the tenfold decrease between 230 and 1100K.) T h e c o m p u t e d CrQ'Sagree well with the r o o m t e m p e r a t u r e measurements used to determine a and P, and are generally within 20% o f the measurements near l l00K. We can compare them with values m e a s u r e d in flames, using the fluorescence intensity from O H excited by a Bi atomic l a m p (the prelaser counterpart o f LIF). Carrington 22 worked in a lowpressure C2H2/O2 flame, deriving OQ values of 35, 7 and 16 ~k2 for H20, 02 and CO2, respectively, at 1300K. A comparison with the values d e t e r m i n e d here (31, 7.3 and 16) shows a g r e e m e n t beyond that w a r r a n t e d in the calculation. Hooymayers and A l k e m a d e 23 determined values ofcyQ'S of 37 + 6, 10 +- 2 and 7 +-- 1 /~2 for H20, 02 and N2 respectively, at T = 1700K. These may be c o m p a r e d with computed values o f 26, 5.8 and 0.4 ~2. Here there is agreement except in the case o f N2, for which the direct determination o f 0.7/~ 2 at 1100K 13'14 shows that the flame value is too large. These calculated aQ'S a p p e a r reasonable for estimating O H q u a n t u m yields in flames. However, they should be r e g a r d e d with caution due to the lack of data concerning the temperature d e p e n d e n c e of the a and P. As will be seen below (Fig. 1), neglect o f any rotational dependence, i.e., setting a =0, produces a 30% difference in Q. T h e r e f o r e , neglect of the t e m p e r a t u r e d e p e n d e n c e o f a will produce an

1698

COMBUSTION DIAGNOSTICS

error in Q of smaller than 30%. T h e effects of any t e m p e r a t u r e d e p e n d e n c e of P are h a r d e r to estimate since P does not a p p e a r to vary much for CO2, Hg, a n d 09 but does for N2 quenchingJ 5 For NH a n d CH, the smaller cross sections (save for the polar NH~) and varied temperature d e p e n d e n c e indicate a different quenching process than in O H . At present, attempts to calculate ~rQ's akin to those for O H would be entirely speculative.

5. Quenching in flame environments. We can now make estimates of quenching rates in actual flames, and address several questions. First, how smooth is the variation o f Q with temperature? T h a t is, in a given flame, can we obtain a good estimate of Q simply by knowing T (which must be measured simultaneously in any event)? Second, for a given flame system (i.e., N H J O 2 o r CH4/air) how d e p e n d e n t is Q u p o n the initial mixture ratio? This question is o f particular importance for imaging in turbulent diffusion flames; across the image the local mixture may vary considerably in fuel/oxidant ratio. Finally, how crucial are the assumptions on the t e m p e r a t u r e dependence of cyQ? Major species profiles were taken from several flames described in the literature. We considered f o u r methane/oxygen flames at reduced pressure', those described by Peeters and Mahnen 24 b u r n i n g at 20 Torr, by Fristrom et al. 25 at 76 T o r r , and two 40 T o r r flames (~ = 0.92 and 1.13) by Zabielski and Seery 96. We also examined three ammonia/oxygen flames at 20 T o r r investigated by McLean and W a g n e r 97, having a m m o n i a fractions of 45% (lean), 57% (stoichiometric) a n d 65% (rich). T h e profiles o f the major species had been measured as a function of distance above the b u r n e r using mass spectrometric detection, and t e m p e r a t u r e was d e t e r m i n e d using thermocouples. Using ~Q's calculated as described above, together with the major species profiles, quenching rates were c o m p u t e d for each flame. Although it is possible that there are radicals present in the b u r n t gases which contribute to the quenching, any such contribution is ignored here. For example, H 2 0 can dissociate to H, O, and OH. Suppose each radical had a cross section that is the same as that for H (measured at room t e m p e r a t u r e to be 26 A9 (ref. 28)). I f the total radical concentration were less than 10% of the water concentration, 25 Q would be < 3% higher than shown in the figures. This is not a significant difference given the lack of

