VibrationtoVibration Energy Transfer in Hydrogen Bromide MixturesHaoLin Chen Citation: The Journal of Chemical Physics 55, 5557 (1971); doi: 10.1063/1.1675723 View online: http://dx.doi.org/10.1063/1.1675723 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/55/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Vibrationtovibration energy transfer in nearresonant collisions J. Chem. Phys. 60, 1064 (1974); 10.1063/1.1681114 Temperature dependence of vibrationtovibration energy transfer in HCl and HBr J. Chem. Phys. 59, 970 (1973); 10.1063/1.1680125 Vibrationtovibration energy transfer in HCl and HBr J. Chem. Phys. 58, 3519 (1973); 10.1063/1.1679684 VibrationtoVibration Energy Transfer in Gas Mixtures Containing Nitrous Oxide J. Chem. Phys. 49, 2816 (1968); 10.1063/1.1670489 Intramolecular VibrationtoVibration Energy Transfer in Carbon Dioxide J. Chem. Phys. 46, 4491 (1967); 10.1063/1.1840573

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THE JOURNAL OF CHEMICAL PHYSICS VOLUME 55, NUMBER 12 15 DECEMBER 1971

Vibration-to-Vibration Energy Transfer in Hydrogen Bromide Mixtures

HAO-LIN CHEN

Department of Chemistry, The Catholic University of America, Washington, D. C. 20017 and Department of Chemistry, University of California, Berkeley, California 94720

(Received 26 April 1971)

The laser-excited vibrational fluorescence technique has been used to determine the rate constants for vibration-to-vibration energy transfer from HBr to other molecules in gaseous mixtures. Cross sections at room temperature have been found:

O"HBr-N2= (1.78±O.17) X 10-2 12, O"HBr-CO= (S.S±O.3) X 10-2 12,

O"D2- HBr= (9.10±O.96) X 10-3 12, O"HBr-O, S (9.3±O.6) X 10-4 12.

The cross section for vibration-to-rotation or translation energy transfer between HBr and D2 has also been determined as O"HBr-D2= (O.96±O.1) X 10-4 12. The dependence of cross section on V-.V energy level differences is about the same magnitude as in the analogous HCl systems but considerably larger than it is in other diatomic-diatomic systems. Strong intermolecular forces and larger amplitudes of hydrogen atom stretching vibration are likely to be the dominant reason for the observed phenomena.

INTRODUCTION

In the preceding paper! rates of HBr vibrational re­laxation in hydrogen halide mixtures have been de­scribed. Vibrational energy has been found to be trans­ferred mostly into rotation of the vibrator. In this paper, measurements of vibration-to-vibration (V~V) energy transfer from HBr to simple diatomic molecules such as D2, N2, O2, and CO are presented. Rapid V~V energy transfer between chemically formed vibration­ally excited hydrogen halides and CO2 produces the most powerful, efficient, and totally inverted CO2

lasers2 to date. In partially inverted chemical lasers, V~V energy transfer has also been found to play an important role in the course of construction and de­struction of inversion in vibrational population.3

In the past studies4.5 of V~V energy transfer in HCl mixtures, cross sections are found to be larger for hy­drogen halides than for other diatomic molecules. Com­paring with other diatomic molecules, cross sections are also observed to decrease considerably slower with increased energy difference between vibrational levels. A plausible explanation for these results involves (1) strong interaction forces, (2) the larger amplitude of H atom vibration, and (3) energy transferred into rotation. For the hydrogen halide partners, detailed studies of other hydrogen halide systems like HBr, DCl, HI, and DBr may provide additional clues to the nature of the hydrogen halide interaction.

EXPERIMENTAL

with HBr. For observation of CO fluorescence, a nar­row bandpath interference filter was used. For mixtures of HBr with D 2, N2, and CO gases, slow rates! were first determined for pressures in the range 50-500 torr. Fast rates were determined at a lower pressure to eliminate possible error contributed from the risetime of detector and amplifier.

