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Chemiluminescent spectra and light yeilds from several low-pressure diffusion flames of alkaline-earth metal vapors
CHEMILUMINESCENT SPECTRA AND LIGHT YIELDS FROM SEVERAL LOW-PRESSURE DIFFUSION FLAMES OF ALKALINE-EARTH METAL VAPORS HOWARD B. PALMER, WILLIAM D. KRUGH, AND CI:[UNG-JEN HSU Fuel Science Scetion, Department of Material Sciences, Pennsylvania State University, Pennsylvania The chemiluminescent emi~ion from diffusion flames of several oxidant~s reacting with alkaline-earth metal vapors has been s~udied at pressure~ between about 2X10-s and 0.2 Torr. Spectra have been recorded in the uv, visible, and near ir regions, and photon yiekks have been determined. B'aO(A-X) photon yields from the reactions of Ba atoms with N~O and with NO~ are found to be presslLre-dependen~,indicating a complex mechanistic route to BaO (A~Z+). By combining our results with those at higher and lower pressures, oin~ined in other laboratories, it is pcxssible to construct a preliminary kinetic model of these reaction systems and obtain seine information on their electronic-sta~e branching ratios, efficiencies of electronic-state transfer proc~ses, and quenching efliciencies. Photon yields also have been measured in flames of Ba, Ca, or Sr with ONBr, and Ba or Ca with ONC1. The yields are generally of the order of l0 -3 or less at p~2-5X10 -~ Tort. They increase somewhat with total press~Lre (3X10 a to 0.25 Torr) in the two cases studied mos~ extensively (Ba, Ca-I-ONCI), but scatter in the data has thus far prevented quantitative determination of the pressure dependence. Introduction mechanistic model for the emission from two flames. Alkaline-earth-plus-oxidant flames were seVisible-ultraviolet (electronic) molecular chemiluminescence from gaseous reactions has perhaps lected for study as a result of the molecular beam been known longer (especially by combustion work of 0ttlnger and Zare13 (a~ld later stndies in Zare's laboratory14) on reactions between Ba scientists) than its infrared analog, but is less well understood. Photon yields of C~ Swan Band (and Ca) and the oxidants Ne0 and N0:. They emission in hydrocarbon flames l and from elec- observed chemilumineseent emission from these tronically excited CO~ in carbon monoxide flames~ systems, identified some of it (e.g., Ba0 A1F.-XI~ were measured some years ago. However, kinetic from Bad-NO.o), and determined (or set limits interpretation of the results was qualitative be- on) the total reaction cross-sections. They did not cause the details of the excitation mechanisms measure light yields, a prime objective of the were not known and the concentrations of the present work. Aside from one brief study of Bad-02, s all precnrsor species could not be measured in the flames being studied. The general direction of systems exa~ained by us have involved triatomic more recent work, for example the studies of oxidants reacting with alkahne-earth vapors. Clyne, Thrush, and co-workers a-6 has been to- These were chosen because (a) there are a number ward simpler reaction systems in which these of triatomies that have weakly bonded atoms limitations are largely removed. (0~, N~O, N02, ONC1, ONBr); (b) alkaline-earth We report here studies of the non-thermal monoxides and monohalides have moderately emission of fight from diffusion flames of several strong bonds (BaO, BaC1, Ca0, etc.); and (e) the oxidants reacting with alkaline-earth metal second products of the reactions (N2 from N~O, vapors. This paper revises and extends ~ m e NO from NO~ and nitrosyl halides) arc stable previous results7-~ and includes a kinetic- molecules that do not react readily with alkaline
951
952
ELEMENTARY ltEACTIONS +
~uuP
FI~. 1. (a) Low-pre~sure reactor for metal-oxidant flames. (b) System for measurement of photon emission from low-pressure flames. earth metals in the gas phase and that do not have low-lying electronic states to complicate the emission or the electronic state distribution.
Apparatus and Measurements The apparatus used is shown in Fig. 1. Diffusion flames are formed in a quartz-windowed reactor (Fig. 1) made of Pyrex glass. Metal is vaporized from an alumina crucible surrounded by az~ electric resistance heater held at about ll00~ The oxidant enters at room temperature through inlmt nozzle A, at a sufficiently slow flow rate that the metal vapor is clearly in excess (this can be seen by eye, from the distribution of the emission and by dcposition of metal on the reactor waft). The input nozzle is about 5 cm above the vaporizer. The opening iu the tip is about 1 mm in diameter. The oxidant flow rate is measured~ since it is a measure of the total reaction rate (all oxidant is consumed by the excess metal, the flux of which is calculated from the vapor pressure to be typically 100 times the oxidant flux). Inert gas can be added with the oxidant, through input B, or next to the quartz window. Flame spectra are recorded with an f/6.3 plane-grating speetrograt)h (20 ~ / m m in the first order). The light flux is measured as indicated in Fig. lb. The photomultiplier (RCA 931A, S-4 response) is calibrated for response to light flux at a chosen wavelength within the spectral region covered by the emission, using an interterence filter, and then the measured flux is corrected by folding in the observed (on plates) wavelength distribution of the emission and the sensitivity curve of the PMT. A tungsten stripfilament lamp, brightness temperature measured with an L&N optical i)yrometer, is the calibra-
tion source. Light from the flame passes through a 45 ~ sector chopper, then through a 1 cin diameter slit to the PMT, from which the output signal goes to a lock-in amplifier and recorder. The referenc~ signal for the lock-in is provided by a photoresistor on the chopping wheel. The emission received by the PMT is treated as ff it issued from a point souree~ for purposes of fommlating the geometric multiplying factor that relates the measured light flux to the total. The assumption is reasonably good; most of the emission at pressures above about ]X 10-3 Torr can be seen (by eye and from photographs) to issue from the spatial region within 1 cm of tile nozzle, while the PMT is 36.5 em from the nozzle. There is no lefts in the optical system. The photon yield is defined as the rate of photon emission divided by the rate of chemical reaction, i.e., by the rate of inflow of oxidant into the reactor. Spectra of the emission Mways are taken before the flux measurements in oMer to identify the emitting species and to assess the distribution of emitted intensity as a function of wavelength. This permits (a) correction of the total photon flux to take into accmmt the variation of photomultiplier sensitivity with wavelength; and (b) determination of tim relative contributions of various states (electronic or vibrational) when more than one state contributes emission and when the contributions are separable. From the calibrations, the geometry, and the oxidant flow rate, combined with the recorded PMT signal, the photon yield, 9 (photons emitted per molecule of oxidant consumed) is obtained:
~= SVG/F, where S = corrected PMT sensitivity (photons counted/see/volt output), V= measured PMT
C H E M I L U M I N E S C E N T SPECTRA
953
TABLE I Summary of present observatlotrs on chemilumineseent emission from flames of alkaline-earth vapors with several oxidants ~ietal
Oxidant
Spectra observed
Photon yield (q~)
Ba
O2
BaO (AtZ-Xtz) plus new system assigned to BaO ( A ~ I I - X ~ ) .
Not measured. Qualitatively observed to increase with increasing pressure of added m'gon.
Ba
N20
Extensive emission from BaO ( A - X ) and ( A ' - X ) . Analysis of A ' - X systern carried out on this spectrum. A - X heads replaced by many*line spectrum at very low pressure.
Measured as function of pressure (using Ar), from 4X10 -3 to 0.2 Torr. 4~ irmreases from 2X10 a to 2.5X 10 -2 over the range.
Ba
NO2
Same ~s Ba+O~, except A - X intensity distribution shifted toward the red.
Measured from 2 X10 -3 to 0.1 Torr. 4~ increases from 1.5X10 ~ to 1 X 10-~ over the range.
