absorption cross-sections and absolute concentration of singlet methylene in methane/air flames

5 November 1999

Ž .Chemical Physics Letters 313 1999 121–128www.elsevier.nlrlocatercplett

Absorption cross-sections and absolute concentration of singletmethylene in methanerair flames

Igor Derzy a, Vladimir A. Lozovsky a,b, Sergey Cheskis a,)

a School of Chemistry, Sackler Faculty of Exact Sciences, Tel AÕiÕ UniÕersity, Ramat AÕiÕ, Tel AÕiÕ 69978, Israelb SemenoÕ Institute of Chemical Physics, Russian Academy of Sciences, 4 Kosygin str., Moscow 117977, Russian Federation

Received 3 June 1999; in final form 7 September 1999

Abstract

Absorption spectra of methylene in the singlet electronic state were measured by intracavity laser absorption spec-Ž . Ž .troscopy in low pressure methanerair flames. Spectra were measured in the region of the 0, 14, 0 – 0, 0, 0 transition

Ž .590–593 nm , including the lines with available Einstein coefficients. Comparing the line intensities, the absorptionŽ . Ž . Ž . Ž .Einstein coefficients and cross-sections for lines of both the 0, 14, 0 – 0, 0, 0 and 0, 13, 0 – 0, 0, 0 transitions were

obtained. The absolute concentration profiles of 1CH were obtained using the measured Einstein coefficients. These2

profiles are compared with model calculations and found to be in reasonable agreement. The population of the vibrationallyŽ .excited 0, 1, 0 level was also determined and found to be slightly higher than the equilibrium value. q 1999 Elsevier

Science B.V. All rights reserved.

1. Introduction

Methylene, CH , is a very important radical in2

combustion chemistry. It participates in the mainchain of hydrocarbon oxidation especially in rich

w xflames 1 , and also plays an important role in nitro-w xgen oxide reburn, reacting with NO 2 . It is also a

very important intermediate in the mechanism ofw xdiamond chemical vapor deposition 3 . Methylene

has two low-lying electronic states, the triplet ground˜3 1state, X B , and the metastable singlet state, a A .˜1 1

Since the singlet state lies only 3147 cmy1 above thew xground state 4 it has a noticeable population in

flames, even under the assumption of thermal equi-

) Corresponding author. Fax: q972-3-6412773; e-mail:[email protected]

Ž .librium ;3% at 1700 K . The reactivity of thesetwo states differs dramatically, singlet methylenereaction rates are usually much faster than theirtriplet analogs, sometimes by more than two orders

w xof magnitude 1,5,6 . Thus singlet and triplet statesof methylene are considered as two different

Ž1 3 .molecules CH and CH in combustion mecha-2 2

nisms. The separated measurement of the 1CH con-2

centration can be handled only by spectroscopictechniques. The 1CH radical can be detected using2

˜1 1the b B §a A transition which has many bands in˜1 1

the visible range. 1CH has been detected in flames2

using this transition by laser induced fluorescenceŽ . w xLIF 7 , intracavity laser absorption spectroscopyŽ . w xICLAS 8,9 and cavity ring-down laser absorption

Ž . w xspectroscopy CRLAS 10 . The line-off sight ab-Ž .sorption spectroscopy methods ICLAS and CRLAS

are better suited for CH measurements in flames,2

0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0009-2614 99 01045-3

( )I. Derzy et al.rChemical Physics Letters 313 1999 121–128122

because LIF suffers from rapid fluorescence quench-ing. In a 5 Torr methane flame, only one fluores-

w xcence photon was detected every 3–5 laser shots 7 .The quantum yield of fluorescence is approximatelyinversely proportional to pressure, which hampersthe use of LIF at pressures higher than 5 Torr. Thesignal to noise ratio provided by ICLAS and CRLASis much better, and it is practically not affected bypressure. Indeed, detection of 1CH at atmospheric2

w xpressure was demonstrated by ICLAS 8 . The ab-sorption spectroscopy methods have an additionalimportant advantage. Absolute concentration mea-surements can be performed very easily by suchmethods provided that the absorption cross-section isknown. Unfortunately, the measurement of the ab-sorption cross-section of 1CH is not a simple task.2

The spectroscopy of 1CH is complicated due to the2˜strong perturbation of a and b states by the triplet˜

ground states and by each other. As a result, in spite1 wof the extensive studies of CH spectroscopy 11–2

x16 , 95% of the lines in the visible spectrum ofmethylene remain unassigned. Another problem iscaused by the high removal rate of metastable astate, which in many cases is close to the gas colli-

