J. Phys. Chem. 1988, 92, 4384-4389
4384
system with similar parameters. In conclusion, the N 0 2 / N 2 0 4system represents a model for association/dissociation reactions with small threshold energy. As a consequence low high-pressure rate constants and very steep k(E,J) curves with maxima at low energies are obtained. The SACM provides a convenient and realistic approach for a theoretical rationalization of these effects.
Acknowledgment. We thank Professor J. Troe for stimulation and helpful discussions, Dr. H. Hippler for his involvement in the experiments, and Dr. L. Brouwer for the preparation of programs and some calculations. P.B. thanks the Royal Society of London and the Deutsche Akademische Austauschdienst for grants. This work was supported by the Deutsche Forschungsgemeinschaft within the Sonderforschungsbereich 93 “Photochemie mit Lasern”. Appendix A
Effective Morse Parameters of Reaction Channel Potentials. In simplified SACM calculations the energy pattern is considered ~ e p a r a t e l y I ~of * ~each ’ oscillator which disappears together with that in the reaction coordinate. The amounts of energy in all other molecular modes influence the effective channel potential for the oscillator just under consideration. To take this into account the Morse parameter p and D of the reaction channel potential are modified into pCffand Deff,all related by &(E,J) = @[D/D,fr (E,J)]o.5.Der = D’+ E, includes a rotational energy correction in D’ = D + Eo(J) - Eo - BJ(J 1).17,35The remaining term, E,, represents a superposition of energy terms from the other (mainly from the likewise disappearing) modes and can be applied to very different degrees of approximation. We have tried various expressions for E,, using eq 2,13 of ref 17 ( I ) , the more general result of ref 35, eq Al-A3 (11), and an alternative expression developed along the same lines of reasoning as the previous D,ff = D ’ + ( E - Eo)(b - l ) / b (S - 2 ) M / 2 ( ~- l ) M [ l + 4N(E - Eo)(b - 1)/bM2]o.5 - 1) (111)
+
+
The nomenclature used here is that of ref 35, Appendix A. The k(E,J) results given above were calculated with Def#II). The first alternative (I), shown to be quite sufficient in several cases,33 deviates by about a factor IO over much of the k(E,J) curves and in k , from calculations with the latter two more detailed corrections, which differ only somewhat at high energies but agree within 10% on the thermal averaged k,. However, it was found that the results on the basis of 111, which treats individually the contributions from all modes, could also be well reproduced for all k(E,J) by using the simple expression
4
D,ff
D ’ - ( b - 1 ) [ E - Eo - B,J(J
+ l)]/s
(IV)
Appendix B
Molecular Parametersfor Modelling N2O4 Bond Fission. N2O4 frequencies (in cm-’): 1368, 812, 266, 79, 1709, 475, 422, 659, 1742, 375, 1251, 743, from ref 41 and 42. Barrier for internal rotation: 875 cm-1!3 NO2 frequencies (in cm-’): 1665.5, 1357.8, 756.8.44 Rotational constants (in cm-I): NZO4, 0.2713, 0.1 174, 0.0804 (calculated from the geometry of ref 45); NOz, 8.0012, 0.4336, 0.4104.44 Threshold energy AHo’ = 53.2 kJ Reaction coordinate: 266 cm-l. Force constant for the N-N bond Correlations of transitional modes (in cm-I): 375 0.3 mdyn A-1.41 0.4336, 659 8.0012, 475 8.0012, 422 0.4336, 79 0.4104, 0.2173 0.4104. Lennard-Jones parameters: N2O4, u = 4.62 A, elk = 347 K; NOz, u = 3.77 A, elk = 210 K; Nz, u = 3.74 A, elk = 82 K. Registry No. NO2, 10102-44-0; N204,10544-72-6.
-
--
-
-
-
(41) Laane, J.; Ohlsen, J. R. Prog. Inorg. Chem. 1980, 27, 465. (42) Holland, R. F.; Maier 11, W. B. J . Chem. Phys. 1983, 78, 2928. (43) Bibaut, C. H.; Ewing, G . E. J . Chem. Phys. 1974,61, 1284. (44) Stoll, D. R., Prophet, H., Eds. JANAF Thermochemical Tables; NSRDS-NBS 37, 2nd ed.; National Bureau of Standards: Washington, D. C . , 1971. (45) McClelland, B. W.; Gunderson, G.; Hedberg, K. J . Chem. Phys. 1972, 56,4541.