Ba
ONCI
BaC1 (C~H-X2z). A - X and B - X not observed (in near Jr) but reported by others to be present. TM
9 (C-X) ~ 2 X 1 0 4 at p = 2 X l O -~ Torr. Into'eases wit,h pressure bill details not established.
Ba
ONBr
BaBr ( ~ I I - X 2 z ) . A - X and B X not known; probab]y in n e w ir.
(o(C X) ~ 3 X I 0 -~ at p ~ 2 X l 0 -a Torr. Not yes studied as function of pressure.
Ca
ONC1
CaC1 (A~II-X2Y,) and (B~Z--X2Z).
r
Ca
ONBr
CaBr (A:ffI-X2Z) mid (B2~-X=~).
No 4~ measurements. Plates show that ( A - X ) >>~ ( B - X ) .
Sr
ONBr
SrBr (A~H-X~Z) and (B~-X2Z).
9 ( A - X ) ~7q~(B-X). Total r 10-~ at p ~ 4 X 10-~ Torr. Not studied as function of pressure.
output voltage, G = geometric factor for light collection from the flame, F = oxidant flow rate (mole/see).
Results and Discussion A s u m m a r y of the experimental results obtained in the present work is presented in Table I. The systems studied in m o s t detail have been Ba-}-N~O ( + A r ) , B a + N O ~ ( + A r ) , and B a or C a + O N C 1 ( + A t ) . T h e measured (with a bare, 9 uncorrected fine thermocouple) temperatures of these flames are in the range 400~176 indicating that all of the visible emission is chemiluminescent. T h e temperatures are not accurate; however they are in the same range as thug reported by Jones and Broida 16 for the B a + N 2 0
=2.54,(B-X). Total ~ = 8 X 10 -4 at p - 2 X 10-2 Torr. Increases with pressure but details not established.
flame at higher pressm'e. The discussion t h a t follows mainly concerns these three reaction systems. Ba-~-N~O. This system has been studied b y four groups, to our knowledge: Zare's group 1r determined an upper limit (27 ~2) for' the total reaction cross section as studied in beams and observed the ehemilmninescent reaction to be first-order in both B a and N20 between about 10-* and 10-s Torr. Jones and Broidg ~6have detm~fincd the photon yield over the pressure range, 1 32 Torr. Their total photon yield results are includ~l in Fig. 2. T h e y report A - X BaO emission and many-line emission, the latter being important at 1 Tm'r b u t quite small at 24 Tort. Field, et al., a have discussed the prohahle reaction mechanism. Benson's group 15 determined the photon yield
954
ELE:~CIENTARY 100
........
I
........
I
REACTIONS . . . . . . . .
,
. . . . . . . .
I
'
, ' ....
,-, I0 / Ill
>Z 0
1.0
0 "in
0.1 / .,./ 0.001
I
0.01
,
I
0.1
,
,
I
1.0
JI
I0.0
,,,
I00.0
PRESSURE (t0rr) Fro. 2. BaO(A-X) photon yields as functions of pressure. B~+N20: O corrected data, present work; t uncorrected dat% present work; 9 Jones and Broida~6; [] Eekstrom, et al. ~ Ba+NO~: A corrected data, pr6sent work; 9 uncorrected data, present work; [] Jones and Broida. ~' Solid curves are the results of mectmnistic modeling. Dashed curves show the falloff behavior attributed to mean free path effects. at 2.2 Torr. Their result, shown in Fig. 2, agrees fairly well (within a factor of 2) with Broida's. We have studied the spectra and determined the photon 5delds at pressures from 4X 10-4 to 0.2 Torr, with results shown in Fig. 2. The pressurizing gas used was argon (helium gives nearly the same results, but the data are more scattered). Using the photon yields from all laboratories, we have been able to model the reaction over about a 100-fold span in yield and a 3X 10S-fold span in pressure (from 10-4 Torr to 30 Torr). Modeling requires an understanding of the probable roles of the accessible electronic states. TM Michels TM has calculated the potential curves of the XtY,, AIX, and aZrl states of BaO, and Field has calculated RKR potentials for the X, A, a, and A'~H states. 2~Their results agree quite well. The electronic spectra observed will be discussed briefly before developing the mechanism. (i) At pressures of 2-4X 10-3 Torr, we find a spectacular many-line spectrum extending from the near uv throughout the visible region. The A - X bands emerge from this spectrum as the pressure rises, and dominate the emission above 2-4X10 -e Torr. We have been able to show u tlmt the many-line spectrum earmot be due to a2H-XiZ. However, it could be due either to
A ' - X or A - X . The fact that A ' - X fie~ls (see below) are visible at p = 4X 10-4 Torr (where the many-fine spectrmn dominates the emission), plus the fact that the many-line emission covers essentially the same wavelength region as the A - X bands seen at higher pressures, suggests that the many-line spectrum probably is A - X emission in which the A state possesses huge rotational excitation. Recent work by Schultz and Zare~ supports this tentative conclusion. Thus the emission at all pressures probably is dominated by A - X emission. (ii) At all pressures covered (2X10-L0.2 Torr), we observe two weak progressions of single-headed bands in the violet and near uv. With the aid of a study by Field 2~ of perturbations in the A - X system, we have analyzed these bands ~ (which are also seen with the oxidants NO~ and 02, but are not as extensive as with N20). They are assiglmd ~ to A'III-X*Y,. They contribute very tittle to the total emission at any pressure. (iii) A - X band heads first become identifiable against the ninny-line spectrum at ~ 2 X 1 0 -2 Torr. They are almost free of the many-line spectrmn at 8X 10-2 Tort. At 0.2 Tort, A - X heads are quite well developed and the many-fine
CHE.~ILUMINESCENT SPECTRA spectrum is no longer observed on our plates. The rotational fine structure appears to be essentially thermal. The observed increase of the A - X phot.on yield with pressure can be explah~ed if most of the BaO produced by the biimolecular process is in an electronic state that can be transformed to AiZ, by collision, This process was first suggested by Field et 02.iT'is The intermediate electronic state is likely to be the aZH, according to FieM. Although this state has not been directly observed, our spectroscopic support for Field's calculation of the location of the AnH state prorides further confidence in the essential correctness of his~~and Michels 'm calculated location of the a '~II state, and of its likely role in the reaction between Ba and N~O. Our mechanistic niodel is based on this important hypothesis. The model consists of eight elementary steps. Three are atom-exchange reactions populating the X, A, and a states:
955
since competition between step 4 and steps 5 and 6 accounts in large part for the pressure dependence. The A - X photon yield can be derived by considering the probabilities of the various steps in the mechanism, as shown in the Appendix (where it is also shown t h a t photon yields can be determined from measurements on diffusion flames). The expression for the A - X photon yield is
q~A-x= { P3+ P#[-I+ (kh+ k6)/taM]} { i/El
+ (ksM/~)]}
where P~ and P~ are the probabilities of steps 3 and 2, respectively; e.g., P3 is the probability that a reactive encomlter between N20 and Ba will produce BaO(A~2;). This is the branching ratio for the A state. This expression does not take into account the expected falloff in the experimental value of the photon yield at low pressures that will occur because of a mean-free-path effect. That is, a Ba-~- NeO---~BaO(XIE) -~-N~ (1) photon cannot be observed unless N20 undergoes a reactive collision with Ba before leaving the field of view (,~2.5 cm radius). We write ~a~p= Ba+N20---~BaO(a3Ii)+ N2 (2) 4~(1-- W), where ~p~p,is the apparent yield defined by (I,~pp=(Light flux)/(Oxldant flow rate), 9 is B a + N'20---~BaO(ALE)+ N,~ (37 the true yield, and (l-W) is the probability t h a t the oxidant (N~O, here) will sustain a reactive One is the crucial a-A collisional transformation: collision as it passes through the observed region (note that if it does trot, it will still react eventuBaO(a~ll)+ M--*BaO (A~E)+ M (4) Mly, but mainly with Ba on the vessel wall). A one-dimensional treatment of W, which is probably adequate for our purposes, gives it as W = Three are radiative processes: exp(--x/L), where x is the distance traveled and L is the mean free path for reactive collisions. If BaO (a'~II)--~Ba0 (X~N)+ hv (5) the reactive cross section is much less than the elastic collision cross section, the correction BaO (a'~H)--+BaO(z*?)+ h~, (6) factor (l-W) should be replaced by a factor derived from considerations of diffusion. HowBaO(AW,)--~BaO(X~Z)+tw (7) ever, the work in Zare's laboratorylaaa suggests that most reactions of the type under study here have reactive cross sections of the same order as, and one is quenching of the A state: or larger than, elastic collision cross sections. For B a + N 2 0 , we have u ~ d a reactive cross secBaO(A~Z )+M--*BaO (X~Z) + M (8) tion of 25 .~2, slightly below the upper limit figure obtained by Jonah, et al., 14 to correct the yiekls. The model is obviously oversimplified. Thus it The corrected results are shown by open circles omits processes such as the back reaction of step in Fig. 2. Corrections at pressures above 2X 10-: 4~direct production of the Anti star% the produc- Torr are negligible. The uncorrected data are tion of AnH by coilisional transformation of aaII, also shown to illustrate the mean free path effect. There will also be a mean free path or diffusion production of A~Z by transfer from high vibrational levels of the ground state, and quenching effect on the electronic-state transfer, step 4. An of a3H. Several of these processes may ultimately estimate of this effect shows that it will only be prove to be significant. significant in our observations if the aSH state is In the radiative steps we include an allowed metastatic, i.e., if the sum of ks and k6 is less transition from the aSH to a lower triplet state than about 104 see-~. Since this is unlikely, the (presumably aZ)~o This is an important process, effect is not hmluded in the fitting procedure.