Žsion rate. Therefore it is very difficult to prepare for.example by photolysis a known concentration of

1 ŽCH with a known rovibrational distribution for2.example under conditions of thermal equilibrium .

w xGarcia-Moreno and Moore 12 measured the Ein-stein coefficient based on the radiative lifetimes of

Ž . Ž .different rotational lines of the 0, 14, 0 and 0, 15, 0˜ w xvibrational levels of the b electronic state 17 . They

observed dispersed fluorescence after excitation ofthe CH radical in the single rovibrational state of2

˜the upper electronic state b. In order to obtain abso-lute emission Einstein coefficients, A, for an individ-ual rovibronic transition they measured the branch-ing ratio for all allowed transitions from the particu-lar excited rovibrational level to different rotationaland vibrational levels of the lowest singlet state a.˜The absolute Einstein coefficients were only reportedw x Ž .12 for transitions from the 2 level of the 0, 14, 002

Ž .vibration and the 2 level of the 0, 15, 0 vibration11˜ Ž .of the b electronic state see Fig. 1 . The absorption

1 w xspectra of CH measured in flames 8,10 where in2Ž . Ž .the region of the 0, 13, 0 – 0, 0, 0 transition and

therefore the measured Einstein coefficients couldnot be directly used in these works.

1 w xFig. 1. A schematic diagram of the CH levels with reported 122

absolute Einstein A coefficients. The distances between rota-tional, vibrational and electronic levels are not to scale.Wavenumbers of the transitions are given in cmy1.

In the present work, the spectrum of the 1CH 2

radical was measured by ICLAS in the methanerairŽ . Ž .flame in the region of the 0, 14, 0 – 0, 0, 0 transi-

Ž .tion 590–593 nm , including the lines with mea-sured Einstein coefficients. The measurements wereperformed under flame conditions identical to those

w xused in our previous work 8 . It allows us to calcu-late absorption Einstein coefficients and cross-sec-

Ž . Ž .tions for lines of both the 0, 14, 0 – 0, 0, 0 andŽ . Ž .0, 13, 0 – 0, 0, 0 transitions and to place the mea-sured concentration profiles of 1CH on an absolute2

basis. In addition, the ICLAS spectrum was alsoŽ . Ž .measured in the range of the 0, 14, 0 – 0, 1, 0 tran-

Ž .sition 640–645 nm where Einstein coefficients for

( )I. Derzy et al.rChemical Physics Letters 313 1999 121–128 123

the hot vibrational bands have also been measuredw x12 . As a result, the population of the vibrational

Ž .excited 0, 1, 0 level in the a A state was deter-˜1 1

mined.

2. Experimental

The experimental apparatus is practically the sameas that used in previous studies of the ICLAS spectra

1 2 w xof HCO and CH in flat flames. 8,9 . A flat flameproduced by a 6 cm diameter McKenna burner wasplaced inside of the cavity of a home made dye laser.

ŽThe laser was pumped by an argon laser Coherent.Innova 90-6 . The flame burner operates at low

Ž .pressure 30"0.3 Torr and the low-pressure appa-ratus is isolated from other parts of the laser cavityby two wedged windows placed at the Brewsterangle. The burner can be moved along of the verticalaxes with an accuracy of 50 mm.

An ICLAS spectrum can be approximated, withgood accuracy, by the Lambert–Beer law:

I Õ s I n exp ys n n L 1Ž . Ž . Ž . Ž .Ý0 i i effi

Ž .where I n is the observed laser intensity at the endŽ .of generation time t ; I n is the analog ‘blank’g 0

Ž .spectrum in classical absorption spectroscopy; s ni

is the absorption cross-section of the observed rovi-brational transition from a level with a population n .iThe effective optical length ICLAS, L , is governedeff

by the generation time t :g

lL s cteff gL

where ls6 cm is the optical length of the absorbingcompound, here the flame diameter; Ls96 cm isthe length of the laser cavity and c is the velocity oflight. In order to control the optical length, L , theeff

pumping argon laser beam was chopped by anacousto-optic modulator and the dye laser beam isdeflected to a spectrograph by a second acousto-opticmodulator after a time t from the beginning of theg

generation pulse during a short sampling time, D ts10 ms. We used t s40 or 80 ms, corresponding tog