knowledge o f actual ~Q for radicals at high temperature. In Fig. 1 is plotted vs. t e m p e r a t u r e the O H quenching rate for the @ = 1.13 methane/oxygen flame described in Ref. 26. (Ar makes up about half the total gas density in these flames, but has a small kq29 o f 3.4 x 10 -13 cm 3 s -1 and does not contribute noticeably to Q.) T h e two profiles illustrate the importance of incorporating the rotational d e p e n d e n c e of ~Q, Eq. (3), in o r d e r to estimate Q within a factor of two. We do not know how a varies with T, so there remains an uncertainty o f the o r d e r of 30% due to that effect alone. Q is quite constant over the region (T > 500 K) where the radicals exist. Thus one expects little error in estimating relative values of Q in flames such as this, for the purpose of determining radical profiles in stable flames, or individual single-shot measurements on a relative basis. T h e results for the ~b = 0.92 flame are nearly as constant. This is in good agreement with the measurements t h r o u g h low pressure p r o p a n e / o x y g e n flames of Stepowski and Cottereau. s T h e y found Q to be constant within 10% t h r o u g h o u t the entire flame, for three different mixing ratios. Fig. 2 is a plot o f Q for the three ammonia/ oxygen flames. 27 Also shown are profiles for OH and N H absorption in the stoichiometric flame (the spatial resolution was unspecified in Ref. 27). Here, Q varies more with t e m p e r a t u r e than in the m e t h a n e flame although the variation is smooth. O f particular interest r e g a r d i n g measurements in diffusion flames is the relatively small difference in Q at a given T for the three initial mixing ratios. Here, differences of the o r d e r of +20% will result for a mixture between 40% a n d 65% ammonia, due in part to the fact that the fuel and principal product, H20, both have large ~Q. Fig. 3 illustrates the sensitivity o f Q to the temperature d e p e n d e n c e of ~Q. T h e example chosen is CH quenching in the methane/oxygen flame of Ref. 24. T h r e e forms of the temperature d e p e n d e n c e o f O'Q for CH are chosen: 1) a constant ~Q using the measured high temperature values o f Ref. 18 (see Table II); 2) an Arrhenius form of an increasing ~Q, using 1 - 2 kcal barriers as indicated by a comparison of the results Of Refs. 18 and 21; and 3) crQ decreasing with T as with OH, here simulated using A r r h e n i u s form with 2 kcal negative activation energies. In each case it was assumed that O'Q(H20) =O'Q(NH~), since quenching o f CH by H20 has never been measured. Q varies by 30% for each o f the forms for T > 1000 K; however, note that the value at the center of the plot, 1400 K, is the same for all cases.

COLLISIONAL Q U E N C H I N G OF ELECTRONICALLY EXCITED SPECIES 8

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T E M P E R A T U R E (K)

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T E M P E R A T U R E (K)

Fie. 1. Calculated OH quenching rate as a function of temperature illustrating the effects of the rotational level dependence of ~Q. This is for a CH4/O2/Ar flame with c~ = 1.13, at 35 T o r r (Ref. 26). The triangles are the quenching rates calculated with the cross sections from Eq. (4), neglecting the dependence of ~Q on rotational level. The rates given by the squares use ~Q which incorporate the rotational dependence, Eq. (3), and average over a thermal rotational distribution.