Simulation of OH Radical ProfHes in Premixed Atmospheric-Pressure Flat Flames E. W. Kaiser Chemistry Department, Research StafJ: Ford Motor Company, Dearborn, Michigan 481 21 -2053 (Received: December 8, 1987)
OH profiles measured in the postflame gases of three propaneair (6= 0.63,1.17, 1.46) flames and one (4 = 1.01) methaneair flame at atmospheric pressure are compared with computer-simulated profiles generated by using a 15-reaction chemical mechanism. The simulated profiles deviate from the measured data by less than 15% for all four flames. Sensitivity analyses verify that reactions of the H 0 2 radical determine the shape of the OH decay profile for the lean flame. For stoichiometric and rich flames, the radical recombination reaction (H + OH + M) strongly influences the OH radical profile. Experimental measurements of the CO, H2, and O2profiles in lean and stoichiometric flames are also simulated correctly by the mechanism. For the stoichiometric flame, the experimental results verify that the H2, 0 2 , and OH densities are in partial equilibrium in the postflame gases as predicted. These results provide a set of reaction rate constants and diffusion coefficients which correctly simulate the observed data over a wide range of fuel-air equivalence ratios.
(1) (a) Westbrook, C. K.; Dryer, F. L. Prog. Energy Combust. Sci. 1984, 10, 1. (b) Kee, R. J.; Grcar, J. F.; Smooke, M. D.; Miller, J. A. Sandia National Laboratories, Livermore, CA, Report SAND85-8240, 1985.
0022-3654/88/2092-4384$01 S O / O
(2) Kaiser, E. W.; Marko, K.;Klick, D.; Rimai, L.; Wang, C. C.; Shirinzadeh, B.; Zhou, D. Combust. Sci. Technol. 1986, 50, 163.
0 1988 American Chemical Society
OH Radical Profiles in Flat Flames
The Journal of Physical Chemistry, Vol. 92, No. 15, 1988 4385
TABLE I: Reaction Mechanism for Simulation of Pmfflame Species Profiles reaction
log A
forward’ b
E
log A
1. H 0 2 = 0 + OH 2 . 0 + H2 = H + O H 3. O H OH = H2O + 0 4. O H H2 = H20 H 5. O H CO = H + C02 6. H 0 2 M = HO2 MC 7. O + HO2 = 0 2 + O H 8. H H02 = O H OH 9. H + H02 = H2 + 0 2 lO.OH+ H 0 2 = H 2 0 + 0 2 11. H + O H M = H 2 0 + Md 12. H H M = H2 + Me 13. H + CO M = HCO + MI 14. O H HCO = H20 C O 15. H + HCO = H2 + C O
14.39 4.03 8.32 13.68 7.18 18.81 13.24 14.23 13.40 16.85 22.34 18.73 20.80 14.04 13.84
0 2.8 1.4 0 1.3 -1 .o 0 0 0 -1.3 -2.0 -1.3 -1.82 0 0
17272 5921 -397 6092 -765 0 -228 875 700 0 0 0 3688 0 0
13.28 3.68 9.32 14.31 9.26 22.56 13.33 13.20 13.85 17.96 27.25 23.01 24.31 15.41 14.57
+
+ +
+ + +
+
+
+
+
+ + + + +
+
reverse‘ b 0 2.8 1.4 0 1.3 -2.0 0 0 0 -1.3 -3.0 -2.3 -2.82 0 0
E
rep
1157 3 826 16 850 21 250 21 420 51 979 52942 37 969 55 919 70 368 122 600 107 400 22916 103 346 88 164
15 13 13, 6 15 16 17 18 6 19 20 21 13, 6, g 6 22 23
“Units: mol/cm3, s, and kcal; k = AF exp(-E/RT). *References are for the forward rate constants; reverse rate constants are calculated from thermodynamic data contained in the JANAF’ tables for all species except HCO and H 0 2 for which tabulations in ref 6 were used. CRelative third-body efficiencies: H 2 0 , 10.3 (ref 18); all others, 1.0. dRelativethird-body efficiencies: H 2 0 , 6.36 (ref 21); all others, 1.0. ‘Relative third-body efficiencies: H20, 15.0; H2, 2.5 (ref 13); all others 1.0. /All relative third-body efficiencies equal 1.0. #See discussion in text (section d). Description of Simulation
The H C T (Hydrodynamics, Chemistry and Transport) computer code was used to generate the simulated profiles. This code was develowd at Lawrence Livermore National Laboratory3 and has been adapted at Ford Motor Co. for use on an FPS-M64/60 computer. The H C T code normally calculates complete species and temperature profiles based on input flow rate, initial species densities, and kinetic, thermodynamic, and transport parameters. Because of uncertainties in these input parameters, the profiles generated by the computer simulation will not be identical with those measured in the flame. In particular, the peak values of the species densities in the flame zone are strongly influenced by the many reactions involving organic radicals and molecules, some of whose rate constants are not well-known. In the postflame gas, however, the organic species have reached low levels in the flames modeled here, and the postflame reaction mechanism is much simpler. For this reason, a complete simulation of the entire flame was not used. Instead, the simulation was performed only for the postflame burned-gas region. The entire temperature profile in the postflame gas2 and the density of the hydroxyl radical at the first point measured in the burned gas (typically a height of 2.5-3.0 mm above the