L s750 and 1500 m, respectively. The spectrumeff

of the dye laser radiation was analyzed with a highŽ .resolution 1 m monochromator SPEX 1000 M

which has a 100 grooves per mm echelle grating,works in the 29th order and has a 2048-element

Ž . Žphotodiode charge coupled device PCCD ALTON.model LS-2000 . The repetition rate of the laser

pulses produced by acousto-optical chopping was 20kHz and 11 kHz for generation times of 40 and 80ms, respectively. The exposure time of the PCCDwas set to 50 ms, thus 500–1000 pulses averagedduring each exposure. The information from thePCCD was sent to a computer where an additionalaveraging of 50–200 spectra was performed. Thetotal time which was required to record an ICLASspectrum after 2=105 averaging was less than 15 s.The spectral resolution was about 0.003 nm, asmeasured by observing the He–Ne laser line. Thespectra of 1CH were recorded in the three different2

ranges: 590–593 nm, 613–633 nm and 640–645 nm.Rodamin 6G, Kiton Red and DCM dyes were usedfor these ranges, respectively. The tuning of the laserto the required wavelength range was assured byusing the appropriate dyes and mirror sets. In severalspectral ranges, additional tuning by a pellicle beam-splitter placed into the laser cavity was used. Gener-ally we preferred to work without any special tuningelement, due to the narrowing of the spectral width

Ž .of the ‘blank spectrum’, I n , and some degrada-0

tion of the quality of spectra. The raw ICLAS spec-trum includes both spectra of molecules in the flame

Žand in the other parts of laser cavity mainly waterovertones due to the water vapor in the laboratory

.room . In order to isolate the CH spectrum, which2

is present only at specific places in the flame, allspectra were divided by the spectrum which wasrecorded about 20 mm above the burner. At thisdistance, the ICLAS spectrum does not contain the1CH radical features. Such a procedure allowed us2

to obtain a baseline which does not practically de-pend on the wavelength.

3. Results and discussion

w xGarcia-Moreno and Moore 12 reported absoluteemission coefficients for three rotational lines of theŽ . Ž . Ž0, 14, 0 – 0, 0, 0 transition: 2 –1 16 955.36302 10

y1 . Ž y1 .cm ; 2 –2 16 927.113 cm , and 2 –302 12 02 12Ž y1 .16 854.688 cm . Fig. 2 shows three parts of theICLAS spectrum including these lines recorded in amethanerair flame. Identification and assignment of


Ž . Ž . 1Fig. 2. ICLAS spectra of the 0, 14, 0 – 0, 0, 0 transition of CH .2w xThe lines marked with asterisks are lines with reported 12

Einstein coefficients. P and Q branches were recorded with ageneration time of 75 ms, which corresponds to the L s1.45eff

km, the R branch was recorded with a generation time of 195 msŽ .L s3.65 km .eff

the spectral lines were performed using lines fromŽthe water overtone spectrum HITRAN database

w x. 118 . Calculated CH line positions agree with2w xpublished ones 11–15 with an accuracy better than

0.1 cmy1. Typical deviations were about "0.05cmy1, or 1 pixel of the CCD array. Note that forseveral lines the reported wavenumbers differs byabout 0.07 cmy1.

In order to calculate the absolute concentration of1CH using these values and the measured ab-2

sorbances for these lines, one needs to know thevibrational and rotational distribution of 1CH in the2

flame. Most of the molecules are in thermal equilib-rium in the flame. However, in several cases devia-tions from a Boltzmann vibrational distribution were

Žobserved in flames for example for OH below thew x.flame front zone 19 . In order to check the validity

of assumption of vibrational equilibrium, we mea-sured the spectrum of the 1CH radical in the range2

640–645 nm where the absolute Einstein A coeffi-cients were measured for three lines from theŽ . Ž .0, 14, 0 – 0, 1, 0 transition. The spectrum which in-cludes two of these lines is shown in Fig. 3. Thispart of the 1CH spectrum also includes several lines2

Ž . Ž .from the 0, 13, 0 – 0, 0, 0 transition; however, theEinstein coefficients for these lines are not known.

Ž . Ž .Fig. 3. ICLAS spectrum of the 0, 14, 0 – 0, 1, 0 transition of1 w xCH . The lines marked with asterisks are lines with reported 122

Einstein coefficients. The spectrum was recorded with a genera-tion time of 75 ms. The spectrum also involves several lines of theŽ . Ž .0, 13, 0 – 0, 0, 0 transition.