RESULTS

v ~ V Energy Transfer Between HBr and D2

When vibrationally excited HBr molecules are pro­duced in HBr-D2 mixtures by absorption of a laser pulse, vibrational energy is rapidly redistributed be­tween HBr(V=I) and D 2(V=I) levels until a con­centration ratio

[D2(V = 1) ]/[HBr(V = 1)]= (XD2/XHBr)

Xexp[ -h(PD2- PHRr) /kT]=0.125 (XD2/XHBr)

is reached, where X D2 and XHBr are the mole fractions of D2 and HBr, respectively. Following this rapid vi­brational energy exchange, both levels are deactivated simultaneously into the ground state through various V~T, R processes. Figure 1 shows the vibrational energy level diagram for the HBr-D2 system. A typical fluorescence signal from HBr( V = 1~0) is shown in Fig. 2. Two exponentials are resolved. The physical significance for rates of both fast and slow relaxation has been exhaustively discussed previously.4 Data are presented in Table I for two different HBr-D2 mixtures.

The experimental setup for HBr vibrational fluores- The rate kD2- D • is expected to be slow,7 and makes cence measurements has been discussed in the preced- a negligible contribution to the observed fluorescence ing paper.! Only additional information concerning par- decay; any value of kD2- D'~ 1 sec!·torC! gives less ticular gaseous mixtures is included here. Due to the than a 5% contribution to the rates measured. Using rapidity of V~V energy transfer between HBr and the kHBr-HBr value reported in the preceding paper CO2 molecules,6 contamination of CO2 has been carefully and assuming kD2-D2~ 1 sec-I·torr-r, the combined guarded against. Matheson c.P. grade D2 (99.5%), slow rate constants can be given as (kHBr-D2+kD,-HRrX research grade N2, CO, and ultrahigh purity O2 from 0.125) =40 secI.torr-I. Air Co. were used. All these samples were withdrawn Since hydrogen halides usually have larger V~T, R from glass bulbs at 77°K for preparation of mixtures cross sections than other simple diatomic molecules,

5557

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5558 HAO-LIN CHEN

TABLE I. Vibrational relaxation rates in HBr mixtures.

(P'Tfast)-1 (P'T.low)-1 k, • AB X AB X HBr (sec-I. tore') (sec-" torr-I) (sec-I·torel )

0.991 0.009 483±20 3.57±0.20 455±20 0.977 0.023 555±60 8.40±0.30 476±50

0.946 0.054 3120±300 3220±300 0.885 0.115 2920±100 3150±110 0.990 0.010 3120±300 3160±300 0.975 0.025 3140±100 3180±100

CO 0.918 0.082 2.15±0.05 0.966 0.034 0.840±0.035 0.949 0.051 1.39±0.04 0.963 0.037 9530±450 9850±490 0.713 0.287 7350±320 9800±430

0.982 0.018 160±60b 154±lOc

0.9913 0.0087 174±15b 170±15c

• Rate constant for V ..... V energy transfer from HBr to AB. For the HBr-O, system. where the distinction between V ..... V and V ..... T. R is not apparent. the combined rate constant is listed.

kD2-HBr is not likely to be larger than kHBr- D" or kD2- HBrX 0.125 will make a negligible contribution to this combined rate constant. Under this assumption we get kHBr_D,=40±5 secl·torel for the V~T, R rate and ke(HBr_D2)=476±SO or ke(D2-HBr) = 3800±400 secl·torel for the fast V~V exchange rates.

v ~ V Energy Transfer Between HBr and CO

Vibrational fluorescence is observed from both HBr and CO following laser excitation of HBr-CO mixtures. A rapid rise and slow fall are observed in the CO fluo­rescence signal. The rate of rapid rise is found to be the same as that of decay in the HBr fluorescence signal. Table I shows data for five different HBr-CO mixtures. The slow rates are due primarily to deactiva­tion of HBr(V=1) by CO, and CO(V=1) by HBr,

kHBr-eo HBr(V=1)+CO(V=0) )HBr(V=O)