~

z~

2

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[] O 0 0 0

2

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o []

~3

Z~ ~.Z~Z~AA

1900

2300

T E M P E R A T U R E (K)

FIG. 2. Calculated OH quenching rates as a function of temperature in 20 torr lean (L), stoichiometric (S), and rich (R) ammonia/oxygen flames from Ref. 27. Also shown are profiles of OH and NH radical absorption for the stoichiometric flame. Finally, we c o m p a r e calculated O's for O H with those m e a s u r e d usi~lg direct fluorescence decay. Stepowski a n d C o t t e r e a u 4 m e a s u r e d Q = 3 . 6 x 1-07 s - l ; a n d we calculate a Q = 4 . 0 • 107. T h e m e a s u r e m e n t 7 o n m e t h a n e / a i r at a t m o s p h e r i c p r e s s u r e with a picosecond laser gave Q = 5 . 6 • l0 s s -~, a n d we calculate a value o f 4.5 x 108. In each case, the calculated Q for O H is within 25% o f that m e a s u r e d . T h e q u e n c h i n g rate for C H has also b e e n

FIG. 3. Calculated quenching rates for CH as a function of temperature T for the 20 torr methane/ oxygen flame of Ref. 24, for three different assumptions about the temperature dependence of O'Q(CH). Triangles: ~Q increasing with T, calculated in Arrhenius form with 1 to 2 kcal barriers; squares: eQ constant at the values measured at 1400K; circles: crQ decreasing with T, represented by an Arrhenius form with negative 1.5 kcal activation energies. m e a s u r e d using direct fluorescence decay in a m e t h a n e / o x y g e n flame at r e d u c e d p r e s s u r e 5. We calculated Q at 3.5 m m above the b u r n e r , the point o f m a x i m u m [CH], using the rep o r t e d m a j o r species c o n c e n t r a t i o n s in the 20 T o r r flame. A value o f 3.3 + 0.7 x 107 s -1 was obtained, the spread d e p e n d i n g on the choice o f the t e m p e r a t u r e d e p e n d e n c e o f the O'Q (the slowest value is c o m p u t e d for the decreasing cross section). This is twice the c o r r e s p o n d i n g e x p e r i m e n t a l value o f 1.6 x 107 s -]. T h e same result is f o u n d for a d i f f e r e n t C H e x p e r i m e n t . K o h s e - H 6 i n g h a u s et al. 6 have m e a s u r e d the fluorescence time d e p e n d e n c e , w o r k i n g in a C2H2/02 flame with cI) = 1.2 at 10 T o r r . A value Q = 1 x 107 s -1 was f o u n d to p r o d u c e a g o o d fit in a m o d e l o f the time d e p e n d e n c e of both the rotational relaxation a n d q u e n c h i n g . We calculate Q = 1.7 -+ 0.4 x 107 s -1, w h e r e the spread again reflects the choice o f t e m p e r a t u r e d e p e n dence. I n both flames, the c o m p u t e d Q is larger than that d e t e r m i n e d e x p e r i m e n t a l l y , by about 80%. T h e discrepancy may be d u e to the lack of k n o w l e d g e o f the t e m p e r a t u r e d e p e n d e n c e of aQ. It is, however, m o r e likely d u e to the use of O'Q(NHs) to describe the H 2 0 q u e n c h i n g ; in each flame H 2 0 m a k e s u p a b o u t 55% o f the total gas density a n d in the calculation accounts for a b o u t 85% o f the q u e n c h i n g . 6. C o n c l u s i o n s

We have s u r v e y e d the c u r r e n t k n o w l e d g e o f q u e n c h i n g cross sections for diatomic hydrides,

1700

COMBUSTION DIAGNOSTICS

needed for analysis of LIF or emission data in flames. For OH, sufficient data exists at different temperatures to furnish a reasonable framework for estimation of quenching rates and q u a n t u m yields for a variety of flame conditions. This follows from the a p p a r e n t ability to understand OH quenching on the basis of attractive interactions. Definite gaps do remain; of particular note are the temperature dependence of o'Q(N2) over a larger range of T, and the T-dependence of the rotational dependence. OH quenching rates have been calculated for a variety of exemplary flames and compared with two directly d e t e r m i n e d absolute values. We conclude that, for at least the CH4 and NH3 flames examined here, it is reasonable to expect estimates of Q as a function of temperature good to within perhaps +30%, given the composition of the local environment, and better than a factor of two over a wide range of u n k n o w n concentration in the ammonia case. At present, too little information about the quenching of NH and CH is available for the same kind of application. This limits the ability to estimate Q to perhaps a factor of three; this appears possible using the ~Q at 1400K, in the midrange of temperatures of importance, so long as values are available for all colliders of importance. T h e discrepancies in the case of CH indicate the importance of measurement of the H20 cross section for these radicals, at more than one temperature.

