Vibration→Rotation Energy Transfer in Hydrogen ChlorideHaoLin Chen and C. Bradley Moore Citation: The Journal of Chemical Physics 54, 4072 (1971); doi: 10.1063/1.1675468 View online: http://dx.doi.org/10.1063/1.1675468 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/54/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Vibration–rotation transfer in molecular super rotors J. Chem. Phys. 113, 10947 (2000); 10.1063/1.1326072 Quasiresonant vibration–rotation transfer: A kinematic interpretation J. Chem. Phys. 111, 7697 (1999); 10.1063/1.480107 Mechanism of quasiresonant vibration–rotation energy transfer in atom–diatom encounters J. Chem. Phys. 97, 3348 (1992); 10.1063/1.462972 Vibration→Vibration Energy Transfer in Hydrogen Chloride Mixtures J. Chem. Phys. 54, 4080 (1971); 10.1063/1.1675469 Vibration—Rotation Energy Transfer J. Chem. Phys. 43, 2979 (1965); 10.1063/1.1697261

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THE JOURNAL OF CHEMICAL PHYSICS VOLUME 54, NUMBER 9 1 MAY 1971

Vibration -7Rotation Energy Transfer in Hydrogen Chloride

HAO-LIN CHEN* AND C. BRADLEY MOOREt

Department of Clwlllistry, University of California, Berkeley, California 94720

(Received 10 July 1970)

A pulsed HCI chemical laser source has been used to carry out laser-excited vibrational fluorescence experiments on HCI and mixtures of HCI with DCI, n-H2 , p-H" rare gases, and H20. The following cross sections <TA-B for vibrational deactivation of A by B at room temperature have been found: <THCI-HCI= (4.2±0.4) X 10-19 cm2, <TDCI-DCI = (1.3+0.2, -0.4) X 10-19 cm2, <TDCI-HCI = (2.9±0.3) X 10-19 cm2, <THCI-n-H2 = <THCI-p-H2= (2.9±0.S) X 10-20 cm2, <THCI-",e gaS < 1O-21cm2, and <THCI-H20 = (2± 1) X 10-16 cm2. The cross sections for HCI-HCI and DCI-DCI are about 16 times larger than predicted by linear extrap­olation of the shock tube data between 2000° and 10000K on a log <T VS T-1I3 plot. The isotopic changes in vibrational relaxation rates lead to the conclusions that: (1) Vibrational energy is transferred almost entirely into rotation in hydrogen chloride-hydrogen chloride collisions, and (2) for HCI-HCI and DCI-DCI collisions most of the vibrational energy is transferred into the rotation of the molecule which is initially vibrationally excited. A plausible explanation for these results is provided by the hydrogen-bonding inter­action between two HCI molecules.

INTRODUCTION

The vibrational relaxation rates of hydrogen halide molecules are of particular interest in the study of energy transfer between vibrational and rotational degrees of freedom. The relative velocity of impact between the vibrating H atom of an HX molecule and a heavy collision partner is predominantly the molecular rotational velocity of the H atom. Thus the coupling of energy into rotation rather than into translation is particularly favored for the hydrogen halide mole­cules. I

•2 Shock tube observations of vibrational re­

laxation in HCI,3.4 in DCI,3 and in mixtures of Ch with HCI and DCI5 give isotope effects and relaxation rates quite incompatible with any formulation of vibration­to-translation (V-7T) energy transfer theory but rather similar to expectations for vibration-to-rotation (V-7R) energy transfer.

:\ieasurements of the vibrational relaxation rates reported here for pure HCI and mixtures with HCI are made possible by the laser-excited vibrational fluor­escence method.6 A pulse of light from an Hel chemical laser vibration ally excites gaseous HCI molecules. The relaxation of the system is followed by measuring the decay of infrared fluorescence intensity after the exci­tation pulse. The rates obtained in these experiments are useful in the analysis of chemiluminescence meas­urements of the vibrational excitation in chemical reaction products7 and in the analysis and prediction of chemical laser kinetics.6 ,8,9

Data arc given here on vibrational relaxation of HCI in collisions with HCI, n-H2, p-H2 • rare gases, and H20 and for relaxation of DCI by HCI and DCI. The effects of isotopic substitution on rate and the com­parisons of halide and nonhalide collision partners yield information on the distribution of vibrational energy between the rotational degrees of freedom of the collision partners, and on the interaction potentials which cause the energy transfer.

EXPERIMENTAL

The experimental apparatus used in this work con­sists of three major parts: the HCI laser, the fluor­escence detector and electronics, and the fluorescence cell and sample preparation system. An over-all schematic diagram is given in Fig. 1.

