- Email: [email protected]
Electronic quenching and vibrational relaxation of no A2Σ(υ′=1 and υ′=0) by collisions with H2O
J. Quant. Spectrosc. Radiat. Trans/er Vol. 42, No. 6, pp. 499-508, 1989 Printed in Great Britain
ELECTRONIC
QUENCHING
RELAXATION BY
OF
NO
COLLISIONS
0022-4073/89 $3.00+0.00 Pergamon Press pie
AND
VIBRATIONAL
A22;(v' = 1 and WITH
v'=
0)
H20
ROBERT J. CATTOLICA, THOMAS G . MATAGA, a n d JOHN A. CAVOLOWSKY Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94550, U.S.A. (Received 3 April 1989)
Abstract--Temporally-resolved measurements of laser-induced fluorescence from the A21g state of nitric oxide in a series of low-pressure (19, 38, and 76 torr), stoichiometric H2/O~/Ar flames were used to obtain electronic quenching and vibrational energy-transfer rates. Using a three-level rate-equation system to model the evolution of the fluorescence signal from the directly excited A 2Y.(v'= 1) state and the collisionally-populated A:Y,(v'= 0) state, we have determined the electronic quenching cross sections for the v ' = 1 (36 + 2/~ 2) and v' = 0 (35 + 3 A2) levels, as well as the vibrational energy transfer (v" = 1-0) cross section (1.8 + 0.4/~ 2) for NO due to collisions with H:O at 1340 K. With the temperature lowered from 1340 to 1050 K, the electronic quenching cross sections remain nearly constant while the vibrational energy transfer cross section increased to 3.2 ___0.5/~.
INTRODUCTION For combustion applications of laser-induced fluorescence (LIF) from nitric oxide, energy-transfer rates are needed at combustion temperatures, so that signal strength, laser-saturation power, and detectability limits can be estimated. F o r nitric oxide in the X211 electronic ground state, energy-transfer rates are available over a wide range of temperatures (150-7000 K). ~ In the A2E state, however, electronic quenching and vibrational energy transfer rates are available only at ambient temperature (298 K). 2-5 In our previous study of low-pressure (76torr) NO-doped H2/O2/Ar flames, we reported 6 de-excitation rates for the A2Y,(v'= 1) state, over a range of equivalence ratios from • = 0.88 to 1.50, that were used to correct the N O fluorescence signal to obtain concentration. For the stoichiometric flame condition in that study, in which H 2 0 was the only primary collision partner, we reported an effective de-excitation cross section of 38/~2 at 1350 K. This de-excitation cross section includes both electronic quenching as well as vibrational energy transfer. To refine our understanding of this de-excitation process, we have performed transient-fluorescence measurements on N O in a series of stoichiometric ( ~ = 1.0) H2/O2/Ar flames at low pressure (19, 38, and 76 torr). We observed the temporal development of the fluorescence from the directly laser-excited v' = 1 level and the collisionally populated v' = 0 level in the A 2E state of NO, and compared these measurements with a three-level rate-equation model to describe the excitation/fluorescenceemission process. F r o m a least-squares fit of the model prediction to the experimental data, we were able to determine the electronic quenching cross sections from the v ' = 1 and 0 levels, and the vibrational energy transfer cross section from v' = 1 to 0 for collisions of N O in the A 2y. state with water molecules. EXPERIMENTAL
STUDIES
The hydrogen/oxygen flames in this study were stabilized on a 6.0-cm-dia. sintered stainless-steel burner located in a vacuum chamber with optical access. The burner and vacuum chamber have been described in detail previously. 6 The chamber pressure in the experiment was maintained at constant pressure (19, 38, or 76 torr), independent of gas flow rate, with a feedback-controlled valve connecting the low-pressure chamber to the vacuum pumping system. The volumetric flow rate 499
500
ROBERT J. CATTOLICA et al V t
1
w
A2T~
0
Q2(26) + R12(2S) 214,34 nm
(1,4) band 252,2 nm
(0,1) band 234.5 nm V ~
4
u
-
X2]-[
_
3
2 1 0
Fig. 1. Laser-excitation and fluorescence-emission detection scheme for monitoring the v" = 0 and 1 levels o f the a2Z state of nitric oxide.
through the burner was 7.93 1/min at NTP, with a volumetric mixture ratio for H2 : 02 : Ar of 2 : 1 : 3.05. The nitric oxide was introduced into the flames as a trace constituent (1.74%) in argon. In the burned-gas region of the flames the nitric oxide concentration was 1%. The laser-excitation scheme (see Fig. 1) for nitric oxide follows the same approach used in our previous experiments.6 We excite a single rotational level from the X2II(v" = 0) ground state to the A 2E(v" = 1) state using the Q2 (26) transition at 214.34 nm. This transition is advantageous because the rotational level involved (J = 25.5) is nearly a constant fraction ( _ 3%) of the total nitric oxide number density from 1000 to 1700 K. There is, however, spin splitting of the energy level in the A 2Z excited state. This energy-level splitting is very small, and therefore the Qz(26) transition is directly overlapped by the weaker Rlz (26) satellite transition. To follow the excitation/fluorescenceemission process, we observed the directly populated v ' = 1 level by monitoring the NO(v' = 1, v" = 4) band at 252.2 nm, or the cotlisionally populated v' = 0 level by monitoring the N O ( v ' = 0 , v " = 1) band at 234.5 nm. These bands were chosen because of their favourable branching ratios 7"8and minimal interference with other bands. By observing emission over the entire band, we averaged over the rotational levels and did not distinguish the rotational structure. The fact that the R12(26) transition weakly populates a second rotational level in the excited state has no significant consequences in our experiments, since some rotational energy transfer within the observed vibrational levels is to be expected. In addition, since both the radiative lifetime and low-temperature quenching rates for NO in the A 2E appear to be independent of rotational level,4 the dynamics of the excitation/fluorescence process observed from the vibrational band fluorescence should not be affected by rotational energy transfer. The optical system used for the nitric oxide fluorescence experiments is illustrated schematically in Fig. 2. The laser system for the experiments consisted of a frequency-doubled (532-nm, 220-mJ, 10-Hz) N d : Y A G laser (Quanta-Ray DCR-1A) pumping a dye laser (oscillator plus amplifier), followed by frequency-doubling and Raman shifting in a hydrogen cell. To excite the NO (1, 0) Q2(26) + R12(26) transition, we used the frequency-doubled output of kiton red, Raman shifted to the third anti-Stokes wavelength, 214.34 nm (70 p J). The laser pulse shape was measured with a 500-psec vacuum diode (ITT F4018). The laser was routed around the optical table, as indicated in Fig. 2, by 90%turning prisms to provide a 12-nsec delay between the laser-pulse shape measurement and the fluorescence measurement. The laser beam was focused to a 0.75 mm dia in the vacuum chamber 40 mm above the burner surface with a 500-ram focal-length u.v. lens. The fluorescence signal from nitric oxide in the burned-gas region above the burner was collected and focused onto the entrance slit (1-mm slit width, 8-mm slit height) of a 0.25-m monochromator (3-mm bandwidth) with a single 150-mm focal-length u.v. lens used at f/4. The monochromator was positioned in wavelength on either the NO(I, 4) band at 252.2 nm or the NO(0, 1) band at 234.5 nm. The fluorescence signal from the monochromator was measured using a photomultiplier tube (Hamamatsu R955) with a nonuniform dynode-voltage distribution to obtain 2-nsec temporal resolution. The fluorescence signal from the photomultiplier and the laser-pulse shape from the
Electronic quenching and vibrational relaxation
501
charge pre-amp __J~ transient digitizer ......
