A laser induced fluorescence study of vibrational energy transfer processes in cyclopropane

Cliemical ?hysics 27 (1978)_6$-_71 0 North-HollandPublishingCompany

A LA&Z

INDUCED FLPORESCENCE

STUDY OF VIBRATIONAL ENERGY

TRANSFER PROCESSES IN CYCLOPROPANE G&n T.FIiJUIOTO *-and Eric WEITZ Department ofChemistry and iUnteriaIs Research Center, North westem University. Evanston. Illinois

60201. USA

Received24 June 1977

Results of infrared laser induced fluorescence studies on cyclopropane are presented. Molecules were excited from fit Don either the P(14) or P(20) transition g&m+ state to the vle level of cyclopropane using a Q-switched CO2 laser operati% of the 9.6 fl branch. Fluorescence was observed from the vg, vg, ~10 + vlt and Q + yIo levels of cyclopropane. The selfdeactivation of vibrationally excited cyclopropane through V + T/R processes was found to have a rate of 8.0 f 1.5 ms-’ torr-’ . Deactivation by rare gas collisions was also studied with comparison to simple V + T tid V+ R theories. V+ V equilibration processes are discussed involving the “6, “8, qe, qt, and qe + “11 levels.

1. Introduction The technique of laser induced fluorescence has become a standard technique for the study of vibrational energy transfer and relaxation processes and has yielded a great deal of information about these processes in small molecules [ 11. Using this technique vibrational energy transfer and relaxation processes have been investigated in cyclopropane. Cyclopropane is one of the first molecules studied by the laser induced fluorescence technique, which has been the subject of extensive investigations of its unimolecular reactive behavior. Cyclopropane undergoes a unimolecular reaction to propene with an activation energy of ~6.5 kcal/mole [2] $_ From a theoretical standpoint this reaction has been extensively modeled using the RRKM approach [3,4] and the Water” approach [5-71. The reaction has been studied in thermally heated reactors [2,8] and in shock tubes [9-l I]. Recently Dorko et al. [l l] studied the cyclopropane isomerization reaction in shock tubes and concluded *NSF predoctorai fellow. * Ref. [2] was the first in-depth study on the cyclopropaae isomerizationreaction with refs. [3-lo] givinga representative sampieof-the numerous referenceson the reaction.

that the isomerization behavior could be explained by invoking a vibrational bottleneck, the rate of reaction depending on the rate of population of the bottleneck level. In Independent studies Fenn et al. [12] and Kennedy and Kohl [ 131 also indicate that vibratiqnal excitation may be intimately involved in the isomerization reaction. Cyclopropane has also recently been the subject of a number of studies involving CO, TEA laser excitation [ 141. In these studies cyclopropane is pumped into a highly excited vibrational state by means of a multi-photon absorption process leading to reaction of the absorbing cyclopropane. Due to the

multitude of studies and the interest in cyclopropane, it was felt that cyclopropane would be a particularly interesting system in which to study vibrational energy transfer and relaxation process and that these studies might provide information which would bear on the nature and pathways of the aforementioned thermal and laser induced reactions. A preliminary report of this work has been previously presented [I 51.

2. Experimental

The basic experiment consists of monitoring the time dependence of 3 /.rand 5 ~1fluorescence originating

#

He -Ne

LASER

iyt OSCILLOSCOPE

Fig. :. Experimental apparatusused for Iaser induced fkzorescence experiments. from the v6