burner) were fixed in the simulation a t their measured mean values. This provided a starting point which agreed with the experimental data for testing of the reaction mechanism in the postflame burned-gas region only. The calculated decay profile of OH toward equilibrium was then compared to that observed by using the best available rate constants for the reactions included in the mechanism. When experimental data for other stable species in the postflame gas such as CO, C02, H2, or O2were available, the densities of these species were also fixed at their measured values for the same height at which the initial OH density in the simulation was fixed. Measured densities of CO and C02were available for all flames studied. These measured C O and C02densities remained constant at their equilibrium values to within experimental error for the rich flames throughout the region of the postflame gas simulated. The equilibrium values were used in the simulation of the postflame gases for these flames. For the lean and stoichiometric flames, the measured CO density in the postflame region decreased significantly with increasing height, and the initial C O density in the simulation was fixed at its measured value at the same height a t which OH was fixed in the calculation. The H2density used in the simulation of the rich flames was set equal to its equilibrium value, which agreed with the measured density. For the stoichiometric flame, the measured H2 density decreased as a function of height in the postflame gas and was set equal to the measured value at the height chosen for fixing
the initial OH. In the lean flame, the H2 density was too low to be detected and was allowed to be partially equilibrated with the OH in the calculation. The validity of this assumption was checked by carrying out a full flame calculation, which predicted that partial equilibration does occur for this lean flame. The measured O2density was used to establish the initial O2 in the calculation for both the lean and stoichiometric flames, again at the height at which the OH density was fixed. For the rich flames where O2could not be measured, the initial O2was allowed to attain partial equilibrium with the OH in the calculation. This assumption is reasonable for the cases studied, in which no appreciable hydrocarbon density remains in the postflame gas and the measured CO and COz have reached their equilibrium values. Any excess O2 would be rapidly consumed by reaction with H atoms in the first 1-1 mm of the simulation. The H20concentration was never measured directly. However,
reaction mechanism used. During the course of these simulations, sensitivity studies were performed in order to determine which reactions ar6 of the greatest importance in controlling the decay rate of the hydroxyl radical in the postflame region. For each set of initial cofiditions, the decay of the OH radical in the postflame gas was initially simulated by using a reaction mechanism containing the approximately 170 reactions expected to occur in a propane-air flame.4 The simulated decay profile was then compared with that generated by the reduced reaction set presented in Table I. This set contains the reactions expected to be important in the postflame gases of lean and moderately rich flames, which do not contain appreciable amounts of hydrocarbons. In each case, the reduced mechanism produced an O H decay profile which was identical with that generated by the full mechanism. In Table I, the rate constant for each forward reaction was obtained from the reference presented in the table. The reverse rate was calculated from the thermodynamics of the reaction. The free energies of formation used in these thermodynamic calculations were obtained from the JANAF tablesS for all species except H C O and H02. For these two species, a more recent tabulation6 was used. Four of the reactions require the (4)
(3) Lund, C.M. NTIS Report UCRL-52504, 1978.
Westbrook, C. K.; Pitz, W. J. Combust. Sci. Technol. 1984, 37, 117. Prophet, H. JANAF Thermochemical Tables; US.
( 5 ) Stull, D. R.;
Government Printing Office: Washington, DC, 197 1; NSRDS-NBS37.
4386 The Journal of Physical Chemistry, Vol. 92, No. 15, I988
Kaiser
__
TABLE II: Sample Binary Diffusion Coefficients (cm*/s) with N20 species 300 K 1800 K species 300 K 1800 K H 1.238 27.00 HCO 0.158 3.79 Hz 0.797 3.51 CO2 0.158 15.90 N2 0.210 5.74 H20 0.226 4.34 0 0.327 6.70 OH 0.321 6.57 02 0.210 4.36 H02 0.208 4.33 CO 0.208 4.30
SIM U MTED
a Representative binary diffusion coefficients calculated by the computer code described in ref 8. Mixture diffusion coefficients were used in the simulation.
