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Vibrational relaxation of NO(X 2Π, ν=3) by NO, O2 and CH4
2 September 1994
ELSEVIER
CHEMICAL PHYSJCS LETTERS
Chemical Physics Letters 227 (1994) 69-73
Vibrational relaxation of NO (X 211,v= 3 ) by NO, O2 and CH4 Ingrid J. Wysong Hughes STX, PL/WA,
Edwards AFB, CA 93524-7660, USA
Received 25 May 1994
Abstract
A two-laser (IR overtone pump and UV laser-induced fluorescence probe) technique has been used to measure vibrational relaxation for NO(X *II, v= 3) colliding with NO, 02, and CH4 at 295 K. The total removal rate coefficients are: (3.26 k 0.24) X 10-‘2cm3s-‘forNO,(1.46f0.15)~10-’3cm3s-’for02,and(1.20+0.12)x10-‘3cm3s-‘forCH,.
1. Introduction An understanding of vibrational energy transfer (VET) is needed for modeling of nonequilibrium gas flows such as bow shocks, arcjet thrusters, rocket
plumes, materials processing plasmas, gas lasers, and the excited upper atmosphere. One aspect of VET where few measurements are available is vibrational relaxation rates as a function of vibrational quantum number. Even fewer measurements are available where only a single vibrational level is initially populated. Both types of vibrational relaxation may be important in nonequilibrium systems: V-V transfer, where the bulk of the energy from the vibrational quantum goes into one quantum of vibrational energy in the collider molecule, and the remaining AE (the ‘energy defect’) goes into translation, and V-T transfer, where the entire energy from one vibrational quantum goes into translation and rotation. A recent study [ 1 ] has been performed on the ZJ=2 and u= 1 vibrational levels of NO (X ‘II), using a twolaser pump-and-probe technique. Infrared overtone pumping was used to excite ground state NO into the v=2 level and a second laser was used to probe the time-dependent u=2 and 1 populations using UV laser-induced fluorescence (LIF) . The cross section
for NO-NO V-V transfer for v= 2 (process ( 1) below) was measured from 240 to 295 K and shown to increase at lower temperatures, indicating the importance of attractive forces in this process. It is not surprising that attractive forces play a key role here, since it is a near-resonant process. In the present study, the laser overtone pumping technique is extended to excite the v= 3 level of NO via the second overtone transition (v=O+ 3). Infrared absorption studies [ 2 ] have shown that the second overtone transition in NO is about fifty times weaker than the first overtone, which in turn is about fifty times weaker than the fundamental. In order to obtain sufficient signal, it is necessary to focus the IR beam; tests are performed as described below to ensure that collisions between excited NO molecules are negligible. Removal rates for v= 3 are obtained only for two species other than NO, two of the most favorable (with respect to signal) colliders: CH4 and Oz. This is the first reported measurement of removal rates for NO v= 3 where v= 3 is the only vibrational level initially excited.
0009-2614/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDlOOO9-2614(94)00783-7
70
I.J. Wysong/Chemical
Physics Letters 227 (1994) 69-73
2. Experiment
The experimental apparatus has been given in detail in the previous paper [ 11, and so will only be described briefly here. An IR laser pulse is tuned to 1.8 urn to resonantly excite NO (v= 3) by pumping the second overtone. A second laser excites the NO molecules to the A electronic state so that LIF may be used to monitor the population in the ground electronic state as a function of time delay. Tunable radiation near 1.8 urn is generated by difference-frequency mixing a Nd:YAG-pumped dye laser at 667 nm with the residual 1064 nm from the pump laser. This produces approximately 0.3 mJ per 8 ns pulse. The IR beam is focused into the cell with a 200 mm focal length CaF, lens. The pump laser excites one particular rotational level within the v= 3 vibrational level, but RET is extremely fast compared with VET, so that within 50 ns (a negligible time on the scale of these experiments) a thermally-equilibrated rotational distribution is attained within the v= 3 level. The probe laser is the doubled output of an excimer-pumped dye laser with a 25 ns pulse, shaped into a round beam of 2 mm diameter. The UV laser may be tuned to 259 nm to monitor NO( v= 3) through the A-X (0, 3) band or to 236 nm to monitor NO (v= 1) through the A-X (0, 1) band. LIF is detected through a filtered photomultiplier tube (PMT). The output of the PMT goes into a gated integrator which is read after every pulse by a laboratory computer through a digitizing board. The computer also controls the time delay between the pump and probe laser pulses through a digital delay generator. Relaxation data are obtained with at least 20 Torr of argon buffer gas in the cell. This slows the diffusion of the NO molecules and ensures that any population decay due to diffusion losses from the probe volume during the 300 us maximum delay time is small. A purified sample of NO is obtained by trap-to-trap distillation and then pumping on the frozen sample. The purified NO is then placed in a sample bulb; argon (ultra-high purity) is added to make a 10% mixture, and the bulb is allowed to sit at least overnight to ensure mixing. Each sample bulb is checked using FTIR to verify the purity. The NO/Ar mixture and other gases used in the experiment pass through mass flow meters before entering the cell, where a slow gas
flow is maintained. The data on O2 and CH4 colliders are obtained using ultra-high purity collider gases and a small partial pressure of NO, so that NO-NO collisions are negligible and collisions with the added collider species dominate the time decays.
