Concentration profiles for radical species in a methane-oxygen-argon flame

COMBUS]~ION AIVD FLAME 21, 371-382 fl973)

371

Concentration Profiles for Radical Species in a Methane-Oxygen-Argon [ l,:tm CHARLES P. LAZZARA, JOAN C. BIORDI. and JOHN F. PAPP Fires a~ld Explosio~ts tlro~lp, Pittsburgh Mining and Safety Research Center, h'ureau of Mines'. Pittsburgh. Pa.

Concentration profile~ tbrougb Ibe reaction zone of ~ h,w-pressure. ~lighlly lean mt.tl':~ne-oxygenargon flame bare been measured, hi sitt¢, for the following unstable species: oxygen altmls, hydrogen atoms, hydroxyl radicals, metllyl radicals, and formyl radicals. The conditions of me~ nmment, means of identification, and method for estimating lhe concentrations of tile ratiicals are dtscribed. The ohserved maximum mole fractions are 2.3 X 10 -2 lbr H, 1.1 × 10 -2 for art, and 0.8 × 10 -2 for ('), Ibe maxima occurring in the recombination zone for these species. 7lie ma~dmum values are in excess of equilibrium ,:ortcentratiota by lactors of ~10~103. Methyl and formyi ~dicals have maximum mole . trac DOnSIn ' Ic reaction lone of z.2 × 0-3 and 6 × O s , l espec lye y. IS,qulll~rmm canstants, calculated from the appropriate measurl.d species eoncentratitms for the fast~.'sIreactions of the I~I--CO--Q2 I'~ame,which is tb..~last slage of !his Ilydro~a~bon flame, suggesls that these reactions are essentially balanced in this part of lhe flame.

Introduction The past fifteen years have produced, principally via flame structure studies, significant advance. ment in our understanding of the reactions occur. ring in hydrocarbon flames [ I ] . Nevertheless, these systems are not well enough cbaracterized to permit straightforward answers to some important practical questions about combustion, e.g., re. garding the mechanisms by which the so-called chemical ijflfibitors act to retard propagation. This is due in part to the experimental difficulIies encountered in determining, in Silll, tile concet~. tration histories of the species responsible for tile chain reaction~ tllat sustain flame propagation. Determination of species concentration profiles for the, presumably, most abund,~ns radicals in methane flames (O, OH, H) Itas beeu limited to either a complete profile for a single species (e.g., OH, via specific spectroscopic techniques [2] ) or to determi~lations of relative conceutrations in a limited region of the flame, usually the burnt gas region [3"1. Only indications of tile presence of methyl radicals have been reported [4, 5] and no complete profile of HCO has been reported. Peeters and Mahnen [lb] have presented impressive profile data for all of the species, with

upper limits ff)r tile concentration of HCO reported, but relatively little in the way of experimental detail and procedure is gen ~rally available. Reported here are species concentration profiles ohtained for O, OH, H, and CH 3 through the reaction zone of a low pressure C H , ~ - - O , - - A r flame and evidence for the HCO radical together with its profile. Apparatus F:tgure 1 is a schematic diagram of tile molecular beam-mass spectrometer apparatus, which has been described in considerable detail elsewhere [6]. Briefiy,'CH4 (9.6%)--O,. (21.3%)--At (69.1%) flames are burned at 32 To,rr on a cooled, porous plug fiat-flame burner. The vacuum burner housing interfaces witll a differentially pumped quadrupole naass spectrometer (Extranuclear Labs EMBA I!) ~ia a conical quarrz probe having an ortfi:e between 75 ,u and 1:25 ~t at its tip. Cones of our own construction fraying overall outside angles between 38 ° and 70 ° were used. The g ~ entering tire orifice expands rapidly~ the flow chan~ng it, nature, from tile slip-transit ion region (0.02 < Knudsen number <~0.2 for the range of temperature and Copyright © 1973 ~y Thz Corabustion Institute Published by Americar~ Elsevier Publishing Company, Inc.

CHAR.LES P. LAZZARA, JOAN C. BIORDI, and JOHN F. PAPP

372

_ _

Mau

(Ody~ f ~ ] [,l............ Jl . . . . . . . . . . . . [ l ~ _ _ i

45,?