and us fundamentals and the (vs + vlO) and (vlu + vll) combination bands of cycIopropane following excitation by a 9.6 fl Q-switched CO, laser. A diagram of the experimental setup used in &is work is presented in fip. 1. The infrared laser used consisted of a 2-l/2 meter water cooled tube with Brewster angle N&f windows mounted at each end. A flowing CO,-N,-He mixture and a longitudinal discharge of approximately 16 kV and 20 mA were maintained in the tube. The laser was Q-switched using a mirror (focal length 10 m) rotating at 100 Hz. A grating blazed for 10.0 ,u completed the cavity and allowed the selection of a smgIe vibration-rotation lasing transition of approximately 3 mJipulse as measured by a calibrated thermopile. The output of the laser operating on either P(20) or P(l4) of the 9.6 jr CO, laser band was passed through a cylindrical aluminnm sampfe cell (12 dia), with-fluorescence from the vibrationahy excited cyclopropane observed through a KBr window pe~e~~cui~ to the laser output. An indium-antiminide detector (Spectronics) was primarily used in these studies. The detector output after ampiitZcation was digitized using a Biomation 610B transient recorder and fed to a hardwired digital signal averager. The averager output is then passed to a Data General NOVA 3 computer for analysis. To determine the response time of the InSb detector and electronics, fluorescence signals from a sample of CO, werebbserved. The CO, was excited using a .

P.bra@r tra&ition of the9.6 blC02 laser output snd cyclopro&ne was added toitbie-cell to in&ease the : relaxation rate df the mixture. Using~this procedure it was determined that the InSb detector and entire electronic chain had a response t&e of Biproximateiy 0.9w. : I. 1- ^_ -- . Two samples of cyclopropane specified as 99.5% pure were purchased_from Ohio-Medical Products, Cleveland, Ohio and used without further purif!cation. Analysis using a.GC-MS With an ethyl N~~~e~y~oxamate column(lO%on 100/120ChromasorbPAW), indicated that propene was the major ~pu~~.-One sample contained = I% propene &rile the other contamed fess than 0.3%. The results of experimental runs made with these samples were indistinguishable. Rare gases were purchased from Matheson Gas Products and used without further purification (He 99.9999%, Ne 99.?95%, Ar 999995%, Kr 99995%, Xe 99.995%). For rare gas studies the cyclopropane and the rare gas being studied were placed in the cell and allowed to mix thoroughly before observing the fluorescence signal. Pressure was measured using a capacitance manometer connected directly to the fluorescence cell with care being taken to minimize the tot+ volume of the system. The sample cell and associated vacuum system had an outgas rate of under 5 mto~~hour. Experiments were done at an ambient temperature of 22” * 1°C.

3. Results The frequency of both the P(20) and P(14) 9.6 p CO, laser transitions are such that they overlap the R branch of the ~10 mode of cyclopropane [ 161. Kk P(14) absorption is the stronger of the two and cyclopropane was found to absorb this line with an absorption coefficient of 0.014k 0.001 cm-l torr-l. This number is somewhat dependent on the expe~e~t~ conditions [17] and is offered only as a measure of approximately how mutih vibrational energy it is possible to pump into the vibrational manifold of cyclopropane under the reported conditions. Fluorescence was observed from the levels shown in fig_ 2. Interference filters v&e used to isolate flueresee& from a Single level _andto vex&y that the levels

.

67

G. T. Fujimoto. E. Weitz/Inftared laser induced fluorescence studies on cycloptopane

n

il

v5+“10

Gi Wfl-vll

-

VI

--2

ji

I

’

I

’

I

’

I

’

I

’

I

CYCLOPROPANEENERGYLEVELS

Fig. 2. Energy level diagram. Downward arrows indicate fiuorescence to the ground state.

were in the appropriate wavelength regions. A comparison of the fluorescent wavelengths with the absorption spectra of cyclopropane indicates that the fluorescing states are the vs and v8 states in the 3000 cm-1 region and the v5 + vlo and vlo + vll combination bands in the 2000 cm-l region Cold gas fnter studies indicate that the fluorescing transitions terminate in the ground state and thus confirm the above assignments. In the case of the v6 and v8 states, the tluorescence is too close in wavelength to be resolved by our interference filters and these levels are treated as a single fluorescing level. Both of these levels are C-H stretching modes and such close lying levels have been found to have similar relaxation behavior in other systems [Is]. Two interference fnters were available for study of one or both of the combination bands. One filter (4.5 y long pass) passed both combination bands without significant attenuation while the other (4.95 p long pass) would be expected to attenuate emission from the us + vIo band by =95%. When the fluorescence signal was observed through the two filters the amplitude remained unchanged except for a slight correction due to filter transmission. This would indicate that the large majority of fluorescence in the 5 u region is due to the vIo + vII combination band. No further work was done on the us + vIo band. The majority of the reported measurements resulted