3. Kinetic analysis The VET processes that are important in the experiment are kE, e NO(2) +NO(O) kZ
NO(l)+NO(l) +28 cm-‘, N0(2)+NO(
(1) kZ 1) = N0(3)+NO(O) kW
+56 cm-‘, N0(3)+NO(O)
(2) ‘& & NO(2) +NO(O) ‘&
+ 1820 cm-’ ,
N0(2)+NO(O)
(3) k& & NO(l)+NO(O) k?‘&
+ 1848 cm-’ , NO( l)+NO(O) +1876cm-‘.
(4) k?a 6 NO(O)+NO(O) k;‘ib (5)
A number of simulations have been performed by numerically solving the coupled differential equations resulting from the above processes to obtain time-dependent vibrational populations; the initial fractions of NO in v= 1 and 2 are thermal and the initial laser-pumped v= 3 population is varied over a wide range. A number of simplifications and assumptions are included. It is assumed that only Au= 1 transitions occur, as has been supported by previous studies [ 1,3] for low vibrational levels. It is also assumed that the V-T rate constants are linearly dependent on vibrational quantum number, as is predicted by SSH theory and supported by Yang et al.
71
I.J. Wysong /Chemical Physics Letters 227 (1994) 69- 73
[ 31. This allows us to make the following substitutions: k& =2/c?! and k& =3k?;lo. The rate constant k?;lo has been measured many times, and the value used here [4] is 2500 s-r Torr-‘. The reverse rates k’, which are related to the forward rates by microscopic reversibility for the exothermicity of the reaction, are: k$Y,=0.76 kz:,; k;Y, =0.87 kL; k’& = 0.00011 k‘;$ at room temperature. Radiative removal, with lifetimes of around 80 ms, will be negligibly slow compared with the above processes at the pressures used here and has been ignored, as have the reverse V-T processes kz, and kT2. The simulations leave out the argon buffer gas, as it is known to have too slow a relaxation rate coefficient [4,5] ( ~0.4 s-r Torr-‘) to have any detectable effect at the pressures used here. When another collider species is added to the flow, the above equations are simply modified by adding a relaxation term for the collider to the equation for each vibrational level. A number of other V-V processes are possible if we consider the collision of a NO ( v= 3 ) with another excited species (v= 1, 2, or 3), but simulations for the present conditions show that these are negligible when the initial fraction of NO ( v= 3 ) is < 0.1%. Under those conditions, the decay of v= 3 is a single exponential with a rate coefficient simply equal to k;T2 + k&. A second result from the simulations is that the v= 1 population (x) has the following time dependence x=a+b[exp(
-ct)-exp(
-dt)]
,
(6)
where a represents the constant background population of v= 1 due to the thermal Boltzmann fraction, b is the magnitude of the transient v= 1 population due to laser pumping, and c and d are the rates for transfer into and out of v= 1. The value of b is equal to about three times the initial v= 3 population, as we would expect since the kinetics are dominated by Eqs. (l)and(2).AscanbeseenfromEqs.(l)and(2), each molecule in v= 3 that only undergoes collisions with molecules in v= 0 will produce three molecules inv=l.
