J. Phys. Chem. 1988, 92, 5507-5514
5507
UV Absorption Study of Colllslonal Energy Transfer In Vlbratlonally Highly Excited SOz Molecules M. Heymann, H. Hippler, D. Nahr, H. J. Plach, and J. Troe* Institut f u r Physikalische Chemie der Universitat Gottingen, Tammannstrasse 6, 0-3400 Gottingen, West Germany (Received: January 4, 1988; In Final Form: March 29, 1988)
Transient UV absorption spectra after UV laser excitation of SOz were recorded and analyzed with respect to collisional energy transfer. By use of previously determined calibration curves, the absorption-time signals were converted into average energy-number of collision profiles. Energy-dependent average energies transferred per collision ( P E ) were derived for 22 different collision partners. The temperature dependence of (Ai?)was determined Over the range 300-1500 K by experiments in a C 0 2 CW laser-heated reactor and in shock waves.
Introduction Collisional energy transfer of highly excited large polyatomic molecules for several systems has been studied by “indirect” techniques with competition between energy transfer and uniby “direct” techniques following the decrease molecular reactions,’~ of internal energy after laser excitation, by time-resolved “calibrated” IR emission3 and UV absorption ~pectroscopy,4*~ and by classical trajectory calculations? It would be desirable to have similar series of experimental and theoretical investigations for highly excited triatomic molecules. However, such studies so far are much less complete. Competitive measurements were made in NOz fluorescence’ and photolysis.* Likewise, relative collision efficiencies were determined in NO2 dissociation and recombination.I0 However, direct measurements and theoretical calculations for this system are absent. On the other hand, direct results are available for excited CS2molecules.”Jz Trajectory calculations are presently being made for this system as well.I3 Nevertheless, indirect kinetic studies for this system do not exist. For SO2,there appears the chance to compare indirect and direct experimental studies with classical trajectory results. For this molecule, relative collision efficiency measurements in thermal rec~mbination,’~ as well as classical trajectory calculation^'^ are available. The present work completes the picture by following collisional energy transfer of highly excited molecules after laser excitation. Quite analogous to the earlier direct studies on CS2, the marked dependence of the UV absorption spectrum on the excitation energy, which was analyzed in the preceding article,I6 is used to monitor the collisional deactivation sequence. Apart from the fundamental aspect of verifying and understanding the details of the individual energy-transfer process, there is more applied interest in the energy transfer of excited triatomic molecules. Thermal decomposition and recombination of these (1) Luu, S. H.; Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1974, 78, 766. Troe, J.; Wieters, W. J. Chem. Phys. 1979, 71, 3931. (2) Damm, M.; Hippler, H.; Troe, J. J . Chem. Phys. 1988, 88, 3564. (3) Rossi, M. J.; Pladziewicz, J. R.; Barker, J. R. J . Chem. Phys. 1983, 78, 6695. Barker, J. R. J . Phys. Chem. 1984,88, 11. (4) Hippler, H.; Troe, J.; Wendelken, H. J. J. Chem. Phys. 1983,78,6709, 6718.
( 5 ) Hippler, H.; Lindemann, L.; Troe, J. J. Chem. Phys. 1985,83, 3906. Hippler, H.; Otto, B.; Troe, J., manuscript in preparation. (6) Gilbert, R. G.; Lim, K. J. Chem. Phys. 1986,84, 6129. (7) Keyser, L. F.; Levine, S.Z.; Kaufman, F. J. Chem. Phys. 1971, 54, 355. (8) Gaedtke, H.; Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1975, 79, 184. (9) Endo, H.; GlHnzer, K.; Troe, J. J. Phys. Chem. 1979,83, 2083. (10) Hippler, H.; Schippert, C.; Troe, J. Inr. J. Chem. Kiner. 1975, Symp. No. 1 , 27. (11) Dove, J. E.; Hippler, H.; Troe, J. J . Chem. Phys. 1985, 82, 1907. (12) Heymann, M.; Hippler, H.; Plach, H. J.; Troe, J. J . Chem. Phys. 1987.87. -. - . , - . , -3867. .- . . (13) Schatz, G., private communication, 1987. (14) Cobos, C. J.; Hippler, H.; Troc, J. J. Phys. Chem. 1985, 89, 1778. (15) Hippler, H.;Schranz, H. W.; Troe, J. J. Phys. Chem. 1986,90, 6158. Schranz, H.-W.; Troe, J. J. Phys. Chem. 1986, 90, 6168. (16) Hippler, H.; Nahr, D.; Plach, H. J.; Troe, J. J. Phys. Chem., pre-
ceding paper in this issue.