9,56
ELEMENTARY REACTIONS
Lt ealcnl~ti3x~ the mean free path effect, we have considered ordy the case of N~0 moving through Ba vapor. The (calculated) flux of Ba from the crucible is at least 100 times the (measured) flow rate of N~O, so production of Ban and N~ produces little change in the composition. Ful%hermore, addition of argon (at the end of the reactor, Fig. la) to increase the pressure seems to confine the Ba vapor more and more closely to the central region of the reactor (as indicated by the extent of wall deposition of Ba). Thns the t~ressurizing argon may I~o~extensively dilute the Ba, but rather confine it, in which ease N.~O issuing from the nozzle encounters mainly Ba atoms over most of the 2.5-era-radius observation region. The four parameters in the phofxm-yield expression ~Pa, P,.,, (k~+k~)/ko, and ks/kT] have been determined from the corrected yield data by a trial-and-error procedure. The data at low pressures (Fig. 2) show that Pa must lie between about 3X10 -~ and 5X10 -'~ if, as required by Zare's beam observations,T M the pressm'e dependence of 9 is to be very weak at pressures below about lX10 ~ Torr. Examination of the high-pressure region showed, in trial calculations, that the fa]loff duc to quenching would be best reproduced if P: were as large as possible: i.e., P2~-~I. Using this value (actually P~=0.996) and Pa=4X10 a, (k~+k~)/k~ has been determined by finding the best fit (judged by eye) to the data in the low-pressure region (up to ca. 0.1 Torr), where quenching is insignificant. The value of ks/~ has been routed by requiring r f~) equal 0.25 at p= 10 Torr (here we ascribe all of the emission observed by Jones and Broida~ to A-X). The results are: P a - 4 X 1 0 - a ; P~=0.996; (Pv-~O) ; (ka+ka)/k4-1.2X 10-7 mole/cm~; k~/~= 7.1X 10~ eroS/mole. The fit is represented by the solid curve in Fig. 2. The dashed curve shows the falloff resulting from the mean free path effect at low pressures. Uncertainties in the above parameters are due to the limite~ions (ff the model, to unccrtainties in the experimental results, and to the necessity of making some compromise in ordcr to fit all the available data reasonably wen. I t is difficult to estimate the total uncertainty. We believe that P3 is probably correct to within =1=25percent; P~ (which cannot exceed unity) is not likely to be any smaller than about 0.75; and P~ has the largest relative error, since its upper lhnlt thus appears to bc about 0.25. The branching ratios Pz, P2, and Pt imply that the three corresponding electronic states (A, a, and X) are populated by the elementary reaction between Ba and N~O in the approximate prob-
ability ratios 4:996:0. Thus it appears that nearly all of the BaO is produced in the aSII state, which supports the postulate of Field et al., 17 and is a very interesting result. From ~=3X106 sec-1, we obtain ks~2Xl@ s eroS/mole sec, implying that quenching of the A state occurs on about one collision out of every ten. The result agrees quite well with the quenching cross sections ( ~ 1 2 .~2) obtained by Johns o n , 22
Estimation of k4 is much less certain because neither k~ nor ke is known. The a-x transition is allowed, but probably lies in the infrared, so ka may be considerably smaller than k7 (3X108 se~l). ~ If the arguments of Field, et al., 17 are correct, ks+k~ may be of the order of 10~ sec-~. This would imply k4~10 ~2 em3/mole see ~nd indicate that the a - A transformation occurs in ab(mt 0.5 percent of a - M collisions in this system. Ba+NO2. This flame does not emit a manyline spectrum. Zarc's group13'14 did not observe one, nor did Jones and Broida, TM nor have we. The intensity distribution of the A - X emission is strongly shifted toward the red, in accord with the much lower cxothermicity of the overall reaction ("overall" because it is complex). The A ' - X progression is weak, and the v' values do not go as high as for Ba+N~O. Actually, the exnthermicity of Ba+N0~--~BaO+NO is insufficient to populate even those vibrational levels of O~e A' state that are seen; and we also see~even at 2X 10-~ Torr--weak eulission from vibratiomd levels of the A state that lie beyond the available exothermieity. Thus there ms}" be Some energy-pooling or energy transfer processes, as yet unidentified, that are responsible. However, tlm processes clearly arc not very important with respect to the A - X photon yield. For Ba+NOe we have assmned the same model as used for Ba+N20, retaining the same rate constant for quenching of the A state b u t obtaining the other parameters by trial-and-error fitting of the data. The apparent photon yields at low pressures were corrected to the true values using a reactive collision cross section of 165 .~ from the work of Jonah, et al34 Corrections at pressures above 4X 10-'~ Torr are negligible. The results are :/'3= 1.7X 10-3; P2 = 0.059 ; (P1 = 0.94) ; (k~+k6)/k4= 1.2X 10 s. The fit is shown in Fig. 2. The two points at higher pressures than ours were reported by Jones and Broida) ~ Their result at p = 1 Tort seems to be incompatible with our experimental data and we have not used it hr tile curve-fitting. Their point at 8 Torr is in the middle of their pressure range and should be the more reliable of t,he two. The values of P'z and of (k:~+ke)/k4 depend rather strongly on the high-pressure point. If the point at 1 Torr is in
CHEMILUMINESCENT SPECTRA fact con~ct, then the model assumed here must be severely inadcquate. The A-state branching ratio obtained is quite similar to that for Ba+N~O, but the ratio for the aslI state is much lower; thus it appears that in the Ba+NO2 reaction, more than 90 percent of the product BaO is created in the ground state. The value of (k~d-k6)/k4 gives a value of k4 equal to N10~s cmS/mole sec if (/~.