of v= 3. It could be a considered a trivial problem to assure that less than O.l”h of the NO molecules are pumped into v= 3, since the second overtone transition is extremely weak, but it is important to be sure, since a high concentration of excited molecules will allow uppumping collisions and change the apparent decay rate coefficient. A sample time scan of v= 1 is shown in Fig. 1. For these scans, the UV probe beam is focused so that it probes about the same volume as is pumped by the IR laser. When the probe beam is focused, the values of c and d will be strongly influenced by diffusion and cannot be meaningfully interpreted. The value of b, however, should still be proportional to the total population passing through v= 1 as a result of laser pumping. Since a will be proportional to the thermal population of v= 1, a fit of the v= 1 time dependence to the form given in Eq. (6) above will yield a ratio of thermal to laser-pumped v= 1 densities. The thermal population of NO( v= 1) is known at a given temperature based on a Boltzmann fraction ( 1x 10e4 at 295 K for NO), and the laser-pumped population passing through v= 1 will be three times the initial laser-pumped population in v=3. Thus we can obtain the fraction of NO molecules that are initially pumped into v= 3 by the laser pulse. Simulations show that collisions between excited NO molecules will begin to become significant when the initially pumped fraction is more than 10e3. As shown in Fig. 1, the energy density obtained in the present study with a focused laser beam yields an initially pumped fraction of 2x 10m4. Under these 2ooo0
0
4. Results
,...‘....‘....‘....‘....‘....‘....(
0
50
loo
150
200
2!Kl
3lxl
Timedday~s)
Some time scans of v= 1 have been obtained in order to estimate the initial laser-pumped population
Fig. 1. Time-dependent population of NO(u= 1) for 0.9 Torr. The pump pulse that populates NO ( u= 3 ) occurs at t = 0.
12
I.J. Wysong / Chemical Physics Letters 227 (1994) 69- 73
conditions, the v= 3 population is dominated by collisions with NO v= 0. A sample time-dependent v= 3 population plot is shown in Fig. 2. It shows that the decay follows an exponential form and yields a decay rate for the given partial pressure of NO. Data from a number of these decay plots at various partial pressures are combined in Fig. 3, and the slope gives the rate coefficient for removal of v= 3. The intercept is expected to be zero, except for contributions by losses due to diffusion or relaxation due to background gases. The technique used here measures the total removal from the v= 3 level and does not distinguish between V-V and VT transfer processes. The observed rate coefficient for removal of NO ( v= 3 ) by NO is 107 f 8 ms- ’ Torr- ’ (all uncertainties represent 20). It follows that the V-V removal rate coefficient kz2 is 99.5 + 8 ms -’
100
5’ 10
NO v=3 relaxation 55o%xp(-.0272t)
x =
1
. . . . . . .
..‘.........‘.....*...’
0
100
50 The
150
delayus )
Fig. 2. Time-dependent population of NO(u= 3) for 0.2 Torr; a simple exponential decay is observed.
._
ni _.- r
w
NO v=3 relaxation
/” I’a
0.08
y.!s0.06
e
-a
3
0.04
0.02
_JJ
x p/
1 1 ,d
Od X/b 0
X4
P 53
0~‘“‘““‘““““” 0
0.2
’
0
00 0 y = 0.107x + 0.005
0.4
0.6
0.8
1
PressureNO (Tom)
Fig. 3. Pressure dependence of NO( v= 3) relaxation rate. Different symbols show data sets taken on three separate days.
Torr-’ or (3.03 20.24) x lo-i2 cm3 s-’ at 295 K if we assume the V-T rate coefficient is kg2 = 7.5 ms - ’ Torr- ’ = 3kzo. It is reasonable to assume this, as SSH theory for V-T transfer predicts k: a vto first order, and a recent study by Yang et al. shows that k: = vk?! for v= 8 to 12. Given Yang’s results, any deviation from kz2 = 3kCo will be small and will cause a change in the stated value for k$Y2that is well within the experimental uncertainty. The corresponding forward rate constant for kZ2 is 131+ 10 ms-’ Torr-’ or (4.OkO.3) x lo-l2 cm3 s-i.
5. Discussion The only previous measurement of the NO v= 3 removal rate coefficient is due to Horiguchi and .Tsuchiya [6]. (HT),withavalueofkz2=89+9ms-’ Torr-‘. HT give this value as the rate coefficient for k;Y’z, but they note that it actually represents the total removal due to V-V and V-T processes, as is the case in the present measurement. It was noted previously [ 1 ] that the laser pump/probe result for kc1 was significantly higher than HT ‘s result which was based on Hg(6 3P,) excitation of NO(v= 1-15). HT state that their analysis ignores collisions between two excited molecules and thus is likely to underestimate the removal rate coefficients, but their results are in reasonable agreement with the present study. One method of predicting VET probabilities is SSH theory [ 7 1, which is based on a purely repulsive interaction, but includes an attractive part of the potential to the extent of increasing the relative velocity of the colliding particles. The probability is defined as the rate constant for the process divided by Z, where Z is the gas kinetic collision rate constant. Dunnwald et al. [ 8 ] have used a kinetic model using semi-empirical rate coefficients for V-V and V-T transfer (as well as expressions for radiative emission and V-E transfer) to model the time-dependent anharmonic V-V pumping in NO following strong laser pumping of v= 1. A convenient formulation of the SSH theory for V-V transfer, as modified by Keck and Carrier [ 9 1, is included in their paper, using a value of 0.2 A for the range parameter of the repulsive potential wall and including an empirical factor which matches the predicted value for k2, of NO to
73
I.J. Wysong/Chemical Physics Letters 227 (1994) 69-73
Table 1 Total removal rate coefficients and probabilities for NO(X, II= 3,2 and 1) for Oz and CH, at 295 K. Rate coefftcients for v= 3 are results of the present study Collision pair
Relaxation rate coeff. k(x10”cm3s-I)
Reduced probability Plv(x104)
AE (cm-‘)
NO(v=l)-0s NO(v=2)-Oz NO(v=3)-Or NO( v= 1 )-CH., NO(v=2)-CH4 NO(v=3)-CH,
0.24+ 0.04 a 0.74*0.10 a 1.46kO.15 2.0f0.2” 5.3kO.5 a 12.0& 1.2
1.0 1.5 2.0 6.3 8.4 13
320 292 264 343 314 286
“Ref. [l].