inclusion of third-body chaperons [(6), (1 l), (12), (13)], and the relative efficiencies of the species in the flame gas used in the simulation are presented in footnotes to Table I. Only those species for which efficiencies are reasonably well established have been included; unknown efficiencies were set equal to 1 in all cases. The flow velocity in the postflame gas for use in the simulations was obtained from the measured cold gas volumetric flow rate, the stoichiometry of the reaction, and the measured temperature of the burned gas by assuming that the flow velocity is uniform across the surface of the burner. Previous hot wire anemometer velocity measurements of the cold gas have shown that this assumption is reasonable.' To model species profiles, molecular diffusion must be correctly simulated because, for lighter species such as the H atom, the diffusion velocity can be comparable to the convective velocity in regions of steep density gradients8 Thus, diffusion can influence the species profiles significantly. The diffusion coefficients used in the simulation are mixture diffusion coefficients calculated by a computer code developed at Sandia National L a b ~ r a t o r y . ~ Binary diffusion coefficients with N2calculated by this computer code for the species present in the simulation are listed in Table I1 at two temperatures for reference in comparing to other data (e.g., ref 10). Results Experimental OH and CO decay profiles along the burner center line are presented in Figures 1-5 for propane-air flames at three fuel-air equivalence ratios (4 = 0.63, 1.17, and 1.46) and for a near-stoichiometric methane-air flame, all operated at atmospheric pressure. The experimental data points, which are plotted as individual points in the figures, were obtained by UV absorption spectroscopy* and have an estimated relative accuracy of ~ 5 near % the burner surface and 220% at the maximum heights measured. In the case of the 4 = 0.63 flame, data points in addition to those published in ref 2 have been included. For every set of experimental conditions, the OH radical is present at densities far above thermal equilibrium (shown as dotted lines) near the flame zone and decays toward equilibrium in the postflame gases. In each figure, the simulated decay curve based on the mechanism in Table I is shown as a dashed line. ( a ) 4 = 0.63,Propant-Air. For the fuel-lean flame presented in Figure 1, the simulated OH profile in the postflame gas agrees well with the measured data. In this flame, repeat measurements of the OH density were made for four heights above the burner. The average values at these heights (3.0,4.5,9.5, and 10.0 mm) are plotted in Figure 1 with error bars representing two standard deviations from the mean for these multiple measurements (8, 5, 5 , and 4 measurements, respectively). All other points in the figure represent single measurements. The OH density decreases by a factor of 7.3 over a distance of 15 mm, approaching equilibrium at the maximum height measured. (6) Tsang, W.; Hampon, R. F. J. Phys. Chem. Ref. Data 1986, IS, 1087. (7) Kaiser, E. W.; Rothschild, W. G.; Lavoie, G. A. Combust. Sci. Technol. 1983, 33, 123. (8) Fristrom, R. M.; Westenberg, A. A. Flame Structure; McGraw-Hill: New York, 1965; p 312. (9) Kee, R. J.; Warnatz, J.; Miller, J. A. Sandia National Laboratories, Livermore, CA, Report SAND83-8209, 1983. (IO) (a) Slattery, J. C.; Bird, R. B. MChE J . 1958, 4, 137. (b) Marrero, T R.; Mason, E. A. J. Phys. Chem. Ref. Data 1972, 1 , 3.
00
2
4
6
8
10 12 1 4
6 18 200
HEIGHT ABOVE BURNER ( M M )
Figure 1. Comparison of experimental OH profile to that simulated (-- -) by the reaction mechanism in Table I for a fuel-lean (6 = 0.63) propane-air flame. Simulated curves A, B, and C were obtained by multiplying the rate of reaction 6 by 3, 0.33, and 0.0, respectively. Position of flame = 1.4 mm. Error bars on experimental data points represent 2a from the mean for repeat measurements. Linear flow velocity at 2.5 mm = 68.5 cm/s and T = 1720 K.
In order to determine which of the reactions in Table I influence the decay profile of O H in this flame, the rates of reactions 6-1 5 were set to zero individually or in selected groups. These sensitivity studies demonstrated that reaction 6 followed by (7), (8), (9), or (10) is crucial in controlling the OH decay profile. As shown in Figure 1, removing reaction 6 [or (7), (8), (9), and (lo)] from the mechanism (curve C) decreases the decay rate of OH as a function of height by approximately a factor of 6. The effect of these reactions on the chemistry alone is larger, accounting for more than 90% of the total OH consumption. However, the presence of diffusion makes the effect on the decay rate as a function of distance less pronounced. In this flame, diffusion contributes an effective velocity at a height of 3 mm which is approximately equal to the convective flow as demonstrated by setting all diffusion coefficients to zero. Reducing the chemical rate of decay decreases the distance decay rate. This decreases the diffusion velocity, which in turn increases the decay rate as a function of distance. The