0022-3654/88/2092-S507$01.50/0
molecules under normal conditions are governed by collisional energy transfer. An independent understanding of collisional energy transfer would allow for a more rigorous analysis” of thermal dissociation’*-z2and re~ombination’~ results. The temperature dependence of energy transfer appears to be of particular relevance in this respect. Earlier indirect conclusions were drawn from thermal dissociation-recombination results.2’ Like in CS2,lZ our present direct measurements of energy transfer for SO2were made in C W C02-laser-heated reactors and behind reflected shock waves. In this way, earlier indirect conclusions from dissociation studies can be verified. In addition to the temperature dependence of energy transfer, the energy dependence is of great interest. A strong energy dependence was observed in CS2,11 being markedly more pronounced than in excited large polyatomic molecules. However, the experiments in CS2could not be extended to such low energies that the range of vibrational relaxation studies was reached. In the present work on SOz, a connection with the vibrational relaxation range was possible such that information on energy transfer is available from the dissociation energy down to low energy. With this complete picture over a large energy range, the old problem of the establishment of a steady state in thermal dissociation and recombination experiments (see, e.g., ref 23-26) can be considered again on the basis of real experimental information. Classical trajectory calculations of rovibrational energy transfer in excited SO2were made in a very detailed way.15 A comparison with the present “direct” experimental results appears most interesting. The problem of the adequate representation of the simultaneous rotational and vibrational energy transfer in trajectory calculations as well as in experimental systems involving sequences of collisions so far has not been treated sufficiently accurately such that an unambiguous analysis would be available. Our present work may help to advance a solution of this problem. Our experiments involved pulsed laser excitation of SO2at 248 and 308 nm into strongly mixed electronic states. The collisional deactivation sequence of the excited molecules then was monitored by using calibrated16 hot UV absorption spectroscopy. The experiments were done in static cells a t room temperature, in C W C02-laser-heated reactors, and behind shock waves. In the fol~
~
~
~~~~
(17) Troe, J. J. Chem. Phys. 1977, 66,4745. (18) Kiefer, J. H.J . Chem. Phys. 1975, 62, 1354. (19) Just, Th.; Rimpel, B. Proceedings of the 11th International Sympo-
sium on Shock Tubes and Waves, 1977; University of Washington Press: Seattle. 1978: D 226. (20jPlach,HyJ.; Troe, J. Int. J. Chem. Kinet. 1984, 16, 1531. (21) Troe, J. J . Phys. Chem. 1979,83, 114. (22) Kiefer, J. H.; Ramaprabhu, R. Chem. Phys. Lett. 1982, 86, 499. (23) McElwain, D. K. S.;Pritchard, H. 0. J . Am. Chem. Sac. 1969, 91, 7693; 13th International Symposium on Combustion; Combustion Institute: Pittsburgh, 1971; p 37. (24) Brau, C. A.; Keck, J. C.; Carrier, G. Phys. Fluids 1966, 9, 1885. (25) Dove, J. E.; Troe, J. Chem. Phys. 1978, 35, 1. (26) Troe, J. Annu. Rev. Phys. Chem. 1978, 29, 223.
0 1988 American Chemical Society
Heymann et al.
5508 The Journal of Physical Chemistry, Vol. 92, No. 19, 1988
0
0
5
IO
15
20
15
20
r
I
I
0
1
2
I
I
t /,US
1
1
5
O I
I
t /ps
Figure 1. Absorption-time profile of SO2 at A = 240 nm after laser excitation at 308 nm. Upper curve: experiment at 300 K with 0.85 Torr of SO2, pulse energy 8 mJ/cm2, length of reaction cell 48 cm, average over 1024 shots. Lower curve: experiment at 300 K with 10.2 Torr of SO2,pulse energy 17 mJ/cm2, length of reaction cell 5 cm, average over 64 shots.
lo
*O
t /,us
3
I
W3O
I
1
4
5
I
1
40
50
Figure 2. Absorption-time profile of SO2 at h = 240 nm after laser excitation at 308 nm. Upper curve: 300 K, 0.21 Torr of SO2in 97.1 Torr of Ar, pulse energy 15 mJ/cm2, length of reaction cell 48 cm, average over 256 shots. Lower curve: 300 K, 11.3 Torr of SO2 in 88.5 Torr of Ar, pulse energy 14 mJ/cm2,length of reaction cell 5 cm, average over
16 shots.
lowing, the three types of experiments will be described separately. Experiments in Static Reaction Cells at Room Temperature
Our experimental apparatus and technique have been described in detail in ref 11 and 16. Only a short summary will be given here. The reaction cell was a cylindrical glass tube of 48-cm length closed by quartz windows. The molecules were excited by 10-ns pulses from an excimer laser passing along the axis through the tube. The time-dependent absorption of the molecules after the pulse was recorded by a lamp, monochromator, photomultiplier, and transient digitizer. Excitation and analysis light beams were conducted collinearly through the tube and separated by dichroic mirrors. Figure 1 shows typical absorption-time profiles recorded at 240 nm after excitation at 308 nm. The decrease of the average vibrational energy ( E ) of the molecules according to the calibration experiments in ref 16 at first is accompanied by an increase of the absorption coefficient e, The maximum of e corresponds to an average vibrational energy ( E ) = 100 kJ mol-'. Starting from an initial energy of 390 kJ mol-', at the SO2pressure of 0.85 Torr of Figure 1 (upper curve), it takes about 5 ps, corresponding to about 55 collisions, to reach this point. The average energy transferred per collision over this energy range thus corresponds to about -400 cm-I. At lower excitation energies, the collisional energy loss slows down markedly. Therefore, the slow final relaxation at energies below 100 kJ mol-' can be studied more conveniently by using higher gas pressures. Figure 1 (lower curve) shows the period after reaching the absorption maximum for an SO2 pressure of 10.2 Torr. Here, it takes about 900 collisions (about 7 w s ) to reach half of the maximum absorption which corresponds to an energy loss from 100 to 30 kJ mol-'. Over this range the average energy transferred per collision has changed to -6.5 cm-I. The final relaxation slows down even further. Experiments with other colliders have to be performed with sufficient excess of the bath gas since SO2 is a fairly efficient collider. Figure 2 demonstrates such experiments with M = Ar. In order to measure the initial period shown in Figure 2 (upper curve), an Ar concentration 500 times larger than that of SO2 was used. In this case the contribution of SOz* + SO2collisions can be neglected. The experiment in Figure 2 (lower curve) in the slow later stage of the deactivation, was performed with an
rodius / nrr
Figure 3. Radial temperature profile in CW C 0 2laser-heated reaction cell (gas in the cell N2 + SF6;absorbed laser power 10 W; (a) cell length 502 mm; (b) cell length 200 mm).