the value measured by Stephenson [ 41. This model predicts a ratio of 1.19 for &‘Yz//CT:,, lower than the present measured ratio of 1.36. The discrepancy may well be due to the attractive forces which have been shown [ 1 ] to be important in NO-NO V-V transfer. Semiclassical VET calculations using an attractiverepulsive potential and including rotation have been performed by Cacciatore and Billing [ lo] for COCO and by Billing and Kolesnick [ 111 for 02-O2 which agree quite well with available data. No such calculations have been performed for NO-NO VET as yet. The present results for removal from NO ( v= 3 ) by O2 and CH4 are shown in Table 1, along with values from the previous study for removal from v= 1 and 2. Again, these values represent total removal, the sum of V-V and V-T processes. The energy defects are shown, along with the reduced probabilities, P(v) /v. The values are consistent with SSH theory, which predicts that P(v) increases with v due to the linear increase in transition matrix elements, and also increases as the energy defect decreases. The fact that CH4 is a more efficient relaxer for the same vibrational level and approximately the same energy defect is not fully understood and has been discussed briefly in the previous study. No previous measurement has been made of the removal of NO (v= 3 ) by CH4, but removal of NO ( Y= l-7) by O2 has been measured by Green et al. [ 121 using electron beam excitation at 300 K, yielding a rate coefficient for v= 3 of (1.2-1.5)x10-” cm3 s-r (lower and upper bounds, respectively). The previous measurement agrees with the present result.
The present results demonstrate the value of the overtone pumping technique to obtain state-specific VET rate constants for levels up to v=3. Removal rate constants for NO ( v= 3 ) have been measured for the first time in isolation from other excited vibrational levels.
References [ 1 ] I.J. Wysong, J. Chem. Phys., in press. [2] B. Schmitt and R.E. Ellis, J. Chem. Phys. 45 (1966) 2528. [ 3 ] X. Yang, E.H. Kim and A.M. Wodtke, J. Chem. Phys. 96 (1992) 5111. [4] J.C. Stephenson, J. Chem. Phys. 59 (1973) 1523. [ 51 J. Kosanetzky, U. List, W. Urban, H. Vormann and E.H. Fink, Chem. Phys. 50 ( 1980) 36 1. [6] H. Horiguchi and S. Tsuchiya, Japan. J. Applied Phys. 18 (1979) 1207. [7] R.N. Schwartz, Z.I. Slawsky and K.F. Herzfeld, J. Chem. Phys. 20 (1952) 1591; R.N. Schwartz and ICE Hetzfeld, J. Chem. Phys. 22 (1954) 767; KF. Herzfeld and T.A. Litovitz, Absorption and dispersion of ultrasonic waves (Academic Press, New York, 1959). [ 8 ] S. Saupe, I. Adamovich, M.J. Grassi, J.W. Rich and R.C. Bergman, Chem. Phys. 174 ( 1993) 2 19; H. Dunnwald, E. Siegel, W. Urban, J.W. Rich, G.F. Homicz andM.J. Williams, Chem. Phys. 94 (1985) 195. [9] J. Keck and G. Carrier, J. Chem. Phys. 43 ( 1965) 2284. [ lo] M. Cacciatore and G.D. Billing, Chem. Phys. 58 ( 1981) 395. [ 111 G.D. Billing and R.E. Kolesnick, Chem. Phys. Letters 200 (1992) 382. [ 12 ] B.D. Green, G.E. Caledonia, R.E. Murphy and F.X. Robert, J. Chem. Phys. 76 (1982) 2441.