from excitation of cyclopropane via the P(14) 9.6 ~1 transition. However, the rates of both the fast and slow decays of combination band fluorescence from pure cyclopropane resulting from P(20) and P(14) 9.6 p excitation were measured and were found to be identical within experimental error. This would be anticipated due to expected rapid equilibration of the vlo rotational manifold. Similar results were obtained for the decay of fluorescence from the v,+8 bands. Fluorescence from all of the above states exhibits a heating signal similar to that observed in SF6 [ 191. Superimposed on this was a rapidly rising and relatively slow decaying exponential. From the vro + vll combination band a more rapid exponential was superimposed on the two decays described above. A sample of the signal observed from the combination band is shown in fig. 3. The slower of the two non-heating signals exhibits the rate of 8.0 f 1.5 ms-l torr-l from either the vr+8 level or the combination band. This rate was measured in the presence of argon which is necessary to suppress the heating signal. Based on a hard sphere radius of 4.6 A * this corresponds to 1450 collisions for decay. This decay rate is in reasonable agreement with the measured ultrasonic rate for V + T/R relaxation in cyclopropane and is attributed to this process [22]. The deactivation rate constant was also measured *Rare gas data is from ref. [ZO],

WI.

cyciopropanedata from ref.

168‘:.

_;

C. X Eu@noto, E. W&&#rured

faser induced fluorescence studies 09 cye&vpne

exhibited&e same de~tiva~on rates for cyciopqknerare g;i~;eoIlisions. The de~~~vatio~ of vibl_a&on8Ly excited cyclopropane-in_ cycL~propane+e g&sco& sions is presented in fig. S where the deactivatkm rate is plotted as a fur&ion of the square root of reduced mass of the coifisio$ pair. . The &cay rate of the fast exponential present in vlo + q1 combination band fluorescence ~8s measured and”where necessary,tbe rate was corrected forthe response time of the system, and the presence-ofthe V + T/R e?cponentialde&y. With these corrections the rate is 240 + 20 msLL toiPi. .. _ The risetime of signals from both the rq@g states and the ~omb~ation bands were too rapid to measure even at pressures as low as 0.4 torr.

I1

I 20

ill

I 40

PRESSURE

60

III 00

ARGON (TORR)

Fig. 4. Data from the argon dependenct%study of the V -+ T/R deactivation of cyclopropane.

4. Discussian Most polyatomic molecules studied to date have been characterized by rapid V + V and slower V + T/R processes_ For the parts of the cyclopropane: vibrational manifold reported on in this paper, &is behavior holds true. The rates of activation of the r+&t mode was too rapid to measure under current experimentat condttions, This implies a conservative lower Emit for the rate of activation ofZZS0 ms-1 to+. There are a variety of possible mechanisms for propagation of ener,qy up the vibrational manifold from the initi4ly pumped Iev~l to the 3000 cm-l region. These possibilities include “up the iadder” transfer within a single mode followed by cross-over to the v6/v8 mode;

C3~c3~xo)+c;~~o~c3~~i36/vs~+~3~~fo)Fig. 5.

Relativeprobabiity of deactivatioionas a Function of

the square root of the reduced mass. The circles represent experimental results. The line comes from a SSH cakuhtion based on refs. 127,281.

for cyclopropane-rare gas collisions. An example of this data is presented in fig. 4 with the results of the rare gas studies presented iri table I _All levek stuked

w ‘l&is process is near-_tesonant and thus would be expected to hd to rapid population of the ~~f~~‘leveks. This type ofprocesshas been postulated as possibly Leading to G-LL stretching mode adtivation in CH$l, CL%& aiId CH3L [23]. Howe&, for cyclopropme @ha processes are also possible?L%ese-ide . :. ___ ’

.

