J. Phys. Chem. 1984, 88, 6397-6406
6397
Ground-State Photochemistry of Tetramethyldioxetane. 1. Energy Distribution among Molecules Excited by Infrared Multiple Photon Absorption S. Ruhman, 0. Anner, and Y. Haas* Department of Physical Chemistry and The Fritz Haber Centre for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (Received: April 23, 1984)
Tetramethyldioxetane (TMD) was dissociated under nearly collision-free conditions following infrared multiple-photon excitation (IRMPE) or overtone excitation (OTE)of the C-H vibrational stretching mode. The kinetics of the ensuing chemiluminescence were observed in real time. A quantitative comparison of the rise and decay curves allows the determination of the approximate energy distribution among molecules excited by IRMPE to beyond the dissociation limit. In addition, the actual yield of dissociating molecules is determined as a function of fluence. These data are compared with models based on the widely used rate equations approach. In these models, energy-dependentabsorption cross sections a(E) are used, which are allowed to vary smoothly with energy. It is found that the yield can be fitted by a number of different functional forms of cr(E). In contrast, none could be used to reproduce the energy distributions. This result indicates that yield data alone are insufficient to derive population distributions generated by IRMPE. More sensitive experimental parameters need be determined, which in turn will lead to a better description of the molecular parameters contributing to IRMPE.
1. Introduction
Infrared multiple-photon dissociation (IRMPD) of mediumsized and large molecules is now a well-established method for inducing molecular dissociation under collision-free conditions.' Although the detailed mechanism by which an isolated molecule absorbs a large number of low-energy photons is not completely understood, approximation methods have been developed that reproduce quantities such as the total yield and the average number of photons absorbed reasonably well. A widely used modeP4 assumes that photons are absorbed sequentially in the molecule and that the situation can be faithfully represented by a set of rate equations (1) dP,/dt = I[Un-lPpl + b ' n + l P n + l - (an + u'n)PnI - knPn Here the energy levels of the molecules are represented by an equally spaced set E, = nhv where Y is the laser frequency. The population of the level n is designated as P, and its degeneracy (density of states) is p,. The absorption cross section and the stimulated emission cross section from level n are an and a', respectively. I is the laser's intensity and k, is the unimolecular dissociation rate constant. an-,is related to a', by the detailed balance condition ~n-~an= - ~ Pndn (2) and k, is usually obtained from the RRKM expression
(3) where L+ is the reaction channel degeneracy and N+the sum of states of the activated complex at energy E,. Equation 1 constitutes a drastic approximation to the real equations of motion of the system. It not only neglects any coherent effects and simultaneous multiphoton transitions but also assumes the existence of a well-defined, energy-dependent absorption cross section. It thus ignores the possibility that degenerate states can interact differently with the electromagnetic radiation. Furthermore, usually levels within a width of about 1000 cm-' (the COzlaser photon's energy) can be grouped together and assigned the same u,. Likewise, each of these energy groups (1). (a) Ben-shaul, A,; Haas, Y.; Kompa, K. L.; Levine, R. D. "Lasers and Chemical Change"; Springer-Verlag: West Berlin, 1981. (b) Quack, M. Adu. Chem. Phys. 1982,50,395. (c) King, D. S.Adv. Chem. Phys. 1982,50,105. (d) Cureton, C . G.; Goodal, D. M. Adu. Infrared Raman Spectrosc. 1983,
10, 307. (e) Steinfeld, J. I., Ed. "Laser Induced Chemical Processes"; Plenum Press: New York, 1981. (2) Lyman, J. L. J . Chem. Phys. 1977, 67, 1868. (3) Grant, E. R.; Schulz, P. A.; Sudbo, Aa. S.;Shen, Y . R.; Lee, Y . T. Phys. Rev. Lett. 1978, 40, 115. (4) Quack, M. J . Chem. Phys. 1978, 69, 1282.