ELSEVIER
CHEMICAL PHYSJCS LETTERS
Chemical Physics Letters 227 (1994) 69-73
Vibrational relaxation of NO (X 211,v= 3 ) by NO, O2 and CH4 Ingrid J. Wysong Hughes STX, PL/WA,
Edwards AFB, CA 93524-7660, USA
Received 25 May 1994
Abstract
A two-laser (IR overtone pump and UV laser-induced fluorescence probe) technique has been used to measure vibrational relaxation for NO(X *II, v= 3) colliding with NO, 02, and CH4 at 295 K. The total removal rate coefficients are: (3.26 k 0.24) X 10-‘2cm3s-‘forNO,(1.46f0.15)~10-’3cm3s-’for02,and(1.20+0.12)x10-‘3cm3s-‘forCH,.
1. Introduction An understanding of vibrational energy transfer (VET) is needed for modeling of nonequilibrium gas flows such as bow shocks, arcjet thrusters, rocket
plumes, materials processing plasmas, gas lasers, and the excited upper atmosphere. One aspect of VET where few measurements are available is vibrational relaxation rates as a function of vibrational quantum number. Even fewer measurements are available where only a single vibrational level is initially populated. Both types of vibrational relaxation may be important in nonequilibrium systems: V-V transfer, where the bulk of the energy from the vibrational quantum goes into one quantum of vibrational energy in the collider molecule, and the remaining AE (the ‘energy defect’) goes into translation, and V-T transfer, where the entire energy from one vibrational quantum goes into translation and rotation. A recent study [ 1 ] has been performed on the ZJ=2 and u= 1 vibrational levels of NO (X ‘II), using a twolaser pump-and-probe technique. Infrared overtone pumping was used to excite ground state NO into the v=2 level and a second laser was used to probe the time-dependent u=2 and 1 populations using UV laser-induced fluorescence (LIF) . The cross section
for NO-NO V-V transfer for v= 2 (process ( 1) below) was measured from 240 to 295 K and shown to increase at lower temperatures, indicating the importance of attractive forces in this process. It is not surprising that attractive forces play a key role here, since it is a near-resonant process. In the present study, the laser overtone pumping technique is extended to excite the v= 3 level of NO via the second overtone transition (v=O+ 3). Infrared absorption studies [ 2 ] have shown that the second overtone transition in NO is about fifty times weaker than the first overtone, which in turn is about fifty times weaker than the fundamental. In order to obtain sufficient signal, it is necessary to focus the IR beam; tests are performed as described below to ensure that collisions between excited NO molecules are negligible. Removal rates for v= 3 are obtained only for two species other than NO, two of the most favorable (with respect to signal) colliders: CH4 and Oz. This is the first reported measurement of removal rates for NO v= 3 where v= 3 is the only vibrational level initially excited.
0009-2614/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDlOOO9-2614(94)00783-7
70
I.J. Wysong/Chemical
Physics Letters 227 (1994) 69-73
2. Experiment
The experimental apparatus has been given in detail in the previous paper [ 11, and so will only be described briefly here. An IR laser pulse is tuned to 1.8 urn to resonantly excite NO (v= 3) by pumping the second overtone. A second laser excites the NO molecules to the A electronic state so that LIF may be used to monitor the population in the ground electronic state as a function of time delay. Tunable radiation near 1.8 urn is generated by difference-frequency mixing a Nd:YAG-pumped dye laser at 667 nm with the residual 1064 nm from the pump laser. This produces approximately 0.3 mJ per 8 ns pulse. The IR beam is focused into the cell with a 200 mm focal length CaF, lens. The pump laser excites one particular rotational level within the v= 3 vibrational level, but RET is extremely fast compared with VET, so that within 50 ns (a negligible time on the scale of these experiments) a thermally-equilibrated rotational distribution is attained within the v= 3 level. The probe laser is the doubled output of an excimer-pumped dye laser with a 25 ns pulse, shaped into a round beam of 2 mm diameter. The UV laser may be tuned to 259 nm to monitor NO( v= 3) through the A-X (0, 3) band or to 236 nm to monitor NO (v= 1) through the A-X (0, 1) band. LIF is detected through a filtered photomultiplier tube (PMT). The output of the PMT goes into a gated integrator which is read after every pulse by a laboratory computer through a digitizing board. The computer also controls the time delay between the pump and probe laser pulses through a digital delay generator. Relaxation data are obtained with at least 20 Torr of argon buffer gas in the cell. This slows the diffusion of the NO molecules and ensures that any population decay due to diffusion losses from the probe volume during the 300 us maximum delay time is small. A purified sample of NO is obtained by trap-to-trap distillation and then pumping on the frozen sample. The purified NO is then placed in a sample bulb; argon (ultra-high purity) is added to make a 10% mixture, and the bulb is allowed to sit at least overnight to ensure mixing. Each sample bulb is checked using FTIR to verify the purity. The NO/Ar mixture and other gases used in the experiment pass through mass flow meters before entering the cell, where a slow gas
flow is maintained. The data on O2 and CH4 colliders are obtained using ultra-high purity collider gases and a small partial pressure of NO, so that NO-NO collisions are negligible and collisions with the added collider species dominate the time decays.