Ar:S02 ratio of 1O:l. In this case, the known contribution of SO2* SO2 collisions still has to be taken into account. Like in our CS2 experiments, the time scale of the absorption-time profiles was proportional to the pressure of the dominating collision partner. There was no evidence for a pressureindependent contribution which might have to be attributed to temporal trapping in excited electronic states. The evaluation of figures like 1 and 2, for a series of different bath gases, will be given below.
+
Experiments in CW C02-Laser-Heated Reaction Cell at Temperatures up to 1000 K In experiments between 300 and 1000 K the gas was heated by a CW CO, laser. Traces of sF6were added to the gas mixture in the reaction cell, absorbing the IR radiation at 10.6 Km. SF6
is a good absorber at this wavelength and thermally stable until far above 1000 K. It is furthermore transparent between 200 and 300 nm under our conditions. The CO, laser radiation was guided through the reaction cell described before by using KCI windows and Ge beam splitters. The determination of the temperature and density profiles, produced by C 0 2laser heating, has been described before in detai112~27 and is not repeated here. Measurements of energy transfer after UV excimer laser pulses were made in a narrow beam along the axis of the cell, for which the heating (27) Heymann, M.; Hippler, H.; Troe, J. J . Chem. Phys. 1984,80, 1853.
Collisional Energy Transfer in Excited SO2 Molecules
The Journal of Physical Chemistry, Vol. 92, No. 19, 1988 5509
V
2
0
obs PowerIWatt
Figure 4. Maximum temperature in C W C 0 2 laser-heated reaction cell (gas in the cell N2 SF6; (a) cell length 502 mm; (b) cell length 200
+
mm).
conditions were homogeneous and particularly well defined. Figures 3 and 4 illustrate radial temperature profile in the cell and maximum temperatures at various laser powers. Room temperature experiments could only be made with an excimer laser wavelength of 308 nm, since the room temperature absorption coefficient at 248 nm is too small for an efficient excitation. The situation markedly improves in heated gases since c at 248 nm increases strongly with increasing gas temperature. Figure 5 (upper curve) shows an example with an excitation wavelength of 248 nm and a gas temperature of 700 (*50 K). The temperature was determined by means of the change of the SO2light absorption at 300 nm during C 0 2 laser heating (using the known temperature dependence of e (ref 16)). The initial excitation energy of SO2 after the excimer pulse corresponds to 40830 cm-' (photon energy plus thermal energy). This value is about 8000 cm-I higher than in the room temperature experiments but still about 5000 cm-I lower than the SO2dissociation energy.28 Excited SO2 molecules thus do not dissociate appreciably. The initial and the later stages of the collisional deactivation in Figure 5 (upper curve) can be monitored in the same experiment. However, the changes of the SO2 absorption are less pronounced in the high-temperature experiments than at 300 K. The absorption coefficient e at 240 nm varies between 10 and 500 L mol-' cm-' at 300 K and between 100 and 500 L mol-' cm-' at 1000 K. In evaluating the C 0 2 laser experiments, the contributions from SO; deactivation by the added SF6 always had to be taken into account besides the effects of SOz* SO2and SO2* + M (e.g., M = Ar) collisions. This was done by experiments of varying concentrations. Within our uncertainties, the effects of the three components of the gas mixture were additive in the decrease of the average energy, ( E ) , with time.
+
Experiments in Incident and Reflected Shock Waves at Temperatures up to 1500 K
By exciting SO2 molecules with excimer laser pulses behind incident and reflected shock waves, even higher temperatures could be reached than in the C02-laser-heated reaction cell. Our technique has been described in detail for the earlier CS2 experirnents.l2 In principle, experiments with SO2can be extended up to 4000 K in this way without dissociating the molecules appreciably during the time of a laser experiment. However, the quality of the signals deteriorates with increasing temperature in such a way that 1500 K was about the maximum useful temperature of our experiments. This limitation is due to the following effects: In the range of large SO2 absorption coefficients, e, at short wavelengths, the variations of e between laser excitation and final thermal equilibrium are small at high temperatures. The averaging of only a limited number of shots appears technically feasible in a simple way. The relatively high pressures applied and the comparably fast deactivation rates at high excitation energies soon lead to an overlap of the laser pulse and the ab-
I
'
0
0.2
0
6
4 t /IS
I
I
0.8
I
I
0.6
0.4
05
I
15
t Ips
Figure 5. Absorption-time profile of SO2 at X = 240 nm after laser excitation. Upper curve: laser excitation at 248 nm. Experiment in C W C 0 2 laser-heated reaction cell at 700 50 K with 15 Torr of S02, 2.2 Torr of SF6, and 150 Torr of Ar. Pulse energy 85 mJ/cm2, length of reaction cell 8 em, average over 64 shots. Center curve: laser excitation at 308 nm. Experiment in reflected shock wave at 950 K with 20 mbar of SO2and 2.9 bar of Ar, pulse energy 50 mJ/cm2, length of observation volume 10 em, single shot. Lower curve: laser excitation at 308 nm. Temperature 1200 K, 31 mbar of SO2, and 3.1 bar of Ar. Other conditions same as those for center curve.