0022-3654/84/2088-6397$01.50/0
is assigned a single reaction rate constant, k,. This is in line with statistical theories of unimolecular dissociation, but uses a coarser graining than most treatments. This oversimplifed model has been surprisingly successful in accounting for the gross features of IR multiphoton excited reactions. Its main merit has been the mathematical simplicity, and the fact that a limited number of parameters are required. As energy is accumulated in the molecule, k, increases until further up-pumping is practically terminated when k, >> uJ. Even so, typically several tens of absorption cross sections are required in order to solve (l), making a meaningful analysis doubtful. The accepted method for dealing with the problem is to assume a simple analytical form for a, as a function of n, allowing for only one or two independent parameter^.^-* It has been noted that since all the equations are linear in I , the total yield under collision-free conditions is approximately9 proportional to the fluence, F, defined as F = S I dt, where integration is over the total duration of the laser pulse. Experimentally, the total yield was often shown5-*to be mainly a function of the fluence only. Recently, it was demonstrated for model systems1° that direct integration of the equations of motion leads to incoherent absorption and to fluence, rather than intensity, dependence of yield and average number of photons absorbed. This results from chaotic behavior of the system arising from nonconservation of the molecular angular momentum. This is due to strong interaction with the radiation field. A property that has so far eluded extensive experimental investigation is the energy distribution among the reaction molecules. The first moment of the total distribution (including nonreacting molecules) can be determined by measuring the average number of photons absorbed per molecule. This quantity can be obtained by direct or by optoacoustic techniques"-I6 and ( 5 ) Jang, J. C.; Setser, D. W.; Danen, W. C. J . Am. Chem. SOC.1982,104,
5440. (6) Barker, J. R. J . Chem. Phys. 1980, 72, 3686. (7) Weston, R. E.; J. Phys. Chem. 1982, 86, 4864. (8) Fuss, W. Chem. Phys. 1979, 36, 135. (9) A small correction is called for to account for the dissociation of molecules during the laser pulse. (10) Galbraith, H. W.; Ackerhalt, J. R.; Millonni, P. W. J . Chem. Phys. 1983, 79, 5345. Ackerhalt, J. R.; Galbraith, H. W.; Milonni, P. W. Phys. Reu. Lett. 1983, 51, 1259. (11) Danen, W. C.; Rio, V. C.; Setser, D. W. J . A m . Chem. SOC.1982, 104, 5431.
(12) Marling, J. B.; Herman, I. P.; Thomas, S.J. J . Chem. Phys. 1980, 72, 5603. (13) Evans, D. K.; McAlpine, R. D.; Adams, H. M. J . Chem. Phys. 1982, 77, 3551. (14) Bagratashvili, V. N.; Knyazev, I. N.; Letokhov, U. S . ; Lobko, V. V. Opt. Commun. 1976, 18, 525.
0 1984 American Chemical Society
6398 The Journal of Physical Chemistry, Vol. 88, No. 25, 1984 has also been accounted for by the rate equation model. Although the total yield provides some information on higher moments, direct determination of these is almost totally absent from literature reports. In the only attempt of which we are aware, Welge and co-workers deduced the energy distribution of SF5+ ions from the time of flight of the daughter SF4+ions." This experiment was limited to one fluence model only and was not compared with a theoretical simulation. Modeling is hampered by the lack of information on the initial energy distribution in the SF5+ions, as well as their low-intensity infrared absorption cross section. In a preliminary report,18 we suggested that comparison with overtone induced dissociation could be used to deduce IRMPE created energy distributions. The molecule chosen as a first candidate to demonstrate the method was tetramethyldioxetane (TMD). Its dissociation leads to the emission of bright chemiluminescence, allowing facile real time monitoring of the reaction kinetics. A low activation barrier makes it a natural candidate for extensive OTE studies, as was recently reported by Cannon and Crim.zz This paper presents a detailed account of the measurements and calculations carried out to obtain IRMPE-created distributions using this method. 11. Methodology
The basis of the present method is the assumption that intramolecular energy scrambling is rapid compared to the unimolecular reactions rate. This hypothesis is well established in conventional chemical kineticsI9 and, despite some early speculations to the contrary,20gz'is generally also accepted for laserinduced processes. More specifically we take this to mean that a molecule excited to within the same energy range from E to E d E by IRMPE or OTE will give rise to identical reaction dynamics. If we assume the ideal case of instantaneous IRMPE and collision-free conditions, the distribution of internal energies in the excited molecules completely determines the subsequent reaction dynamics. If only a single product is formed, the probability for its formation at time t is