opposite effects of diffusion and the rate of chemical consumption of OH, therefore, reduce the effect of changes in chemical rate constants on the density-distance profiles. Reactions 1-4 are very fast. Their rate constants are known to within a factor of 2, and their equilibrium constants are well-established. These reactions are very important because they maintain the species in partial equilibrium with one another." However, the decay rate of OH does not depend critically on the rates of these four reactions. Decreasing all four of these rates simultaneously by a factor of 10, while maintaining the same equilibrium constants, produces no change in the simulated decay profile of OH. Of the other reactions in the mechanism, reaction 11 contributes a significant additional amount (7%) to the observed initial decay rate of the OH radical in the postflame gas. The presence of reaction 5 in the mechanism acts to inhibit the OH decay slightly. Removal of this reaction from the mechanism increases the initial slope of the OH decay profile by approximately 10%. Thus, under very lean conditions, formation and subsequent reactions of the H 0 2 radical control the rate of decay of the superequilibrium radical pool toward thermal equilibrium in the postflame gas. As this process occurs, the concentrations of H, 0, and OH are maintained in partial equilibrium with one another by reactions 1-4. The CO density in this lean flame, which was determined by withdrawing samples through a microprobe,'* is also far above (,I 1) Dixon-Lewis, G. In Combustion Chemistry; Gardiner, W C., Jr., Ed.; Springer-Verlag: New York, 1984; p 106
The Journal of Physical Chemistry, Vol. 92, No. 15, 1988 4387
OH Radical Profiles in Flat Flames
10
--
\ \ \ 0
1
1
1
/
1
1
1
l
I
/
I
/
SIM~JLATED EXPERIMENT
in \
I
0
,
I
I
/
,
I
SIMULATED EXPERIMENT
0
a-
\
,
--
L
\
2________ DELETE 6,l1
\
\ \
\P
\ \
O\
6-
\
,
'9
I
4-
'1
" I
2
I
3
I
0
0
4
Figure 2. Comparison of experimental CO profile to that simulated (---) by the reaction mechanism in Table I for a fuel-lean (4 = 0.63) pro-
pane-air flame. thermal equilibrium in the postflame gas at a distance of 2.5 mm above the burner. The simulated CO decay profile in the postflame gas agrees very well with the experimental data, as shown in Figure 2. The CO density decreases toward equilibrium by reaction with OH in accordance with reaction 5. This reaction is near but not at partial equilibrium, with the forward reaction proceeding at a rate approximately 45% faster than the reverse at a height of 3 mm above the burner. The C O density was not measured for heights greater than 4 mm because it was approaching the limit for which accurate density measurements were possible. The fact that the simulated OH and CO profiles both agree with the respective experimental data is an important observation. Because the sampling of species profiles by a physical probe could perturb the true species concentrations, data obtained by a physical probe should ideally be compared to that measured by a nonperturbing technique in order to assess the extent of possible errors induced by the probe. The agreement of both the stimulated CO and OH decay profiles with the experimental data confirms that, at least in the postflame gas, the probe sampling technique does not perturb the CO density measurement significantly. The simulation permits the rate constant of reaction 6 to be tested and error limits established a t 1600-1700 K. In Figure 1, the two curves bracketing the best simulated curve were obtained by multiplying both the forward and reverse rate coefficients of reaction 6 by 3.0 (labeled A) or 0.33 (labeled B). These changes in the rate of reaction 6 produce simulated curves which deviate significantly from the observed data set. Note that the effect produced by increasing the rate constants is smaller than that obtained by decreasing the rate constants. This occurs because reaction 6 is within a factor of 5 of being equilibrated under these experimental conditions [rate (6)/rate (-6) = 51. Thus, increasing the rate constant will bring the reaction nearer to equilibrium and will, therefore, produce a smaller change in the slope of the simulated OH decay profile than would be expected if the reverse reaction were negligible. Reducing the rate constant will move the reaction farther from equilibrium and will result in a somewhat larger change in the OH profile. There are two potential sources of error in this examination of the rate constant of reaction 6 which must be considered. First, uncertainty in the diffusion coefficients could affect the simulated OH decay profile. In order to estimate this error, all of the diffusion coefficients were simultaneously increased or decreased by a factor of 1.5 (Le., for species i, 0,' = 1.50, or 0.670,). Changes of this magnitude in the diffusion coefficients produce simulated OH profiles which deviate from the best simulated curve by amounts which are equivalent to changing the rate constant of reaction 6 by a factor of N 1.5. It is likely that the diffusion (12) Kaiser, E. W.; Rothschild, W. G.; Lavoie, G. A. Combust. Sci. Technol. 1984,41, 27 1.