Acknowledgements We thank Gregory Smith, Paul Fairchild, Richard Copeland, Mark Dyer and Jay Jeffries, each of whom has made part of the quenching measurements described here and has participated in many discussions about the collision mechanism as well as applications to LIF detection. This study of quenching in flames was supported by the Basic Research Department of the Gas Research Institute.

REFERENCES 1. CROSLEY, D. R. AND SMITH, G. P.: Opt. Engr. 22,

545 (1983); BECHTEL,J. H., DASCH, C. J. and TEETS, R.: in Laser Applications (E~, R. K. and READY,J. F.: Eds.), Academic Press, New York, 1983; LUCHT, R. P.: in Laser Spectroscopy and Its Applications (RADzIEMSKI,L.J., SOLARZ,R. W. and PAISNER,J. A.: Eds.), Marcel Dekker, New York, 1986. 2. CROSLEY,D. R.: Opt. Engr. 20, 511 (1981). 3. STEPOWSKI, D. AND COTTEREAU,M. J.: Comb. Flame 40, 65 (1981).

4. STEPOWSKI, D. AND COTTEREAU,M. J.: j. Chem. Phys. 74, 6674 (1981). 5. CATTOLICA,R.J., STEPOWSKI, D., PUECHBERTY,D. ANDCOTWE~AUM. J.: J. Quant. Spectros. Radiat. Transfer 32, 363 (1984). 6. KOHSE-HOINGHAUS,K., PERC, W. ANDTH. JUST: Ber. Bunsen Ph. Ch. 87, 1052 (1983). 7. BERGANO,N. S., JAANIMAC,I, P. A., SALOUR,M. M. AND BECHTEL,J. H.: Opt. Len. 8, 443 (1983). 8. DAILY,J. W.: Appl. Opt. 15, 955 (1976); LUCHT, R. P., SWEENEY, D. W., LAURENDEAU,N. M., DRAKE, M. C., LAPP, M. and PITZ, R. W.: Opt. Lett. 9, 90 (1984); KOHSE-HOINGHAUS, K., HEIDENREICH, R. and JusT, Th.: Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1985, p. 1177. 9. ALD]~N,M., EDNER, H., HOLMSTEDT, G., SVANBERG, S. AND HOGBERG, T.: Appl. Opt. 21, 1236 (1982); DYER, M. J. and CROSLEY, D. R.: Opt. Lett. 7, 382 (1982); KYCHAKOFF,G., HOWE,R. D., HANSON, R. K. and MCDANIEL,J. C.: Appl. Opt. 21, 3225 (1982); CATTOLICA,R. J. and VOSEN,S. R.: Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1985, p. 1273. 10. JEFFRIES,J. B. AND CROSLEY, D. R.: Comb. Flame, 64, 55 (1986). 11. COPELAND, R. A. AND CROSLEY, D. R.: Chem. Phys. Lett. 107, 295 (1984). 12. COPELAND, R. A., DYER, M. J. AND CROSLEY, D. R.: J. Chem. Phys. 82, 4022 (1985). 13. FAIRCHILD, P. W., SMITH, G. P. AND CROSLEY, D. R.:J. Chem. Phys. 79, 1795 (1983). 14. SMITH,G. P. AND CROSLEY, O. R.:J. Chem. Phys. 85, 3896 (1986) 15. COPELAND, R. A, AND CROSLEY, D. R.; J. Chem. Phys., 84, 3099 (1986). 16. JEFFRIES,J. B., COPELAND, R. A. AND CROSLEY, D. R.: J. Chem. Phys. 85, 1898 (1986). 17. GARLAND, N. L., JEFFRIES, J. B., CROSLEY, D. R., SMITH, G. P. AND COPELAND, R. A.: j. Chem.