I
:
I
l
Nd:YAQ=.,
I
~ ..........................
I : I
t '~'-'[~t
0.25meter monochromator
-IX
II vacuum DioUe
VacuumDiode
,
U
........ O't- Ramanshitter" Hz" t'0-~
?--I [J-] charge transient pre-amp digitizer charge transient pre-amp digitizer Fig. 2. Schematic of the experimental setup for the temporally-resolved laser-fluorescencemeasurements of nitric oxide in low-pressure H2/O2/Ar flames. vacuum diode were recorded with a Tektronix 7912AD transient digitizer at a 5-GHz sampling rate and stored on a computer. The temporally resolved measurements of the excitation-laser pulse and the subsequent fluorescence emission from the NO(v' = 1, v" = 4 ) band and the NO(v' = 0, v " = 1) band are plotted in Fig. 3 for the stoichiometric H2/O2/Ar flames at three different pressures: 19, 38, and 76 torr. For each flame the data are obtained from averaging 128 laser shots. Because of the low signal strength from the NO(0, 1) band, it was necessary to perform a zero-signal baseline measurement and correction to the fluorescence signals. For clarity, only every tenth data point 4
3
(a)
4
(b)
~,o, ,~
.... ~,,~,.M~,~ . . . . . . . . . . . . . . . . . .
NCt(1,4)model 3-
NO(t,4) fluore~ence
~ ~
................
NO(1,4}model
L~ N0[1,4)fluor,uceoce
iF i,
3-
I-
0
~d
0
10
20
30
40
50
60
70
80
20
30
time (nsec)
40
50
eo
70
time (nsec)
4-
-3
(c) ......~,,~ ~
NO(1,41model
[\
z~ NO(1.4~ftuo~em:ence
i~
3-
...............
N(~O,1) fluorescence • 10
2-
,-
i
10
-
i
i
20
30
,
i
i
40
50
•
i
60
•
i
70
80
t i m e (nsec)
Fig. 3. Laser-induced fluorescence signals from the A2~ state of nitric oxide in low-pressure H2/O2/Ar flames: (a) 76 torr, (b) 38 torr, and (c) 19 torr. The symbols A and x indicate the measured fluorescence emission from the NO(l, 4) and NO(0, l) bands of the A2~,-~X2II transition at every tenth data point. The least-squares fit of the integration of a three-level rate-equation model is shown with a solid line for the NO(l, 4) fluorescence and a broken line for the NO(0, 4) fluorescence. Q.S.R.T. 4216--E
80
502
RoBErcrJ. CATTOL1CAet al
from the fluorescence signal has been plotted. Two general qualitative observations can be extracted from the raw data: first, the fluorescence from the directly excited NO(l, 4) band is much stronger than the collisionally populated NO(0, 1) band, by about a factor o f 30, and second, as the pressure in the vacuum chamber was reduced from 76 to 19 torr, the decay o f the fluorescence slows. The radiative lifetime Trad for the nitric oxide A 2]E state is 210 and 205 nsec for the v ' = 1 and 0 levels, respectively. The rapid fluorescence decays, compared to the radiative lifetime, indicate that collisional de-excitation is still the dominant process, even at 19 torr. To determine the electronic quenching rates and vibrational energy transfer rates from these data we must model the laser excitation/fluorescence emission process. THREE-LEVEL RATE-EQUATION
MODEL
The process of laser-induced fluorescence from the NO molecule, including vibrational energy transfer, can be described by a simple three-level model as illustrated in F i g . 4. The sum of populations in the ground state N~, the laser-excited state N2, and the collisionaUy-excited state N3 is equal to the initial total population No, i.e. No = N, (t) + N2(t) + N3(t).
(1)
Prior to laser-excitation, the entire population is in the ground-state level N~ (0) = No,
N2(0) = 0,
N3 (0) = 0.
(2)
The time-dependent populations in these three levels are described by a coupled set o f first-order differential equations. The rate equation for the population of Nz is d N 2 / d t = N I B l 2 I l z ( t ) - N2B21 ll2(t) -- A z l N 2 - Q21~v2 - - V 2 3 N 2 q- V32N3,
(3)
and the rate equation for N3 is d N 3 / d t = V23N2 -- V32N3 - A31N3 - Q31N3,
(4)
where I~2(t) is the spectral energy density, B~2 and B2t are the Einstein coefficients for absorption and stimulated emission, A21 and A3~ are the spontaneous emission rates for the N2 and N3 levels, Qz~ and Q3t are the quenching rate constants, and V32 and Vz3 are the vibrational energy-transfer rates between the N2 and N3 levels. The Einstein coefficients are related by the degeneracies of the ground state and the excited state as follows: (5)
B12gl = Bzig2.
The vibrational transfer rates are related through detailed balance. At equilibrium, N2eq/N3~ = (g2/g3) e x p [ - (E2 -- E3 )/kT].
(6)
At equilibrium, the rate o f transfer between the two states must be equal, viz. N2eq V23 N~
=
N3eq 1/32.
Level 2
(7) A~ (v',, 1)
112B12
t v" t ,,,~,il
X2i-!
Fig. 4. Three-levelmodel of the processes involved in the laser excitation of NO from the X2II ground state and fluorescenceemission from the v' = 0 and 1 levels of the A 2Z excited state.
Electronic quenching and vibrational relaxation
503
For vibrational levels, the degeneracies are g2 = g3 = 1. We may combine Eqs. (6) and (7) and obtain V32 exp( - AE23/kT) V23,
(8)
=
where AE23 is the energy-level difference between v ' = 1 and 0 in the NOA 2E state, and T is the temperature. To reduce Eqs. (1)-(4) to a simplified form suitable for numerical integration, we normalize the populations in the three levels by the initial total population and write nl = Ni/No,
n2= N2/N o,
n3= N 3 / N o.
(9)
To take into account the laser spectral line shape and the absorption-line shape, an effective absorption coefficient, b~2, is introduced, which includes a laser line-shape factor q(6v~, 6va): b¿2 -~- q ( f v l ,
Ova)Bl2
(10)
Since the laser spectral halfwidth 6v~ (--,0.35 cm -I) is larger than the primarily Doppler-broadened absorption halfwidth 6va(~ 0.2 cm-~), the laser-line shape factor is nearly constant over the range of temperature in our experiments (1000-1400 K). By using Eqs. (1), (5), and (8) to eliminate Nl, B21, and V32 from Eqs. (1) and (3), the N2 rate equation becomes dn2dt- LF1 -- n2 -- n 3 - n 2 ( g ' ) ] b , 2 I i 2 - (Az, + Q2, "4" V23)n2 "1"- V23exp(--AE23/kT)n3,
\g2,/_J
(11)
and the N3 rate equation becomes dn3 = V23n2 - [V23e x p ( - A E 2 3 / k T ) + A31 + Q3t]na, dt
(12)
with the initial conditions n2(0) = 0,
n3(0) = 0.
