Volume 73, number 3 CHEMICAL PHYSICS LETTERS 1 August 1980

VIBRATIONAL ENERGY RELAXATION IN CH3X MOLECULES

J. SCHUURMAN and G.H. WEGDAM Laboratory for Physxal Chemlsny. Umversuy of Amsterdam. Amsterdam, i?he Netherlands

Received 9 May 1980

Opto-acoustic techmques have been used to measure vibrational energy relaxation tn methyl halides and their mixtures

wth tnert gases Under certain condihons tune-resolved measurements gwe direct evidence of a V-R-T relaxation channel parallel to the V-T relaxation channel Comparison with infrared fluorescence data confirms thus conclusioa

1. Introduction

One of the most wrdely used techmques in the study of vrbrational relaxation in molecular gases is the laser-induced fluorescence method. This method is especrally powerful in probirrg the initial equrlibra- tron among the various vibratronal modes by fast V-V transfer [I]. However, measurement of the relaxanon of this exerted vibratronal manifold to the ground state by thrs technique gives less detarled mformation -just an average time for the conversion of vibra- tional mto rotational and/or translatronal energy and a long trme tad due to heat conduction [L-4].

Information about the relative importance of these two relaxatron channels, V-T versus V-R-T relaxa- tion, can be found only mdlrectly by comparing dif- ferent molecular gases or mixtures with inert gases. The vast amount of data available certainly indicate an important role of rotation rn the deactivation of vlbrahonally excited molecules [S-7], at least for molecules with small moments of inertia. Moreover, lthe conversion of vrbratronal mto rotational energy can give rise to long-hved rotational distnbutions in the vrbratlonal ground states [8]. Since the relaxation for high rotational states is comparable with mea- aured relaxation times for the vibrations, the excess nbrational energy can be stored in the rotations be- fore rt 1s released to the translations. Therefore, com- Elementary informatron about the vibrational deacti- mtion process can be obtained by measuring the final

stage of the relaxation, the response of the translations to the time development of a vibrational disturbance. Measurement of the risetime of the translational tem- perature as a result of vibrational excitation by opto- acoustic techniques and comparison with the viira- tionai relaxation times measured by the fluorescence method can thus reveal more about the role of the rotations in the relaxation process. The methyl hali- des look promising in this respect. The fluorescence data are available and point to the rotations as an irn- portant relaxation channel [9]. in this paper we pre- sent opt*acoustic measurements on the pure methyI halides and then mixtures with inert gases.

2. Experimental

Two methods were used to measure the acoustic

response to a vrbrational disturbance, i.e. the phase lag and the pulse method.

In the first method, which has been described ex- tensively [lo], one measures the phase lag between the pressure wave as probed by a microphone and a modulated hght wave. In our experiment a low-power cw CO, laser was used as the light source. The output of the CO, laser was kept to a level of a few milli- watts or less to prevent heating of the sample. The laser was used to pump the vibrations of the CH3X molecules, where X stands for F, Cl, Br, and I. The systems measured are the pure gases and dilute mix-

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Volume 73, number 3 CHEZhUCAL PHYSICS LETTERS 1 August 1980

tures of CH,X wrth the inert gases. Before use, the gases, of spectroscoprc quaky, were dned carefully. CeII dunensions, modulation frequency and density were chosen such that effects of heat conduction could be excluded.. Measuring the phase a&e rb as a function of modulation frequency Y and denslty p, the relaxa- tion time T was obtained from the relation

The pressure range was chosen between t and 50 Torr whlIe the moduia~on frequency was vaned between 100 and 1200 Hz.

For the mixtures with the mert gases, we assumed the retatron

where rE is the relaxation ttme determmed from ex- periment and XA and XB are the mole fractions of CH,X and the inert gas respectively. Smce m our ex- penment XA = JO-2 this formed only a small correc- tton to the value of TAB_ The deac t&a&on rates k = f/r are shown for CN3Br m fig. 1 as a funcuon of pres- sure and coihs~on partner. The v&es for the relaxa- tron tunes obtamed thrs way are collected in tabfe I. They are gzven as rate constants k rather than relaxa- tlon times to stress the fact that they are not neces- sanly equal to V-T relaxation tunes, but are a mea- sure for the average rate of energy transfer into the translations.