2
4
6
8
10 12 14 16 18
20
HEIGHT ABOVE BURNER (MM)
HEIGHT ABOVE BURNER (MM)
Figure 3. Comparison of experimental OH profile to that simulated (---) by the reaction mechanism in Table I for a near-stoichiometric (6 = l.Ol),methane-air flame. Also presented is the simulated profile when
reactions 6 and 11 are deleted from the mechanism. Flame position = 1.4 mm. Linear flow velocity at 3 mm = 94.1 cm/s and T = 1940 K. TABLE III: Stable Species Densities in the Postflame Cas of a Q = 1.01 Methane-Air Flame height," density! 10l6molecules/cm3 mm H, 0, co co, 2.7 1.85 (f0.2) 1.37 (f0.14) 3.47 (f0.17) 33.5 (11.7) 1.72 1.40 3.70 32.4 6.7 1.29 (f0.2) 0.76 (f0.15) 2.5 (f0.12) 34.8 (f1.7) 1.38 0.8 1 2.89 33.8 9.7 1.12 (f0.2) 0.73 (f0.18) 2.19 (fO.ll) 35.7 (f1.7)
1.26
0.60
2.60
34.6
'Height above burner surface. bThe upper and lower entries refer to the observed and simulated densities, respectively. coefficients for the species of importance to this simulation are accurate to better than 50%, and, therefore, the error introduced in the calculation of the OH profile is significantly less. A second possible source of error is uncertainty in the rates of reactions 7-10, whose estimated error factors are 1.25,2,2, and 2, respectively. Simultaneously increasing or decreasing the rates of all four reactions by the above factors changes the simulated curve by an amount equivalent to changing the rate of reaction 6 by a factor of 1.5. This represents an upper limit to this contribution to the uncertainty in the rate constant of reaction 6, because it is unlikely that reactions 7-10 would all be in error by the maximum or minimum values of their respective error limits. Thus, overall the rate constant of reaction 6 in Table I is consistent with the experimental OH decay profile with an uncertainty of a factor of approximately 2, including errors in the experimental data, diffusion coefficients, and other critical reactions. (b) 4 = 1.01, Methane-Air. Figure 3 compares the simulated OH profile with measured data for a near-stoichiometric methane-air flame. Again the agreement is excellent. For this stoichiometric flame, reactions 6 and 11 produce 90% of the observed OH decay rate as a function of height as shown in Figure 3. Individual removal of these reactions from the mechanism indicates that each contributes approximately equally to the initial OH radical decay rate. For a stoichiometric flame, it is possible to measure both the H2and O2densities in the postflame gas, while in rich or lean flames it is very difficult to accurately determine both densities because one is always present at very low concentration. The observed densities of these molecules as well as CO and C 0 2 in the postflame gas are compared with those calculated by the computer simulation at three heights in Table 111. Within experimental error, all of the trends in the postflame gas are simulated cdrrectly for these species. The simultaneous measurement of O2 and H2 in this flame allows a test to be made of the partial equilibration of reactions
4388 The Journal of Physical Chemistry, Vol. 92, No. 15, I988
Kaiser
TABLE I V Comparison of the Experimental OH Density to That Calculated from tbe Measured 0, and H2in a Q = 1.01 Methane-Air Flame Assuming Partial Equilibrium' OH density, molecules/cm'
height? mm 2.7 6.7 9.7
experimental 8.3 x 1015 5.1 x 1015 4.2 x 1015
1
'
1
'
l
'
l
~
l
'
l
'
l
'
1 I ' ~1
SIMULATED EXPERIMENT
c-O-
partial equilibrium 8.3 (f0.9)X 1015 5.0 (*0.9) X 1015 4.4 ( ~ 1 . 0 )x 1015
"Thermodynamic constants from ref 5 were used in calculating the partially equilibrated OH density from the measured O2and H1 concentrations assqming the reaction stoichiometry O2+ Hz = OH + OH. Height above burner surface.
1 and 2. These reactions are predicted to be at equilibrium in the simulation, and the sum of reactions 1 and 2 produces the overall reaction H2 + 02 = 2 0 H (A)
In Table IV, the OH density calculated from the measured 02,
H2, and the equilibrium constant of reaction A determined from the JANAF tabless is compared to the measured OH density a t three heights. Within the experimental error estimated for determining the hydrogen and oxygen densities, the agreement is perfect, verifying that reactions 1 and 2 are partially equilibrated. This also suggests that measurement of the O2and H2densities in a stoichiometric flame could provide a convenient calibration for the fluorescence determination of OH densities. (c) d, = 1.17, Propane-Air. The OH profile simulated by the reaction mechanism in Table I is compared with experimental data for a fuel-rich (d, = 1.17) flame in Figure 4. The agreement is good for an OH density decrease spanning a factor of 10 although the simulated curve does decrease slightly faster than the observed data. Note that, for this flame, the measured OH concentration remains substantially above equilibrium at the maximum height observed. Deleting reactions 6,11, 12, 14,and 15 decreases the initial OH decay rate vs distance by a factor of 10 (curve C), indicating that these reactions contribute virtually all of the chemical cansumption of OH at this equivalence ratio. Sensitivity analyses indicate that, at a height of 3 mm, reaction 1 1 accounts for =75% of the chemical decay rate, while reactions 6, 12,and 14 15 each contribute lo%, lo%, and 5%, respectively. The importance of reaction 6 decreases raapidly with increasing height above the burner because of the drop in the partially equilibrated O2density with increasing height in this rich flame. Thus, over the 17-mm height range for which the density was measured, reaction 1 1 produces an average of 80-85% of the chemical rate of OH consumption in the postflame gas. The curves bracketing the best simulated profile in Figure 4 were obtained by multipyling the rate of reaction 1 1 by either 1.5 (curve A) or 0.67 (curve B). These curves differ by a significant amount from the best simulated curve, indicating that a deviation greater than -25% should be visible. In fact, a rate constant for reaction 11 that is 25% smaller than that presented in Table I would fit the data better, but such a small change is of marginal significance because of other possible errors. The profile changes caused by a *SO% error in the same direction for all mixture diffusion coefficients would be equivalent to a change of ef30% in the rate constant of reaction 11. Thus, overall the rate constant for reaction 1 1 presented in Table I, weighted by the stated third-body efficiencies, agrees with the experimental O H decay profile to within an uncertainty of approximately a factor of 1.5 a t temperatures between 1750 and 1850 K. (6)d, = 1.46, Propane-Air. Figure 5 presents a comparison of the experimental OH decay profile (points) to that simulated by the mechanism in Table I (dashed curve) for a second fuel-rich propaneair flame. At this equivalence ratio (d, = 1-46),reactions 11, 12,and 15 [and (to a much smaller extent) (14)] coupled with the partially equilibrated reaction 13 are the most important in controlling the simulated decay profile. Based on sensitivity analyses, reactions 11, 12,and 14 15 contribute =60%, 20%, and 20%, respectively, to the initial chemical consumption of OH in this flame.