sorption-time profile. The center and lower curves of Figure 5 demonstrate the obtainable absorption-time profiles from single experiments at 950 and 1200 K. The averaging of up to 20 shots allowed improvement of the evaluation; nevertheless, experiments at T > 1500 K showed signal-to-noise ratios too poor to be useful. The results of the shock tube experiments agreed well with those from CO, laser heating when the same conditions were applied. As observed earlier, the time scale of the signals always varied with pressure. Also, the dependence on the SO2 concentrations in the carrier Ar followed the trends seen before. Shock-wave experiments were only done with S 0 2 / A r mixtures, and results for only these two collision partners were extended up to 1500 K. Evaluation of the Absorption-Time Profiles
The recorded absorption-time profiles were evaluated in the following way. The absorption signals at 240 nm were converted into average vibrational energies using the e( ( E ) )calibration curve for ref 16. The change of the average energy ( E ) with time in mixtures of i collision partners always followed the simple relation~hip~~ d ( E ) / d t = x(AE)iZLJi[M]i i
(1)
where ZLj denotes the Lennard-Jones collision frequency ZLJ=
(28) Demtr6der. W.; Kullmer, R. J . Chem. Phys. 1986,84,3672. Brand, J. C. D.; Hardwick, J. L.; Humphrey, D. R.; Hamada, Y.;Merer, A. J. Can. J . Phys. 1976, 54, 186. Okabe, H. J . Am. Chem. SOC.1971, 93, 7095.
I
P U S O ~ - M (~ ~
~ T / P ~ S O * - M ) ' / ~ ~(2)~ ~ ~ ~ M
(29) Troe, J. J . Chem. Phys. 1982, 77, 3485.
5510 The Journal of Physical Chemistry, Vol. 92, No. 19, 1988
t
2
0
1
I
I
4
6
8
Heymann et al.
1 10
I
0
1000 2.
z,p.t/104
Figure 6. Energy-loss profiles for SO2* + M collisions (M = rare gases, ( E ) = average vibrational energy, zpt = Zw[M]t = number of collisions, T = 300 K).
2000
p. t
I 3000
Figure 9. Energy-loss profiles for SO2* + M collisions (M = alkanes, (E) = average vibrational energy, zpt = Zw[M]t = number of collisions, T = 300 K).
'OS
\
I -
HCL
1 0
2
l
2
4
co
02
I
1
6
8
10
z.p.t/t~4
Figure 7. Energy-loss profiles for SO2* + M collisions (M = diatomic colliders, ( E ) = average vibrational energy, zpt = ZLJ[M]t= number of collisions, T = 300 K).
1000
0
2000
z.p,t
Figure 10. Energy-loss profiles for SO2* + M collisions (M = perfluoro substances, ( E ) = average vibrational energy, zpt = Z,[M]r = number of collisions, T = 300 K).
so;
103
I
3000
.
Ar
I
L
I
1
0
2000
4000
0
t .
3
2 . p . t / 104
6
+
Figure 11. Energy-loss profiles for SO2* M collisions (M = Ar, (E) = average vibrational energy, zpt = ZLJ[M]~ = number of collisions, T = 300 K).
energy transferred per collision, ( AE),were a linear function of ( E ) ,linear plots in Figures 6-10 would be obtained. This is quite clearly not the case. The energy-loss rate decreases more strongly with decreasing energy than given by a ( A E ) for highly excited large polyatomic molecules. Analogous to our results on CS2, the derived properties of ( AE) show very specific variations which go beyond a simple dependence on the number of atoms in the collider. The differences between H2 and D2as well as the great efficiency of HC1 appear worth mentioning. H2Sis markedly more efficient than SO2and C 0 2 . The efficiency of the alkanes increase with increasing complexity; however, perfluorocarbons are more efficient than hydrocarbons. CF4 is more efficient than SF,.
The Journal of Physical Chemistry, Vol. 92, No. 19, 1988 5511
Collisional Energy Transfer in Excited SO2 Molecules
lo4
SO;
+
1'
I
I
I
CH,,
\ A
w
10 -
4
moo
0
4ooo
6000
2.p.t
+
Figure 12. Energy-loss profiles for SO2* M collisions (M = CH4, ( E ) = average vibrational energy, zpt = ZLJ[M]t= number of collisions, T = 300 K). Figure 14. Energy dependence of the average energy, (AE), transferred per collision of excited SO2 (various collision partners, T = 300 K).
0
1000
500
1500
2000
2.p.t
Figure 13. Energy-loss profiles for SO2* + M collisions (M = SOz, ( E ) = average vibrational energy, zpt = ZLIIM]t= number of collisions, T
= 300 K). The temperature dependence of the energy-loss profiles is illustrated in Figures 11-13 for SO2* + Ar, SO2* + CH4, and SO2* SOzcollisions. The temperature effects obviously are strongest during the approach of the final thermal equilibrium whereas much weaker effects are observed near the high initial excitation energy.