+
A(t) = I m P ( E )(1 Ea
- e--k(E)f) dE
(4)
Here P ( E ) is the probability of finding the excited molecule at energy E, E, is the threshold energy, and k(E) is the energydependent reaction rate constant. Were A ( t ) directly observable in real time, and k ( E ) known for all E > E,, then P(E) could be derived from (4)by a proper variational method. However, these conditions are actually never obtained in practice. More than one product is usually formed (by this we also mean several distinct states of a given product). The formation kinetics of A ( t ) is generally not measured directly but rather deduced from an experimental observation via an assumed mechanism. Technically, the quantity directly measured is not the probability of observing A, but a property related to it. In the present work, chemiluminescence (CL) was used, as it offers a facile and sensitive means of observing the reaction kinetics. Let S(E,t) be the CL signal observed after an instantaneous excitation of all irradiated molecules to an internal energy E. It follows that the signal after IRMPE can be written as (5) (15) Black, J. G.; Kolodner, P.; Schulz, M. J.; Yablonovitch, E.; Bloemberger, N. Phys. Rev.A 1979, 19, 704. (16) Presser, N.; Barker, J. R.; Gordon, R. J. J. Chem. Phys. 1983, 78, 2163. (17) von Hellfeld, A.; Arndt, B.; Feldmann, D.; Fournier, P.; Welge, K. H. Appl. Phys. 1980, 21, 9. Gershuni, S.; Haas, Y. Chem. Phys. Lett. (18) Ruhman, S.; Anner, 0.; 1983, 99, 28 1. (19). (a) Robinson, P. J.; Holbrook, K. A. "Unimolecular Reactions"; Wiley Interscience: London, 1972. (b) Forst, W. 'Theory of Unimolecular Reactions"; Academic Press: New York, 1973. (20) Hall, R. B.; Kaldor, A. J . Chem. Phys. 1979, 70, 4027. (21) Reddy, K. V.; Berry, M. J. Chem. Phys. Lett. 1979, 66, 223.
,
Ruhman et al. NUMBER OF ABSORBED COz LASER PHOTONS :I I; 12 13 14 15 16 I I I I 1
INTERNAL
ENERGY ( c r n - 1 )
Figure 1. The shape of the energy distributions created by overtone excitation of the CH stretch to v = 3, 4, and 5 for room temperature TMD, assuming that the Boltzmann distribution is shifted upward by the energy content of the absorbed photon. For comparison purposes, the number of absorbed COzlaser photons in the same energy interval is also shown.
Here &RMpE($,t) is the C L signal obtained by a laser pulse of energy 4. Equation 5 can be used instead of 4 to derive P(E) as a function of I#J,without needing to know anything about the mechanism leading to S(E,t). The statistical assumption ensyres that S(E,t) is indeed a function of the internal energy only. Measurement of S(E,t) involves devising a method for exciting TMD to any well-defined region above threshold, on a time scale short compared to the subsequent reaction rate. The single-photon OTE time-resolved excitation studies initiated by Cannon and CrimZZ(CC) provide a practical approximation to this ideal. At present, signal-to-noise considerations restrict this metfiod to a small number of overtone transitions. Cannon and Crim used the third, fourth, and fifth overtone transitions of the C-H stretching mode. The energy ranges reached by these absorption bands will be designated as u = 3, 4, and 5, respectively. Figure 1 shows the energy distributions obtained. They were calculated by assuming that the cross section for OTE of each molecule is independent of its initial energy. The resulting distributions are nominally about 2500-cm-' apart, but due to their large widths (- 1000 cm-l fwhm) are seen to span continuously (not uniformly) a large energy interval. Cannon and Crim have analyzed the dissociation dynamics using a kinetic model based on RRKM theory and the production of two distinct nascent emitting products. As a result of this analysis the time evolution of the chemiluminescence could be predicted as a function of internal energy E, to within a scaling factor. The dependence of this factor on E is still unknown due to the fact that not all relevant rate constants are known. Thus, an analytic model cannot be used at present in conjunction with ( 5 ) to calculate an approximate P(E). For a more detailed discussion of this point, see section IV. Rather than using further mechanistic assumptions, we propose to approximate (5) using a coarse energy graining by approximating P(E) above threshold as a linear combination of the three distributions displayed in Figure 1. Let SOTE(u,t)designate the C L signal measured after total excitation to the u'th overtone. If S(E,t) is a slowly varying function of E, we can approximate ( 5 ) by U
where the optimal P(u)'s constitute a coarse approximation for P ( E ) . Our method consists therefore of a direct quantitative (22) Cannon, B. D.; Crim, F. F. J . Chem. Phys. 1981, 75, 1752; J . Am. Chem. SOC.1981, 103, 6722. Cannon, B. D. Ph.D. Thesis, University of Wisconsin, Madison, 1981.