+
+
2
6
4
10 1 2 14 16 18 2C
8
HEIGHT ABOVE BURNER (MM) F i e 4. Comparison of experimental OH profile to that simulated (-- -) by the reaction mechanism in Table I for a fuel-rich (6 = 1.17) propane-air flame. Curves A and B were obtained by multiplying the rate of reaction 1 1 by factors of 1.5 and 0.67,respectively. Curve C: remove reactions 6,11, 12, 14,and 15. At 20-mmheight, [OH], = 6.4 X 10" molecules/cm3. Linear flow velocity at 3 mm = 84.7cm/s and T = 1860
K.
i
o
/ 0
~ 2
, 4
~ 6
, 8
~
,
~
,
~
, I~
,
~
10 12 1 4 1 6 18 20
HEIGHT ABOVE BURNER (MM) Figure 5. Comparison of experimental OH profile to that simulated (-- -) by the reaction mechanism in Table I for a fuel-rich (6 = 1.46)propane-air flame: (curve A) multiply rate of reaction 12 by 2.2(see text); (curve B) change thermochemistry of HCO radical (see text); (curve C) delete reactions 1 1, 12, 14,and 15. Position of flame = 1.4mm. Linear flow velocity at 3 mm = 94.1 cm/s and T = 1920 K.
The agreement between the experimental and simulated curves is acceptable although the simulation does decrease somewhat too slowly particularly in the initial stage, where the data should be the most accurate. A possible explanation for this small deviation may lie in the value chosen for the rate constant of reaction 12, which is that presented for N2 as the third body in a review article by Cohen and Westberg.13 Their estimate was derived from only three data points in the temperature range 77-300 K. Considerably more data over a wide temperature range (77-2000 K) are available for Ar as the chaperon. If the same temperature dependence is assumed for N 2 as is observed for Ar, the best straight line through the low-temperature N2 data yields a rate constant of 1.5 X lO'*T' cm6/(mo12-s)for reaction 12. The rate at 1900 K derived from this choice of rate constant is 2.2times faster than that obtained from the formula in Table I. Using this rate constant for reaction 12 produces the curve labeled A in Figure 5. This agrees well with the observed OH profile in the region 0-1 cm above the burner. Thus, it is possible that the value of k12at high temperature is larger than suggested by Cohen and Westberg for N2 diluent. However, either choice produces an (13) Cohen, N.; Westberg, K.R.J . Phys. Chem. Ref. Doto. 1983, Z2, 531.
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J . Phys. Chem. 1988, 92, 4389-4396
overall fit which is acceptable, and no certain conclusion regarding the rate of reaction 12 can be drawn. As mentioned previously, the establishment of a partially equilibrated HCO density via reaction 13 and subsequent reactions of the HCO radical, particularly with H atoms (reaction 15), contribute to the OH decay in this moderately rich flame. Because reaction 13 is near equilibrium, the OH decay rate responds primarily to the equilibrium constant of this reaction and not to the absolute forward and reverse rate constants. Decreasing the rates of both the forward and reverse processes of reaction 13 by a factor of 10 produces no change in the observed OH decay rate as a function of distance. Changing the equilibrium constant, however, does affect the OH profile, although the relatively small contribution of HCO reactions to the radical consumption rates in this flame means that only a large change causes a significant perturbation. As an example, early estimates of the thermochemistry of the H C O radical5 yielded an equilibrium constant for reaction 13 which is 30 times smaller than more recent estimate~!.'~ The OH decay profile calculated by use of this early HCO thermochemistry is presented as curve B in Figure 5. This simulated curve decreases much faster toward equilibrium than does the experimental data, providing additional confirmation that the earlier thermochemistry of the HCO radical is incorrect. Note that for reaction 13 the third-body efficiencies are assumed to be one for all species. This assumption was made because little data are available concerning such efficiencies for this reaction. However, as mentioned above, this reaction is nearly equilibrated, and the absolute rate of the reaction does not affect the simulation significantly. (14) Chase, M. W.; Curnutt, J. L.; Hu, A. T.; Prophet, H.; Syverud, A. N.; Walker, L. C. J . Phys. Chem. Ref. Data 1974, 3, 311. (15) Frank, P.; Just, Th. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 181. (16) Baulch, D. L.; Drysdale, D. D. Combust. Flame 1974, 23, 215. (17) Baulch, D. L.; Cox, R. A.; Hampson, Jr., R. F.; Kerr, J. A.; Troe, J.; Watson, R. T. J. Phys. Chem. Ref Data 1984, 13, 1259. (18) Nicovich, J. M.; Wine, P. H. J . Phys. Chem. 1987, 91, 5118. (19) Warnatz, J. In Combustion Chemistry; Gardiner, W. G., jr., Ed.; Springer-Verlag: New York, 1984; p 106. (20) Sridharan, U. C.; Qiu, L. X.;Kaufman, F. J . Phys. Chem. 1984.88, 1281. (21) Baulch, D. L.; Drysdale, D. D.; Horne, D. G.; Lloyd, A. C. Evaluated Kinetic Data for High Temperature Reactions; Butterworth: London, 1972; Vol. 1, p 327.