Fig. 1. Molecularbeam-mass spectrometer and low pressure flame system. Dimensionsfor a 70* cone are shown. Skimmer tip to cone tip = 7.6; skimmer t~p to ionizer = 9,4; skimmer Lip din. = 0.25; cone tip din. = 75 ,~. All dim,r'~sionsare in centimeters,

orifices used in the ~ m e ) to free molecular flow. "Ilze central core of the flow is "skimmed" by a second cone, and the resultant molecular beam is d~reeted along the axis o f the .:onize~'of the mass spectrometer. The beam is mudui~ed by a toothed wheel upstream of the ioff,ze~, and phasesensitive detection permits disdacti0.n between fire beam and background signals. The ll~Lsershown in Fig. 1 i~ used for alignment of the system only. Ir~ th~s system the probe is fixed, and the burner moves in a verti=zl dir,.'ction to obt~,in composition profiles along a coordinate (called Z in the figures) perpendicular to the flame sarfaee, The mass spectrometer was calibrated directly fc)r stable species from mixtures of known composition passed through the burner, '~adthout ignition, and aampled in exactly the ~ame manner as with the flame. The method used for determining concentrations of radical species will be described in detail below. R.=sults Stable Species Concentration profiles for the major flame species, CHa, 0 ~ , CO, H~, CO7, and H~ O, were

0.24

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t.I..-~,~ ,~g~.~,u~.o~~o~

'~/v"--"

"~'2o " "

.......

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Z,6URNFJZSU~'~CETO PROBE1riP.I~TANCE,¢m

F~I~.2. Composition profilesfor the major species of a 9.6% CH4-2 ~.3% O2-69.1% At flame. P = ~2 Tort; l.otai flow rate = 3.149 ee (NT]P)/see ,:.In2 oF hutner surface; initial linear flow velocity = 131.5 ¢m see"~ when Tinitial = 293°K; final flame temperature = 18500K; 70° cone.

RADICAL PROFILES IN A CH4--O2--AR FLAME

373

obtained, and typical results are shown in Fig. 2. Procedures for obtaining these profiles as well as detailed discussion of the effect of the probe on the flame have been given elsewhere [6], and this figure is presented to facilitate comparison with the radical profiles. Profiles for the following intermediate stable species were also obtained for the flarr ~: H2CO, C2H6, C2H4, C2H2, CH30H. Except for formaldehyde, the instrument was uot calibrated directly for these species, but relative sensitivity data permit estimated maximum mole fractions of 2X 10-4,4X 10-4,1 X 10-';,2 X 10"4 for C2 H6, C2H4, C2 H2, CHaOH, respectively. ~oo

,

i

.

i

,

Formaldehyae had a mole fraction of 1.4 X I0 -3 at i~s mafimum. AppearancePotentia! Measurements The electron energy distribution in the high efficiency ionizer of the Ex~ranuclear M[as:~ Spectrometer is broader thall that of conventional ion sources. This is due, in part, to the fact that there are no electron beam collimating slits and this results in an electron energy spread due to the potential drop acres:: the flku-aent (about 3 V here), in addition to the usual sources of electron energy inhomogeneity. In principle, one might expect an energy spread at lea~t equivalent to the i

i

~.0

I~0

--i-----r---

io.ooo

II

8.0

IQO

12.0

le,O

L~30

Fig. 3. Ion current vs. electron energy data for masses29 artd 40 in the

flame, The electron energysc~Jehas been correctedaccordingto th,~argon appearancepotential of 15.76 eV [9].

CHARLES P. LAZZARA, JOAN C. BIORDI, and JOHN F. PAPP

374

potential drop across the filament but (and for renstms not well understood by us) tile effective electron energy distribution is, in fact, not that broad. This can be seen by inspection of the argon ionization efficiency curve in Fig. 3. From file second derivative o f the ionization efficiency curve found for helium we have obtained thq; electron euergy distribution function in arbitrary units. It was found to have a half-width of 2eV. Because of this relatively broad elec.'.ron energy ,:listribution, an analytical method w a .a~d to render uniform the criteria for choosing threshold ionization energies. The electron energy distribution difference [7] method lEEr)D] was originally intended to allow observation of the fine structure of ionization efficiency curves and zs~umes that the energy distribution o f the ionizing electrons is of a simple quasi-Maxwell-Boltzmann type. Used on more realistic experimental electron energy distributions, it has been shown that the EEDD mefltod will usualiy only reduce tailing, and make the initial break more visible [8]. This is file spirit in which file method was applied here, and no significance was attached to "fine Stl'UCtUre." Estimates of the appearance potential for the species observed at masres 1, 15, 16, 17, and 29 in the flame were performed using the argon constituent of the flame to calibrate the electron energy scale. Table 1 lists the observed appearance potentials. The limits shown indicate the precision of these TABLE 1 Observed Appearance Potentials for Flame Speeies'a Mass no.