~+k~)~105 s e ~ ~. This would imply transformation of a into A on roughly every twentieth a-M collision. The energy lcvcls of the a state that are populated by the B a + N 0 2 reaction are relatively low-lying because of the lower exothermicity. Field, st al.,17 have pointed out that the electronic transfer from several of the lower levels of the a state into the A state should occur with cross sections that are of the order of 88189of gas-kinetic, because of strong mutual perturbations. The trend in k4 from B a + N 2 0 to Ba+NO~ thus seems to lse in the right dil'cction. The absolute magnitude of k4 remains uncertain. Although our B a + N 0 2 data are more precise than those for Ba+NeO, they may not be as accurate; the undertainty may be about 4-50%. The reason is that the correction for the lack of photomultipller sensitivity ial the far red region is nmch larger and less certain than ill the case of Ba+X:O. A-X emission from Ba+NO2 can be followed on plates all the way to about 8700 :X., where the plate sensitivity drops sharply. Presumably it continues further; we have assumed that tim contribution will be minor, but experiments should be extended well into the ir for this system (and for others). Ba and Ca-{-ONCI. From the flame of Ba with ONC1 we have observed radiation enly from the C~2H-~VaEtransition of BaCi. We have made many measurements of the C-X photon yield over pressures from about 2X 10-a to 0.25 Torr. There are persistent inconsistencies in the results from ran to run (caused, we now think, by ONCI corroding our flow meter) thai, prevent us from presenting a figure showing thc pressure dependence. Thc C-X yield at p = 2X 10~ Torr is about 2(4-1)X 10-4. The yield generally increases with pressure (in a few runs we have found a plateau). Benson's group*~ has reported yiehls from BaCI(A-X plus B X ) , C-X, and D-X for this reaction at a pressure of 1.5 Torr. Their C-X yield is 4.8X 10~ , which provides some support for our observed dependence of (I) upon pressure. From the flame of Ca with ONC1 we see elnission from CaCI(A2II X~X and B"X-XeZ). Plates of the spectra show that ~P(A-X)~2.5cO(B-X) at p ~ 5 X 1 0 - z Torr. The total photon yield (A-X plus B-X) at p-.~2X 10-~ Torr is about 8(:t:2)X10 -4. We are again troubled by hlcon-
957
sistencies in detelzninations of the pressure dependence, but the total ~I, generally increases with pressure. I t is premature to speculate oil a possible reaction mechanism that could account for such behavior. General Comments
Photon yield measurements and simple modeling have been possible in two flame systems described here because one can (a) identify with some confidence the chemistry, the relevant electronic states, and the probable main features of the mechanism; and (b) make simultaneous measuremegts of the total reaction rate and the photon flux. Extension of the methodology to nmrc conventional flame systems may be quite difficult. The present work underscores somc of the mechanistic features that will have to be considered, such as electronic branching in elementary steps and elect,ronic-state transfer, in addition to the more obvious processes of radiativc relaxation and quenching.
Appendix Derivation of the Expression for the BaO(A-X) Photon Yield from the Reaction of Ba with N~O or NO2
Assume the mechanism 1,2,3
Bad-N~O (or NO2) --* BaO(X, a, or A) d-~:~ (or NO) where the branching ratios, or probabilities, are P1 for X, P,~ for a, and P3 for A. 4
a+M-->A+M,
electronic state transfer
a----)X+Ap 6
a----~x+hv
radiation
7
A - + X + hv 8
A+M--~X+M,
quenching of A
The probability of prr
an A - X photon
958 from BaO(A) is
E L E M E N T A R Y REACTIONS REFERENCES
1. GAX~ON,A. G. AND WOI,VHARE,H. G.: Prec. R. See. Lend. A20I, 570 (1950). 2. KONDRATIEV, V. N.: Spectroscopic Study of Chemical Gas Reactions, Acad. Sci. U.S.S.R., The probability of transforming a to A is 1944; as cited in ~i~ONDRATIEV~V. N.: Chemical Kinetics of Gas Reactions, p. 673, Pergamon, 1964. 3. CLYN~, M. A. A. A~o TnRUSK, B. A.: Ninth SymposiRm (International) on Combustion, p. Thus the total probability of producing an 177, Academic Press, 1963. A - X photon as a consequence of the initial reac4. CLX~E, M. A. A. AND COXON, J. A.: Chem. tion event (i.e., the photon yield) is Commun. 1966, 285. 5. HxI~TV~u), C. J. AND TnRUSR, B. A.: Prec. R. See. Lend. A295, 380 (1966). 6. CLOI~G~, P. N. A N D TRnus~L B. A.: Trans. Faraday Soc. 63, 915 (1967). +~,)~[~/(k~+ksM)]. 7. OBENAUF, R. H., Hsu, C. J., A~'D PALMER, H. B.: J. Chem. Phys. 57, 5607 (1972) and erratum, = [1/(l+ksM/kT)~(P~+ P.{ 1/[1 J. Chem. Phys. 58, 2674 (1973). + (k~+~)/k~i~}) 8. OBENAIFF~1~. H., Hsu, C. J., AND PALMER, H. B.: Chem. Phys. Lett. 17, 455 (1972). 9. OBENAUFI R. H., HSU, C. J., AND PALMER, H. Transport or mixing rates have no influence on B.: J. Chem. Phys. 58, 4693 (1973). this expression, except as they m a y affect tile 10. OBENAUF, R. H., HsIJ, C. J., AND PALMER, H. nature of M. Both k4 and ks could be functions B.: Combustion Inslitule European Symposium of the nature of species M. The fact that there 1973, p. 4l, Academic Press, 1973. appears experimentally to be a smooth transition 11. HEy, C. J., KRVGU, W. D., AND PALMER,H. B.: from low-pressure data, taken where M is mainly J. Chem. Phys. 60, 5118 (1974). BR, BaO, a~td some Ar to higher-pressure data 12. Hsw, C. J., KR~IC~, W. D., PAI,MER, H. B., where M is mainly Ar, suggests that k, is at most OnE~X'AUF, R. H., ANn ATEN, C. F.: J. Moh weakly dependent upon the nature of M. Quench~ Spectrosc., 53, 273 (1974). Lag (ks) is only very significant at pressures above 13. OTTINGP.X,C. Ah'D EARS, R. N.: Chem. Phys. 1 Torr. In experiments in t h a t region, M has Lett. 5, 243 (1970). been mainly Ar. 14. Jo:,rA~, C. D., ZARFo R. N., AND OTTINO~a, OH.: One of tile most important features of the J. Chem. Phys. 56, 263 (1972). expression for 9 is t h a t it follows entirely from 15. ECKSTROM, D. J., EDELSTEIN, S. A., ANn BENconsiderations of probabilities. No steady-state soN, S. W.: J. Chem. Phys. 60, 2930 (1974). assumptions are introduced. I t turns out that one 16. Jo~rEs, C. R. ANn BaolnA, H. P.: J. Chem. obtains the same expression ff one assumes t t ~ t Phys. 59, 6877 (1973) mid 60, 4369 (1974). a and A aa'e in steady states; but that is not iT. FIv~LD, R. W., Jowws, C. R., A~D BROIDA~ H. necessary. P. : J. Chem. Phys. 60, 4377 (1974). I t rc~y be useful to note t h a t at mIy pressures 18. The probable role of the a~II state in the mechabove beam conditions, measurements in these anism was fu's~ suggested to us by R. W. Field of reaction systems are Laevitably made on a difthe Quantum Institute, Univ. of California, fusion flame. The total reaction cross section in Santa Barbara. the B a + N 2 0 reaction is close to gas-khletic, while the cross section for Baq-NO~ greatly 19. MICnELS, H.: United Aircraft Research Laboratories, E. Hartford, Connecticut, unpublished. exceeds the gas kinetic value. For such reactions, it is impossible to mix reactants before they 20. FIaT,D, R. W.: J. Chem. Phys. 60, 2400 (1974). A. A~n ZAnS,, R. N.: J. Chem. Phys. react, no m a t t e r how vigorously the system is 21. Sr stirred. In this Appendix, we h a v e shown thal; GO, 5120 (1974). measurements on such systems m a y not be 22. JOHNSOn, S. E.: J. Chem. Phys. 56, 149 (1972). seriously distorted by non-uniformities in com- 23. DAGDIGIAN,P. J., CRUSE, It. W., AND ZAR~, R. N.: J. Chem. Phys. 60, 2330 (1974). position.