+
Average Energies, ( AE ), Transferred per Collision
We further represent our results in terms of average energies, (Ai?), transferred per collision via the slopes of Figures 6-1 3 ( m )= d ( E ) /(dZLJ[Mlt) (3) Figure 14 shows (AE)as a function of ( E ) in a double-logarithm plot. With the chosen scales of the axis, a 45' slope corresponds to a square dependence Equation 4 well characterizes the general behavior although minor deviations are also observed such as an apparent "leveling off" at high energies for SOz. Obviously, eq 4 cannot describe the whole energy range, in particular not the final approach of the thermal equilibrium energy (i?)th, where (Ai?) 0 for ( E ) ( E ) t h . This becomes more prominent at elevated temperatures such as demonstrated in Figure 15 for SO2and Ar. At high temperatures, a "high-energy leveling off" here also becomes apparent for Ar. Since eq 4, therefore, appears to provide a not completely satisfactory basis for the representation of our results, like for CS212 we have chosen the form
-
[ {
-
- ( A E ) = A 1 - exp -
< E > / cm" Figure 15. Energy dependence of the average energy, ( AE),transferred per collision of excited SOz (temperature dependence for SO2* SO2 and SO2* Ar collisions).
+
+
nevertheless, eq 5 allows for a detailed representation of all of the present observations. The temperature dependence of the parameter C again12 follows a simple relationship
C = Co(T/300 K)"
(6)
+
Figure 16 documents eq 6 for SO2* Ar collisions in a log C-log T plot. Experiments at room temperature, in the C02-laser-heated cell, and in shock waves fit well together. Our results for the representation of ( AE) by eq 5 and 6 are tabulated in Table I together with the relevant SO2 + M Lennard-Jones collision frequencies. The energy and temperature dependences of ( AE) are documented for selected values in Table 11. Table I1 also contains extrapolations via eq 5 of ( AE) to the dissociation energy 45 600 cm-'. The latter value is given for comparison with thermal dissociation-recombination experiments. The absolute accuracy of the derived ( A E ) values (or the products ( AE)ZLJ) is difficult to establish. The reconstruction of the measured adsorption-time profiles, using eq 1-6 together with the parameters of Table I and the calibration curve of the spectrum from ref 16, was always within the noise of &lo% of the recorded signals.
--p)"}] (5)
which implies a high-energy leveling off of ( AE).This behavior certainly is not documented well enough by the present data;
Discussion
Comparison with Measurements of Vibrational Relaxation. A quantitative comparison of the present energy-loss profiles with
The Journal of Physical Chemistry, Vol. 92, No. 19, 1988
5512
1oc
Heymann et al. TABLE 11: Average Energies, ( a (in ) cni'), Transferred per Collision of Excited SOz at Average Vibrational Energy, ( E ) (in cm-I), and Temperature, T (in K) -(AI?) at ( E ) = M T 2500 5000 10000 20000 45600
8C
He
40
.
Ne
20
Kr
r 7
0
Ar
"
Xe
H2 10
300
500
1000
T/K
1500
D2
2000
N2
Figure 16. Temperature dependence of parameter C in eq 5 for SO2*
+ Ar collisions.
co HC1
TABLE I: Lennard-Jones Collision Frequencies (in lo6 Torr-' s-l) and Parameters ( A in cm-', Coin cm-') of (AE)Representation via Eq 5 and 6O M 2,,(300 K) Zu(lOOO K) A n Co/103 m
He Ne Ar Kr
Xe H2 D2 N2
co
HCI H2S
co2 so2
SF6 CHI C2H6 C3H8 ClH16
cF4 C2F6
C3FB C7F16
13.4 8.16 9.52 9.12 9.83 25.1 18.0 10.8 11.2 11.6 13.6 11.9 12.7 12.3 15.3 15.5 16.3 20.0 10.6 12.3 13.6 19.4
6.05 3.54 3.70 3.36 3.50 10.4 4.34 4.39 3.95 4.31 4.30 4.44 5.74
3.96
540 180 150 150 150 320 320 170 230 210 420 420 840 840 8400 8400 8400 8400 5900 5900 5900 5900
'Lennard-Jones parameters of SO,: For other colliders. see ref 4 and 11.
u
2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.0 2.2 2.2 3.0 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
125.0 78.6 77.8 78.6 68.5 58.5 106.0 52.7 59.4 31.8 19.6 40.1 18.4 35.1 66.9 65.2 61.8 46.8 42.6 28.4 30.1 25.1
-1.05 -0.94 -0.97 -0.98 -0.79 -0.35
-0.40 0.13 0.0 -0.01
-0.28
vibrational relaxation studies at low energies is difficult. Measurements of the vibrational relaxation by ultrasonic absorption,M laser schlieren studies?l and laser-induced f l ~ o r e s c e n c ehave ~ ~ led to the conclusion that the transitions SO2(O,0,l) SO2(O,1,0) between the energies 1361 and 1151 cm-I and SO2(O,1,0) SO2(2,O,0)between the energies 1151 and 1036 cm-I are markedly slower than the lowest transition SO,(l,O,O) SO,(O,O,O) between 518 and 0 cm-I. Expressing the relaxation results near 1000 cm-l by a total average energy transferred per Lennard-Jones collision (including up and down transitions), one arrives at the same order of magnitude of (0) as observed in the present work, i.e., -( AE) = 0.1 cm-I for S02-S02 collisions and 0.01 cm-I for S02-Ar collisions. One should, however, keep in mind that the present
-
co2 so2 F6
CH4 C2H6
-0.65 -0.47 -0.49
= 4.112 A, c / k = 336 K.
-+
H2S
-
(30) Stevens, B. Collisional Activation in Gases; Pergamon: Oxford, 1967. Lambert, J. D. Vibrational and Rotational Relaxation in Gases; Clarendon: Oxford, 1977; p 90. (31) Kishore, V. V. N.; Babu, S.V.; Rao, V. S.Chem. Phys. 1980,46, 297. (32) Siebert, D. R.; Grabiner, F. R.; Flynn, G. W. J . Chem. Phys. 1974, 60, 1564. Siebert, D. R.; Flynn,G. W. J. Chem. Phys. 1975,62, 1212. West, G. A.; Weston, R. E.; Flynn, G. W. J . Chem. Phys. 1977,67, 4873. Lester, M. I.; Flynn, G. W. J . Chem. Phys. 1977, 67, 4873.