(13)
The time-dependent spectral energy density of the laser II2(t) is evaluated from the measured laser-pulse shape and a measurement of the pulse energy. It was found that there was little variation in the averaged laser-pulse shape throughout the experiment, so that a representative profile was used. The measured laser profile was normalized by its integrated area and scaled by the measured laser-pulse energy Elase r :
[ )/;o
I12(t) = E,a~r ItRexp(t
]
1,2exp(t)dt .
(14)
The unknown parameters in Eqs. (11) and (12) are the quenching rates Q21 and Q31 and vibrational energy transfer rate I"23. All of the other parameters are known spectroscopic constants. The gas temperature enters into the problem through the detailed-balance assumption relating Vz3 and I"32 and is measured separately from quenching-corrected LIF spectra of O H . 9 To determine the electronic quenching rates Qzl and Q31 and the rate for vibrational energy transfer V23, we compare the results of the numerical integration of Eqs. (11) and (12) with the measured fluorescence signals from the NO(l,4) and NO(0, 1) bands. The time-dependent fluorescence photon flux In~/(t) from each level follows the time-dependent population in that level, viz. f~
1%(,) = rl• 4---~VA o.No n~(t )
(15)
where f~ is the solid angle of the light-collection system from a fluorescence volume V that is viewed with a detector of sensitivity r/ij; A 0 is the spontaneous emission rate for the observed band. The time-dependent fluorescence signal ln,~(t) is recorded on a transient digitizer with a 400-MHz bandwidth that includes both the detector and amplifier frequency response. This finite bandwidth will broaden the observed fluorescence signal. To account for this instrument bandwidth effect, the
504
ROBERT J. CATTOLICA et al
predicted time-dependent fluorescence signal must be convoluted by the instrument bandwidth function to yield the measured fluorescence signal [n~ (t) =
:0
Ii,~t(t -- z)I,~ (z) dz.
(16)
The instrument-bandwidth function/~n~t (t - z) was determined by measuring the response of the transient recording system to a 100-psec pulse from a diode laser. The time-dependent fluorescence signal, lab(t), follows the temporal development of the population n~(t) through Eq. (15). We therefore perform the convolution indicated in Eq. (16) on the predicted populations ni(t) and obtain ~(t) =
t' /i.~t(t- ~)n~(r) dl:.
(17)
do
The temporal evolution of the measured fluorescence signal then follows the instrument-broadened population history
[n~(t) = rl,+-~ VAoNofz,(t).
(18)
Since only a fraction of the population in the excited levels fluoresce in the NO(l, 4) and NO(0, 1) bands, the spontaneous emission rate, A~: for each band is determined from the radiative lifetime for the level and the branching ratios:
A U= flO/T~d.
(19)
Introducing the branching-ratio relation and rearranging terms, we obtain
fi~exp(t) = [fl(t)/Iqi:-~ V(flq/%ad)No ].
(20,
Since f~, V, No are the same for fluorescence signals from both NO(I, 4) and NO(0, 1) and since the r~,d are nearly identical, we can put the fluorescence signals in a form suitable for comparison with the convolution of the numerical solutions for n~ and n2 as follows: r~,~p(t) = const. ×
[n(t)/(qi:fl~).
(21)
The fluorescence signals must be scaled and shifted for comparison with the numerical solution to account for the gain of the transient digitizer and the time-delay offset between the laser and fluorescence. The fluorescence signal for the N2 level, in[NO(l, 4)], is normalized and time-shifted as indicated: ~i:exp= A x Tn[NO(1, 4)](t + B).
(22)
The constant A is set so that the peak signal of the experimental profile matches the peak signal of the convolution of the numerical solution for n2. The constant B is used to align the numerical and experimental signals in time, and accounts for the time delay between the measured laser pulse shape and fluorescence. A similar equation is used for the fluorescence signal from the N3 level to remove the time delay offset and to account for the difference in the branching ratios for the two levels: t~3exp= A ×
(r121132,/r13~[331)[,[NO(O, 1)](t
+ B).
(23)
The constants A and B are the same as in Eq. (22). The detector sensitivities q0 are determined from measurements of a calibrated deuterium lamp. It is now possible to compare the convoluted numerical solution with the scaled and shifted experimental profiles. There are three fitting parameters, namely, the quenching rates Q~I and Q31 and the vibrational energy transfer rate V23for the two experimental profiles. The parameters are fitted by establishing a ~2 error for each of the fluorescence profiles and minimizing this error by adjusting the fitting
Electronic quenching and vibrational relaxation
505
parameters. Two semi-independent X2 are used for each experimental profile to estimate the error between the numerical and experimental profiles. The Z22 error for the ~2 signal is given by
The Z 2 error for the ~3 signal is given by
z2(a)=~[:3exp--n3(li;Q31'g23)12"i= '
0"3
(25)
Since the n3 signal is about a factor of 30 below the n2 signal, the g 2 is minimized by varying only the quenching rate, Q2,. The other two parameters are fitted using the X23for the rJ3 signal. In both cases, the 3(2 error is weighted by the standard deviation of the fluorescence signals found from Poisson statistics, i.e. 0"2= ~
and
0"3= x//-~3.
(26)
The Z 2 are then minimized by a method of steepest descent using the gradient of Z2. The gradient of the X2 with respect to the fitting variables determines the next value of the variables through anext = acu r - -
constant x VZ 2,
(27)
where a represents a vector of the fitting parameters. The gradient for the X2 error is V• 2 = OZ~/OQ2,,
(28)
and the gradient for the Z] error is V~(~ = (0~(2/0 V23 )~'23 "~
(OzE#~Q3,)t)3,-
(29)
The parameters Qz,, Q3,, and V23 are found by repeating the numerical integration of the rate equations using Eq. (27) to determine new values of the parameters until the Z z errors reach a stable minimum. RESULTS
AND
DISCUSSION
The comparison of the three-level rate-equation model with the temporally resolved fluorescence from the NO(I, 4) and NO(0, 1) bands is presented in Fig. 3. An excellent fit to the measured fluorescence signals is obtained. For the 76-torr flame in Fig. 3(a), the least-squares fit gives values for the electronic quenching rate from the A2E state of Q2, = 1.22 x 108 sec -l for the v ' = 1 level, Q3, = 1.21 x l08 s e c - ' for v' = 0, and a vibrational energy transfer rate of V:3 = 6.1 x l06 sec-'. The quenching rates for the 19-, 38-, and 76-torr flames, which are summarized in Table 1, are much faster than the spontaneous emission rate for the fluorescence, 5 x 10 6 s e c -1. The vibrational energy transfer rates, also summarized in Table 1, are about a factor of 20 slower than the quenching rates. Table 1. Quenching and vibrational energy transfer rates and cross sections from least-squares fits of the three-level rate-equation model to NO transient fluorescence data for three low-pressure H2/O2/Ar flames. P0 (tort)
76
38
19
T (K)
1340
1124
1050
Q21 (s'l) Q3! (s -1) V23 (s"1) oQ21 (A2) ~Q3t (A2) ~V23 (A2)
1.22 x 108 1.21 x 108 6.1 x 106 365:2 355:3 1.8 ± 0.4
0.64 x 108
0.40 x 108
0.60 x 108
0.33 × 108
3.7 x 106 35+2
3.0 x 106 41 + 2
32±3
34-I-3
2.0 5:0.4
3.2 5:0.5
ROBERT J. CATTOLICA et al
506
3
(o)
4 "
le~eri~nal
(b)
model
3
~p, ,~.4 i~
rnod~
-21
+t0%
2-
-1 1-
.....