Ground State Photochemistry of Tetramethyldioxetane
The Journal of Physical Chemistry, Vol. 88, No. 25, 1984 6399
TABLE I: Details on Laser Sources Used in OTE Experiments
C-H vibrational excitation energy per state excited wavelength, pm pulse, mJ v = 3
1.167
v=4
0.904
method of generation second Stokes in 350 PSI H2 from 70 mJ Kiton red at 5919 A 4.5 f 0.5 first Stokes in 280 PSI H2from 50 mJ DCM at 2 f 0.3
6575 A
v=5
0.740
14.5 f 1
fundamental of oxazine 725
optical filters used Schott RG 715;Schott RG 780;Corning 7-56 Schott RB 780;Schott RG 715 Schott RG 715
comparison of IRMPE and OTE results for TMD, recorded under identical experimental conditions. The validity of this approach and the technical problems involved are discussed in sections I11 and V. The basic virtue of the method is the fact that it circumvents the necessity of an elaborate model for describing the kinetics of the emission signals and is based only on quantities directly measurable in real time. 111. Experimental Results
A . Experimental Details. Sample Handling. TMD crystals, synthesized by Kopecky's method,23 were placed in the sidearm of a Pyrex flow cell. They were held in an ice-water bath, thus facilitating the maintaining of a constant sample pressure which was controlled by needle valves and measured by a 1-torr capacitance manometer (MKS Baratron Model 220-3A1-1). The flow rate was such that almost complete replenishment of the sample took place between laser pulses in the IRMPE experiments. A 30-cm long cell equipped with BaF2 or quartz laser beam entrance and exit windows and a quartz observation window was used. A wood's horn opposite the observation window helped reduce the scattering light level. All experiments were conducted at room temperature. Laser Sources. For OTE experiments and Nd:YAG laser pumped dye laser was used (Quanta Ray's DCR-1: PDL laser system). Raman shifting was used to obtain the necessary wavelengths, cf. Table I. Raman-shifted radiation was isolated from shorter wavelength radiation by optical filters. Higher-order Stokes lines were minimized by adjusting the pressure in the H2 Raman cell. Their intensity was kept at least an order of magnitude lower than the band used. The laser beam was collimated to 3 mm diameter, minimizing nonlinear intensity effects. These were sought for and not observed-the signal was always linear with the laser power. A thyratron triggered tunable TEA C 0 2 laser was used in the IRMPE experiments. The lOR(20) line at 10.247 nm was used throughout. The laser was operated in the TEM,, mode, with pulse energies up to 40 mJ. The usual "tail" was eliminated by using nitrogen-lean gas feed mixtures, resulting in a 120-ns fwhm pulse, with negligible intensity beyond 350 ns (see Figure 3). In the IRMPE experiments, a 500-mm focal length BaFz lens was used to focus the radiation into the cell center. The Raleigh range of the beam was 5 cm, and the luminescence was collected only from a region of a total length of 2 cm near the center, ensuring nearly constant energy density conditions. This precaution was not taken in the preliminary report.'* The total C 0 2 laser energy reaching the sample was controlled by a liquid attenuation cell equipped with BaFz windows and adjustable between 0 and 5 mm. Cyclohexane was used as the attenuation liquid, yielding a facile and reproducible control method with no discernible change in the spatial or temporal characteristics of the pulse. The Gaussian beam profile at the focus was determined by measuring the energy transmitted through a set of pinholes of different radii, situated at the focus. The energy transmitted (ER) through the pinholes of radius R was detected by a photon drag detector. For a pinhole of radius R, ER is given by ER = ET[1 - exp(-R2/w2)] where ET is the initial energy, and w the l / e beam waist. Figure 2 shows the results expressed as a linearized form of eq 6 along (23)Kopecky, K. R.;Filby, J. E.; Mumford, C.; Lockwood, P. A.; Ding, J.-Y. Can. J . Chem. 1973,53, 1103.