CHEMILUMINESCENT SPECTRA
959
COMMENTS L. F. Phillips, University of Canterbury, New Zea/and. Has ozone been used as an oxidant? (Presumably it should also populate the triplet, as nitrous oxide is believed to, unlike nitrogen dioxide.)
Authors' Reply. We are preparing to make yield measurements with 03. The results may shed some light on the spin-conservation arguments, regarding the nature and distribution of product states. Zam and Schultz have recently studied the emission from Ba~-Oa in a beam system. Interestingly, they find what appears to be the same ma~y-line emission that was
previously observed in Ba-[-N20 but not in Ba-bNO~.
A. Fontijn, Aerochvm, USA. There is another precedent for the formation of an emitting singlet-state molecule by colhsion from a molecule in a triplet state. We folmd evidence (J. Chem. Phys., 15 December 1973) t h a t such a mechanism is responsible for most of the CO fourth positive emission in the O/C2H~ reaction. Slanger and Black have directly demonstrated the occurrence of such "cross-relaxation" processes in CO. The selective V-R population resulting from cross-relaxation is of com'se an attractive feature for chemical laser candidate reaction systems.
951
952
ELEMENTARY ltEACTIONS +
~uuP
FI~. 1. (a) Low-pre~sure reactor for metal-oxidant flames. (b) System for measurement of photon emission from low-pressure flames. earth metals in the gas phase and that do not have low-lying electronic states to complicate the emission or the electronic state distribution.
Apparatus and Measurements The apparatus used is shown in Fig. 1. Diffusion flames are formed in a quartz-windowed reactor (Fig. 1) made of Pyrex glass. Metal is vaporized from an alumina crucible surrounded by az~ electric resistance heater held at about ll00~ The oxidant enters at room temperature through inlmt nozzle A, at a sufficiently slow flow rate that the metal vapor is clearly in excess (this can be seen by eye, from the distribution of the emission and by dcposition of metal on the reactor waft). The input nozzle is about 5 cm above the vaporizer. The opening iu the tip is about 1 mm in diameter. The oxidant flow rate is measured~ since it is a measure of the total reaction rate (all oxidant is consumed by the excess metal, the flux of which is calculated from the vapor pressure to be typically 100 times the oxidant flux). Inert gas can be added with the oxidant, through input B, or next to the quartz window. Flame spectra are recorded with an f/6.3 plane-grating speetrograt)h (20 ~ / m m in the first order). The light flux is measured as indicated in Fig. lb. The photomultiplier (RCA 931A, S-4 response) is calibrated for response to light flux at a chosen wavelength within the spectral region covered by the emission, using an interterence filter, and then the measured flux is corrected by folding in the observed (on plates) wavelength distribution of the emission and the sensitivity curve of the PMT. A tungsten stripfilament lamp, brightness temperature measured with an L&N optical i)yrometer, is the calibra-
tion source. Light from the flame passes through a 45 ~ sector chopper, then through a 1 cin diameter slit to the PMT, from which the output signal goes to a lock-in amplifier and recorder. The referenc~ signal for the lock-in is provided by a photoresistor on the chopping wheel. The emission received by the PMT is treated as ff it issued from a point souree~ for purposes of fommlating the geometric multiplying factor that relates the measured light flux to the total. The assumption is reasonably good; most of the emission at pressures above about ]X 10-3 Torr can be seen (by eye and from photographs) to issue from the spatial region within 1 cm of tile nozzle, while the PMT is 36.5 em from the nozzle. There is no lefts in the optical system. The photon yield is defined as the rate of photon emission divided by the rate of chemical reaction, i.e., by the rate of inflow of oxidant into the reactor. Spectra of the emission Mways are taken before the flux measurements in oMer to identify the emitting species and to assess the distribution of emitted intensity as a function of wavelength. This permits (a) correction of the total photon flux to take into accmmt the variation of photomultiplier sensitivity with wavelength; and (b) determination of tim relative contributions of various states (electronic or vibrational) when more than one state contributes emission and when the contributions are separable. From the calibrations, the geometry, and the oxidant flow rate, combined with the recorded PMT signal, the photon yield, 9 (photons emitted per molecule of oxidant consumed) is obtained:
~= SVG/F, where S = corrected PMT sensitivity (photons counted/see/volt output), V= measured PMT
C H E M I L U M I N E S C E N T SPECTRA
953
TABLE I Summary of present observatlotrs on chemilumineseent emission from flames of alkaline-earth vapors with several oxidants ~ietal
Oxidant
Spectra observed
Photon yield (q~)
Ba
O2
BaO (AtZ-Xtz) plus new system assigned to BaO ( A ~ I I - X ~ ) .
Not measured. Qualitatively observed to increase with increasing pressure of added m'gon.
Ba
N20
Extensive emission from BaO ( A - X ) and ( A ' - X ) . Analysis of A ' - X systern carried out on this spectrum. A - X heads replaced by many*line spectrum at very low pressure.
Measured as function of pressure (using Ar), from 4X10 -3 to 0.2 Torr. 4~ irmreases from 2X10 a to 2.5X 10 -2 over the range.
Ba
NO2
Same ~s Ba+O~, except A - X intensity distribution shifted toward the red.
Measured from 2 X10 -3 to 0.1 Torr. 4~ increases from 1.5X10 ~ to 1 X 10-~ over the range.
Ba
ONCI
BaC1 (C~H-X2z). A - X and B - X not observed (in near Jr) but reported by others to be present. TM
9 (C-X) ~ 2 X 1 0 4 at p = 2 X l O -~ Torr. Into'eases wit,h pressure bill details not established.
Ba
ONBr
BaBr ( ~ I I - X 2 z ) . A - X and B X not known; probab]y in n e w ir.
(o(C X) ~ 3 X I 0 -~ at p ~ 2 X l 0 -a Torr. Not yes studied as function of pressure.
Ca
ONC1
CaC1 (A~II-X2Y,) and (B~Z--X2Z).
r
Ca
ONBr
CaBr (A:ffI-X2Z) mid (B2~-X=~).
No 4~ measurements. Plates show that ( A - X ) >>~ ( B - X ) .
Sr
ONBr
SrBr (A~H-X~Z) and (B~-X2Z).
9 ( A - X ) ~7q~(B-X). Total r 10-~ at p ~ 4 X 10-~ Torr. Not studied as function of pressure.
output voltage, G = geometric factor for light collection from the flame, F = oxidant flow rate (mole/see).