Appearance potential, eV

Assigned to-

1

13.7 ± 0.1

H

2 15 16 17 18 29

15.3 -~0.1 10.2 -~0.3 13.7 • 0.4 13.1 • u.i 12.4 :' 0.1 9.5 ± 0.1

H2 CH3 O OH H20 HCO

Literature b values, eV 13.6 15A. 9.8 13.6 13.2 12.6 <9.8

aAn appearance potential of 15.76 eV for argon was ~.,,ed in the calibration c£ the electron energy scale. bValues quoted are from optical speetros~:opic determinations where a,ai~able [9].

measurements vlfly (two to four determinations were made for each species) and imply nothing about their acct;racy. Aq indication of the accuracy of the m~:asurements is given by the val,es of the appearance potentials obtained r~oth in the flame and "cold") for tile stable specLe!cH2 and H20. For H, O, and OH, the measurements were made at values o f Z / > 0.9 cm; for CE[3 and HCO they 'were made at the value of Z eort'esponding to their observed maxima in the flame. With the exception o f H, in each .ease the ie,a eum,~nt vs. electron energy curves show structur, ~,which, by a simp]e linear extrapolation, are seen to ilave appearance potentials characteristic of the expected interferring peaks to within -+0.5 eV. For H, the concentration of hydrogen arums is nearly equal to that of hydrogen molecules in the region of the flame where the appearance potential was measured. During these measurements, lhe intensities at buff1 masses I and 2 were monitored as a function of electron energy. At 70 eV, sampling Hz - - A t mixtures, we or, serve the intensity at I ainu to be about 1.5% that of 2 amu. Assuming, as a worst ease, that 1.5% is applicable also at lower electron energies, the observed intensity at 2 ainu in the flame is such that, at most, only about 2% of the observed intensity at 1 ainu in the flame could have been derived from H2. Thus it is not surprising that we cannot distinguish structure due to dissociative ionization of H2 in the appearance potential curve for hydrogetl atoms. Figures 3 ~ and 4 are examples of the raw ion current vs. electron energy curves obtained. Figure 3 shows the curve obtained for mass 29, taken at Z = 0.45 cm in the flame, and also the argon curve, which was used to correct the eleetrtm energy sea]re. The appearance potential of riCO '~ from H2CO has been reported variously as 13.0 eV [9] and 12.6 eV [10]. In Fig. 4, the electron energy scale ie uncorrected, and shown are ,Lhe ion current curves fur masses 17 and 18 in the flame at large Z. The appearance potential for OH* from H 2 0 is 18.3 eV [9]. The agreement between observed and literature i In this a,ad all subsequent fignres, the flame eomposilieu, flow :'ate, and temperature are those described in tile legend of 1.'is. 2.

RADICAL PROFILES IN A CHa--Ox---AR FLAME z'2oo

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1

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o o

ioo

02 ELECT~IN

O4

0,6

oe

to

i~

ENElIGY,~ tJamorl~.lt~lI~ok~

Fig. 4. Ionization efficiency curves for masses 17 and 18 in the i~ame at 2' > 0.9 era. The eleetr~an e~ergy scale ts uncorrected. t v~lues of the appearance potential for these species is good. Howe.,~er, some of the observed appearance i?otendals (e.g., for Ha O*) are lower than, ~nstead of higher than the spectroscopic values, which is more usually the ease for electron impact measurements. Tiffs could be due to the choice ,of 1.5.76 eV for the argon app,.~arance pn. tential in the c'-tlibration of the electron energy, scale. The tlt~ureshold we observe for At*, in both the EEDD curves and by linear extrapolation, as in Fig. 3, may be more realistically that due to the 2p~/2 state of the ion rather than the ground state. The appearance potential for Ar+ (2Pt/~) is 15,94 eV [9], and this would inerea.~,e the appearance potentials in Table 1 by 0.18 eV. In general, we regard the appearance potential data as strong, but not exclusive, evidence for the veracity of the radical profiles. Hydroxyl Radical, Hydrogen Atom, and Oxygen Atom The flame profiIes obtained for OH, H, and O are shown in Fig. 5 together with the methane p:rof'de for the probe used. In each case the profile was taken at an actual electron energy of 15.6 eV and the peaks monitored were 17, 1, and 16 an , for OH, H, and O, respectively. In addition to OH, two other fla.rne speeie:~ may

IrWin,, 5. C o n c e n t r a t i o n profiles f o r o x y g e n ate, ms, h y d r o -

gt.n atoms, and hy0.roxyl radicals through the flame. Electron energy = i 5.6 eV, 70 ° co~e. rtormally b.~"expected to contribu'~e to the 17 peak, OH* from fragmentation of H~O and C 13H~ in the re#on where the methane concentration is non-zero. At 15.6 eV, the contribution to rmass 17 from water was determined to be zero from o0servations on water vapor in argon carrier introduced t ~ o u g h the san~pling system at room temperature. No difference was observed in the ratio of intensities of masses 17 and 18 (I: 7/118 ) Cot "cold" water and water in the post flame gases at high electron energies. Assuming that the temp~'~rature independence of the fragmentation pat lern is valid also at low electron energy, then, a, 15.6 eV, no interference at mass 17 from war .~r :s expected. The co ntribution from C ta H,~ is not eliminated by reducing electron energy, since CII~ from methane has an appearance potential of 12.9 eV. In order to correct for this interference, the ratio I t 7/11 s was determined at 1 5 £ eV close to the burner, where [OH] is zero and only methane contributes to these peaks. Then, while the profile was taken, both masses 15 and 17 were mon:*ored, and file latter was corrected using the pred
376