The rotational levels seem to be in equilibrium,because rotational equilibrium is usually accom-plished much faster than vibrational equilibrium. Wecan prove this by comparing the observed intensitiesof the different rotational lines with those reported

w xby Garcia-Moreno and Moore 12 . Unfortunately,the differences in the rotational energies of the levelswhich have reported Einstein coefficients are notlarge enough in order to measure the rotational tem-perature. However, in all cases the observed ratios ofintensities agree with the rotational equilibrium as-sumption. Fig. 4 shows the spectrum including the

Ž . Ž . 1lines of the 0, 13, 0 – 0, 0, 0 transition of CH 2

Ž . Ž .Fig. 4. ICLAS spectrum including lines of the 0, 13, 0 – 0, 0, 0transition of 1CH .2


Table 1Flame parameters

Reactant gas ws0.8 ws1.0 ws1.2

Ž . Ž . Ž .Flow rate sccm Mole % Flow rate sccm Mole % Flow rate sccm Mole %

CH 360 8.5 450 10.4 540 12.24

O 900 21.2 900 20.7 900 20.32

N 2990 70.3 2990 68.9 2990 67.52

w x w x 3The fuel equivalence ratio, ws2 CH r O . Total pressure: 30.0"0.3 Torr. Sccm is a cm under standard conditions per minute.4 2

which used previously for concentration measure-w xments 8,10 .

In our experiments we used three ‘standard’ flamesŽ .see Table 1 with temperature profiles measured by

w xcavity ring-down spectroscopy of OH 20,21 . Usingthese temperature profiles, the relative populations niŽ Ž ..see Eq. 1 for different rovibrational levels can beobtained and the relative absorption cross-sections

Table 2Absorption Einstein coefficients of several 1CH lines2

X Y y1 y8Ž .J yJ n cm s B=10K K K K relativea c a c

Ž . Ž .0, 14, 0 § 0, 0, 02 –2 16 927.1 1.00 8.502 12

3 –3 16 927.7 0.42 3.603 13

4 –4 16 928.9 1.41 12.104 14

5 –5 16 932.3 0.75 6.405 15

2 –3 16 854.7 0.49 4.202 12

2 –3 16 857.0 0.49 4.202 12

2 –1 16 955.4 0.87 7.502 10

Ž . Ž .0, 13, 0 § 0, 0, 06 –7 15 805.3 0.27 2.415 25

7 –8 15 842.6 0.35 3.217 27

3 –2 15 849.3 0.94 8.631 21

5 –4 15 883.4 0.33 3.033 23

4 –5 15 569.8 0.76 7.131 41

4 –4 16 057.1 0.49 4.414 04

7 –7 16 068.5 0.95 8.617 07

Ž . Ž .0, 14, 0 § 0, 1, 02 –2 15 573.1 1.00 10.902 12

4 –4 15 575.7 1.27 13.904 14

6 –6 15 587.0 0.73 8.006 16

2 –1 15 600.9 0.77 8.402 10

2 –1 15 603.2 0.77 8.402 10

3 –2 15 608.5 0.89 9.703 11

4 –3 15 612.3 0.78 8.504 12

5 –4 15 614.0 1.89 20.705 13

6 –5 15 617.6 0.52 5.706 14

8 –7 15 635.1 0.23 2.508 16

( ) ( )0, 15, 0 § 0, 1, 03 –4 16 306.2 1.83 19.112 04

s is a cross-section normalized by the cross-sections of the 2 –2 lines; Einstein absorption coefficient B is in m2 Jy1 sy1.rel 02 12

Cross-section values were obtained by averaging of line intensities measured in different experiments and in flames with different equivalentratios. The statistical error was less than 20%.


can be calculated from the measured spectra. Therelative absorption cross-sections obtained for theline-centers are shown in Table 2.