Phys., 84, 4970 (1986). 18. GARLAND,N. L. ANnCROSLEY,D. R.: Chem. Phys. Len., in press. 19. McDER~ID, I. S. AND LAUDENSLAGER,J. B.: J. Chem. Phys. 76, 1824 (1982). 20. HOFZUMAHAUS,A. ANDSTUHL,F.: j. Chem. Phys. 82, 3152 (1985). 21. NOKES, C., GILBERT, G. AND DONOVAN, R. J.: Chem. Phys. Lett. 99, 491 (1983); NoKEs, C. J. and DONOVAN,R. J.: Chem. Phys. 90, 167 (1984). 22. CARRINGTON,T.: J. Chem. Phys. 30, 1087 (1959). 23. HOOYMAYERS,H. P. ANDALKEMADE,C.,JusT, TH.: J. Quant. Spectros. Radiat. Transfer 7, 495 (1967). 24. PEETERS,J. AND MAHNEN, G.: Fourteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1973, p. 133. 25. FRISTROM,R. M., GRUNFELDER,C. ANDFAVIN,S.: J. Phys. Chem. 64, 1386 (1960).

COLLISIONAL QUENCHING OF ELECTRONICALLY EXCITED SPECIES 26. ZABIELSKI, M. F. AND SEERY, D. J.: Gas Research Institute Final Report, NTIS No. PB-85-129690, 1985. 27. MACLEAN, D. I. AND WAGNER, H. Gg.: Eleventh Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1967, p. 871.

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28. BECKER, K. H., HAAKS, D. AND TATARCZYK, T.: Chem. Phys. Lett. 25, 564 (1974). 29. HOGAN, P. AND DAVIS, D. D.: J. Chem. Phys. 62, 4574 (1975); LENGEL, R. K. and CROSLEY, D. R.: J. Chem. Phys. 64, 3900 (1976).

COMMENTS Hans M. Hertz, Lund lnst; of Tech., Sweden. You have measured and calculated the quenching cross-section (Tq) for OH for temperatures below approximately 1500 K. What is known about Tq for OH at higher temperatures? Author's Reply. All that is known about OH is that tyQ decreases up to 1500K. This temperature is as high as we can go with our laser pyrolysis apparatus. So long as attractive forces are important, the cross section will decrease with increasing collision velocity and thus with temperature. All of the cross sections in the paper are calculated assuming this quenching mechanism. At very high collision velocities, however, one may begin to sample the short-range repulsive part of the potential, and then the thermally averaged cross section would begin to increase with further increase in temperature. In the study ~of quenching of OH by NH3, tyq was constant to within error bars between 900 and 1400K. We postulated that this may indicate the onset of such a second mechanism, but that is entirely spectulative at present. Measurements at yet higher temperature are needed to examine this question.

REFERENCE

1. JEEERIES,J. B., COPELAND, R. A. AND CROSLEY,D. R., J. Chem. Phys. 85, 1898

Th. Just, DFVLR, W. Germany. Could you extract information on rate coefficients for state to state energy transfer? Author's Reply. In the paper we consider only quenching, that is, total removal of the electronically excited state and the resulting overall fluorescence quantum yield. Energy transfer within the excited state can be important, however, in determining the quantum yield for fluorescent emission within a given spectral bandpass of the detector. We have made other measurements, not covered in the paper, on state-to-state energy transfer in A2~ § OH. In much earlier work we examined rotational I and vibrational 2