Results and Discussion A s u m m a r y of the experimental results obtained in the present work is presented in Table I. The systems studied in m o s t detail have been Ba-}-N~O ( + A r ) , B a + N O ~ ( + A r ) , and B a or C a + O N C 1 ( + A t ) . T h e measured (with a bare, 9 uncorrected fine thermocouple) temperatures of these flames are in the range 400~176 indicating that all of the visible emission is chemiluminescent. T h e temperatures are not accurate; however they are in the same range as thug reported by Jones and Broida 16 for the B a + N 2 0
=2.54,(B-X). Total ~ = 8 X 10 -4 at p - 2 X 10-2 Torr. Increases with pressure but details not established.
flame at higher pressm'e. The discussion t h a t follows mainly concerns these three reaction systems. Ba-~-N~O. This system has been studied b y four groups, to our knowledge: Zare's group 1r determined an upper limit (27 ~2) for' the total reaction cross section as studied in beams and observed the ehemilmninescent reaction to be first-order in both B a and N20 between about 10-* and 10-s Torr. Jones and Broidg ~6have detm~fincd the photon yield over the pressure range, 1 32 Torr. Their total photon yield results are includ~l in Fig. 2. T h e y report A - X BaO emission and many-line emission, the latter being important at 1 Tm'r b u t quite small at 24 Tort. Field, et al., a have discussed the prohahle reaction mechanism. Benson's group 15 determined the photon yield
954
ELE:~CIENTARY 100
........
I
........
I
REACTIONS . . . . . . . .
,
. . . . . . . .
I
'
, ' ....
,-, I0 / Ill
>Z 0
1.0
0 "in
0.1 / .,./ 0.001
I
0.01
,
I
0.1
,
,
I
1.0
JI
I0.0
,,,
I00.0
PRESSURE (t0rr) Fro. 2. BaO(A-X) photon yields as functions of pressure. B~+N20: O corrected data, present work; t uncorrected dat% present work; 9 Jones and Broida~6; [] Eekstrom, et al. ~ Ba+NO~: A corrected data, pr6sent work; 9 uncorrected data, present work; [] Jones and Broida. ~' Solid curves are the results of mectmnistic modeling. Dashed curves show the falloff behavior attributed to mean free path effects. at 2.2 Torr. Their result, shown in Fig. 2, agrees fairly well (within a factor of 2) with Broida's. We have studied the spectra and determined the photon 5delds at pressures from 4X 10-4 to 0.2 Torr, with results shown in Fig. 2. The pressurizing gas used was argon (helium gives nearly the same results, but the data are more scattered). Using the photon yields from all laboratories, we have been able to model the reaction over about a 100-fold span in yield and a 3X 10S-fold span in pressure (from 10-4 Torr to 30 Torr). Modeling requires an understanding of the probable roles of the accessible electronic states. TM Michels TM has calculated the potential curves of the XtY,, AIX, and aZrl states of BaO, and Field has calculated RKR potentials for the X, A, a, and A'~H states. 2~Their results agree quite well. The electronic spectra observed will be discussed briefly before developing the mechanism. (i) At pressures of 2-4X 10-3 Torr, we find a spectacular many-line spectrum extending from the near uv throughout the visible region. The A - X bands emerge from this spectrum as the pressure rises, and dominate the emission above 2-4X10 -e Torr. We have been able to show u tlmt the many-line spectrum earmot be due to a2H-XiZ. However, it could be due either to
A ' - X or A - X . The fact that A ' - X fie~ls (see below) are visible at p = 4X 10-4 Torr (where the many-fine spectrmn dominates the emission), plus the fact that the many-line emission covers essentially the same wavelength region as the A - X bands seen at higher pressures, suggests that the many-line spectrum probably is A - X emission in which the A state possesses huge rotational excitation. Recent work by Schultz and Zare~ supports this tentative conclusion. Thus the emission at all pressures probably is dominated by A - X emission. (ii) At all pressures covered (2X10-L0.2 Torr), we observe two weak progressions of single-headed bands in the violet and near uv. With the aid of a study by Field 2~ of perturbations in the A - X system, we have analyzed these bands ~ (which are also seen with the oxidants NO~ and 02, but are not as extensive as with N20). They are assiglmd ~ to A'III-X*Y,. They contribute very tittle to the total emission at any pressure. (iii) A - X band heads first become identifiable against the ninny-line spectrum at ~ 2 X 1 0 -2 Torr. They are almost free of the many-line spectrmn at 8X 10-2 Tort. At 0.2 Tort, A - X heads are quite well developed and the many-fine
CHE.~ILUMINESCENT SPECTRA spectrum is no longer observed on our plates. The rotational fine structure appears to be essentially thermal. The observed increase of the A - X phot.on yield with pressure can be explah~ed if most of the BaO produced by the biimolecular process is in an electronic state that can be transformed to AiZ, by collision, This process was first suggested by Field et 02.iT'is The intermediate electronic state is likely to be the aZH, according to FieM. Although this state has not been directly observed, our spectroscopic support for Field's calculation of the location of the AnH state prorides further confidence in the essential correctness of his~~and Michels 'm calculated location of the a '~II state, and of its likely role in the reaction between Ba and N~O. Our mechanistic niodel is based on this important hypothesis. The model consists of eight elementary steps. Three are atom-exchange reactions populating the X, A, and a states:
955
since competition between step 4 and steps 5 and 6 accounts in large part for the pressure dependence. The A - X photon yield can be derived by considering the probabilities of the various steps in the mechanism, as shown in the Appendix (where it is also shown t h a t photon yields can be determined from measurements on diffusion flames). The expression for the A - X photon yield is
q~A-x= { P3+ P#[-I+ (kh+ k6)/taM]} { i/El
+ (ksM/~)]}
where P~ and P~ are the probabilities of steps 3 and 2, respectively; e.g., P3 is the probability that a reactive encomlter between N20 and Ba will produce BaO(A~2;). This is the branching ratio for the A state. This expression does not take into account the expected falloff in the experimental value of the photon yield at low pressures that will occur because of a mean-free-path effect. That is, a Ba-~- NeO---~BaO(XIE) -~-N~ (1) photon cannot be observed unless N20 undergoes a reactive collision with Ba before leaving the field of view (,~2.5 cm radius). We write ~a~p= Ba+N20---~BaO(a3Ii)+ N2 (2) 4~(1-- W), where ~p~p,is the apparent yield defined by (I,~pp=(Light flux)/(Oxldant flow rate), 9 is B a + N'20---~BaO(ALE)+ N,~ (37 the true yield, and (l-W) is the probability t h a t the oxidant (N~O, here) will sustain a reactive One is the crucial a-A collisional transformation: collision as it passes through the observed region (note that if it does trot, it will still react eventuBaO(a~ll)+ M--*BaO (A~E)+ M (4) Mly, but mainly with Ba on the vessel wall). A one-dimensional treatment of W, which is probably adequate for our purposes, gives it as W = Three are radiative processes: exp(--x/L), where x is the distance traveled and L is the mean free path for reactive collisions. If BaO (a'~II)--~Ba0 (X~N)+ hv (5) the reactive cross section is much less than the elastic collision cross section, the correction BaO (a'~H)--+BaO(z*?)+ h~, (6) factor (l-W) should be replaced by a factor derived from considerations of diffusion. HowBaO(AW,)--~BaO(X~Z)+tw (7) ever, the work in Zare's laboratorylaaa suggests that most reactions of the type under study here have reactive cross sections of the same order as, and one is quenching of the A state: or larger than, elastic collision cross sections. For B a + N 2 0 , we have u ~ d a reactive cross secBaO(A~Z )+M--*BaO (X~Z) + M (8) tion of 25 .~2, slightly below the upper limit figure obtained by Jonah, et al., 14 to correct the yiekls. The model is obviously oversimplified. Thus it The corrected results are shown by open circles omits processes such as the back reaction of step in Fig. 2. Corrections at pressures above 2X 10-: 4~direct production of the Anti star% the produc- Torr are negligible. The uncorrected data are tion of AnH by coilisional transformation of aaII, also shown to illustrate the mean free path effect. There will also be a mean free path or diffusion production of A~Z by transfer from high vibrational levels of the ground state, and quenching effect on the electronic-state transfer, step 4. An of a3H. Several of these processes may ultimately estimate of this effect shows that it will only be prove to be significant. significant in our observations if the aSH state is In the radiative steps we include an allowed metastatic, i.e., if the sum of ks and k6 is less transition from the aSH to a lower triplet state than about 104 see-~. Since this is unlikely, the (presumably aZ)~o This is an important process, effect is not hmluded in the fitting procedure.