The Einstein B coefficient is related to thei k

absorption cross-section by the following expression:

`1B s s nyn dn 2Ž . Ž .Hi k 0hn 00

Here the absorption coefficient B has the unitsi k

m2 Jy1 sy1 and n is a wavenumber of the center of0

the line. Assuming a Gaussian lineshape:

'1 pB s s n dn 3Ž . Ž .i k 0'hn 2 ln 20

Ž .where dn is a linewidth FWHM . In our experi-ments dns0.2"0.04 cmy1. This is larger than a

Ž y1 .Doppler linewidth 0.13 cm for 1700 K andrepresents the overlap of the actual line shape with

Ž .the spectrograph apparatus function. Eq. 3 allowsus to calculate relative B coefficients from the mea-sured absorption cross-section. Note that analogousresults can be obtained even without any assumptionabout lineshape if the linewidth dn is constant. TheEinstein coefficient B is related to the emissioncoefficient A:

g Ak k iB si k 3g 8phcni 0

Using known absolute A coefficients for the mostintense line, 2 –2 , from the three lines mentioned02 12

above, the absolute B coefficients can be obtainedfor this line as well as for all non superimposed lineswith measured relative B coefficients. The resultsare shown in Table 2. The relative intensities of thethree lines measured by Garcia-Moreno and Mooreare in reasonable agreement with the results of thiswork. Table 2 also shows the calculated B coeffi-cients for the transitions originating from the vibra-

Ž .tionally excited level 0, 1, 0 . These coefficients wereobtained in a similar way, using the published Acoefficient value for the 2 –2 line.02 12

Ž . Ž .The ratio of population of the 0, 1, 0 and 0, 0, 0vibrational levels of 1CH can be readily obtained2

using B coefficients from Table 2 and the measuredŽ .absorbances of the lines related to the 0, 14, 0 –

Ž . Ž . Ž .0, 0, 0 and 0, 14, 0 – 0,1, 0 transitions. The ratiow x w xobtained was found to be 0, 1, 0 r 0, 0, 0 s0.45"

0.1 at the maximum of the concentration profiles. Itis somewhat higher than ;0.3, which would beexpected at a temperature of 1650 K. The obtainedpopulation ratio corresponds to a vibrational temper-ature of 2400"600 K. On the one hand, somedifference is not surprising. The GRI mechanismpredicts the population of the electronically excitedsinglet state of CH to be at least five times higher2

than the equilibrium value. The rate of vibrationalrelaxation for 1CH seems to be lower than that of2

electronic relaxation because the latter approachesthe gas kinetic collision rate. On the other hand, themain reaction which produces 1CH in a methane2

flame is the reaction

OHqCH ™1CH qH O3 2 2

The enthalpy of this reaction is close to zero, andtherefore it is difficult to expect a high population of

Fig. 5. Absolute concentration profiles of 1CH radicals in three2

different flames. The profiles were obtained using Einstein coeffi-cients from Table 2. Solid lines without symbols represents modelprediction based on the GRI-Mech ver 2.11 mechanism. Lineswith circles, triangles, and squares are data measured in flames

Ž .with w s1, 0.8 and 1.2, respectively see Table 1 .


vibrationally excited levels of 1CH . Unfortunately,2

the accuracy of determining the population ratio isnot high, due to the low intensity of the vibrationallyexited state lines. This did not allow us to measurethe dependence of the population ratio on the loca-tion in the flame, because the errors are higher at theconcentration profile edges where the total 1CH 2

concentration is lower. Nevertheless, this inaccuracydoes not significantly affect the determination of thetotal absolute concentration of 1CH , because most2

of the radicals are in the ground vibrational state inthe flame.

The absolute 1CH concentration was determined2

using the absorption B coefficients obtained. Theabsolute concentration profiles of 1CH for the three2

studied flames are shown in Fig. 5, along with theresults of the calculations. The calculations were

w xperformed using the PREMIX code 22 and thew xGRI-Mech 2.11 mechanism 5 . The experimental

curves shown in Fig. 5 are similar to those publishedby us earlier and differ only by multiplication by theappropriate value. The experimental absolute valuesare about 2 times lower than the calculated ones forall three flames. This is in contrast with the previous

w xestimate 8,21 that the experimental value is muchhigher than the calculations. The previous estimate

w xwas obtained from the analysis of Petek et al. 15 .They reported that the minimum detectable 1CH 2

concentration is 1=108 molecules cmy3 per quan-tum-state at 300 K which corresponds to an ab-sorbance of 10y5 for a single pass configuration. Itis difficult to estimate the total population of 1CH 2

from these data, because the specific level, related tothis number, its degeneracy and energy are not

w xknown. Moreover, the authors 15 pointed out thatthe 1=108 value is actually only the upper limitdue to uncertainty in the energy distribution of 1CH 2

after flash photolysis. This leads to the underestima-tion of the absorption cross-section and therefore tothe overestimation of the 1CH concentration. We2

believe that the results obtained in this work andbased on the measurements of the radiative lifetimesw x12 provide a much more reliable estimate of the1 w xCH concentration. McIlroy 10 reported that he2

obtained Einstein A coefficients for the lines 4 –414 04Ž . Ž .and 7 –7 of the 0, 13, 0 – 0, 0, 0 vibrational tran-17 07

sition to be 4 and 8 msy1, respectively assuming thatabsolute concentrations of 1CH are equal to their2

calculated values. The Einstein coefficients fromTable 2 lead to the Einstein A coefficients of 9.1 and17.8 msy1, respectively. This results in absoluteconcentrations about two times lower, in agreementwith this work.