011
d2 d.3 014 d.5 R , PINHOLE RADIUS ( m r n )
Figure 2. The spatial Gaussian shape of the C02 laser pulse, obtained from the analysis of beam intensity transmitted through calibrated pinholes. See text for details.
LASER
, -&+i+++++*+++++++
>t-
H
cn Z
W t-
Z H
L
-0.25
I
0.81
I
1.87
I
--1
2.94
4.00
TIME(microseconds> Figure 3. The temporal evolution of the rise of the chemiluminescence induced by the C02 laser. The pulse shape of the laser is also shown. In this experiment, the total fluorescence was observed with the photomultiplier placed next to the observation window and TMD pressure was 10 mtorr. with the beam shape deduced from them, with w = 0.41 f 0.02 mm. Detection System. Chemiluminescence was observed through a blue-green filter (Corning 4-96) by an EM1 9558QB photomultiplier. A f / l lens was used to image the luminescence onto a 20-mm aperture placed in front of the PM's photocathode in the IRMPE experiments, as described above. In the OTE experiments, the P M was placed as close as possible to the observation window. The anode signal was digitized (Biomation 8100), averaged (Nicolet 1170), and stored in a VAX 750 computer for further analysis. B. Chemiluminescence Kinetics. Figure 3 shows the C 0 2 laser pulse temporal profile, along with the rising portion of the chemiluminescent signal obtained upon IRMPE. It is seen that even at the highest laser energy used (23 mJ per pulse) most of the reaction takes place after termination of the laser pulse. The total luminescence kinetics at two time scales for IRMPE are shown in Figure 4. For clarity, only two out of the eight pulse
Ruhman et al.
6400 The Journal of Physical Chemistry, Vol. 88, No. 25, 1984
TMD-OTE
TMD- IRMPE
Z c (
Z
I
-1.00
11.8
I
I
37.2
50.0
1
24.5
10
24.5
li.8
3j.2
56.0
.,.., , . ... , 5.7mJ -19.6mJ
I
I . I '2.
iis.
245. 3j3. 560. TIMECmicroseconds) Figure 5. TMD luminescence kinetics at 3 mtorr, after excitation to C-H 0
t
-10 0
I
I
I
245. 373. TIME(microseconds>
118
1
500.