9,56
ELEMENTARY REACTIONS
Lt ealcnl~ti3x~ the mean free path effect, we have considered ordy the case of N~0 moving through Ba vapor. The (calculated) flux of Ba from the crucible is at least 100 times the (measured) flow rate of N~O, so production of Ban and N~ produces little change in the composition. Ful%hermore, addition of argon (at the end of the reactor, Fig. la) to increase the pressure seems to confine the Ba vapor more and more closely to the central region of the reactor (as indicated by the extent of wall deposition of Ba). Thns the t~ressurizing argon may I~o~extensively dilute the Ba, but rather confine it, in which ease N.~O issuing from the nozzle encounters mainly Ba atoms over most of the 2.5-era-radius observation region. The four parameters in the phofxm-yield expression ~Pa, P,.,, (k~+k~)/ko, and ks/kT] have been determined from the corrected yield data by a trial-and-error procedure. The data at low pressures (Fig. 2) show that Pa must lie between about 3X10 -~ and 5X10 -'~ if, as required by Zare's beam observations,T M the pressm'e dependence of 9 is to be very weak at pressures below about lX10 ~ Torr. Examination of the high-pressure region showed, in trial calculations, that the fa]loff duc to quenching would be best reproduced if P: were as large as possible: i.e., P2~-~I. Using this value (actually P~=0.996) and Pa=4X10 a, (k~+k~)/k~ has been determined by finding the best fit (judged by eye) to the data in the low-pressure region (up to ca. 0.1 Torr), where quenching is insignificant. The value of ks/~ has been routed by requiring r f~) equal 0.25 at p= 10 Torr (here we ascribe all of the emission observed by Jones and Broida~ to A-X). The results are: P a - 4 X 1 0 - a ; P~=0.996; (Pv-~O) ; (ka+ka)/k4-1.2X 10-7 mole/cm~; k~/~= 7.1X 10~ eroS/mole. The fit is represented by the solid curve in Fig. 2. The dashed curve shows the falloff resulting from the mean free path effect at low pressures. Uncertainties in the above parameters are due to the limite~ions (ff the model, to unccrtainties in the experimental results, and to the necessity of making some compromise in ordcr to fit all the available data reasonably wen. I t is difficult to estimate the total uncertainty. We believe that P3 is probably correct to within =1=25percent; P~ (which cannot exceed unity) is not likely to be any smaller than about 0.75; and P~ has the largest relative error, since its upper lhnlt thus appears to bc about 0.25. The branching ratios Pz, P2, and Pt imply that the three corresponding electronic states (A, a, and X) are populated by the elementary reaction between Ba and N~O in the approximate prob-
ability ratios 4:996:0. Thus it appears that nearly all of the BaO is produced in the aSII state, which supports the postulate of Field et al., 17 and is a very interesting result. From ~=3X106 sec-1, we obtain ks~2Xl@ s eroS/mole sec, implying that quenching of the A state occurs on about one collision out of every ten. The result agrees quite well with the quenching cross sections ( ~ 1 2 .~2) obtained by Johns o n , 22
Estimation of k4 is much less certain because neither k~ nor ke is known. The a-x transition is allowed, but probably lies in the infrared, so ka may be considerably smaller than k7 (3X108 se~l). ~ If the arguments of Field, et al., 17 are correct, ks+k~ may be of the order of 10~ sec-~. This would imply k4~10 ~2 em3/mole see ~nd indicate that the a - A transformation occurs in ab(mt 0.5 percent of a - M collisions in this system. Ba+NO2. This flame does not emit a manyline spectrum. Zarc's group13'14 did not observe one, nor did Jones and Broida, TM nor have we. The intensity distribution of the A - X emission is strongly shifted toward the red, in accord with the much lower cxothermicity of the overall reaction ("overall" because it is complex). The A ' - X progression is weak, and the v' values do not go as high as for Ba+N~O. Actually, the exnthermicity of Ba+N0~--~BaO+NO is insufficient to populate even those vibrational levels of O~e A' state that are seen; and we also see~even at 2X 10-~ Torr--weak eulission from vibratiomd levels of the A state that lie beyond the available exothermieity. Thus there ms}" be Some energy-pooling or energy transfer processes, as yet unidentified, that are responsible. However, tlm processes clearly arc not very important with respect to the A - X photon yield. For Ba+NOe we have assmned the same model as used for Ba+N20, retaining the same rate constant for quenching of the A state b u t obtaining the other parameters by trial-and-error fitting of the data. The apparent photon yields at low pressures were corrected to the true values using a reactive collision cross section of 165 .~ from the work of Jonah, et al34 Corrections at pressures above 4X 10-'~ Torr are negligible. The results are :/'3= 1.7X 10-3; P2 = 0.059 ; (P1 = 0.94) ; (k~+k6)/k4= 1.2X 10 s. The fit is shown in Fig. 2. The two points at higher pressures than ours were reported by Jones and Broida) ~ Their result at p = 1 Tort seems to be incompatible with our experimental data and we have not used it hr tile curve-fitting. Their point at 8 Torr is in the middle of their pressure range and should be the more reliable of t,he two. The values of P'z and of (k:~+ke)/k4 depend rather strongly on the high-pressure point. If the point at 1 Torr is in
CHEMILUMINESCENT SPECTRA fact con~ct, then the model assumed here must be severely inadcquate. The A-state branching ratio obtained is quite similar to that for Ba+N~O, but the ratio for the aslI state is much lower; thus it appears that in the Ba+NO2 reaction, more than 90 percent of the product BaO is created in the ground state. The value of (k~d-k6)/k4 gives a value of k4 equal to N10~s cmS/mole sec if (/~.~+k~)~105 s e ~ ~. This would imply transformation of a into A on roughly every twentieth a-M collision. The energy lcvcls of the a state that are populated by the B a + N 0 2 reaction are relatively low-lying because of the lower exothermicity. Field, st al.,17 have pointed out that the electronic transfer from several of the lower levels of the a state into the A state should occur with cross sections that are of the order of 88189of gas-kinetic, because of strong mutual perturbations. The trend in k4 from B a + N 2 0 to Ba+NO~ thus seems to lse in the right dil'cction. The absolute magnitude of k4 remains uncertain. Although our B a + N 0 2 data are more precise than those for Ba+NeO, they may not be as accurate; the undertainty may be about 4-50%. The reason is that the correction for the lack of photomultipller sensitivity ial the far red region is nmch larger and less certain than ill the case of Ba+X:O. A-X emission from Ba+NO2 can be followed on plates all the way to about 8700 :X., where the plate sensitivity drops sharply. Presumably it continues further; we have assumed that tim contribution will be minor, but experiments should be extended well into the ir for this system (and for others). Ba and Ca-{-ONCI. From the flame of Ba with ONC1 we have observed radiation enly from the C~2H-~VaEtransition of BaCi. We have made many measurements of the C-X photon yield over pressures from about 2X 10-a to 0.25 Torr. There are persistent inconsistencies in the results from ran to run (caused, we now think, by ONCI corroding our flow meter) thai, prevent us from presenting a figure showing thc pressure dependence. Thc C-X yield at p = 2X 10~ Torr is about 2(4-1)X 10-4. The yield generally increases with pressure (in a few runs we have found a plateau). Benson's group*~ has reported yiehls from BaCI(A-X plus B X ) , C-X, and D-X for this reaction at a pressure of 1.5 Torr. Their C-X yield is 4.8X 10~ , which provides some support for our observed dependence of (I) upon pressure. From the flame of Ca with ONC1 we see elnission from CaCI(A2II X~X and B"X-XeZ). Plates of the spectra show that ~P(A-X)~2.5cO(B-X) at p ~ 5 X 1 0 - z Torr. The total photon yield (A-X plus B-X) at p-.~2X 10-~ Torr is about 8(:t:2)X10 -4. We are again troubled by hlcon-
957
sistencies in detelzninations of the pressure dependence, but the total ~I, generally increases with pressure. I t is premature to speculate oil a possible reaction mechanism that could account for such behavior. General Comments
Photon yield measurements and simple modeling have been possible in two flame systems described here because one can (a) identify with some confidence the chemistry, the relevant electronic states, and the probable main features of the mechanism; and (b) make simultaneous measuremegts of the total reaction rate and the photon flux. Extension of the methodology to nmrc conventional flame systems may be quite difficult. The present work underscores somc of the mechanistic features that will have to be considered, such as electronic branching in elementary steps and elect,ronic-state transfer, in addition to the more obvious processes of radiativc relaxation and quenching.