Acknowledgements

This research was supported partially by the JamesFranck, German-Israeli Binational Program in LaserMatter Interaction.

References

w x1 J. Warnatz, Rate coefficients in the CrHrO system, in:Ž .W.C. Gardiner Ed. , Combustion Chemistry, Springer, New

York, 1984, pp. 197–360.w x2 J.A. Miller, C.T. Bowman, Prog. Energ. Comb. Sci. 15

Ž .1989 287.w x3 R.B. Jackman, L.H. Chua, J.S. Foord, Diam. Relat. Mater. 4

Ž .1995 740.w x Ž .4 P. Jensen, P.R. Bunker, J. Chem. Phys. 89 1988 1327.w x5 C.T. Bowman, R.K. Hanson, D.F. Davidson, W.C. Gardiner,

V. Lissianski, G.P. Smith, D.M. Golden, M. Frenklach, H.Wang, M. Goldenberg, http:rrwww.me.berkeley.edurgri_mech, 1997.

w x6 H. Okabe, Photochemistry of Small Molecules, John Wileyand Sons, New York, 1978.

w x7 A.D. Sappey, D.R. Crosley, R.A. Copeland, Appl. Phys. BŽ .50 1990 463.

w x8 S. Cheskis, I. Derzy, V.A. Lozovsky, A. Kachanov, F.Ž .Stoeckel, Chem. Phys. Lett. 277 1997 423.

w x9 V.A. Lozovsky, S. Cheskis, A. Kachanov, F. Stoeckel, J.Ž .Chem. Phys. 106 1997 8384.

w x Ž .10 A. Mcilroy, Chem. Phys. Lett. 296 1998 151.w x11 M.N.R. Ashfold, M.A. Fullstone, G. Hancock, G.W. Ketley,

Ž .Chem. Phys. 55 1981 245.w x Ž .12 I. Garcia-Moreno, C.B. Moore, J. Chem. Phys. 99 1993

6429.w x13 W.H. Green Jr., I.-C. Chen, H. Bitto, D.R. Guyer, C.B.

Ž .Moore, J. Mol. Spect. 138 1989 614.w x Ž .14 G. Herzberg, J.W.C. Johns, Proc. R. Soc. A 295 1966 107.w x15 H. Petek, D.J. Nesbit, D.C. Darwin, C.B. Moore, J. Chem.

Ž .Phys. 86 1987 1172.w x Ž .16 W. Xie, C. Harkin, H.L. Dai, J. Chem. Phys. 93 1990 4615.w x17 I. Garcia-Moreno, E.R. Lovejoy, C.B. Moore, J. Chem. Phys.

Ž .98 1993 873.w x18 L.S. Rothman, C.P. Rinsland, A. Goldman, S.T. Massie, D.P.

Edwards, J.M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana,J.Y. Mandin, J. Schroeder, A. McCann, R.R. Gamache, R.B.


Wattson, K. Yoshino, K.V. Chance, K.W. Jucks, L.R. Brown,V. Nemtchinov, P. Varanasi, J. Quant. Spectr. Rad. Trans. 60Ž .1998 665.

w x19 V.A. Lozovsky, I. Derzy, S. Cheskis, Chem. Phys. Lett. 284Ž .1998 407.

w x20 S. Cheskis, I. Derzy, V.A. Lozovsky, A. Kachanov, D.Ž .Romanini, Appl. Phys. B 66 1998 377.

w x21 V.A. Lozovsky, I. Derzy, S. Cheskis, Twenty-Seventh Sym-Ž .posium International on Combustion, The Combustion In-

stitute, Pittsburgh, PA, 1999, p. 445.w x22 R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, A Fortran

Program for Modelling Steady Laminar One-DimentionalPremixed Flames, Report SAND85-8240, Sandia NationalLaboratories, Livermore, CA, 1991.

absorption cross-sections and absolute concentration of singlet methylene in methane/air flames

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