4389
Summary In this paper, computer-simulated O H profiles in the postflame gas of atmospheric-pressure propane- and methane-air flames have been compared in detail to those measured by UV absorption spectroscopy. The chemical mechanism used in the simulation, which consists of 15 reactions, predicts the O H profiles as they decay toward equilibrium from superequilibrium densities in the flame zone with errors of less than 15% when compared to the experimental data. The flames studied cover a wide range of equivalence ratios varying from 4 = 0.63 (fuel-lean) to 4 = 1.45 (fuel-rich). The results of sensitivity analyses show that the formation and subsequent reactions of the H 0 2 radical determine the shape of the OH profile for very lean flames. For a moderately rich flame (4 = 1.17), the recombination of H atoms with O H radicals is of primary importance. In a richer flame (4 = 1.46), recombination of H atoms and reactions of the H C O radical begin to be significant in addition to the (H + O H ) recombination. The results of these simulations provide sensitive tests of the rates of addition of H atoms to O2and of the recombination of H atoms with O H radicals. Finally, measurements of the H1, 02,and O H density profiles in the postflame gas of a stoichiometric methane-air flame show that the OH radical is in partial equilibrium with H2 and O2as predicted by the chemical mechanism. Therefore, the reaction mechanism and rate constants shown in Table I, coupled with the diffusion coefficients summarized in Table 11, constitute a set of parameters which can simulate O H profiles in the postflame gases of atmospheric-pressure flames over a wide span of fuel-air equivalence ratios. Acknowledgment. I thank C. K. Westbrook for generously providing the H C T computer code. I also thank A. Schoene for adapting the program for use on the FPS M64/60 computer and D. Anderson for his invaluable assistance during the adaptation process. Registry No. C,H8, 74-98-6; CH,, 74-82-8; OH, 3352-57-6; HOz, 3170-83-0. (22) Temps, F.; Wagner, H. Gg. Eer. Bunsen-Ges. Phys. Chem. 1984,88, 415. (23) Timonen, R. S.;Ratajczak, E.; Gutman, D. J . Phys. Chem. 1987,91, 692.
Hot Toluene as an Intermediate of UV Multiphoton Dissociation Nobuaki Nakashima,*vt Noriaki Ikeda,t and Keitaro Yoshihara Institute for Molecular Science, Myodaiji, Okazaki 444, Japan (Received: December 17, 1987)
The primary process of excited toluene irradiated by using ArF laser light (193.2 nm) is internal conversion to the ground state in the gas phase. This process produces hot toluene. Hot toluene shows strong absorption in the UV region and hence absorbs a second photon which causes dissociation into a benzyl radical. The apparent yield is 0.24 under a laser fluence of 11.5 mJ cm-2. This is the first observation of UV multiphoton chemistry via a hot molecule. This mechanism is also operative in the ArF laser photolysis of alkylbenzenes.
I. Introduction This paper demonstrates that hot molecules can be one of the intermediates in UV multiphoton chemistry. The hot molecule (denoted as so**)is formed by internal conversion to the ground
electronic state and carries a high vibrational energy, which is to the photon energy absorbed. Hot molecules have been detected by laser flash photolysis of cycloheptatriene,'P2 b e n ~ e n e alkylbenzenes? ,~ and olefins.s Hot
t Present address: Institute of Laser Engineering, Osaka University, 2-6 Yamada-oka Suita, Osaka 565, Japan. *Present address: Chemistry Department, College of General Education, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560, Japan.
(1) Srinivasan, R. J . Am. Chem. SOC.1962, 84, 3432, 4141. Thrush, B. A.; Zwolenik, J. J. Bull. SOC.Chim. Belg. 1962, 71, 642. (2) Hippler, H.; Luther, K.; Troe, J.; Wendelken, H. J. J . Chem. Phys. 1983, 79, 239.
0022-3654/88/2092-4389$01.50/0
0 1988 American Chemical Society