C3H8 C1H16
C F4 C2F6
C3FB C7F16
300 1000 300 1000 300 1000 1500 300 1000 300 1000 300 1000 300 300 1000 300 1000 300 1000 300 300 1000 300 1000 1500 300 1000 300 1000 300 300 300 300 1000 300 300 300
0.1 0.5 0.1 0.4 0.1 0.4 0.1 0.1 0.4 0.1 0.3 0.3 0.3 9.1 0.2 0.4 0.2 0.3 0.9 1.6 4.3 0.9 0.9 2.0 0.3 0.02 1.1 0.3 2.1 0.7 2.3 2.6 2.6 4.6 3.4 13 11 17
0.4 4.5 0.4 3.3 0.3 2.9 3.9 0.3 2.9 0.5 2.4 1.4 2.3 0.4 0.9 3.3 1.o 2.1 4.3 11 20 4.2 7.7 16 5.5 2.2 6.2 3.8 12 7.7 13 15 15 27 38 74 64 100
2.0 26 1.9 19 1.6 16 29 1.6 16 2.1 13 6.4 13 1.7 4.3 19 4.5 12 18 49 85 19 43 120 60 38 35 28 71 58 76 88 88 150 280 410 360 560
9.4 120 8.60 77 7.3 67 110 7.2 67 9.6 58 29 62 8 19 76 20 57 66 140 270 81 180 600 420 340 180 160 400 370 420 490 490 820 1570 2000 1770 2540
55 440 47 180 40 150 150 39 150 50 140 140 240 46 88 170 98 190 180 210 420 310 410 840 840 840 720 700 2670 2630 2810 3160 3320 4090 5470 5670 5550 5830
study of stepwise collisional deactivation starting from high energies provides only a very global picture of the final relaxation steps without indicating the specific pathway. It appears plausible that the measured ( A E ) values correspond rather to the (bottleneck) near 1000 cm-I than to the faster relaxation from 500 to 0 cm-'. In any case, the present measurements could be conducted down to energies near 500 cm-I, where direct vibrational relaxation measurements were made, in contrast to CS2 where the energy loss could be followed only" down to about 2500 cm-I. Comparison with Relative Collision Efficiencies in the Thermal SO2 + M . The present enerRecombination 0 + SO + M gy-loss studies at low energies smoothly connect with vibrational relaxation results, although no relation with a specific low-energy transition appears possible. At high energies, they can be extrapolated to the dissociation energy where indirect studies were made by relative collision efficiency measurement^.'^ The analysis of absolute values of thermal dissociation18-20*22 and recombination14 would be more difficult because of the large and not well-defined contribution of excited electronic states to the density of states.I4 However, relative measurements of collision efficiencies p, provide an access to ( A E ) via the relation" p c / ( 1 - &I/*) - ( A E ) / F & T (with FE = 1 near 300 K), when strong collision efficiencies close to unity can be attributed to very efficient colliders. Using @, = 0.85 (or -( AE) = 2200 cm-I) for CsFs, the recombination results of ref 14 were evaluated. They are compared in Table I11 with the present values for 300 K from Table 11. For more than half of the bath gases, the results agree quite satisfactorily within a factor of 2, which is an optimistic estimate of the overall accuracies of the two different approaches. There are, however, also striking differences in H2, D2, CHI, and CF4. For the latter two gases, these are possibly due to an overestimate for
-
The Journal of Physical Chemistry, Vol. 92, No. 19, 1988 5513
Collisional Energy Transfer in Excited SOz Molecules
TABLE III: Average Energies, ( AE ) (in cm-’), Transferred per Collision of SO2 at Dissociation Energy ( E ) = 45 600 cm-’ M He Ne Ar Kr Xe H2 Dz Nz COz CHP CF4
SF6 430 950 1250 (1100) 47 740 39 (410) 27 31 31 39 -(AE)from 8, 90 310 (2700) (4100) 720 50 140 45 55 50 40 40 - ( A E ) from ( E ( r ) ) T = 300 K. First row: relative collision efficiency measurements in recombination 0 + SO + M SO2+ M from ref 14, evaluated with (M = C,Fs) = 0.85 corresponding to - ( A E ) = 2200 cm-I. Second row: energy-loss profiles of this work, extrapolation by eq 5.