CHARLES P. LAZZAP.A,lOAN C. B[ORDI, and JOHN F. PAPP

radi,.'als, in which case tile contribution to mass 17 i:~smaller than the albrementioned determined ratio. Second, the r~.~hane fragmentation pattern is temperature.dependent [1 ]I], favoring the fragmentation at high temperatnres, and this would also imply a correction to mass 17 smaller than the aforemenl:ioned ratio. These corrections, which are applicable ordy at low values of Z, are small (increasing [Off[ by, at most, 2 ~ at the lowest values o f Z), but they have been made to the proi'de for OH shown in Fig. 5. For oxygen atoms monitored at 16 ainu, the contribution o f O ÷ from fragmentation ofOz ~s cverywhsre zero at 15.6 eV. For Z ~ 0.7 cm, the contribution from CH~*is also zero since there i~ no methane at tZ~esedi:;tances from the burner. 2 The contribution :o 16 from methane at values of Z between 0.6 and 0.7 cm, where the methane concentration is small but non-negligible, was determined in a manner analogous to that described abo,ve. The ratio (lt6/lts) was determined close to the burner, where [0] is zero, and only methane contrfbutes to these peaks at 15.6 ,~V Masses 15and 16 wem monitored throughout the profile. Mass 15 was first corrected for con. tribution frora the methyI radical where appropriate, and a correction was made to mass 16 taking into account the expected variation with temperature of 116/l~s from methane from the data of Osberghaus mad Taubert [11 ]. This procedure is not sufficiently sensitive to seV'rate the O atom signal from the methane signal at values of Z where the atom concentration is small and that of tile methane is relatively high (i.e., Z < ~ 6.6 cm in Fig. 5). Hence, the O atom profiles appear truncated and oxygen atoms probably do not decay as rapidly as we observe and persist to lower values of Z than obsereed here. No corrections were made to the pt ,~,kat mass l, aSsigned to hydrogen atoms, since at the low electron energy used there is no contribution to ma.-.s I from any flame cOnstituent cont~ning hydrogen. Figure 6 shows the gradual decay of these three species at large distances froh'l the burner. This is

Fotrayl I~dical The profile shown in Fig. 9 is for mass 29 ob~l:ained at I 1.1 ~.V and is assigned to HCO. This profile w.Js the most difficult to obtain, because the maximum intensities are characteristically an order of magnitude lower than those lbr methyl radical. The assignment of this profile to the formyl radi. ca[ is made on the basis of the following obseJrva. tions:

2AI the temperatures involved hea'c,about 1800°K, the inlensity of the fragmentation peak a~ 15 arnu is greater than thai of the parent ion fox nlethan¢ [ 1~I. AI the highest instrument sensitivity we t)bserve[Is = 0 at Z :'~ 0.7 cra.

(1) the appearance potential observed for fhis species, wbd~e higher than current opinions of Att:OtCO*) would predict [12], is still severed electron vol~s lower than those characteristic nf HCO* front the expet ted interfering species,

~.he so-called recombination zone of a laminar flame, all of the rapid reaction of fuel having occurred over the first few millimeters of Z (Fig. 5). The temperature d,ops about 200 ° from iits max/mum va)ue, measured to be 1850°K in th,~ absence of the sampling probe, about 150 ° cooler with the probe [6]. The concentrations of Oz and H2 al~o were observed to decay slowly toward eqvillbrium in this tog/on, while that of water changes nearly irnperce,ptibly if anything, perhaps rising by 1% or 2%. Methyl Radied Figure 7 shows the appearance of the "methane" ion intensity profile monitored at 15 ainu as the electron energy is decreased. At high electron energy, the imensity at mass 15 is due almost exclusively to CHf from CH4 and, indeed, tht~ 15 peak is used to monitor the methane concentration in the stable species profile [61 . The peak, which grows in with decreasing electron energy, is due to methyl radicals, but there is apparendy still some contribution from methane fragmentation, even at ~13 eV. The methyl radical profile shown in Fig. 8 was obtained at an electron energy of 11.1 eV. At this electron energy there is n o contribution to mass 15 from methane. In fact, the intensityat n~ss 16 v e ~ close to the burner, where the n~thane concentration is higi,est, is also zero at this electron energy. Thus there can be no contribution from methane anywhere in the dame, irrespective of temperature effects on fragmentation patterns.