0
,
0
20
30 t~e
~ -
40
50
60
70
0
0
80
m ~ 4
10
20
30
(nsec)
( CI
,
.
40
tPne
20
4o
5o
,
r
60
,
~
0
70
80
(nsec)
....
3-
...::9.~ . . . . . . .
3o
.
kllllN" aignal
+10%
lo
,
50
I l l l ~ lligtlal
•
o
/ ' ~ ' .
~
0
8o
7o
!
.,.:P-~ . . . . . . . . .
i
8o
~
.
i
2o
•
~
ao
t
4o
•
i
6o
t
6o
2
ao
time (nsec) time (nsec) Fig. 5. Three-level rate-equation model results for the NO(I, 4) fluorescenceand N O ( 0 , 4) fluorescence in the 19-torr H 2 / O 2 / A r flame for + 10% variation in the parameters; (a) Q21, (b) V23, (c) Q31, and (d) T.
To illustrate the sensitivity of the least-squares fit of the three-level model to the experimental data, the predicted fluorescence signals for a + 10% variation in the parameters Q21, Q3~,/I23, and T are plotted in Fig. 5 for the 19-torr flame. In Fig. 5(a), the variation of Q2~ affects both the NO(l, 4) and NO(0, 1) fluorescence signal. Because the rate of vibrational energy transfer, V~3, is much slower than Q2~, variation in V23 or Q32 has no significant effect on the behavior of the NO(l, 4) fluorescence in Figs. 5(b) and (c). In the least-squares fitting procedure it is therefore necessary to determine Q21 from the NO(l, 4) signal prior to determining V23 and Q3~. In fitting the NO(0, 1) fluorescence signal, the variation in V23 has a significant effect on the magnitude of the signal in Fig. 5(c). In Fig. 5(b), the variation of Q31 primarily affects the decay rate of the fluorescence in the NO(0, 1) band. A + 10% variation in the temperature in Fig. 5(d) has no effect on either of the fluorescence profiles. Since the temperature enters into the model explicitly only through the detailed balance relation, Eq. (8), relating II23 and I,'32, and since the reverse rate is small at this temperature, a _+ 10% variation has no significant effect. Since the primary collision partner for energy transfer in the burned-gas region of these low-pressure flames is H20, these measured electronic quenching and vibrational energy transfer 110"~
E O
-
-
9 0 -]
•
v" -- 0 McDermid lind Lauden$1aget (19821
0
v'--O
¢,3
~
70
o
50o
e-t-
oe -
30
100 300
500 700 900 1100 1300 1500 t e m D e r a t u r e (K) Fig. 6. Electronic quenching cross section of nitric oxide for v' = 1 a n d 0 by H 2 0 as a function of temperature.
Electronic quenching and vibrational relaxation
507
Table 2. Electronic quenching cross sections for the A 2y state of nitric oxide by gases of interest in combustion.
Species
o (]~2) at 298 K from Refs. 4 and 5
H20
102
(v'=0)
CO2
61
(v'=0)
NO
35 32 27
(v'=0) (v'=l) (v'=2)
O2
22.3
(v'=0)
Ar
0.06
(v'=0)
N2
0.014 0.241 0.122
(v'=0) (v'=l) (v'=2)
o'(/~2) at 1340 K 35 :t: 3 (v'=0) 36 + 2 (v'=l)
rates can be converted to H 2 0 collision cross sections using the known water concentration and the measured gas temperature. The calculated electronic quenching cross sections for the 76-torr flame are 36 _+ 2 ,~2 for the v' = 1 level, and 35 _ 3 ,~2 for the v' = 0 level. The vibrational relaxation cross section from v' = l ~ is 1.8 _ 0.4 A2. These cross sections, along with the results for the other flames, are listed in Table 1. The uncertainties in these measured cross sections were determined from a combination of the errors associated with the fluorescence signals and the temperature measurements. In Fig. 6 we plot the quenching cross section for v' = 1 and 0 as a function of gas temperature for the experiments conducted at all three pressures. These quenching cross sections are relatively constant except for the lowest temperature measurement for v ' - - 1. A comparison in Fig. 6 with the much higher measured cross section (102 A:) for H 2 0 at ambient temperature 7 is indicative of the importance of the role of the attractive part of the intermolecular potential on the electronic quenching of nitric oxide. In Table 2 we present a summary of the previously measured 4"5electronic quenching cross sections for the A 2E state of nitric oxide for a number of collision partners of interest in combustion experiments. At ambient temperature, H 2 0 is the most efficient and Ar the least efficient species in quenching NO. At the higher temperature in our experiments, we assumed that this relationship was still valid and that H 2 0 w a s the dominant quenching species. Although N O has a self-quenching cross section comparable to our measurement for H20, its abundance is only 1/39th of that of H 2 0 in our experiment, so its effect can be neglected. In Table 3 we compare our measured vibrational energy transfer cross sections for the v ' = 1 level of the A :E state of NO with measurements for both the A 2y, state and the X2H ground state at ambient temperature.~'5 In the X2II ground state of NO, the vibrational energy transfer (VET) cross sections for N2 and Ar are very small. The much higher VET rate for NO colliding with itself Table 3. Vibrational energy transfer cross sections for the a2~ state and the X21-I state of nitric oxide by gases of interest in combustion. A2~ (v'= 1) o (/~2) at 298 K (Ref. 5)
X2yI (v'=l) o (,~2) at 298 K (Ref. 1)
N2
0.031
2.13 x 10-5
NO
1.36
0.013
Species
Ar
H20
7.7 x 10.6 1.8 -4-0.4 (1340 K) 2.0 :I:0.4 (1150 K) 3.2,4-0.5 (1024 K)
508
ROBERT J. CATTOLICA et al
has been attributed ~ to the influence of strong attractive forces. In the A2X state, the large VET cross section for N O has been explained 3 by resonance electronic energy exchange. Although such a direct resonant electronic-exchange process cannot explain the large cross section we observed for the vibrational relaxation of N O by H20, the strongly attractive intermolecular force between N O and H 2 0 (as indicated by the large electronic quenching cross section) probably plays a significant role.
Acknowledgements--The authors would like to thank J. Meeks for his excellent technical assistance in the design and implementation of these experiments. This work was supported by the U.S. Department of Energy, Officeof Basic Energy Sciences, Division of Chemical Sciences. REFERENCES L. Doyennette and M. Margottin-Maclou, J. Chem. Phys. 84, 6668 (1986). H. P. Broida and T. Carrington, J. Phys. Chem. 38, 136 (1963). L. A. Melton and W. Klemperer, J. Phys. Chem. 59, 1099 (1973). I. S. McDermid and J. B. Laudensberg, JQSRT 27, 483 (1982). T. Imajo, K. Shibuya, K. Obi, and I. Tanaka, J. Phys. Chem. 90, 6006 (1986). R. J. Cattolica, T. G. Mataga, and J. C. Cavolowsky, in Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburg, in press (1989). 7. T. J. McGee, J. Burris, and J. Barnes, JQSRT 34, 81 (1985). 8. T. J. McGee, G. E. Miller, J. Burris, Jr., and T. J. McIlrath, JQSRT 29, 333 (1983). 9. R. J. Cattolica, T. G. Mataga, and J. A. Cavolowsky, manuscript in preparation.