G.T. Fujimoto. E.-Weitzfhfiaredkxer inducedfluorescencestudieson cyclopropane

-310

cm-l;

(2a)

+ = 10 cm-l,

(2b)

and sC,H,(2g)+C,H,(O)

C$$@g)+C$+$‘g) followed by

- =I60 cm-l,(2c) and similar processes where the vg mode is replaced by the p2 mode. Other possibilities are C&$‘,($+C3&(0)

zC3H6(vi)fC3H6(0)

t

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~9 C3&(ui) +C3Q(~j) + C3H6(2pj) *$H6(0) C3H6(2v$+C3H6@)

@a) WI

9

(3c)

+ C3H6@6153) +C3H6@0) CQ0

where i=3,13,4,5,

j=2,9

_

An analogous process to (3) is responsible For rapid population of C-H stretches in CH,F [18,24]. Currently existing experimental data does not allo-w us to choose among these processes. However, experiments are under way to measure the risetime of the vg level which should shed light on the v& activation process. One of the features that emerges from a wide variety of previous V-V studies is that near resonant processes of the type 2X(Vl) t X(2 v!>f X(0) ,

(44

and X(Pl>+ X@,) f x0Q + vn) + X(O),

W)

are rapid. Thus, under appropriate conditions, the combination bands in a molecule should reflect the behavior of the fundamentals through which they are populated. If we consider the vIo + pII state in C3H6 we can assume that

is more rapid than

C3H6(u10)+C3H6(o+-&-C

69

3 H6 (ull)+C3H6(0)

(5b) due mainly to the much smaller energy defect in‘(5a). Neglecting V + T/R processes which occur on a inuch slower time-scale we can say that vlO, vll states are in dynamic equilibrium with the (vIo + vI1) state or

where N(i) is the population of the ith level and K is the appropriate equilibrium constant. We know that due to eq. (5) the population of vll will rise after the laser pulse while the population of vlo will fall. It can then be shown that in the weak excitation limit, the decay rate of th& vIo + vI1 signal is given by k,,_,, + kll_10 which in our case is measured as 240 * 20 ms-1 torr-l. Thus within this model, the rapid decay observed in the fluorescence from the vlD f vll combination band reflects the equilibration of the fundamentals. This type of behavior should make combination bands very usefui probes of vibrational energy transfer processes. Though this model is very likely, the data currently avai!able is not sufficient to indicate it is unique and defmitive assignment will be provided by direct study of the vll level which is under way. Studies to determine the deactivation of vibrationally excited cyclopropane due to cyclopropane collisions were performed in the presence of argon to reduce the effects of cleating. The deactivation rate is the same for all of the levels studied, implying that any V-V type processes involving these levels occurs on a much faster time scale than the deactivation process. This concurs wi& similar results from laser induced fluorescence studies on small molecules such as the methyl halideldeuteride series [18,23-251 where all of the vibrational levels are tightly coupled. The self-deactivation rate of cyclopropane is slower than that measured in similar 1:ydrocarbons such as propylene [26]. This is probably the result of a low density of states in the low energy reaon of the vibrational manifold which is due to the high symmetry p3,J and fairly rigid ring structure of cyrlopropane. Rare gas studies were performed to gain further insight into ihe deactivation process. Comparison of experimental and theoretical results are presented in table 1. The theoretical values for Pl_o are from an SSH calculation as formulated by Stretton [27], Dickens and Ripamonti [28], which is based on a

70

G. T. Fujimoto. E. Weitz/Infrared her

induced fruorescence studies on eyclopropane

_~

-

Table 1.~.