377

RADICAL PROFILES IN A CH4--O2--AR FLAME 2.4

t

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t

I

I

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/

~

L2

.4

~

~ Oxy~n amm~/

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2

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f

4

n

6

o

,

I

8

t

I I0

,

I 12

i

14

Z, BURNER SURFACE TO PROBE OISTANCE,cm

Fig. 6. Profiles for H, O, and OH at large distances from tile burner, showing the slow

decay of these species in the recombination zone of the l,a.~,c. Elect.'.~.~energy = 15.6 eV. 70° cone. HaCO and CHaOH. It is, however, not very dif. ferent from the only other direct measurement reported for HCO [13] ; (2) at the electron energy used to obtain the profile, the intensity of the 29 pea!,: from HaCO (obtained in an argon carrier by passing the gas over warm pa~'aformaldehyde) is zero; (3) the maxhnum intensity of the 28 peak in the flame at ] ~.1 eV is such tha'. contributions to the 29 peak fro~rn any C 13 -containing species (for example, C2 H4) could account for, at most, only 3% of the observed intens, ty; and (4) assuming, as a worst case, that the signal at mass 28 is due e,rlth'ely to C2 H6 and taking into account the temperature dependence of the ethane fragmentation pattern [ I 1], only 50% of the signal at mass 29 can be accounted for. To the extent that this last item is realistic, the concentrations shown in Fig. 8 could be too high by a factor of 2, in addition to the other uneertaintie~ discussed below.

assigned here to HCO. We have explored ~:h~s possibility from two points of view-appearance potential measurements and reaction kinetics. A review of the appearance potential data fer 29 amu indicates that it cannot accommodate an appearance potential of 8.7 eV, even as an extremely prejudiced low value. The value of 8.7 eV for tile onset of ethyl radical is that most [ikely to be observed by electron impact since the relative cross sections below this voltage are very small [14]. Consideration of possible interferences in the measurement of the onset voltage for '29 amu here, e.g., from ((21~H~C ~2 H 2 )÷ from ethane, and of the choice of an appearance potential fi~r call. bration purposes (see Table 1) favor a higher, rather than lower, value for the threshold energy for mass 29. Thus the appearance potential measurements could not support an assignment of ethyl radical to the observed 29 peak, althoug.h they do not rule out the possibility that Call s could contribute to the observed intensity.

It has been suggested b~; the re,Sewer" that e~hyl radical rn~ght contribute to the peak at 29 arnu

An estimate of the relative concentrations of HCO and C: Hs can be made by eonsideri]~g the

CHARLES P. LAZZARA, JOAN C. BIORDI. and JOHN F. PAPP

378

,

6S

13ov

lls

19

..

o•S , &

r

0342 045~5 Z {cmt

057e

0684

0798

Fig. 7. Iotacurrent in tile flame at 15 ainu as a function of distztuce from the burner surface at various electron energies, the intensities..a'e in arbitrary units which differ tot each electron energy; 70° cone.

detector be calibrated, using sources of known concentration of these species. This fls possible in some cases but involves an experimental effort nearly equivalent to that required heJre for detection and characterization. It is possible, however, to estim~ite mass spectral "sensitivities" for these species by consideration of relative icpnization cross sections and other discrimination effects pertinent to the particular instrument and sampling system used. The procedure used to estimate the radical concentration here is as follows, a For a ~iven radical and its structurally similar "parent" stable mole. eule (e.g.~ OH and Hz O), the intensities for each were mea:~ured at electron energies above their respective ionization potentials by the same amount. The concentration of the stable species is known from previous calibration. The assumption is then made that the ratio of iomzation cross sections (Qi) for the two species at equivalent amounts above their respective ionization potentials is the same as at 70 eV. Thus the concentration of ti~e radical can be estimated as

xR

IR (lr~ + b) Is(e~+b)

as(70 ev3~ . xs, Q,~(70 ~V)

reactions which lead to, the formation and destruction o:~'eaeh. It is assumed ~hat C2Hs is formed by ab~lr~dction reactions of H, O, and OH with ethane and by H atom addition to ethylene, and that it i~ consumed by reactions with H, O, OH, and O2. HCO is assumed to be formed by radical and alorll abseraction from H2CO and consumed in the same way as ethyl radical. At the point in the flare,.• where the 29 peak is a maximum, it is pc,ssi[,le to derive from this reaction scheme expressianl; of [C~ Hs] and [HCO] in terms of rate constan!s and the concentrations of the other reacts.ms. The latter, and ~ e temperature, is known ti'om measurements in the system and the former can be obtained from the literature, or reasonahly estimated. Such a calculation indicates that [~lCO] max is at least 5-10 times greater than

is equivalent to the assumption that the iordzation cross-section curves for *.hose species have the same shape. An attempt was made to check this assumption by using the data of Rapp and Eug-

Estimsti~n of Radical Coneentration~ A diree~ determination of unstable species conceatrati~ts requires that the sampling system and