+CO(V=0)+f).E=2S59 em-I,

keo-HBr CO (V = 1) + HBr( V =O)--~CO( V =0)

+HBr(V=0)+f).E=2143 em-I,

and self-deactivation of both CO and HBr molecules. The self-deactivation rate keo-eo is expected to be very slows and make a negligible contribution to the rate of fluorescence decay. Subtracting out the con­tribution of HBr self-deactivation from the slow rates [using Eq. (2) of Ref. 1J we get the following value for the combined rate: (kHBr-eo+ 7.4kco-HBr) = 154±16 secl·torel. Unfortunately, it is not easy to decide which process is responsible for this observed rate. However, it will be safe to state that kHBr-CO< 154 or

b Observed rate. i.e .• P'Tob •. c V ~V. T. R combined rate constant.

keo-HBr<22 secl·torr-I. Adopting this limiting value for kHBr-eo, we get keHBNco=9850 secl·torr-l for the rate of V~ V energy exchange.

V~V Energy Transfer Between HBr and N2

The vibrational fluorescence signal also shows two exponential decays for HBr-N2 mixtures. The slow rates are hard to measure since the rapid equilibration between HBr( V = 1) and N2 ( V = 1) leaves only a small fraction of energy in the HBr (V = 1) level.4 Hence, the amplitude of the slow decay signal becomes too weak to be determined accurately. Table I shows data for four different HBr-N2 mixtures. The slow rates are due primarily to deactivation processes like

kHBr- N2 HBr(V=1)+N2(V=0) >HBr(V=O)

+N2(V=0)+f).E=25S9 em-I,

kN2-HBr N 2(V=1)+HBr(V=0) >N2(V=0)

+HBr(V=0)+f).E=2331 em-I,

and self-deactivation of both HBr and N2 • The rate kN2-N, is expected to be sma1l9 and makes no contribu­tion to the rate measured. Adopting the kHBr- HBr value determined previously, we get (kHBr-N2+3.0kN,-HBr) < 105±secl·torel for the combined slow rates. Again it is not easy to judge which is the dominating rate. However, it is unlikely that kN,-HBr will be any greater than keo-HBr since V~T, R rates for CO are usually two to a hundred times faster than for N2• At the present time, we can only count this value as a crude upper limit for kN2- HBr, or kN2-HBr<35 sec-I·torr-l. It by no means represents the desired true value. Using

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ENERGY TRANSFER IN HYDROGEN BROMIDE 5559

kHBr-N2< 105 seci • torcI, we obtain k.+kHBr-Nz=3160 3000 or ks=3160 sec-I·torc! where kHBr-N2 contributes less than 3% of the observed fast rates. Any uncertainty in determination of the slow rate is not likely to affect our rate reported here.

Vibrational Relaxation of HBr in HBr-02 Mixtures

Single exponential decay is observed in vibrational fluorescence signals from HBr-02 mixtures. Table I represents the single rates observed at two different gas concentrations. Possible processes involved in the deactivation of vibrationally excited HBr molecules in HBr-02 mixtures could be either

k. HBr(V = 1)+02( V =O)~HBr( V =0) +02(V = 1)

ke' +.1.E=994 crni

TABLE II. Cross sections and probabilities for HBr(V=l)+ AB (V =O)-+HBr(V =0) +AB (V = 1) +!:J.E energy transfers.

k u b !:J.Ec

AB (sec-1• tore1) pa (12) (cm-1)

Dzd 38oo±400 2.9XlO-4 0.0091 435 CO 9850±5oo 1.4XlO-3 0.055 416 HIe 21 4OO±28oo 4.2XlO-3 0.186 329 HCll 35 5OO±3300 6.2XlO-3 0.218 327 N2 3 160±3oo 4.5XlO-4 0.0178 228 02 g 160±1O 2.5Xlo-6 0.00093 995 or 2559