Hopmg for more detaled mformatlon, we apphed the second method, the pulse method, to the same gases. Thrs technique has been described recently by

I He

CH$r

1 10 20 30 40

PressurrRbrrf

Fig. 1. Deactwatlon rates k m s-’ for 1 Torr CH3Br in the Fig 2. Result of the opto-acoustic pulse method for 1 Torr mert gases obtamed from the opt@acoustrc phase method CH3Br rn 20 Torr argon.

Table 1 Measurements of deactivation rates (m ms-t Torr”) for the methyl hahdes m mert gases obtamed by the opto-acoustic phase method. In parentheses the fluorescence data taken from ref- 161 for CH3F, ref [a) for Ci-i3Ci, ref. f 121 for CH3Br 3nd ref_ [Sf for CHsI

He Ne Ar Kr

CH3 F 0 30 (0 78)

CH3Cl 0 35 (3 11

CH3 Br 0.53 (4 IS)

CH3 1 060 (5.6)

0.18 (0 065)

0.19 (0 51)

0 24 (1.24)

030 (1.9)

0.26 (0.039)

0.20 (0 54)

0 25 (I.291

0.27 (2.21

0.25 to 022)

0 19 G3.54)

0.19 (1.01)

0 27 (1 6)

Wrobel and Vala [I 13. In this method the transient acoustic signal resultmg from a short laser pulse is &- rectly momtored by the microphone. The mlcrophotze signal is fed into a PAR stgnaI averager and pfotted on an X-Y recorder. A typical exampIe is shown LR fig. 2 The transient acoustic signal is characterued by a fast rise-tune grvmg the rate of energy &ssipatron m to the tr~sIations and a decay refiectmg the heat conduc- tion to the cell walls The fast modolatlon on top of these gross features IS caused by acoustic resonances m the cell. Their frequencies are determined by the sound velocity of the transrent gas and the celi dunen- sions The acoustic signal shown m fig. 2 IS typtcal for most gases measured, m particular for the heavier methyl hahdes and their nnxtures. For these systems the m&al nse of the transzent signaf gives, wrthm ex- perimental error, the rates measured by the phase lag method.

However for the CH3F/He system a markedly dtf- ferent form of the trarwent signal IS observed, as

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Volume 73, number 3 CHEMKAL PHYSICS LETTERS 1 August 1980

I -_-I

1 2 3 4

TIME (ms)

Fig 3 Result of the opto-acoustic pulse method for 1 Torr CH3F in 100 Torr hehum. The dashed curve IS the result of the three-levelscheme with km = 104, km = 204, kRT = 3 X lo3 and kheat=5 X lo*.

shown III fig. 3. The acoustic resonances are suppressed to get a better overall picture of the general features. A second maxmum IS visible and the imtial rise IS no longer equal to the relaxation time of the phase meth- od. Although the second maximum is found only for CH,F/He, the discrepancy between the rise-time and the relaxation time from the phase measurements 1s observed for CH3F/Ne too. The transient signal of the CH,F/He system strongly suggests energy dissrpation from two different sources mto translation

3. Discussion

In table 1 the data of the spectrophone measure- ments are collected together wrth the relaxatton times measured by Fly~ et al. [2,3,6] and ROM et al. [4,5,12]. There are two striking features. Firstly the relaxation times measured by the two methods are markedly dtfferent. Secondly the relaxation tunes measured by the spectrophone method depend even less on the reduced mass of the collision pan than the fluorescence trmes

The only explanation for the difference m relaxa- tion tunes or rate constants measured by the two methods is that different relaxation processes are probed by the two methods. If the underlying physi- cal process is sunply a direct transfer of vibrational energy mto the translations, both methods would mea- sure the same relaxation time. A parallel relaxation process where vrbrational energy is &ssrpated mto the rotations and subsequently degrades into translational energy seems to suggest itself.