3This procedure was first developed by Dr. J. Peeters and his colleaguesat the Catholic Universitj,of Leuven, .Belgium,and the authc,rs wish to thank them far their generous assistance,

where the subscripts R and S refer to the radical and stable species, respectively, X denotes mole fraction, 1 is the signal intensity, E ° is the ionization potential, Q the ionization cross section, and b isa constant. The value ofb must be chosen, of course, such that there is no contribution to [R from fragmentation of the stable specious. The assumption that

Qs(e~ + b) -- Qs(70 ¢V) air (E,~ + b) oR (70 eV)

379

RADICAL PROFILES II,l A CHn'--O2--AR FLAME 2.4---

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I

t

I

I

I

I

,

o x

0

v

0

J

_

0.10

O20

0,30

0,40

0.50

n6o

t~7~

Z, BIJ~IER SURFACE TO PROBE OIS"i~NC~,cm

Fig. 8. Concentration profile for methyl radicals in the flame. Electron energy = 11.1 eV, 38* cone. lander-G.alden [ 15], who measured ionization cross sections for a number of stable species over a wide range of electron energies. In general, the assumption was found to be quite good (to

5,e

~ 4.o

a.o

I

o

--,J--~' 0,1

I I I 0.2 03 0.4 0.5 0.6 0.7 Z,BURNER SUI:WACE TO PROne OIS1~Nge,¢m

O.a

Fig. 9. Profile at 29 ainu in the flame, assigned to formyl radical Electron energy, = 11.1 eV, 38° cone.

within about 15%) fiat similar species, such :as CO and CO2. It is ,~ithin a factor of 2 or 3 for dissimilar species, such as H~ an~t CO. Thus, i'.' would appear that '1his assumption does not sat th,.~ limit of uncertainty for the procedure; the latter is more likely to be determined by the uncertainty in the individual valL,.:.~for Q. Absolute iomzation cross-section measur~tments have been made for only a few stable naole~:ular and atomic species, and an excellent review of these measurements is available [16]. Various empirical correlations have been suggested for estimating the Q values for species for whirl1 no direct measurements have been made [17, 18, 19]. The values for the cross sections used here were'obtained from the paper of Kieffer and Dunn [16] for O, H, H2, and 02, from Lampe, Franklin. :,nd Field [18] for H20, and from Ral:,p and Eng. lander-Golden [15] for CH4. For OH and CH3 Q's were estimated by additiv~.ty [15] and for I-I~CO and HCO by flue empirical correlations suggested by Beran and Kevan [19]. Taken as a whole, it is reasonable to expect that the concert-

380

CHARLES P. LAZZARA,JOAN C. BIORDI, and JOHN F. PAPP

trations determined here for the major radical species are accurate ~o within a factor of 2. It will be noted that no attempt has been made to quantit~tively account for mass discrimination effects that might be expected to occur in the sampling system, the mass filt~', and the multiplier. It seems established now that, when sampiing from atmospher:'~, pressure or greater with Jelatively large oriflc~: (that is, in the continuum flow region), the discrimination shows a firstpower dependence on molecular weight [20]. However, at low pressures, such as those encoun).ered here, the mass discrimination is much [ess ~.'vere and not well characterized at all. The situation regarding multiplier discrimination is equally unclear; the theoretical (-V~) -l . dependence is apparently applicable only for low energies and high masses [21]. For the accelerator voltage used here (~<4000 V), the discrimination is against higher massas, whatever the functional dependence may be [21]. This is in the opposite sense ,3f any expected discrimination in the molecular beam and, in order of magnitude, not very different ~22]. Therefore, it seems not unreasonable to e:(.pect that the errors involved in ignoring these effects are largely compensating. Regarding the possible discrimination by the filter itself, the instrument us~(I l)ere is such that the resolution mode and transmission of the filter are variable. Thus, it is possible to choose a hybrid r'*solntion mode in such a way that the mass disetimination is negligible over a given mass range (having a width of about 50 mass units for this particular instrument). The required hybrid resolution is conveniently establ.'.~Jtedo'¢er the mass range of interest here, by adjustin,3 transmission so that the ratio of intensities of singly to doubly charged argon, before multiplication, is flRatgiven by the ratio of the ionh,ation cross sections for these ions ,[23]. Discussion The primary significance of the data obtained here is the demonstrated ability Co measure, with good precision, radical concentration profiles within a factor of about 2 through the reaction zone of flames. The methyl radical (Xmax = 2.2 X 10-3)