• P =kZ-1 X 10"'. where Z =2.55 Xd'HBr-AB XILHBr-AB-l/,. dHBr-AB = HdHBr+dAB) and ILHBr-AB is the collision reduced mass. dHBr and dAB are the kinetic theory diameters given by J. O. HirschfeIder. C. F. Curtis. and R. B. Bird. Molecular Theory of Gases and Liquids (Wiley. New York. 1954). p. 1111.

b U =PUkin and Ukin =1/' [(dHBr+dAB) /21'. c Differences between vibrational fundamental freq uencies. d For energy transfer from D, to HBr in the exothermic direction. e Data from Ref. 1. I For energy transfer from HCI to HBr in the exothermic direction. K Data represent vibrational energy transfer from HBr (V = 1) to other

degrees of freedom (V -.V. T. R) by collision with 02 molecule. not just for (V -. V) process.

and/or kHBr- O ,

HBr(V=1)+02(V=0) )HBr(V=O)

+02(V=0)+~E=2S59 em-I.

Since the forward reaction of the first process is 994 cm-I more exothermic than the backward reaction, rapid V~V energy exchange will leave little or almost no energy in the HBr( V = 1) level. This could cause the absence of a second decay in the fluorescence signal. In this case, the observed rate would represent the combination rates (k.+kHBr-02) = 160 seci • torci .

However, if no vibrational energy has been trans­ferred into 02(V=1) level at all, the observed rates would represent mainly kHBr- O, as shown in the second process; kHBr- O , = 160 sec-I. torr-I. Both processes could have rates around the same magnitude as observed.

1000

SLOW V-T,R

AND RADIATION

LASER EXCITATION

SLOW V-T,R

FIG. 1. Vibrational energy levels of HBr and D2•

DISCUSSION

For comparison of the V~V energy transfer rates measured in this work with other diatomic-diatomic systems, the cross sections and probabilities are calcu­lated and presented in Table II. Donovan, Husain, and StevensonlO have also studied part of the HBr system independently with a flash photolysis technique. Agree­ment in both HBr~HCI, HBr~N2 data is observed.

LASER SCATTERED LIGHT

E L ECTR IC PICKU~l'---'\1-~--'~~!!':O!!.( ,.--. •• _tl...!~~;-o!-___ ..!J(.~.,......i/~20 r ~ I I I

EMPTY CELL

HBr FLUORESCENCE

FAST DECAY

o

HBr FLUORESCENCE

SLOW DECAY

FIG. 2. Vibration fluorescence signal of HBr in HBr-D2 mixture. The rapid decay due to V -> V energy transfer from HBr to D2 is shown on the middle trace (the corresponding signal for an empty cell is the top most trace), and the slow decay due to V->T, R energy transfer is shown on the bottom trace. The sample pressure is 155 torr with XgBr=0.023, XD2=0.977, and 1,= lllLsec, t.= 740 ILsec.

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SS60 HAO-LIN CHEN

/0-2

8f-

6

).. 4

!::: :::! III

2 ~ ~ ~ -. ~ 10 r-LJ... 8f-~ 6f-'<t

e: 4f-).. I!) Q:

~ 2 i.LJ ~

1 10-4 -

8-

6-

~ Oz

t,

I

"­"-

200

I

'~ HBr , E1', HI ,

I I

, ,

EI CO

400

I

, , , ,

I

I

, , ,

~ Nz

I

, , ,

I

~', HI ,

I 600

fJ.E.'b

(em-I)

I -

-

-

-

, " ~OCI

" , ~ , CO '

" -

---

I 800

FIG. 3. Probability of vibration-wibration energy transfer between HBr (V = 1) and AB (V = 0) levels vs energy discrepancy !lEo 0. Data for process HCI (V=l)+AB (V=O)~ HCI (V=O)+AB (V=1)j 8, data for process HBr (V=l)+ AB (V=O)~HBr (V=O)+AB (V=l), both presented in the exothermic direction.