-
the most efficient colliders of the A parameters in eq 5 which may produce a leveling off at too high energies. The differences for H 2 and D2are more difficult to explain from the side of the energy-loss experiments. Here the recombination rate coefficients of ref 14 exceed all other values suggesting anomalous reaction behavior. Considering the rare gases, N2, and C02,the agreement between the recombination results from ref 14 and the present energy-loss data appears very satisfactory. Apparently, the present results in a consistent manner fill the gap between the low-energy vibrational relaxation and the high-energy dissociation/recombination range. Role of Excited Electronic States. The overall vibronic density of states near the dissociation energy of SOz in ref 14 was estimated to be 10 times larger than that of the electronic ground state. The corresponding large contribution of excited electronic states to the low-pressure dissociation and recombination reaction is the reason for the anomalously large rate coefficients. It appears not too unplausible that energy transfer in these states near the dissociation energy is characterized by similar collision efficiencies @., The present laser absorption at 308 nm led to SO2excitation a t an energy not too high above the minima of the excited electronic states, where their vibrational densities of states are still fairly small. Nevertheless, the state mixing assured efficient population of the electronic ground state. The consistency of the thermal and laser excitation spectra confirms the dominant role of the electronic ground state in the present work, in spite of the dominance of excited electronic states near the dissociation energy. We have not found any evidence for a different behavior of energy transfer in the present energy-loss experiments, taking place essentially in the electronic ground state, and in thermal recombination, being dominated by excited electronic states in their vibrational quasi-continuum. There was also no evidence for temporal trapping near the minima of excited electronic states, probably because of sufficiently effective state mixing. Temperature Dependence of Energy Transfer. The present measurements indicate that the temperature dependence of ( A E ) in general is stronger at smaller excitation energies ( E ) than at larger energies. The ( A E ) values extrapolated to the dissociation energy in Figure 17 are shown as a function of temperature. Quite similar to the corresponding results in CS2,I2the values of I(AE)I over the investigated range up to 1500 K slightly increase with temperature for the less efficient colliders whereas they are nearly constant (or may even decrease) for the more efficient colliders. The analysis of SO2dissociation rate constantsI4 in Ar over the I range 3000-5000 K, on the other hand, has led to a I(AE)I T decrease after an increase between 300 and 3000 K. Although the latter evaluation was not very direct, similar conclusions in ref 21 were drawn on H 2 0 dissociation in Ar. The present study in any case confirms the hypothesis of only a small temperature coefficient of ( A E ) , being in the range
( A E ) a 7“*’
(7)
This result has important consequences for the temperature dependence of the collision efficiency @, in thermal dissociation and recombination reaction^.'^*^' Consequences of Energy-Dependent ( A E ) in Multistep Systems. Theories of thermal dissociation reactions mostly have been formulated on the basis of energy-independent (AE); see ref 17. However, for small excitation energies, ( AE) a ( E ) 2was found in the present work, ( A E ) ( E ) was determined for large polyatomic excited m o l e c ~ l e s and , ~ ~ transitions ~ between ( AE) a ( E ) zat low and ( A E ) a: ( E ) at high energies were observed in excited molecules of intermediate size like SF6.33 For larger
.- - ..- .
AI
N z --. He
300
y30
l0OU
1500
20a3
T/K Figure 17. Temperature dependence of average energies, (AE),transferred per SOz* + M collision (results at the dissociation energy from Table 11).
energies, a transition to energy-independent (AE)was found in large polyatomic rnolec~les.“3~ With this experimental information on the energy dependence of ( A E ) , it appears worthwhile to consider the consequences on the overall rate in multistep collisional activation or deactivation systems. Following the theoretical analysis for deactivation systems in ref 29, a simple -( AE) i= O ( A E )relationship, ~ such as suggested by Figure 14 and eq 4, via eq 3, leads to
corresponding to a second-order kinetic time law. Taking into account the finite final equilibrium value = (E)th,instead of eq 8 with -(AE) a ’ ( ( E ) - (&))* one would have
A linear -( AE) i= a”( ( E ) - (Eth))relationship, by analogy with a first-order kinetic time law, instead gives ( E ) - (E)th % ( ( E ) - (E)th)l=Oexp(-a’zLJ[Mlt)
(10) whereas a constant -( A E ) = a” leads to a linear energy-loss relation ( E ) - (E)th % ( ( E ) - (Eth))r=O- a’zLJ[Mlt
(1 1) The overall relaxation law obviously will be characterized by transitions between these limiting forms. The energy dependence of ( A E ) can be taken into account in weak collision unimolecular rate theory by inspecting the formalism of diffusion theory.17a-25,34The effects on the low-pressure rate coefficient are not too large, as long as the energy dependence of ( AE) is weaker than that of the equilibrium populationflE). Larger effects obviously are expected for the incubation times. Comparison with Classical Trajectory Calculations. In ref 15 energy transfer for SOz* Ar collisions was treated by classical trajectory calculations, analyzing for simultaneous vibrational and
+
(33) Braun, W.; Scheer, M. D.; Cvetanovic, R. J. J . Chem. Phys. 1988, 88, 3715. Braun, W.; Scheer, M. D.; Kaufman, V. J . Res. Natl. Bur. Stand. 1986, 91, 313. Beck, K. M.; Gordon, R. J. J . Chem. Phys. 1987,87, 000. Gordon, R. J.; Beck, K. M.; Koshi, M.; Vlahoyannis, Y. P. Presented at the 4th International Conference on Multiphoton F’rocesses, Boulder, CO, 1987. (34) Keck, J. C.; Carrier, G. F. J. Chem. Phys. 1965, 43, 2284.