I. 2. 3. 4. 5. 6.
ELECTRONIC
QUENCHING
RELAXATION BY
OF
NO
COLLISIONS
0022-4073/89 $3.00+0.00 Pergamon Press pie
AND
VIBRATIONAL
A22;(v' = 1 and WITH
v'=
0)
H20
ROBERT J. CATTOLICA, THOMAS G . MATAGA, a n d JOHN A. CAVOLOWSKY Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94550, U.S.A. (Received 3 April 1989)
Abstract--Temporally-resolved measurements of laser-induced fluorescence from the A21g state of nitric oxide in a series of low-pressure (19, 38, and 76 torr), stoichiometric H2/O~/Ar flames were used to obtain electronic quenching and vibrational energy-transfer rates. Using a three-level rate-equation system to model the evolution of the fluorescence signal from the directly excited A 2Y.(v'= 1) state and the collisionally-populated A:Y,(v'= 0) state, we have determined the electronic quenching cross sections for the v ' = 1 (36 + 2/~ 2) and v' = 0 (35 + 3 A2) levels, as well as the vibrational energy transfer (v" = 1-0) cross section (1.8 + 0.4/~ 2) for NO due to collisions with H:O at 1340 K. With the temperature lowered from 1340 to 1050 K, the electronic quenching cross sections remain nearly constant while the vibrational energy transfer cross section increased to 3.2 ___0.5/~.
INTRODUCTION For combustion applications of laser-induced fluorescence (LIF) from nitric oxide, energy-transfer rates are needed at combustion temperatures, so that signal strength, laser-saturation power, and detectability limits can be estimated. F o r nitric oxide in the X211 electronic ground state, energy-transfer rates are available over a wide range of temperatures (150-7000 K). ~ In the A2E state, however, electronic quenching and vibrational energy transfer rates are available only at ambient temperature (298 K). 2-5 In our previous study of low-pressure (76torr) NO-doped H2/O2/Ar flames, we reported 6 de-excitation rates for the A2Y,(v'= 1) state, over a range of equivalence ratios from • = 0.88 to 1.50, that were used to correct the N O fluorescence signal to obtain concentration. For the stoichiometric flame condition in that study, in which H 2 0 was the only primary collision partner, we reported an effective de-excitation cross section of 38/~2 at 1350 K. This de-excitation cross section includes both electronic quenching as well as vibrational energy transfer. To refine our understanding of this de-excitation process, we have performed transient-fluorescence measurements on N O in a series of stoichiometric ( ~ = 1.0) H2/O2/Ar flames at low pressure (19, 38, and 76 torr). We observed the temporal development of the fluorescence from the directly laser-excited v' = 1 level and the collisionally populated v' = 0 level in the A 2E state of NO, and compared these measurements with a three-level rate-equation model to describe the excitation/fluorescenceemission process. F r o m a least-squares fit of the model prediction to the experimental data, we were able to determine the electronic quenching cross sections from the v ' = 1 and 0 levels, and the vibrational energy transfer cross section from v' = 1 to 0 for collisions of N O in the A 2y. state with water molecules. EXPERIMENTAL
STUDIES
The hydrogen/oxygen flames in this study were stabilized on a 6.0-cm-dia. sintered stainless-steel burner located in a vacuum chamber with optical access. The burner and vacuum chamber have been described in detail previously. 6 The chamber pressure in the experiment was maintained at constant pressure (19, 38, or 76 torr), independent of gas flow rate, with a feedback-controlled valve connecting the low-pressure chamber to the vacuum pumping system. The volumetric flow rate 499
500
ROBERT J. CATTOLICA et al V t
1
w
A2T~
0
Q2(26) + R12(2S) 214,34 nm
(1,4) band 252,2 nm
(0,1) band 234.5 nm V ~
4
u
-
X2]-[
_
3
2 1 0
Fig. 1. Laser-excitation and fluorescence-emission detection scheme for monitoring the v" = 0 and 1 levels o f the a2Z state of nitric oxide.
through the burner was 7.93 1/min at NTP, with a volumetric mixture ratio for H2 : 02 : Ar of 2 : 1 : 3.05. The nitric oxide was introduced into the flames as a trace constituent (1.74%) in argon. In the burned-gas region of the flames the nitric oxide concentration was 1%. The laser-excitation scheme (see Fig. 1) for nitric oxide follows the same approach used in our previous experiments.6 We excite a single rotational level from the X2II(v" = 0) ground state to the A 2E(v" = 1) state using the Q2 (26) transition at 214.34 nm. This transition is advantageous because the rotational level involved (J = 25.5) is nearly a constant fraction ( _ 3%) of the total nitric oxide number density from 1000 to 1700 K. There is, however, spin splitting of the energy level in the A 2Z excited state. This energy-level splitting is very small, and therefore the Qz(26) transition is directly overlapped by the weaker Rlz (26) satellite transition. To follow the excitation/fluorescenceemission process, we observed the directly populated v ' = 1 level by monitoring the NO(v' = 1, v" = 4) band at 252.2 nm, or the cotlisionally populated v' = 0 level by monitoring the N O ( v ' = 0 , v " = 1) band at 234.5 nm. These bands were chosen because of their favourable branching ratios 7"8and minimal interference with other bands. By observing emission over the entire band, we averaged over the rotational levels and did not distinguish the rotational structure. The fact that the R12(26) transition weakly populates a second rotational level in the excited state has no significant consequences in our experiments, since some rotational energy transfer within the observed vibrational levels is to be expected. In addition, since both the radiative lifetime and low-temperature quenching rates for NO in the A 2E appear to be independent of rotational level,4 the dynamics of the excitation/fluorescence process observed from the vibrational band fluorescence should not be affected by rotational energy transfer. The optical system used for the nitric oxide fluorescence experiments is illustrated schematically in Fig. 2. The laser system for the experiments consisted of a frequency-doubled (532-nm, 220-mJ, 10-Hz) N d : Y A G laser (Quanta-Ray DCR-1A) pumping a dye laser (oscillator plus amplifier), followed by frequency-doubling and Raman shifting in a hydrogen cell. To excite the NO (1, 0) Q2(26) + R12(26) transition, we used the frequency-doubled output of kiton red, Raman shifted to the third anti-Stokes wavelength, 214.34 nm (70 p J). The laser pulse shape was measured with a 500-psec vacuum diode (ITT F4018). The laser was routed around the optical table, as indicated in Fig. 2, by 90%turning prisms to provide a 12-nsec delay between the laser-pulse shape measurement and the fluorescence measurement. The laser beam was focused to a 0.75 mm dia in the vacuum chamber 40 mm above the burner surface with a 500-ram focal-length u.v. lens. The fluorescence signal from nitric oxide in the burned-gas region above the burner was collected and focused onto the entrance slit (1-mm slit width, 8-mm slit height) of a 0.25-m monochromator (3-mm bandwidth) with a single 150-mm focal-length u.v. lens used at f/4. The monochromator was positioned in wavelength on either the NO(I, 4) band at 252.2 nm or the NO(0, 1) band at 234.5 nm. The fluorescence signal from the monochromator was measured using a photomultiplier tube (Hamamatsu R955) with a nonuniform dynode-voltage distribution to obtain 2-nsec temporal resolution. The fluorescence signal from the photomultiplier and the laser-pulse shape from the
Electronic quenching and vibrational relaxation
501
charge pre-amp __J~ transient digitizer ......