The rotations as a hkely relaxation channel were suggested by Mrkiavc and Fisher to explain the much shghter dependence of the fluorescence times OQ the

reduced mass of the collision pair than expected from sunple V-T relaxatron. This vtew is strongly supported by the spectrophone data, which depend even less on the reduced mass.

Under con&hons where the response of the micra- phone to a laser pulse is not simply the resultant of an exponential rise followed by an exponential decay OF the translattonal temperature, one might be able to separate expenmentally different relaxation channels. Therefore the pulsed measurements can give us an ex- penmental means to test models where parallel re- laxation processes are taken into account_ We have simulated the response in the pulsed measurements making use of the formahsm given by Wrobel and Vala [ 1 l] and a model for the molecular relaxation process, where the rotations are introduced as a paral- lel relaxation channel.

The differential equation descnbing the temporal and spatiaI evolutton of a pressure wave is gjven by Wrobel and Vala [ II] as

a’plaC2 - c’Q2p = (7 - I)aQ/af ,

where p 1s the pressure, c the sound velocity, y the heat capacity ratto cr/cV, and aQ/at the source term.

The spatd solutions for the pressure wave are Bessel functions since the cell geometry has cylindri- cal symmetry. The vrbrational energy can be trans- ferred to rotation as well as translation. The rotation m turn transmrts energy to translation, which even- tually comes to equilibrium by heat transfer. The re- sult of the simulations done this way is given in fig_ 3. The three-level scheme (fig. 4) used in the most simple model describes the second hump III the acoustic sig-

I

El/IS

TVR

z &T

B GOT

3

Dz

TRT

ETRANS

&EAT

Fig. 4. The sunple three-level scheme used for the simtitioion of the opto-acousrlc measurements.

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Volume 73. number 3 CHEMICAL PHYSICS LETTERS 1 August 1980

naI observed m sortle of the CH,F/He systems very well. The ratios between the different rates for this system made the experimental observation posnble. The proposed model should be appked to tie other systems as well. There the conditions are such that an average rise and decay tie results from the combined processes Careful analysis and many sunulations w~ih the abovementioned model ~~41 make a quantttatlve determination of the different rates possible. This will be the subject for a future pubhcation.

Acknowledgement

The work described here is part of the research pro- gram of the foundation for Fundamental Research of Matter (F 0-M.) and was made possible by fiianclal support from the Netherlands Orgamzatlon for Pure Research (Z.W.O.)

References

111

[21

I31

[41

[51

[61 I71 WI

R S Sheorey and G.W. Flynn, J Chem. Phys. 72 (1980) 117s; E. Wertz and G.W. Ffynn. J. Chem. Phys. 58 (1973) 2781. V-A Apkaman and E Weltz. J. Chem. Phys 71 (1979) 4359. J.T Knudtsen and G.W. Flynn. J. Chem Phys. 58 (1973) 2684. F-R Grabmer and G.W. F~YM, J Chem Phys 60 (1974) 398. S M Lee and A M ROM, Chem. Phys Letters 22 (1973) 279. J. Langsam, S M. Lee and A&f Ronn, Chem. Phys. 14 (1976) 375. E. Weitz and G W. Flynn, J. Chem. Phys. 58 (1973) 2679 C.B. Moore, J. Chem. Phys 43 (1965) 2979. L. Roodhart and G.H Wegdam, Chem Phys Letters 61 (1979) 449.

[9] A Mtklavc and S F. Fisher, J. Chem Phys 69 (1978)

IlO1

[I11 [I21

281. R. Zygan-hfaus and S.F Rsher, Chem. Phys 41 (1979) 319 L.B. Kreuzer, J. Appl. Phys. 42 (1971) 2934; Y.H. Pao, ed., Opto-acoustic spectroscopy and detection (Acadermc Press, New York, 1977). J. Wrobel and M. Vala. Chem. Phys. 33 (1978) 93 B.L. Earl and A M. Ronn, Chem. Phys. 12 (1976) 113.

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