However, our HBr~CO rate is about two times faster. Figure 3 shows a plot of V ~ V energy transfer prob­ability vs tJ.E (discrepancies between vibrational en­ergy levels). The observed probability for HBr~HI falls right on the line obtained in the hydrogen halide system.4 This accidental matching in probability is actually expected since effective V~V energy transfer requires a strong coupling between the vibrating atoms of the collision partners and for coupling to occur by direct impact between hydrogen halides, H atom must collide with H atom rather than a halogen atom. The effect of interaction forces (i.e., chemical forces) thus becomes less important in V ~ V energy transfer than in V~T, R transfer as discussed previously. However, for collisions between hydrogen halides and other di­atomic molecules such as N2 and CO, the effect of the strong interaction force remains playing an important role in process of V~V transfer. In both (HBr~CO, HBr~N2) and (HCI~CO, HCI~N2) cases, HBr~CO and HCI~CO are found to be three times more prob­able than HBr~N2 and HCI~N2, respectively, in spite of the fact that an additional 188 cm-l of energy is transferred for CO cases. This similarity between HCI and HBr systems also indicates that in hydrogen-halide­diatomic-molecule collisions, V~V energy transfer de-

pends more heavily on interaction forces between the vibrating H atom ano. collision partners rather than interaction forces between two whole molecules. It is obvious that the interaction force between HBr and collision partners (such as CO, N2, O2, D2, and other hydrogen halides) is drastically different. However, for the V~V process, the observed differences in cross section for energy transfer among the hydrogen halides are not significant compared to these drastic differ­ences of interaction potential.

Comparing the slow rates for HBr-D2 and HBr-02 may also reveal the mechanism of HBr relaxation in O2 mixtures. The limiting value for PHBr- D , is 3.1X 10-6

and the observed value for P HBr- O , system is 2.SX 10-5,

and it is not likely that, in V~T, R process, O2 could be more efficient than D2 in deactivating vibrationally excited HBr molecules. Consequently, we conclude that the observed relaxation rate in HBr-02 system repre­sents the combined rates (k.+k HBr- O ,) and possibly less than 10% of this observed rate is due to kHBr-02'

Unfortunately, not enough information on the rates of deactivation of both N2 and CO by hydrogen halides is known. At the present stage, it is not likely to be able to explain the observed slow rate in HBr-N2 and HBr-CO systems. Considerably more information is necessary before any quantitative conclusions and the­oretical calculations can be made.

ACKNOWLEDGMENTS

This work has been supported by the Research Cor­poration, Catholic University Research Foundation and the Advanced Research Projects Agency of the De­partment of Defense (monitored through Professor C. B. Moore by the U.S. Army Research Office­Durham, Box CM, Duke Station, Durham, North Car­olina 27706, under contract No. DAHC04 68 (0044)). The author is most grateful to Professor C. B. Moore for lending the space and equipment for performing part of the measurement. The author is also thankful to Professor C. B. Moore and Mr. P. Zittel for helpful discussions and corrections concerning this manuscript.

1 Hao-Lin Chen, ]. Chem. Phys. 55, 5551 (1971), preceding paper.

2 T. A. Cool and R. R. Stephens, J. Chem. Phys. 52, 3304 (1970).

3 T. A. Cool, R. R. Stephens, and J. A. Shirley, J. App\. Phys. 41, 4038 (1970).

• H. L. Chen and C. B. Moore,]. Chem. Phys. 54,4072 (1971). • H. L. Chen and C. B. Moore,]. Chem. Phys. 54, 4080 (1971). 6 ]. C. Stephenson and C. B. Moore (private communication).

They have measured the V -+ V rate for CO2-HBr mixture using a Q-switch CO2 laser.

1]. H. Kiefer and R. W. Lutz, ]. Chem. Phys. 44, 658 (1966). 8 R. C. Millikan,]. Chem. Phys. 38, 2855 (1963). 9 M. C. Henderson, ]. Acoust. Soc. Am. 34, 349 (1962). 10 R. J. Donovan, D. Husain, and C. D. Stevenson, in (a)

Trans. Faraday Soc. 66, 2148 (1970) and (b) Nature 227, 602 (1970).

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