transfer within the A-state, and some of that work is now being extended 3 to a wider range of collision partners. Very recently we have begun a new experiment4 concerned with quenching, for which only preliminary results are available. The objective is the distribution of population over internal levels of the X2Ili ground state OH, following a quenching collision. The experiment is performed by pumping v'=0 of A2~ + with one laser, and using a second time-delayed laser to probe that the vibrational levels of the X-state which have been populated by quenching and subsequent vibrational energy transfer collisions during the delay. The collider studied was HzO, and we were able to probe v"= 1,2 and 4. The results indicate that the OH is quenched into high-lying v" in the ground state, since all the levels probed were populated only by subsequent vibrational transfer collisions following the quenching. It is clear that a Frank-Condon overlap of initial and final vibrational states as governing propensities for quenching is not an applicable explanation here. 1. LENGEL, R. K. AND CROSLEY, D. R., J. Chem. Phys. 67, 2085 (1977). 2. LENGEL, R. K. AND CROSLEY, D. R., J. Chem. Phys. 68, 5309 (1978). 3. COPELAND, R. A., WISE, M. L., ANn CROSLEY, D. R., to be published. 4. COPELAND,R. A.,JEFFRIES,J. B., AND CROSLEY,D. R., to be published.

Katharina Kohse-Honighaus, DFVLR, W. Germany. Would you comment on the quenching of combustion-relevant atoms by the same quenchers, e.g. on the basis of the N atoms quenching investigated in your laboratory.

Author's Reply. Laser-induced fluorescence in atoms relevant to combustion (H, O and N) can be produced only by two-photon absorption 1 because their lowest excited states lie so high in energy. Little has been done on quenching of these species. In our measurements 2 on nitrogen atoms, the only collider studied which is found in flame gases is molecular Nz. Here the cross section is large, about 55/~2. That is much

1702

COMBUSTION DIAGNOSTICS

larger than for the diatomics. Your own recent results3 for O and H atoms are the most complete set. Again, the cross sections are pretty large, between 30 and 600 ~2. It is very interesting that you found ~rq for H to decrease in going from room temperature to 700K, for the colliders 02 and H~O, One certainly expects hydrogen atoms (in the ground state at least) to form a complex with 02, and maybe with H20.

REFERENCES 1. BISCHEL,W. K., PERRY, B. E. AND CROSLEY,D. R., Chem. Phys. Lett. 82, 85 (I98I); Appl. Opt. 21, 1419 (1982). 2. JEFFRIES,J. B., COPELAND,R. A. AND CROSLEY,D. R., to be published. 3. MEIER, U., KOHSE-HOINGHAOS, K., AND JUST, TH., Chem. Phys. Lett. 126, 567 (1986).

I. Wolfrum, Univ. Heidelberg, W. Germany. Could you measure the competition of reactive and nonreactive channels in the quenching of OH(A) by CO molecules? Author's Reply. All we observe when measuring quenching rate constants for any of the radicals, is the total disappearance of the excited state. This removal could be due to reactive and/or nonreactive quench-

ing, but we cannot distinguish between the two processes. To do so would require an absolute measurement of the concentration of the reaction product and of the initially excited OH.

A. J. Saber, Concordia Univ., Canada. Is there a Mach number limit for use of excited OH as a tracer? The velocity is not uniform within a flame and may change from mixture to mixture or with experimental conditions. With that in mind and based on your data, would you please comment on the accuracy of OH as a tracer for flame structure observation? Author's Reply. Because the quenching cross section depends only on the relative velocity between the excited OH and the collision partner, the speed (Mach number) of the overall flow is immaterial. One must still know the local temperature at the point where the radical is sampled, in order to know that relative velocity. Therefore, any gradients in the overall velocity should also pose no problem, so long as the temperature is known. The OH is quenched so rapidly after excitation (in a ns or so) that only the spatial region (and thus the collisional environment) where it was excited is sampled. One must however, consider overall spatial resolution under conditions where gradients exist--that is, ensure that the laser beam and/or detector do not average a range of conditions such as temperature.