Figure 4. TMD luminescence kinetics at 3 mtorr after excitation by the C 0 2laser. The laser pulse energy was 19.6mJ for the solid line and 5.7 mJ for the dotted one. These were the two extreme values of the laser
energies used. energies used are shown. The actual intensities strongly depend on the laser energy, but are normalized to unit height in the figure. The time evolution of the signals displayed in Figure 4 is similar to that reported by CC for OTE excitation. Our raw data using OTE at 3 mtorr are shown in Figure 5. As observed by CC, the emission decay can be coarsely separated into two parts a fast component, with a decay constant that is strongly pressure dependent, and a slower one whose decay constant is weakly pressure dependent. For a semiquantitative comparison of OTE and IRMPE results, we define two quantities: Tmx and y. T,,, is the time interval between the laser pulse and the point of maximum signal intensity, and y serves as an estimate of the time integrated intensity ratio of the fast component to that of the slow one: y = L6'S(t) d t / I 560 " S ( t ) dt
where t is in microseconds. Table I1 lists T,,, and y for OTE and IRMPE experiments, as well as the relative intensity. The latter was determined from an experiment in which the u = 4 band was excited under exactly the same geometrical conditions as used in the IRMPE experiments, including the imaging lens. The C 0 2 laser energies were chosen in such a way that y and Tmaxwere approximately bracketed by the OTE values for u = 3 and u = 5. It was hoped that this would lead to excitation distributions that can be reasonably well represented by OTE functions (eq sa). This expectation was largely borne out by a more refined analysis, as shown below. Figure 6 shows a Stern-Volmer plot for the fast decay component. It also displays the results of CC, obtained for u = 4 or 5 excitation. The agreement between the two measurements is good, even for high C 0 2 laser energies except for the highest sample pressures.
.......v:5
overtone bands. TABLE I 1 Characteristics of TMD Chemiluminescence Induced by OTE and IRMPE' U yb Tmax?ps re1 peak intC
OTE Experiments 3 4 5
0.7 1.5 3.4
22 f 4 9fl 1.5 f 0.2
0.006 0.035 0.0065
IRMPE Experiments pulse energy: mJ 5.7 6.7 8.0 9.3 10.3 13.7 16.3 19.6
1.1 1.3 I .4 1.45 1.75 2.0 2.2 2.5
10 2 813 712 5f1 4f1 2 & 0.5 2 f 0.3 1.5 f 0.25
1 2.5 f 0.25 7.5 f 0.75 18 f 1.8 33.5 f 3 164 8 310 f 15 535 f 25
'TMD pressure was 3 mtorr. bFor the definition of y and T,,,,,, see text. cUnderidentical viewing conditions, with a laser energy of J. The uncertainty in CL intensity was 10% for u = 3, 5% for u = 4 and 5. "The error in the C 0 2 laser energy measurments was &0.4 mJ. IV. Derivation of I R M P E Energy Distributions Cannon and CrimZZtried to rationalize their OTE data by a mechanism involving two species, the thermalized triplet (T) and the species giving rise to the fast decay, designated as X. X can be assigned as a vibrationally excited S1 acetone or a mixed SI-T1 state. For the purpose of the kinetic discussion, its actual nature is of little consequence. The following kinetic scheme, based on Cc's proposal, has been used by us in a previous report:24
D
D+
-
-
D+ + D X
nhu
-
or hut
D+
2D
optical excitation vibrational deactivation
formation of the fast decaying component
(7) (8) (9)
The Journal of Physical Chemistry, Vol. 88, No. 25, 1984 6401
Ground State Photochemistry of Tetramethyldioxetane D+
-
T
X X
+D
-
T
- ++ A
+D T+D T+D
X
formation of triplet acetone
-+
-
A
-
A
T
-
hv
fluorescence
D
FAST COMPONENT DECAY
(12)
/
0.201 /
collision induced triplet formation (13) A
+D
-
triplet quenching
+ hv
phosphorescence
(14)
/
- 0.151
/
I
o
7v)
So)
(15) (16)
Here D and D+ are cold and vibrationally excited TMD molecules, respectively. A is acetone in the electronic ground state and X and T are defined above. The time dependence of X is obtained upon solution of the kinetic scheme as
I
/'8
(11)
quenching by T M D
intersystem crossing ( T A
(10)
5
0.10
0 W
0.05
1
/
r
/ /
/
:;li' ' , 0
0
2 3 rnJ
0
18 m J
A
6.5 12 m J
-
'A A
where [D+l0is the initial population of vibrationally excited TMD, assumed to be formed instantaneously, and k, = kx[D] k~ = kii
+ k9 + kio
(18)
+ (ki2 + ki3)[D]
0.00
I
I
---0TE Results 1 I
(19)
+