and formyl radical (Xmax = 6 X 10-s) are seen to be transient species in the flame, while the H, O, and OH radicals reach their maxima well outside the zone of primary reaction. The observed maximum concentration for these thre~,~reaction species are in excess of their expected equilibrium concentrations by varying degrees. At 1700=K (which is tile measured final flame temperature less about 150° owing to cooling by probe [6]) fol" this flame, equilibrium calculations (NASA Lewis Code [24] ) give the following mole fractions: 8.0 X l0 -6 for [H], 3.1 X 19-s[O], and 6.2 X 10-a for [OH] to be compared with 2.0 X 10-2,0.8 X 10"~ ,and 1.1 X 1D-2,respectively, measured ~inthe hot gas regiolt of the flame ffig. 6). Tile radical concentrations routed l'Lareare in quite reasonable agreement with tho:;e reported by Petters ,and Mahnen for a similar flarae [lb]. ~hey lislt the ratio of concentrations of various species fbr a stoichiometric CH4/O2/Ar flame vs. a lean C]['14]O2flame (both having 9.5% CH4 and burned at 40 Torr) at a point in the flame where the rate of methane disappearance is a maximum. Assuming that these ratios are also v~didfor the peak radical concentrations they found: X(CH3)ma,t = 3.2 X 10-3 ; X(O)max = 0.9 X ]0 "2 ; X(OH)max = 1.3 X 10-2 ; X(I-I)max = 1.7 X 10"2. The HCO mole fraction is given as a maximum of ~4 X 10-s . Eventually, of course, the system would reach equi!ibrium. Since the three-body radical recombination reactions required to achieve this are slow relative to the rapid bimoleeular raactions occurring in this region, the latter have i~een considered to maintain a ~tate of balance among themselves, in which the relative species concentrations may be described by the equilibrium constant appropriate to the reaction and temperature considered. This view ~eems well established from a variety of direct radical concentration measurements for the post flame gases of hydrogen flumes and, by inference from stable species concentrations, was supposed also to be reasonably valid for post flame gas of a lean methane flame [25]. Petters and Malmen have also confirmed this directly in their lean CH4/O2 flame [lb].

RADICAL PI~OFILES IN A CH~--O2- .-AR FLAME

381

TABLE 2 Experimentally Determined Equilibrium Constants for Reactions in the Post Flame GaSesof a 9.6% CH4-21.3% O7.-69.i % At Flame, P = 32 Tort

Reaction H+O2=OH+O O * Hz = Oil + H OH+H2 =HeO+H CO + OH =C02 +H

Equilibrillm Constant 170ff'K ~500°K Caicd. 1261 Obsvd. Cried. 1261 Obsvd. 0.12 1.3 19.2 5.9

The reactions of interest are as follows H+O2 =OH+O

(1)

O+H2 =OH+H

(2)

OH+H2 =H+H20

(3)

C,O + OH = COe + H .

(4)

For 1.3 cm < Z < 2.0 cm in Fig. 6, the tempera. ture is at its maximum and is constant to within ~15 ° . Considering the cooling effect of the probe, this temperature is taken to be 1700°K [6], and the equilibrium constants for reactions (1)-.(4) may be calculated and compared with values derived from the measured concentrations. Table 2 shows the results. Depending upon one's point of view, the satisfactory agreement between observed and calculated values may be taken as evi. denee that these reactions are indeed balanced in the hot gas region of this flame or that the measured radical ,concentration profiles are reasonal:b, accurate and consistent. Better insight into the degree of balance of reactions (1)-(3) may be realized by simply ob. serving the behavior of the appropriate mass spectrometer intensity ratios as a function of Z in comparison with the behavior of the equilibrium constant over the corresponding range of tempera. ture. This procedure should minimize error by avoiding those errors inherent in the calculations of absolute radical concentrations. For example, the ratio (I~ lrt,o/IoH In ~) is proportional to K,~

0.0~ 1.S 18.0 4.7

0.06 1.2 35.0 -

0.04 1.4 39.4 -

and is observed to increase by about 18% as Z increases from 1.3 to 4.0 cm in Fig. 6. The temperature was observed to drop by about 60 ° over this range of Z. The change in Kywith temperature may also be calculated, and the expected increase i~sabout J ~-%. Similar comparisons may be roade for b:~ and K,. The ratio corresponding to Kz is nearly constant, as tile mild temperature dependence predicts. Kt however, falls off more r:pidly as tW:emeasured intensity ratio than the calculated equilibrium constant over this temperature rang%suggesting that this reaction is not fully balanced in this system. ForZ ~ 14 cm (Fig. 6), the temperature, by extrapolation, is about 15rIO°K, and values for the expected and observed equilibrium constants at this temperature are also given in Table 2 for reactions ( ] ) (3). Interest in this flame is not confined to the recombination region, and the most valuable use of the radical profile data will be in conjunction with complete stable species and temperature profiles for the flarae. [~rovided that the sampling cone can be made to cause minima! (or, at least, accountable) disturbance to the flame, the system may be subjected to analyses using the Hirschfelder model of flame propagation [27] to obtain information regarding the rates and mechanisms of reactions occurring in tile flame.. We believe that the small angle probes, such as those used to obtain the dat~ in Figs. 8 and 9, approach this condition, and we intend to apply these techniques to problems of chemical flame iah.ibition.