Laser action on the 1-70 vibrational transition of HCI results from the reaction of HI molecules with CI atoms produced by a photolysis flash. 8 The laser con­sists of a Pyrex laser tube of 50-cm active length and 20-mm i.d. with NaCI Brewster's angle windows. CI atoms are produced by discharging an 8.5-J.LF capacitor at 7-10 kV through a xenon-filled flash tube of 10-mm i.d. The flash lamp and laser tube are wrapped together with aluminum foil. The laser cavity is formed by a 3-m radius gold-coated mirror at one end and a sapphire flat 130 cm away at the other. Since there is a spontaneous chemical reaction between HI and C12, the gases are continuously pumped through the laser tube by condensation in a liquid N2 trap connected to the laser through a 50-cm long 13-mm i.d. tube. A pressure of 9 torr CI2 and 3 torr HI yields a laser pulse energy, as measured on a calibrated thermopile, of 0.01-0.03 J. The pulses are 10-20 J.Lsec in duration as measured by an InSb PEM detector with a response time less than 10-8 sec. Approximately 40% of the output is in the ~I= 1-70 P branch. The remainder is in 3-72 and 2-71 bands. The strongest 1-70 transitions arc P(9), P(lO), and P(ll). With care pulses are 90% re­producible from shot to shot.

The vibrational fluorescence passes through a narrow­band interference filter and is detected by a Ge:Au photoconductor. The signal is amplified, displayed on an oscilloscope and photographed. For the detection of HCI fluorescence a filter which transmitted the R branch of the 1-70 transition but not the laser P branch transitions was used. The 1 % transmlSSlOn points were 2840 and 3000 cm-I

; 30% at 2870 and 4072

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ENERGY TRANSFER IN HYDROGEN CHLORIDE 4073

2950 cm-I ; and 60% from 2900 to 2930 cm-I. For

DCI fluorescence a filter was chosen which transmitted nearly the entire vibrational band. The transmitted fluorescence is detected by a 3XlO mm area Ge:Au photoconductor at 77°K. The detector surface is 2 cm above the sample cell just behind the entrance window. The signal is amplified by a Keithley Model 103 amplifier with a band pass from 1 to 105 Hz. The overall detection response time is 2.4 JLsec, and the noise equivalent power is about 10-7 watts. The signal was displayed on a Tektronix 565 dual beam oscilloscope and photographed with a Polaroid pack film camera at 1: 1 magnification.

The laser output monitored by a PEM detector is displayed on the second beam. For signals exhibiting two decay times the second beam is often used to display the signal on a different time scale. The oscillo­scope is triggered by the response of a photodiode to the xenon flashlamp. The detector and electronics are located several meters from the flash lamp and power supply. The remaining optical and electrical pick up is illustrated relative to the detector noise level in Fig. 2.

For measurements of HCI fluorescence a cylindrical all quartz cell of 5-cm diameter is used. This cell is heated strongly with a gas-oxygen torch and pumped to below 10-6 torr before use. The degassing rate of the cell and connecting tubing is less than 10-5 torr/h. For observation of DCI fluorescence, NaCI windows were attached to a Pyrex cell using Kel-F wax. The degassing rate of this cell is less than 10-4 torr/h. It was pumped to 10-6 torr before use. The 2.5-cm diam laser beam is directed just below the top surface (fluorescence window) of the cells. Gas pressures are measured with a precision-bore mercury manometer. Measurements were carried out at total gas pressures between 50 and 500 torr. The cell temperature was 23±2°C.

Matheson electronic grade HCl gas (99.99+%) was used. The DCI from Stohler Isotope Chemicals was shown by mass spectral analysis to contain 4.5% HCI. HCI and DCI were purified by degassing and by repeated distillation in a closed system from a trap at -120 to a trap at -196°C. Because H20 is 500 times as effective as HCI itself for vibrational relaxation, its

HI + CI2 Flow

Ge'Au Fluorescence Detector

FIG. 1. HCllaser-excited vibrational fluorescence apparatus. The sample cell for DCI fluorescence is illustrated.