3. Kinetic analysis The VET processes that are important in the experiment are kE, e NO(2) +NO(O) kZ
NO(l)+NO(l) +28 cm-‘, N0(2)+NO(
(1) kZ 1) = N0(3)+NO(O) kW
+56 cm-‘, N0(3)+NO(O)
(2) ‘& & NO(2) +NO(O) ‘&
+ 1820 cm-’ ,
N0(2)+NO(O)
(3) k& & NO(l)+NO(O) k?‘&
+ 1848 cm-’ , NO( l)+NO(O) +1876cm-‘.
(4) k?a 6 NO(O)+NO(O) k;‘ib (5)
A number of simulations have been performed by numerically solving the coupled differential equations resulting from the above processes to obtain time-dependent vibrational populations; the initial fractions of NO in v= 1 and 2 are thermal and the initial laser-pumped v= 3 population is varied over a wide range. A number of simplifications and assumptions are included. It is assumed that only Au= 1 transitions occur, as has been supported by previous studies [ 1,3] for low vibrational levels. It is also assumed that the V-T rate constants are linearly dependent on vibrational quantum number, as is predicted by SSH theory and supported by Yang et al.
71
I.J. Wysong /Chemical Physics Letters 227 (1994) 69- 73
[ 31. This allows us to make the following substitutions: k& =2/c?! and k& =3k?;lo. The rate constant k?;lo has been measured many times, and the value used here [4] is 2500 s-r Torr-‘. The reverse rates k’, which are related to the forward rates by microscopic reversibility for the exothermicity of the reaction, are: k$Y,=0.76 kz:,; k;Y, =0.87 kL; k’& = 0.00011 k‘;$ at room temperature. Radiative removal, with lifetimes of around 80 ms, will be negligibly slow compared with the above processes at the pressures used here and has been ignored, as have the reverse V-T processes kz, and kT2. The simulations leave out the argon buffer gas, as it is known to have too slow a relaxation rate coefficient [4,5] ( ~0.4 s-r Torr-‘) to have any detectable effect at the pressures used here. When another collider species is added to the flow, the above equations are simply modified by adding a relaxation term for the collider to the equation for each vibrational level. A number of other V-V processes are possible if we consider the collision of a NO ( v= 3 ) with another excited species (v= 1, 2, or 3), but simulations for the present conditions show that these are negligible when the initial fraction of NO ( v= 3 ) is < 0.1%. Under those conditions, the decay of v= 3 is a single exponential with a rate coefficient simply equal to k;T2 + k&. A second result from the simulations is that the v= 1 population (x) has the following time dependence x=a+b[exp(
-ct)-exp(
-dt)]
,
(6)
where a represents the constant background population of v= 1 due to the thermal Boltzmann fraction, b is the magnitude of the transient v= 1 population due to laser pumping, and c and d are the rates for transfer into and out of v= 1. The value of b is equal to about three times the initial v= 3 population, as we would expect since the kinetics are dominated by Eqs. (l)and(2).AscanbeseenfromEqs.(l)and(2), each molecule in v= 3 that only undergoes collisions with molecules in v= 0 will produce three molecules inv=l.