Appendix Derivation of the Expression for the BaO(A-X) Photon Yield from the Reaction of Ba with N~O or NO2
Assume the mechanism 1,2,3
Bad-N~O (or NO2) --* BaO(X, a, or A) d-~:~ (or NO) where the branching ratios, or probabilities, are P1 for X, P,~ for a, and P3 for A. 4
a+M-->A+M,
electronic state transfer
a----)X+Ap 6
a----~x+hv
radiation
7
A - + X + hv 8
A+M--~X+M,
quenching of A
The probability of prr
an A - X photon
958 from BaO(A) is
E L E M E N T A R Y REACTIONS REFERENCES
1. GAX~ON,A. G. AND WOI,VHARE,H. G.: Prec. R. See. Lend. A20I, 570 (1950). 2. KONDRATIEV, V. N.: Spectroscopic Study of Chemical Gas Reactions, Acad. Sci. U.S.S.R., The probability of transforming a to A is 1944; as cited in ~i~ONDRATIEV~V. N.: Chemical Kinetics of Gas Reactions, p. 673, Pergamon, 1964. 3. CLYN~, M. A. A. A~o TnRUSK, B. A.: Ninth SymposiRm (International) on Combustion, p. Thus the total probability of producing an 177, Academic Press, 1963. A - X photon as a consequence of the initial reac4. CLX~E, M. A. A. AND COXON, J. A.: Chem. tion event (i.e., the photon yield) is Commun. 1966, 285. 5. HxI~TV~u), C. J. AND TnRUSR, B. A.: Prec. R. See. Lend. A295, 380 (1966). 6. CLOI~G~, P. N. A N D TRnus~L B. A.: Trans. Faraday Soc. 63, 915 (1967). +~,)~[~/(k~+ksM)]. 7. OBENAUF, R. H., Hsu, C. J., A~'D PALMER, H. B.: J. Chem. Phys. 57, 5607 (1972) and erratum, = [1/(l+ksM/kT)~(P~+ P.{ 1/[1 J. Chem. Phys. 58, 2674 (1973). + (k~+~)/k~i~}) 8. OBENAIFF~1~. H., Hsu, C. J., AND PALMER, H. B.: Chem. Phys. Lett. 17, 455 (1972). 9. OBENAUFI R. H., HSU, C. J., AND PALMER, H. Transport or mixing rates have no influence on B.: J. Chem. Phys. 58, 4693 (1973). this expression, except as they m a y affect tile 10. OBENAUF, R. H., HsIJ, C. J., AND PALMER, H. nature of M. Both k4 and ks could be functions B.: Combustion Inslitule European Symposium of the nature of species M. The fact that there 1973, p. 4l, Academic Press, 1973. appears experimentally to be a smooth transition 11. HEy, C. J., KRVGU, W. D., AND PALMER,H. B.: from low-pressure data, taken where M is mainly J. Chem. Phys. 60, 5118 (1974). BR, BaO, a~td some Ar to higher-pressure data 12. Hsw, C. J., KR~IC~, W. D., PAI,MER, H. B., where M is mainly Ar, suggests that k, is at most OnE~X'AUF, R. H., ANn ATEN, C. F.: J. Moh weakly dependent upon the nature of M. Quench~ Spectrosc., 53, 273 (1974). Lag (ks) is only very significant at pressures above 13. OTTINGP.X,C. Ah'D EARS, R. N.: Chem. Phys. 1 Torr. In experiments in t h a t region, M has Lett. 5, 243 (1970). been mainly Ar. 14. Jo:,rA~, C. D., ZARFo R. N., AND OTTINO~a, OH.: One of tile most important features of the J. Chem. Phys. 56, 263 (1972). expression for 9 is t h a t it follows entirely from 15. ECKSTROM, D. J., EDELSTEIN, S. A., ANn BENconsiderations of probabilities. No steady-state soN, S. W.: J. Chem. Phys. 60, 2930 (1974). assumptions are introduced. I t turns out that one 16. Jo~rEs, C. R. ANn BaolnA, H. P.: J. Chem. obtains the same expression ff one assumes t t ~ t Phys. 59, 6877 (1973) mid 60, 4369 (1974). a and A aa'e in steady states; but that is not iT. FIv~LD, R. W., Jowws, C. R., A~D BROIDA~ H. necessary. P. : J. Chem. Phys. 60, 4377 (1974). I t rc~y be useful to note t h a t at mIy pressures 18. The probable role of the a~II state in the mechabove beam conditions, measurements in these anism was fu's~ suggested to us by R. W. Field of reaction systems are Laevitably made on a difthe Quantum Institute, Univ. of California, fusion flame. The total reaction cross section in Santa Barbara. the B a + N 2 0 reaction is close to gas-khletic, while the cross section for Baq-NO~ greatly 19. MICnELS, H.: United Aircraft Research Laboratories, E. Hartford, Connecticut, unpublished. exceeds the gas kinetic value. For such reactions, it is impossible to mix reactants before they 20. FIaT,D, R. W.: J. Chem. Phys. 60, 2400 (1974). A. A~n ZAnS,, R. N.: J. Chem. Phys. react, no m a t t e r how vigorously the system is 21. Sr stirred. In this Appendix, we h a v e shown thal; GO, 5120 (1974). measurements on such systems m a y not be 22. JOHNSOn, S. E.: J. Chem. Phys. 56, 149 (1972). seriously distorted by non-uniformities in com- 23. DAGDIGIAN,P. J., CRUSE, It. W., AND ZAR~, R. N.: J. Chem. Phys. 60, 2330 (1974). position.
CHEMILUMINESCENT SPECTRA
959
COMMENTS L. F. Phillips, University of Canterbury, New Zea/and. Has ozone been used as an oxidant? (Presumably it should also populate the triplet, as nitrous oxide is believed to, unlike nitrogen dioxide.)
Authors' Reply. We are preparing to make yield measurements with 03. The results may shed some light on the spin-conservation arguments, regarding the nature and distribution of product states. Zam and Schultz have recently studied the emission from Ba~-Oa in a beam system. Interestingly, they find what appears to be the same ma~y-line emission that was
previously observed in Ba-[-N20 but not in Ba-bNO~.
A. Fontijn, Aerochvm, USA. There is another precedent for the formation of an emitting singlet-state molecule by colhsion from a molecule in a triplet state. We folmd evidence (J. Chem. Phys., 15 December 1973) t h a t such a mechanism is responsible for most of the CO fourth positive emission in the O/C2H~ reaction. Slanger and Black have directly demonstrated the occurrence of such "cross-relaxation" processes in CO. The selective V-R population resulting from cross-relaxation is of com'se an attractive feature for chemical laser candidate reaction systems.