From this mechanism and ref 22, kx and k12 ki3 are 12.4 X lo6 and 5.6 X lo6 s-' torr-', respectively. The unimolecular decomposition rate constant, k9 klo, was adequately accounted for by RRKM calculations. In their analysis, C C were able to reconstruct the general time dependence of the rise and decay behavior for the emission signals as a function of the internal energy E and the pressure P in the u = 4 and 5 regions. This was achieved by effectively setting k i 3 to zero and treating k9/klo as an adjustable parameter. For the present purpose we need a model that can in addition predict the absolute intensity for emission signals for all energies lying in the range from threshold to about 8000 cm-' above. The cited model cannot be used for this purpose without reliable values for k9/klo and k12Iki3. Direct use of OTE-generated kinetic curves provides a simple way out of these mechanistic difficulties. One need not know the nature of the species formed by the reaction if the total population of vibrationally excited T M D molecules and their energy distribution are known for each O T E experiment. Equation 5a is thus the basis of our analysis, with the penalty of losing detail due to the coarse energy graining. While the kinetic model is incapable of reproducing absolute signal intensities, one kinetic aspect which has been experimentally demonstrated is the strong pressure dependence of the observed emission decay, even at a pressure of a few millitorr. We therefore rewrite (5a) in yet another form, (5b) including the pressure as a relevant parameter:
+
TABLE III: Estimated Absorption Cross Sections for TMD C-H Stretch Overtone Absorotion Bands transition wavelength, pm cross section, cmz 0-3
1.167
0-4
0.904
0-5
0.740
*
(3.8 1.2) X (4.7 f 0.9) x 10-23 (4.3 f 0.9) x 10-24
In order for (5b) to hold, we require that the bimolecular as well as purely unimolecular rate constants governing the shape of the emission signals be identical under OTE and IRMPE conditions. If we bear in mind the fact that P(u) is the probability of finding the molecule excited within the energy range obtained upon excitation to the v'th overtone, SOTE(u,p,t)represents the signal that would be obtained by OTE of the total irradiated population to that energy range. In practice the OTE signals are obtained under conditions where only a very small fraction of the molecules is excited. The bimolecular processes are thus dominated by collisions of excited T M D or its nascent products with room tem-
perature TMD molecules. SOTE(u,p,t)for use in (5b) is obtained from the observed OTE curves by a proper renormalization factor as described below. It therefore represents the signal that would be obtained by exciting a population as large as the total irradiated sample, under conditions where the excited molecules are highly diluted within the bulk. In the IRMPE experiments, particularly at high fluence levels, the number density of vibrationally excited molecules is large. In order for (5b) to hold, we need to ensure that the excited molecule will undergo collisions primarily with cold molecules as in the OTE experiments. One reason for using 3 mtorr was that the calculated mean free path of a molecule perpendicular to the beam axis is an order of magnitude larger than w, the laser beam's I / e radius. This calculation is based on the quenching rate constant obtained by Cannon and Crim.22 Thus, at this pressure even in the IRMPE experiments collisions involving two vibrationally excited molecules are rare. This conclusions is indeed experimentally confirmed, as Figure 6 shows. The pressure dependence of the fast CL decay is similar for OTE and IRMPE, except for the highest pressures in the latter. In order to calculate actual populations created by OTE, we have to use the absorption cross sections for the appropriate transitions. A direct measurement for TMD is difficult because of its low vapor pressure and thermal instability. The cross sections were thus estimated by using the concept of universal intensities in local-mode absorption introduced by Burberry and Albrecht (BA).25 According to this concept, the integrated intensities of an OTE transition depend primarily on the number of C-H oscillators, independent of the nature of the molecule. A survey of available data25.26shows that absorption intensities may be estimated to an accuracy of 50% or better. If the line shape is known, the cross
(24) Ruhman, S.; Anner, 0.; Haas, Y .Discuss. Faraday SOC.1983, 75, 239.
(25) Burberry, M. S.; Albrecht, A. C. J . Chem. Phys. 1979, 7 1 , 4768. (26) Wong, J. S.; Moore, C. B. J . Chem. Phys. 1983, 77, 603.