382

CHARLES P. LAZZARA,JOAN C. B1ORDI, and JOHN F. PAPP

R~fe~lleffs, 1. (a) We.stenberg,A. A., and Fsisttom, R. M., 3".Phys. Chem. 65,591 (1961); (b) Peetets, J., and Mahnen, G., paper presented at the Fourteenth Symposium (International) on Combustion, Pennsylv0niaState University, At,lgust20-25, 1972; (c) Fe:aimor¢,C.P.,andJones, G.W.,Ninth Symposium (International) on Combustion. A=~demicPress, New York (1963) pp. 597- 606; (d) Wewlenb~g,A. A., and Frlstrom, R. M., Tenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, Pa. (i 9~5), pp. 473-487; (e) Eb¢tius, K. H., Hoycrmann, K., and Wagner, H. G., Paper presented at the FourteerRh Symposium (International) on Combustion. Penn:,ylvaniaState University,August 20-25, 1972. 2. Bonne. U , Grewer, T., and Wagner,H. G., Z. Phys. Chem. N.F. 26, 93 (1960). 3. Milan.T. A., and Greene, F., 3'. Chem. Phys. 44, 2,144 (1966). 4. Ftistmm, R. M., Plinth Symposium flnternationaIJ on Combustiol!, Academic Press, New York (1963), pp. 560, aml the Discussion thereafter. 5. Foner~S. N., and Hudson, R. L., d. Chem. Phyx. 2 ! 1374 (1953;. 6. Biordi,$. C., Lazzara, C. P., and Papp, J. F , BuMinas Repol't ~3fIn~testigationsNo. 7223 (1973). 7. WinterssR. E., Collins~J. H., and C.l:mrehene,W. L, J. Chem, Phys. 45,1931 (1966). 8. Geissner~B. G., and Meisels,G. G.,d. Chem. Phys. 55,2269 (1971), 9. Field, F, H., and Franklin, J. L , Electron Impact and foals'arian Phenoraena (RevisedEdition), Academic Press, New York (1970), pp. 239.-493. 10 P:itehard, H. and Harrison, A. G., d. Chem. Pbys. 4B, 2827 (1968). 1I. Osbe~ghaus,O., and Taubcff, R,.,Z. Phys. Chem. N.F.4, 264 (1955).

12. Haney, M. A., and Franklin, L L., Trans. Faraday

Sue. 65,1794 (~969). 13. Reed, R. L, and Brand, J. C. D., rrans Faraday Sue. 54,478 (1958). 14..M~lton, C. E., aJnldHamiB, W. H.,J. Chem.Phys. 41, 3464 (1964). l 5. Rapp, D., and Englander-Golden,P., J. Chem. Phys. 43,1464 (1965). 16. Kieffer, L. L, and Dunn, G. H., Rev. Madam Phys. 38,1 (1966). 17. Ureas, J.W., and StevensOn,D, P.,J. Am. Chem. Sac. 78, 546 (1956). 18. Lampe, F. W., Franklin, J. L., and Field, J. H., J, Am. Chem. Sac. 79, 6129 (1957). 19. Beran,.l.A., and Kevan, L.,J. Phys. Chem. 73, 3866 (1969). 20. Greene, F. T., Btenwer,J.,and Milne,T. A.,J. Chem. Phy.~; 41% 1488 (1964). 21. Inglu:aat,M. G., and Hayden, R. J., Mass Spectrometry, Nuclear Science Series Report No. 14. National Academy of Sciences, National Research Council, Washington, D.C. (1950), pp. 41~g5. 22. Lao, R. C., and Pattie, R. F., P~oc. 18th Ann. Conf. Mass Spectrum. All. Top., Americ,~nSociety for Mass Spectrometry, JuP.e ~4-19, 1970, San Francisco,. Calif (1970), p. B383. 23. Kieff~r, L. 1.,AtomicData I, 19 (1969). 24. Gordon~S., and Zelee..nik,F. J., NASA Technical Note D-1737 (1963). 25. Fenimore, C. P., Chemistry in Premixed Flamas, The MacmillanCompany, New York (11965),Chapts. 2 and 5. 26. Ft'istrom~,R. M., and Weatenberg, A. A., Flame Structure, McGraw Hill, New York (1965), pp. 355. 27. Hitsehfelder, .L O., Curtiss, C. F., ar,d Campbell,D., Fourth Symposium (Internationall o~l Combustion, Williamsand WilkinsCompany, B;dtimore (1953). pp. 190.

(Received May 3, 1973; revised July 15, 1973)