De~ctivation.of.cyclopropane by rare gas collision partners Coilision partner

~1(aa) a)

e/k (K) b)

D (A) b)

_ helium neon

Theoretical

Experimental decay rate (ms-1 torr-1)

Zl-0

c,

krypton’

20.361 28.014

10.22 35.7 124.0 190.0

2.576 2.789 3.418 3.61

7.11 k 0.70 0.360 r 0.021 0.290 c 0.022 0.336-t 0.022

2400 26300 1 31400 24300

xenon

31.868

329.0

4.055

0.231 r 0.024

36700

argon

3.655 13.639

P~_~ d)

1.0

9.2 x 107 7.7 x 107. 1.00 x 10-I 6.6 x lo*

--

P;._~ e)

1 4.7 x 1.7 x 1.38 x 3.4

’ 102 10-s lO-3

x lo*

a) Reduced mass of collision pair (cyclopropaae-rare gas). b) Lenaard-Jones parameters from ref. [20] for the c&ision partner. For cyclopropane from ref. [21], e/k = 370 K, and o = 4.6 A. C) Number of collisions needed for deactivation: Zl_o = $(u, f ub)* (8kT/Tp)‘” (P/kT)/(lO’ X rate X P), whereP =pressure,

T = temperature. d) Relative probability of deactivation per coUision;PI-0 = l/Z~_a_ e, Relative probability of deactivation per collision calculated using SSH method from refs. 127,281. V-T deactivation process. For purposes of the calculation the final deactivation step of the cyclopropane molecule was assumed to be from the q4 level to the ground state. Furthermore the P1_o values were calculated on a relative scale as there are no published values for the “breathing sphere” parameters for C, H6. From tig. 5, it can be seen that the experimental data does not compare favorably with the calculated values through the entire series of rare gases. This is most likely due to the fact that “SW” theory concerns it-

self entirely with the vibrational + translational energy exchange_ Moore [29] and Cottrell [30] have worked on a model which includes the contribution of rotational motion of the molecules to the vibrational deactivation process. In certain systems the relative rotational motion of the collision pair will be large with respect to the relative translational motion of the pair. This is often the case for collisions involving heavy rare gases. A model which includes both V -+ T and V + R procqss does not predict that P1_o should decrease monotonically with increasing reduced mass. This leveling off of P1_o with increasing reduced mass has been observed in CH$l, CH, Br, and CH3 I [23] and is attributed to the importance of the relative rotational motion of the molecules in the deactivation process. If the major deactivation channel in cyclopropane is from the v7 or vll ievels to the ground state, it would be expected that the SSH caIcuIated values forP1_0 would fall off even faster with increasing reduced mass

than shown in fig. 5. This is due to the increased energy gap and thus the conclusion of rotational involvement in the deactivation process would not change.

5. Conclusions The v6/v8 fundamentals and the (vll) combination band of cyclopropane were studied via the laser induced fluorescence technique following C02Q-switched excitation of cyclopropane using &laser operating on either the P(14) or P(20) 9.6 ~1transitions. V+T/R deactivation rate was found to be the s&e from all states 8.0 L 1.5 ms-l torr-l. Rare gas deactivation of vibrationally excited cyclopropane showed that V * R processes become more important as the reduced mass of the collision partner increases, a trend that has been previously observed in the methyl halides and deuterides. Activation of the v6/vg and ~10 + vll bands is very rapid. The ulo + vll combination band has a fast deactivation step which is shown to be linked to the e&ilibration rate of the vlo and vll modes and has a rate of 240 + 20 r&-l torr-l . The absorption coefficient of cyclopropane for P(14) 9.6 p radiation has also been measured. Additional studies of cyclopropie are &der way in an effort to fully map out flows of vibrational energy in this-system. It has been recently pointed out that energy transfer pathways are vital in the understanding of chemistry initiated via ce+in types of laser pump