I
:
I
l
Nd:YAQ=.,
I
~ ..........................
I : I
t '~'-'[~t
0.25meter monochromator
-IX
II vacuum DioUe
VacuumDiode
,
U
........ O't- Ramanshitter" Hz" t'0-~
?--I [J-] charge transient pre-amp digitizer charge transient pre-amp digitizer Fig. 2. Schematic of the experimental setup for the temporally-resolved laser-fluorescencemeasurements of nitric oxide in low-pressure H2/O2/Ar flames. vacuum diode were recorded with a Tektronix 7912AD transient digitizer at a 5-GHz sampling rate and stored on a computer. The temporally resolved measurements of the excitation-laser pulse and the subsequent fluorescence emission from the NO(v' = 1, v" = 4 ) band and the NO(v' = 0, v " = 1) band are plotted in Fig. 3 for the stoichiometric H2/O2/Ar flames at three different pressures: 19, 38, and 76 torr. For each flame the data are obtained from averaging 128 laser shots. Because of the low signal strength from the NO(0, 1) band, it was necessary to perform a zero-signal baseline measurement and correction to the fluorescence signals. For clarity, only every tenth data point 4
3
(a)
4
(b)
~,o, ,~
.... ~,,~,.M~,~ . . . . . . . . . . . . . . . . . .
NCt(1,4)model 3-
NO(t,4) fluore~ence
~ ~
................
NO(1,4}model
L~ N0[1,4)fluor,uceoce
iF i,
3-
I-
0
~d
0
10
20
30
40
50
60
70
80
20
30
time (nsec)
40
50
eo
70
time (nsec)
4-
-3
(c) ......~,,~ ~
NO(1,41model
[\
z~ NO(1.4~ftuo~em:ence
i~
3-
...............
N(~O,1) fluorescence • 10
2-
,-
i
10
-
i
i
20
30
,
i
i
40
50
•
i
60
•
i
70
80
t i m e (nsec)
Fig. 3. Laser-induced fluorescence signals from the A2~ state of nitric oxide in low-pressure H2/O2/Ar flames: (a) 76 torr, (b) 38 torr, and (c) 19 torr. The symbols A and x indicate the measured fluorescence emission from the NO(l, 4) and NO(0, l) bands of the A2~,-~X2II transition at every tenth data point. The least-squares fit of the integration of a three-level rate-equation model is shown with a solid line for the NO(l, 4) fluorescence and a broken line for the NO(0, 4) fluorescence. Q.S.R.T. 4216--E
80
502
RoBErcrJ. CATTOL1CAet al
from the fluorescence signal has been plotted. Two general qualitative observations can be extracted from the raw data: first, the fluorescence from the directly excited NO(l, 4) band is much stronger than the collisionally populated NO(0, 1) band, by about a factor o f 30, and second, as the pressure in the vacuum chamber was reduced from 76 to 19 torr, the decay o f the fluorescence slows. The radiative lifetime Trad for the nitric oxide A 2]E state is 210 and 205 nsec for the v ' = 1 and 0 levels, respectively. The rapid fluorescence decays, compared to the radiative lifetime, indicate that collisional de-excitation is still the dominant process, even at 19 torr. To determine the electronic quenching rates and vibrational energy transfer rates from these data we must model the laser excitation/fluorescence emission process. THREE-LEVEL RATE-EQUATION
MODEL
The process of laser-induced fluorescence from the NO molecule, including vibrational energy transfer, can be described by a simple three-level model as illustrated in F i g . 4. The sum of populations in the ground state N~, the laser-excited state N2, and the collisionaUy-excited state N3 is equal to the initial total population No, i.e. No = N, (t) + N2(t) + N3(t).
(1)
Prior to laser-excitation, the entire population is in the ground-state level N~ (0) = No,
N2(0) = 0,
N3 (0) = 0.
(2)
The time-dependent populations in these three levels are described by a coupled set o f first-order differential equations. The rate equation for the population of Nz is d N 2 / d t = N I B l 2 I l z ( t ) - N2B21 ll2(t) -- A z l N 2 - Q21~v2 - - V 2 3 N 2 q- V32N3,
(3)
and the rate equation for N3 is d N 3 / d t = V23N2 -- V32N3 - A31N3 - Q31N3,
(4)
where I~2(t) is the spectral energy density, B~2 and B2t are the Einstein coefficients for absorption and stimulated emission, A21 and A3~ are the spontaneous emission rates for the N2 and N3 levels, Qz~ and Q3t are the quenching rate constants, and V32 and Vz3 are the vibrational energy-transfer rates between the N2 and N3 levels. The Einstein coefficients are related by the degeneracies of the ground state and the excited state as follows: (5)
B12gl = Bzig2.
The vibrational transfer rates are related through detailed balance. At equilibrium, N2eq/N3~ = (g2/g3) e x p [ - (E2 -- E3 )/kT].
(6)
At equilibrium, the rate o f transfer between the two states must be equal, viz. N2eq V23 N~
=
N3eq 1/32.
Level 2
(7) A~ (v',, 1)
112B12
t v" t ,,,~,il
X2i-!
Fig. 4. Three-levelmodel of the processes involved in the laser excitation of NO from the X2II ground state and fluorescenceemission from the v' = 0 and 1 levels of the A 2Z excited state.
Electronic quenching and vibrational relaxation
503
For vibrational levels, the degeneracies are g2 = g3 = 1. We may combine Eqs. (6) and (7) and obtain V32 exp( - AE23/kT) V23,
(8)
=
where AE23 is the energy-level difference between v ' = 1 and 0 in the NOA 2E state, and T is the temperature. To reduce Eqs. (1)-(4) to a simplified form suitable for numerical integration, we normalize the populations in the three levels by the initial total population and write nl = Ni/No,
n2= N2/N o,
n3= N 3 / N o.
(9)
To take into account the laser spectral line shape and the absorption-line shape, an effective absorption coefficient, b~2, is introduced, which includes a laser line-shape factor q(6v~, 6va): b¿2 -~- q ( f v l ,
Ova)Bl2
(10)
Since the laser spectral halfwidth 6v~ (--,0.35 cm -I) is larger than the primarily Doppler-broadened absorption halfwidth 6va(~ 0.2 cm-~), the laser-line shape factor is nearly constant over the range of temperature in our experiments (1000-1400 K). By using Eqs. (1), (5), and (8) to eliminate Nl, B21, and V32 from Eqs. (1) and (3), the N2 rate equation becomes dn2dt- LF1 -- n2 -- n 3 - n 2 ( g ' ) ] b , 2 I i 2 - (Az, + Q2, "4" V23)n2 "1"- V23exp(--AE23/kT)n3,
\g2,/_J
(11)
and the N3 rate equation becomes dn3 = V23n2 - [V23e x p ( - A E 2 3 / k T ) + A31 + Q3t]na, dt
(12)
with the initial conditions n2(0) = 0,
n3(0) = 0.
(13)
The time-dependent spectral energy density of the laser II2(t) is evaluated from the measured laser-pulse shape and a measurement of the pulse energy. It was found that there was little variation in the averaged laser-pulse shape throughout the experiment, so that a representative profile was used. The measured laser profile was normalized by its integrated area and scaled by the measured laser-pulse energy Elase r :
[ )/;o
I12(t) = E,a~r ItRexp(t
]
1,2exp(t)dt .