of v= 3. It could be a considered a trivial problem to assure that less than O.l”h of the NO molecules are pumped into v= 3, since the second overtone transition is extremely weak, but it is important to be sure, since a high concentration of excited molecules will allow uppumping collisions and change the apparent decay rate coefficient. A sample time scan of v= 1 is shown in Fig. 1. For these scans, the UV probe beam is focused so that it probes about the same volume as is pumped by the IR laser. When the probe beam is focused, the values of c and d will be strongly influenced by diffusion and cannot be meaningfully interpreted. The value of b, however, should still be proportional to the total population passing through v= 1 as a result of laser pumping. Since a will be proportional to the thermal population of v= 1, a fit of the v= 1 time dependence to the form given in Eq. (6) above will yield a ratio of thermal to laser-pumped v= 1 densities. The thermal population of NO( v= 1) is known at a given temperature based on a Boltzmann fraction ( 1x 10e4 at 295 K for NO), and the laser-pumped population passing through v= 1 will be three times the initial laser-pumped population in v=3. Thus we can obtain the fraction of NO molecules that are initially pumped into v= 3 by the laser pulse. Simulations show that collisions between excited NO molecules will begin to become significant when the initially pumped fraction is more than 10e3. As shown in Fig. 1, the energy density obtained in the present study with a focused laser beam yields an initially pumped fraction of 2x 10m4. Under these 2ooo0
0
4. Results
,...‘....‘....‘....‘....‘....‘....(
0
50
loo
150
200
2!Kl
3lxl
Timedday~s)
Some time scans of v= 1 have been obtained in order to estimate the initial laser-pumped population
Fig. 1. Time-dependent population of NO(u= 1) for 0.9 Torr. The pump pulse that populates NO ( u= 3 ) occurs at t = 0.
12
I.J. Wysong / Chemical Physics Letters 227 (1994) 69- 73
conditions, the v= 3 population is dominated by collisions with NO v= 0. A sample time-dependent v= 3 population plot is shown in Fig. 2. It shows that the decay follows an exponential form and yields a decay rate for the given partial pressure of NO. Data from a number of these decay plots at various partial pressures are combined in Fig. 3, and the slope gives the rate coefficient for removal of v= 3. The intercept is expected to be zero, except for contributions by losses due to diffusion or relaxation due to background gases. The technique used here measures the total removal from the v= 3 level and does not distinguish between V-V and VT transfer processes. The observed rate coefficient for removal of NO ( v= 3 ) by NO is 107 f 8 ms- ’ Torr- ’ (all uncertainties represent 20). It follows that the V-V removal rate coefficient kz2 is 99.5 + 8 ms -’
100
5’ 10
NO v=3 relaxation 55o%xp(-.0272t)
x =
1
. . . . . . .
..‘.........‘.....*...’
0
100
50 The
150
delayus )
Fig. 2. Time-dependent population of NO(u= 3) for 0.2 Torr; a simple exponential decay is observed.
._
ni _.- r
w
NO v=3 relaxation
/” I’a
0.08
y.!s0.06
e
-a
3
0.04
0.02
_JJ
x p/
1 1 ,d
Od X/b 0
X4
P 53
0~‘“‘““‘““““” 0
0.2
’
0
00 0 y = 0.107x + 0.005
0.4
0.6
0.8
1
PressureNO (Tom)
Fig. 3. Pressure dependence of NO( v= 3) relaxation rate. Different symbols show data sets taken on three separate days.
Torr-’ or (3.03 20.24) x lo-i2 cm3 s-’ at 295 K if we assume the V-T rate coefficient is kg2 = 7.5 ms - ’ Torr- ’ = 3kzo. It is reasonable to assume this, as SSH theory for V-T transfer predicts k: a vto first order, and a recent study by Yang et al. shows that k: = vk?! for v= 8 to 12. Given Yang’s results, any deviation from kz2 = 3kCo will be small and will cause a change in the stated value for k$Y2that is well within the experimental uncertainty. The corresponding forward rate constant for kZ2 is 131+ 10 ms-’ Torr-’ or (4.OkO.3) x lo-l2 cm3 s-i.
5. Discussion The only previous measurement of the NO v= 3 removal rate coefficient is due to Horiguchi and .Tsuchiya [6]. (HT),withavalueofkz2=89+9ms-’ Torr-‘. HT give this value as the rate coefficient for k;Y’z, but they note that it actually represents the total removal due to V-V and V-T processes, as is the case in the present measurement. It was noted previously [ 1 ] that the laser pump/probe result for kc1 was significantly higher than HT ‘s result which was based on Hg(6 3P,) excitation of NO(v= 1-15). HT state that their analysis ignores collisions between two excited molecules and thus is likely to underestimate the removal rate coefficients, but their results are in reasonable agreement with the present study. One method of predicting VET probabilities is SSH theory [ 7 1, which is based on a purely repulsive interaction, but includes an attractive part of the potential to the extent of increasing the relative velocity of the colliding particles. The probability is defined as the rate constant for the process divided by Z, where Z is the gas kinetic collision rate constant. Dunnwald et al. [ 8 ] have used a kinetic model using semi-empirical rate coefficients for V-V and V-T transfer (as well as expressions for radiative emission and V-E transfer) to model the time-dependent anharmonic V-V pumping in NO following strong laser pumping of v= 1. A convenient formulation of the SSH theory for V-V transfer, as modified by Keck and Carrier [ 9 1, is included in their paper, using a value of 0.2 A for the range parameter of the repulsive potential wall and including an empirical factor which matches the predicted value for k2, of NO to
73
I.J. Wysong/Chemical Physics Letters 227 (1994) 69-73
Table 1 Total removal rate coefficients and probabilities for NO(X, II= 3,2 and 1) for Oz and CH, at 295 K. Rate coefftcients for v= 3 are results of the present study Collision pair
Relaxation rate coeff. k(x10”cm3s-I)
Reduced probability Plv(x104)
AE (cm-‘)
NO(v=l)-0s NO(v=2)-Oz NO(v=3)-Or NO( v= 1 )-CH., NO(v=2)-CH4 NO(v=3)-CH,
0.24+ 0.04 a 0.74*0.10 a 1.46kO.15 2.0f0.2” 5.3kO.5 a 12.0& 1.2
1.0 1.5 2.0 6.3 8.4 13
320 292 264 343 314 286
“Ref. [l].