6402 The Journal of Physical Chemistry, Vol. 88, No. 25, 1984
Ruhman et al.
I I
8.0
L 3 1 4 1 5 l
l -1 10
1
I
24.5
I
16.3
1
3 1 4 1 5 1
ENERGY REGIONS ( I N C -
BEST FIT
11.8
I
I
37.2
1
50.0
TIME(m I croseconds) Figure 7. A graph showing the experimental luminescence signal obtained at three COz laser energies, and the synthesized curve obtained from a combination of the three OTE-generated curves shown in Figure 5.
section at any given wavelength can be obtained. Table 111 lists the cross sections calculated in this way for TMD, using the line shapes obtained by CC.22 These cross sections can now be combined with the data of Table I1 to yield the relative peak intensitiesz7 of OTE generated CL for equal initial populations. At a pressure of 3 mtorr, they are 1, 50, and 100 for u = 3 , 4 and 5, respectively. The low value for u = 3 reflects the fact that, even at 3 mtorr, the average k , is much smaller than k, (cf. eq 17). Work at still lower pressures was not practical in our case but, if performed, would allow us to probe the energy range near u = 3 with better accuracy. The absolute values of the cross sections obtained by BA's method allowed also the calculation of absolute peak intensities of &)TE(u,P,t)that would be obtained upon complete excitation of T M D in the irradiation zone-a cylinder of radius o. These were used in (5b) to obtain the probabilities P(u). A computer optimization routine was used to calculate triads-P(3), P(4), and P(5)-that best reproduce the shape and intensity of the different SIRMPD for each of the pulse energies listed in Table 11. The fitting procedure used the first 50-ps section of the emission signals. This choice was made since the three OTE curves exhibit clearly distinct kinetic behavior within this time interval and all of them reach their maximal intensity within it. At longer times, the decay rate is almost independent of u. At shorter times, the finite CO, laser pulse has to be explicitly considered and deconvolution techniques are called for. The quality of the fit obtained by this procedure may be estimated from the examples shown in Figure 7 . It is seen that the three SoTE curves afford a reasonable reproduction of the shape of the (27) Note that the peak intensity is obtained at different times for OTE into o = 3, 4, or 5.
H QUANTA )
Figure 8. A bar graph showing the energy distribution of reacting molecules created upon IRMPE of T M D by the COz laser with the specified pulse energies (in millijoules). The internal energy is divided into three sections corresponding to population of the three distributions created upon O T E to v = 3, 4, and 5, and shown in Figure 1. The grey areas mark the estimated uncertainty in each energy region. TABLE IV: IRMPE of T M D Fraction of Molecules Excited to Energies Equivalent to That of Y = 4 and Beyond, and the Ratio P(4)/P(5)' COz laser pulse energy, mJ P(41/P(5) Y(v>41 6.7 >10 0.003 f 0.002 8.0 4.0 f 2.5 0.01 f 0.006 9.3 3.0 f 1.5 0.022 f 0.014 10.3 1.5 f 0.8 0.03 f 0.02 13.7 0.5 f 0.3 0.14 f 0.08 16.3 0.24 A 0.2 0.24 f 0.15 19.6 mT, p = 0, f l
(2)
Ruhman et al.
%(F14
+ F14r)/[%(F14
+ F14? +
13
18
n=12
n=14
[flz(F11+ FII') +
c
n-15
Fn
C Fn + F,'I/ C Fn + F,'
+ F,'] (A5)
at the end of the pulse have been summed together since at 3 mtorr almost all molecules excited beyond u = 4 will eventually decompose before suffering a stabilizing collision. The reconciliation of the ideal method assuming instantaneous excitation with our simulations exhibiting nonnegligible decomposition during irradiation is to be found in section VI. Specifically, care was taken to check that the amount of decomposition from region u = 4 did not exceed -8% of the population in this region a t the end of the excitation process. This is the amount of decomposition expected based on the RRKM decomposition rates from this region. Registry No. TMD,35856-82-7.