(14)
The unknown parameters in Eqs. (11) and (12) are the quenching rates Q21 and Q31 and vibrational energy transfer rate I"23. All of the other parameters are known spectroscopic constants. The gas temperature enters into the problem through the detailed-balance assumption relating Vz3 and I"32 and is measured separately from quenching-corrected LIF spectra of O H . 9 To determine the electronic quenching rates Qzl and Q31 and the rate for vibrational energy transfer V23, we compare the results of the numerical integration of Eqs. (11) and (12) with the measured fluorescence signals from the NO(l,4) and NO(0, 1) bands. The time-dependent fluorescence photon flux In~/(t) from each level follows the time-dependent population in that level, viz. f~
1%(,) = rl• 4---~VA o.No n~(t )
(15)
where f~ is the solid angle of the light-collection system from a fluorescence volume V that is viewed with a detector of sensitivity r/ij; A 0 is the spontaneous emission rate for the observed band. The time-dependent fluorescence signal ln,~(t) is recorded on a transient digitizer with a 400-MHz bandwidth that includes both the detector and amplifier frequency response. This finite bandwidth will broaden the observed fluorescence signal. To account for this instrument bandwidth effect, the
504
ROBERT J. CATTOLICA et al
predicted time-dependent fluorescence signal must be convoluted by the instrument bandwidth function to yield the measured fluorescence signal [n~ (t) =
:0
Ii,~t(t -- z)I,~ (z) dz.
(16)
The instrument-bandwidth function/~n~t (t - z) was determined by measuring the response of the transient recording system to a 100-psec pulse from a diode laser. The time-dependent fluorescence signal, lab(t), follows the temporal development of the population n~(t) through Eq. (15). We therefore perform the convolution indicated in Eq. (16) on the predicted populations ni(t) and obtain ~(t) =
t' /i.~t(t- ~)n~(r) dl:.
(17)
do
The temporal evolution of the measured fluorescence signal then follows the instrument-broadened population history
[n~(t) = rl,+-~ VAoNofz,(t).
(18)
Since only a fraction of the population in the excited levels fluoresce in the NO(l, 4) and NO(0, 1) bands, the spontaneous emission rate, A~: for each band is determined from the radiative lifetime for the level and the branching ratios:
A U= flO/T~d.
(19)
Introducing the branching-ratio relation and rearranging terms, we obtain
fi~exp(t) = [fl(t)/Iqi:-~ V(flq/%ad)No ].
(20,
Since f~, V, No are the same for fluorescence signals from both NO(I, 4) and NO(0, 1) and since the r~,d are nearly identical, we can put the fluorescence signals in a form suitable for comparison with the convolution of the numerical solutions for n~ and n2 as follows: r~,~p(t) = const. ×
[n(t)/(qi:fl~).
(21)
The fluorescence signals must be scaled and shifted for comparison with the numerical solution to account for the gain of the transient digitizer and the time-delay offset between the laser and fluorescence. The fluorescence signal for the N2 level, in[NO(l, 4)], is normalized and time-shifted as indicated: ~i:exp= A x Tn[NO(1, 4)](t + B).
(22)
The constant A is set so that the peak signal of the experimental profile matches the peak signal of the convolution of the numerical solution for n2. The constant B is used to align the numerical and experimental signals in time, and accounts for the time delay between the measured laser pulse shape and fluorescence. A similar equation is used for the fluorescence signal from the N3 level to remove the time delay offset and to account for the difference in the branching ratios for the two levels: t~3exp= A ×
(r121132,/r13~[331)[,[NO(O, 1)](t
+ B).
(23)
The constants A and B are the same as in Eq. (22). The detector sensitivities q0 are determined from measurements of a calibrated deuterium lamp. It is now possible to compare the convoluted numerical solution with the scaled and shifted experimental profiles. There are three fitting parameters, namely, the quenching rates Q~I and Q31 and the vibrational energy transfer rate V23for the two experimental profiles. The parameters are fitted by establishing a ~2 error for each of the fluorescence profiles and minimizing this error by adjusting the fitting
Electronic quenching and vibrational relaxation
505
parameters. Two semi-independent X2 are used for each experimental profile to estimate the error between the numerical and experimental profiles. The Z22 error for the ~2 signal is given by
The Z 2 error for the ~3 signal is given by
z2(a)=~[:3exp--n3(li;Q31'g23)12"i= '
0"3
(25)
Since the n3 signal is about a factor of 30 below the n2 signal, the g 2 is minimized by varying only the quenching rate, Q2,. The other two parameters are fitted using the X23for the rJ3 signal. In both cases, the 3(2 error is weighted by the standard deviation of the fluorescence signals found from Poisson statistics, i.e. 0"2= ~
and
0"3= x//-~3.
(26)
The Z 2 are then minimized by a method of steepest descent using the gradient of Z2. The gradient of the X2 with respect to the fitting variables determines the next value of the variables through anext = acu r - -
constant x VZ 2,
(27)
where a represents a vector of the fitting parameters. The gradient for the X2 error is V• 2 = OZ~/OQ2,,
(28)
and the gradient for the Z] error is V~(~ = (0~(2/0 V23 )~'23 "~
(OzE#~Q3,)t)3,-
(29)
The parameters Qz,, Q3,, and V23 are found by repeating the numerical integration of the rate equations using Eq. (27) to determine new values of the parameters until the Z z errors reach a stable minimum. RESULTS
AND
DISCUSSION
The comparison of the three-level rate-equation model with the temporally resolved fluorescence from the NO(I, 4) and NO(0, 1) bands is presented in Fig. 3. An excellent fit to the measured fluorescence signals is obtained. For the 76-torr flame in Fig. 3(a), the least-squares fit gives values for the electronic quenching rate from the A2E state of Q2, = 1.22 x 108 sec -l for the v ' = 1 level, Q3, = 1.21 x l08 s e c - ' for v' = 0, and a vibrational energy transfer rate of V:3 = 6.1 x l06 sec-'. The quenching rates for the 19-, 38-, and 76-torr flames, which are summarized in Table 1, are much faster than the spontaneous emission rate for the fluorescence, 5 x 10 6 s e c -1. The vibrational energy transfer rates, also summarized in Table 1, are about a factor of 20 slower than the quenching rates. Table 1. Quenching and vibrational energy transfer rates and cross sections from least-squares fits of the three-level rate-equation model to NO transient fluorescence data for three low-pressure H2/O2/Ar flames. P0 (tort)
76
38
19
T (K)
1340
1124
1050
Q21 (s'l) Q3! (s -1) V23 (s"1) oQ21 (A2) ~Q3t (A2) ~V23 (A2)
1.22 x 108 1.21 x 108 6.1 x 106 365:2 355:3 1.8 ± 0.4
0.64 x 108
0.40 x 108
0.60 x 108
0.33 × 108
3.7 x 106 35+2
3.0 x 106 41 + 2
32±3
34-I-3
2.0 5:0.4
3.2 5:0.5
ROBERT J. CATTOLICA et al
506
3
(o)
4 "
le~eri~nal
(b)
model
3
~p, ,~.4 i~
rnod~
-21
+t0%
2-
-1 1-
.....