the value measured by Stephenson [ 41. This model predicts a ratio of 1.19 for &‘Yz//CT:,, lower than the present measured ratio of 1.36. The discrepancy may well be due to the attractive forces which have been shown [ 1 ] to be important in NO-NO V-V transfer. Semiclassical VET calculations using an attractiverepulsive potential and including rotation have been performed by Cacciatore and Billing [ lo] for COCO and by Billing and Kolesnick [ 111 for 02-O2 which agree quite well with available data. No such calculations have been performed for NO-NO VET as yet. The present results for removal from NO ( v= 3 ) by O2 and CH4 are shown in Table 1, along with values from the previous study for removal from v= 1 and 2. Again, these values represent total removal, the sum of V-V and V-T processes. The energy defects are shown, along with the reduced probabilities, P(v) /v. The values are consistent with SSH theory, which predicts that P(v) increases with v due to the linear increase in transition matrix elements, and also increases as the energy defect decreases. The fact that CH4 is a more efficient relaxer for the same vibrational level and approximately the same energy defect is not fully understood and has been discussed briefly in the previous study. No previous measurement has been made of the removal of NO (v= 3 ) by CH4, but removal of NO ( Y= l-7) by O2 has been measured by Green et al. [ 121 using electron beam excitation at 300 K, yielding a rate coefficient for v= 3 of (1.2-1.5)x10-” cm3 s-r (lower and upper bounds, respectively). The previous measurement agrees with the present result.
The present results demonstrate the value of the overtone pumping technique to obtain state-specific VET rate constants for levels up to v=3. Removal rate constants for NO ( v= 3 ) have been measured for the first time in isolation from other excited vibrational levels.
References [ 1 ] I.J. Wysong, J. Chem. Phys., in press. [2] B. Schmitt and R.E. Ellis, J. Chem. Phys. 45 (1966) 2528. [ 3 ] X. Yang, E.H. Kim and A.M. Wodtke, J. Chem. Phys. 96 (1992) 5111. [4] J.C. Stephenson, J. Chem. Phys. 59 (1973) 1523. [ 51 J. Kosanetzky, U. List, W. Urban, H. Vormann and E.H. Fink, Chem. Phys. 50 ( 1980) 36 1. [6] H. Horiguchi and S. Tsuchiya, Japan. J. Applied Phys. 18 (1979) 1207. [7] R.N. Schwartz, Z.I. Slawsky and K.F. Herzfeld, J. Chem. Phys. 20 (1952) 1591; R.N. Schwartz and ICE Hetzfeld, J. Chem. Phys. 22 (1954) 767; KF. Herzfeld and T.A. Litovitz, Absorption and dispersion of ultrasonic waves (Academic Press, New York, 1959). [ 8 ] S. Saupe, I. Adamovich, M.J. Grassi, J.W. Rich and R.C. Bergman, Chem. Phys. 174 ( 1993) 2 19; H. Dunnwald, E. Siegel, W. Urban, J.W. Rich, G.F. Homicz andM.J. Williams, Chem. Phys. 94 (1985) 195. [9] J. Keck and G. Carrier, J. Chem. Phys. 43 ( 1965) 2284. [ lo] M. Cacciatore and G.D. Billing, Chem. Phys. 58 ( 1981) 395. [ 111 G.D. Billing and R.E. Kolesnick, Chem. Phys. Letters 200 (1992) 382. [ 12 ] B.D. Green, G.E. Caledonia, R.E. Murphy and F.X. Robert, J. Chem. Phys. 76 (1982) 2441.