J. Phys. Chem. 1988, 92, 5514-5517
5514
rotational energy transfer. The flow pattern, Le., ( AE) values in the vibrational-rotational energy plane, indicates a partial but not very substantial rotational heating during the stepwise energy-loss process of vibrationally highly excited molecules. Therefore, we compare our measured ( AE) values with average vibrational energy transfer in the calculations. The comparison shows that the measured (AE)values are markedly (more than 1 order of magnitude) smaller than the calculated results. Experiments and calculations agree in an only weak temperatures dependence of ( AE). However, whereas the measurements gave (AE)a ( E ) * ,the calculations rather give ( A E ) a ( E ) . The discrepancies, hence, are largest for the smallest energies. This suggests that the neglect of quantization in the classical trajectory calculations is one important reason for the discrepancy. The introduction of quantization into classical calculations of vibrational relaxation of diatomic molecules is well established; see, e.g., ref 30. The generalization of this procedure to polyatomic molecules apparently is not trivial at all, such that no a posteriori quantization of the SO2 Ar results from ref 15 was tried. One might think of neglecting all collisions in which less energy is transferred than the smallest vibrational quantum of 5 18 cm-’. This would cut out a major fraction of the collisions and bring the calculated energy transfer much closer to the experiments. However, there is the question how far the validity of such a “propensity rule” would reach up into the vibrational quasi-continuum. There exists some information from studies of large polyatomic molecule^^^^^^ about the extension of such a propensity rule up to energies which correspond to a fairly dense vibrational quasi-continuum. Similar effects in triatomic molecules should be expected to reach up to much higher energies. For the present case, the comparison of trajectory calculations and the present
measurements suggests that such propensity rules extend up to the dissociation energy. The theory of collisional energy transfer in the relevant transition range from the lowest energy levels and from energies in the dense vibrational quasi-continuum is not well developed at this time. Whereas SSH-type theories can well describe single transitions, at higher densities of the levels probably the envelope of the collisional transition probability function becomes most important. Quantum calculations for the lowest discrete transitions in C3H6from ref 37 have confirmed a nearly exponential envelope of the energy transfer rate coefficients as a function of the energy difference before and after the collision. The width of this envelope function corresponds well to ( AE) measurements of highly excited large polyatomic molecules, whereas the averaged ( M )over the sparse manifold of actual energy levels at low energies is much therefore, possibly can smaller. The energy dependence of (AE), be rationalized in terms of several effects, the sparsity of the energy levels at low energies, the extension of propensity rules up to higher energies, and the properties of the envelope of a continuous collisional-energy-transfer probability. Classical trajectory calculations probably correspond only to the latter contribution. SSH-type quantum calculations should be extended to the range of the sparse vibrational quasi-continuum in order to provide a suitable treatment for the former contributions. Promising approaches in this direction are under way.35-37
(35) Krajnovich, D.J.; Parmenter, C.; Catlett, D. L. Chem. Rev. 1987,87, 237. (36)Thoman, J. W.;Kable, S. H.; Rock, A. B.; Knight, A. E. W. J . Chem. Phys. 1986,85,6234. Knight, A. E.W., manuscript in preparation. Kable, S. H.;Knight, A. E. W. J . Chem. Phys. 1987,86,4709.
335-57-9.
+
Acknowledgment. Financial support of this work by the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich93 “Photochemie mit Lasern”) is gratefully acknowledged. Registry No. SO2, 7446-09-5;He, 7440-59-7;Ne, 7440-01-9;Ar, 7440-37-1; Kr, 7439-90-9; Xe, 7440-63-3;Hz,1333-74-0; Dz,7782-39-0; Nz, 7727-37-9;CO,630-08-0;HC1,7647-01-0;HzS, 7783-06-4;COz, 124-38-9; SF6,255 1-62-4; CH4,74-82-8;C2H6,74-84-0;C3H8,74-98-6; C7H1.5,142-82-5;CF4,75-73-0;CzF6,76-16-4;C,Fs, 76-19-7;C7F1.5, (37)Clary, D.C. J. Am. Chem. Soc. 1984,106,970; J. Phys. Chem. 1988, 92, 3173.
Spectroscopy of the no-3s Rydberg State of Isolated and Clustered Acetaldehyde D. J. Donaldson, Erik C. Richard, S . J. Strickler, and Veronica Vaida* Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-021 5 (Received: December 29, 1987)
The direct absorption spectra of jet-cooled acetaldehyde-do, -dl, and -d4 are reported in the no-3s Rydberg electronic state. Cooling in a jet removes all vibrational hot bands, confirming that there is not a second, “intravalence” transition in this region. Some previously unreported vibrational features are assigned based on a normal-coordinate analysis of the excited state. Cluster-induced changes in the spectrum are observed. These changes are interpreted in light of previous work in which cluster-induced changes in the spectrum provide information about the dissociation dynamics.
Introduction The past decade has witnessed enormous advances in our understanding of molecular photodissociation dynamics.’ These have been spurred largely by improved experimental capabilities: more selective methods of initial-state preparation and new, highly sensitive techniques of product-state analysis. Despite these technical successes, a detailed description of photodissociation dynamics is still elusive for most polyatomic molecules. The major (1)Recent reviews include: Jackson, W. M; Okabe, H. Adv. Phorochem. 1985,13, 1. Simons, J. P.J. Phys. Chem. 1984,88, 1287. Bersohn, R.J. Phys. Chem. 1984,88,5145.Leone,S. R.Adv. Chem. Phys. 1982,50,255. Shapiro, M.;Bersohn, R. Annu. Rev. Phys. Chem. 1982,33, 409. 0022-3654/88/2092-5514$01.50/0
obstacle to a quantitative understanding of photodissociative molecules is an insufficient knowledge about the potential energy surface@) which control the dissociation process. Potential energy surfaces can be derived quite readily for bound systems, by use of high-resolution spectroscopic information. However, by definition, dissociating molecules are short-lived, and so the sensitive spectroscopic techniques appropriate for bound systems become useless. This has led us to developing the technique of direct absorption spectroscopy of molecules cooled in a free expansion.* This method has proven to be particularly powerful in the study of predissociating m o l e c ~ l e s . ~ (2) Vaida, V. Acc. Chem. Res. 1986,19, 114.
0 1988 American Chemical Society