0
,
0
20
30 t~e
~ -
40
50
60
70
0
0
80
m ~ 4
10
20
30
(nsec)
( CI
,
.
40
tPne
20
4o
5o
,
r
60
,
~
0
70
80
(nsec)
....
3-
...::9.~ . . . . . . .
3o
.
kllllN" aignal
+10%
lo
,
50
I l l l ~ lligtlal
•
o
/ ' ~ ' .
~
0
8o
7o
!
.,.:P-~ . . . . . . . . .
i
8o
~
.
i
2o
•
~
ao
t
4o
•
i
6o
t
6o
2
ao
time (nsec) time (nsec) Fig. 5. Three-level rate-equation model results for the NO(I, 4) fluorescenceand N O ( 0 , 4) fluorescence in the 19-torr H 2 / O 2 / A r flame for + 10% variation in the parameters; (a) Q21, (b) V23, (c) Q31, and (d) T.
To illustrate the sensitivity of the least-squares fit of the three-level model to the experimental data, the predicted fluorescence signals for a + 10% variation in the parameters Q21, Q3~,/I23, and T are plotted in Fig. 5 for the 19-torr flame. In Fig. 5(a), the variation of Q2~ affects both the NO(l, 4) and NO(0, 1) fluorescence signal. Because the rate of vibrational energy transfer, V~3, is much slower than Q2~, variation in V23 or Q32 has no significant effect on the behavior of the NO(l, 4) fluorescence in Figs. 5(b) and (c). In the least-squares fitting procedure it is therefore necessary to determine Q21 from the NO(l, 4) signal prior to determining V23 and Q3~. In fitting the NO(0, 1) fluorescence signal, the variation in V23 has a significant effect on the magnitude of the signal in Fig. 5(c). In Fig. 5(b), the variation of Q31 primarily affects the decay rate of the fluorescence in the NO(0, 1) band. A + 10% variation in the temperature in Fig. 5(d) has no effect on either of the fluorescence profiles. Since the temperature enters into the model explicitly only through the detailed balance relation, Eq. (8), relating II23 and I,'32, and since the reverse rate is small at this temperature, a _+ 10% variation has no significant effect. Since the primary collision partner for energy transfer in the burned-gas region of these low-pressure flames is H20, these measured electronic quenching and vibrational energy transfer 110"~
E O
-
-
9 0 -]
•
v" -- 0 McDermid lind Lauden$1aget (19821
0
v'--O
¢,3
~
70
o
50o
e-t-
oe -
30
100 300
500 700 900 1100 1300 1500 t e m D e r a t u r e (K) Fig. 6. Electronic quenching cross section of nitric oxide for v' = 1 a n d 0 by H 2 0 as a function of temperature.
Electronic quenching and vibrational relaxation
507
Table 2. Electronic quenching cross sections for the A 2y state of nitric oxide by gases of interest in combustion.
Species
o (]~2) at 298 K from Refs. 4 and 5
H20
102
(v'=0)
CO2
61
(v'=0)
NO
35 32 27
(v'=0) (v'=l) (v'=2)
O2
22.3
(v'=0)
Ar
0.06
(v'=0)
N2
0.014 0.241 0.122
(v'=0) (v'=l) (v'=2)
o'(/~2) at 1340 K 35 :t: 3 (v'=0) 36 + 2 (v'=l)
rates can be converted to H 2 0 collision cross sections using the known water concentration and the measured gas temperature. The calculated electronic quenching cross sections for the 76-torr flame are 36 _+ 2 ,~2 for the v' = 1 level, and 35 _ 3 ,~2 for the v' = 0 level. The vibrational relaxation cross section from v' = l ~ is 1.8 _ 0.4 A2. These cross sections, along with the results for the other flames, are listed in Table 1. The uncertainties in these measured cross sections were determined from a combination of the errors associated with the fluorescence signals and the temperature measurements. In Fig. 6 we plot the quenching cross section for v' = 1 and 0 as a function of gas temperature for the experiments conducted at all three pressures. These quenching cross sections are relatively constant except for the lowest temperature measurement for v ' - - 1. A comparison in Fig. 6 with the much higher measured cross section (102 A:) for H 2 0 at ambient temperature 7 is indicative of the importance of the role of the attractive part of the intermolecular potential on the electronic quenching of nitric oxide. In Table 2 we present a summary of the previously measured 4"5electronic quenching cross sections for the A 2E state of nitric oxide for a number of collision partners of interest in combustion experiments. At ambient temperature, H 2 0 is the most efficient and Ar the least efficient species in quenching NO. At the higher temperature in our experiments, we assumed that this relationship was still valid and that H 2 0 w a s the dominant quenching species. Although N O has a self-quenching cross section comparable to our measurement for H20, its abundance is only 1/39th of that of H 2 0 in our experiment, so its effect can be neglected. In Table 3 we compare our measured vibrational energy transfer cross sections for the v ' = 1 level of the A :E state of NO with measurements for both the A 2y, state and the X2H ground state at ambient temperature.~'5 In the X2II ground state of NO, the vibrational energy transfer (VET) cross sections for N2 and Ar are very small. The much higher VET rate for NO colliding with itself Table 3. Vibrational energy transfer cross sections for the a2~ state and the X21-I state of nitric oxide by gases of interest in combustion. A2~ (v'= 1) o (/~2) at 298 K (Ref. 5)
X2yI (v'=l) o (,~2) at 298 K (Ref. 1)
N2
0.031
2.13 x 10-5
NO
1.36
0.013
Species
Ar
H20
7.7 x 10.6 1.8 -4-0.4 (1340 K) 2.0 :I:0.4 (1150 K) 3.2,4-0.5 (1024 K)
508
ROBERT J. CATTOLICA et al
has been attributed ~ to the influence of strong attractive forces. In the A2X state, the large VET cross section for N O has been explained 3 by resonance electronic energy exchange. Although such a direct resonant electronic-exchange process cannot explain the large cross section we observed for the vibrational relaxation of N O by H20, the strongly attractive intermolecular force between N O and H 2 0 (as indicated by the large electronic quenching cross section) probably plays a significant role.
Acknowledgements--The authors would like to thank J. Meeks for his excellent technical assistance in the design and implementation of these experiments. This work was supported by the U.S. Department of Energy, Officeof Basic Energy Sciences, Division of Chemical Sciences. REFERENCES L. Doyennette and M. Margottin-Maclou, J. Chem. Phys. 84, 6668 (1986). H. P. Broida and T. Carrington, J. Phys. Chem. 38, 136 (1963). L. A. Melton and W. Klemperer, J. Phys. Chem. 59, 1099 (1973). I. S. McDermid and J. B. Laudensberg, JQSRT 27, 483 (1982). T. Imajo, K. Shibuya, K. Obi, and I. Tanaka, J. Phys. Chem. 90, 6006 (1986). R. J. Cattolica, T. G. Mataga, and J. C. Cavolowsky, in Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburg, in press (1989). 7. T. J. McGee, J. Burris, and J. Barnes, JQSRT 34, 81 (1985). 8. T. J. McGee, G. E. Miller, J. Burris, Jr., and T. J. McIlrath, JQSRT 29, 333 (1983). 9. R. J. Cattolica, T. G. Mataga, and J. A. Cavolowsky, manuscript in preparation.
I. 2. 3. 4. 5. 6.