G. T. Fujimoto. E. Weitz /Infrared Iaser induced Jiuorescence studies on cyclopropane

ing [3 11. We

feel that this linking will become more important in the future and anticipate the possible of this linking into investigations of the reactive behavior of vibrationally excited cyclopropane produced via non-laser mechanisms. extension

Acknowledgement We would like to thank the following agencies for support of this work: The National Science Foilndation under Grant CHE7510333, the Research Corp& ration, and NATO. We thank Ms. C. Halbleib and Mr. RK. Huddleston foi useful discussions. One of us (G-F.) would also like to thank Dr. K. Drake and Dr. S. Roby for assistance with piogramming the NOVA 3 computer.

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A. Kaidor, presented at 2nd Winter Colloquium on Laser

Induced Chemistry, Park City, Utah, 2/13-2/16/77. [U] G.T. Fujimoto and E. Weitz, Bull. Am. Phys. Sot. 22 (1977) 77. [16] J.L. Duncan, J. Mol. Specty. 2.5 (1968) 451; J.L. Duncan and D.C. McKean, J. Mol. Spectry. 27 (1968) 117; T.Y. Chang, Opt. Commun. 2 (1970) 77. [17] E. Weitz, G.W. Flynn and A.M. ROM, J. Appl. Phys. 42 (1971) 5187. [LS] E. Weitz, G.W. Flynn and A.M. Ronn, J. Chem. Phys. 56 (1972) 6060; E. Weitz and G.W. Flynn, J. Chem. Phys. 58 (1973) 2781. [19] R.D. Bates Jr., J.T. Knudtson, G.W. Flynn and A.M. Ronn, J. Chem. Phys. 57 (1972) 4174. [20] J.O. Hirschfelder, CF. Curtiss and R.B. Bird, Molecular theory of gases and liquids (Wiley, New York, 1964) p. 1110. 1211 H.G. David, S.D. Hamam and R.B. Thomas, Austr. J. Chem. 12 (1959) 309. 1221 T.L. Cottrell and J.C. McCoubrey. Molecular energy transfer in gases (Butterworths. London, 1961) pp. 120, 121; P.D. Edmonds and J. Lamb, Proc. Phys. Sot. (London) 72 (1958) 940. [23] J.T. Knudtson and G-W. Flynn, J. Chem. l’hys. 58 (1973) 2684; F.R. Grzbiner and G.W. Flynn, J. Chem. Phys. 60 (1974) 398; B.L. Earl and A.M. Ronn, Chem. Phys. 12 (1976) 113; Y. Langsam, SM. Lee and A.M. Ronn, Chem. Phys. 14 (1976) 375. [24] G.W. Flynn and J.M. Preses, to be published; J.M. Preses, R. Sheorey, R.C. Slater, E. Weitz and G.W. Flynn, to be published. [25] L.A. Gamss, B.H.Kohn, A.M. ROM and G-WV.Flynn, Chem. Phys. Letters 41 (1976) 413; Y. Langsam, S.hI. Lee and A.hl. Ronn, Chem. Phys. 15 (1976) 43; E. Weitz and G.W. Flynn, J. Chem. Phys. 58 (1973) 2679. [26] W. Griffith, I. Appl. Phys. 21 (1950) 1319. 1271 J.L. Stretton, Trans. Faraday Sot. 61 (1965) 1053. [28] P.G. Dickens and A. Ripamonti, Trans. Faraday Sot. 57 (1961) 735. [29] C.B. Mooze, J. Chem;Phys.43 (1965) 2979. [30] T.L. Cottrcll, R.C. Dobbie, I. McLain and A.W. Read, Trans. Faraday Sot. 60 (1964) 241. [31] R.K. Huddleston and E. Weitz, I. Chem. Phys. 66 (1977) 1740; I. Shamah and G.W_ Flynn, J. Am. Chem. Sot. 99 (1977) 3191; S. Mukamel and J. Rdss, J. Chem. Phys. 66 (1977) 5235.