Fluorescence ! Detector

Loser t Time (fLsec)

FIG. 2. Oscilloscope photograph of HCI fluorescence detector response to optical and electronic pickup. Strong electronic pickup at the initiation of the flash lamp has decayed almost completely by the end of the laser pulse (lower trace from PEM detector). The sample amplitude oscillations beyond 60 p.sec are detector noise. A background photograph such as this establishes the zero baseline for fluorescence measurements which may start 35 p'sec after flash initiation, just at the end of the laser pulse.

concentration was checked by mass spectra and by infrared absorption of solid HCI at 77°K. The intensity of the H20 absorption band near 1600 cm-1 w;s measured for several known mixtures. The electronic grade HCI showed less than 0.01% H20. A less pure sample of HCI was purified by the distillations above and yielded a sample with less than 0.01 % H20 and the same relaxation rate as the electronic grade samples. The following Matheson research grade gases were used (impurities >0.5 ppm in ppm): H2(N2<5, O2 < 1, H20= 1); He(Ne<S, N2, O2, Ar, H2< 1, H20=0.6); Ne(He<SO, H2 <S, O2, Nz, Ar< 1, H20 = 1); and Ar(N2 <5, 02,H2<1, H20=0.6). These gases were all withdrawn from glass flasks immersed for more than 1/2 h in liquid N2. Mixtures were prepared in flamed glass vessels and allowed to stand more than three hours. Experiments with mixtures containing less than 0.1 % hydrogen halide were affected by adsorption at the cell walls. Para-H2 was prepared by evaporation of para liquid. Its composition was determined by Raman spectroscopy to be 93% para.

RESULTS

Excitation

The laser pulse excites a sufficient number of HCI molecules for facile observation of the fluorescence signal. The excitation is sufficiently strong that large temperature rises and population of the v = 2 level must be guarded against. At pressures above 5-torr rota­tional relaxation is sufficiently fast that the intensities near 100 W / cm2 used here d~ not significantly bleach the absorption. The fraction of molecules excited or number of quanta absorbed per molecule Q is given by

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4074 H.-L. CHEN AND C. B. MOORE

' ... £ '0

CII ~

,

IOO~------~------~~r---,

80

60

~ll 40 , . .0 0.

oL-----~0~.0~5~--~0.~1----~

XHC1

FIG. 3. Observed fluorescence decay rates for HCI-Ar mixtures as a function of HCI mole fraction. The slope of this curve is equal to kncl-ncl-kncI_A, and the intercept is kncI-A,. The measured rates are kncl-lIcl=870±80 seCI·torr-1 and 1 < kHCI-A,<2 secl·torr-l.

where EJ is the number of photons per laser pulse in line P(J) of the 1---70 transition, A is the area of the laser beam, kJ is the absorption coefficient at the line center for P(J) in square centimeter/molecule, !!.vp and !!.VD = 6 X 10-3 cm-! are the pressure broadened and Doppler linewid ths (FWHM), and kJo = kJ for !!.V p =

0.10 When pressure broadening is negligible Q<0.05. For Hel, !!.vP= 1.4X 10-4 cm-l/torr for P(9) ,ll and thus Q<0.05/[1+0.025 PUC I (torr)]. For Hel dilute in argon !!.vP is about 8 times smaller,I2 and hence Q< 0.05/[1 +5 X 10-3 PAr]. Since the ratio of molecules in z'=2 to those in v=1 is roughly equal to the ratio of molecules in v = 1 to those in v = 0, the v = 2 level is unlikely to affect the kinetics observed here. However, when the vibrational energy is transferred into the translational and rotational degrees of freedom a temperature increase of

!!.T= 41500 K (!XD+iXA)-IQXHCI.

Here 41500 K is the vibrational energy of Hel and XD!

X A , and XHCI are the mole fraction of all diatomics, of all atoms, and of Hel, respectively. Thus for pure Hel at 50 torr, !!.T < 40oK, and in dilute mixtures with argon !!.T is much less. It is important for the validity of this analysis of the excitation that the laser operates on high J transitions and that the beam is unfocused. If the laser is focused, a decrease in fluorescence in­tensity is observed due to saturation of the absorption. If the laser were operated on low J transitions near the maximum of the room temperature Boltzmann distri­bution, k.r and hence Q and !!.T would be about 10 times largerY

Relaxation of HCI (v= 1) by HCI

Vibrational relaxation in Hel-Hel collisions has been studied in pure Hel and in HCI-Ar mixtures. In pure Hel graphs of the logarithm of fluorescence intensity vs time gave straight lines. The product of pressure and relaxation time is PTHCI-HCI = 1.6 JIsec· atm or kncI-licl = 8.0X102 sec-l·torel within the 15% experimental un­certainty limits over the pressure range 50-250 torr. At lower pressures the observed relaxation rate is larger; however, our approximate knowledge of the amount of excitation is not sufficient for a quantitative calculation of the effect in terms of sample heating. The upper pressure limit is imposed by short relaxation times and low fluorescence intensity.

The reported rates did not change when the laser power was decreased by a factor of ten. The radiative lifetime of 30 msecll is very much longer than any of the relaxation times measured here. The diffusion of excited molecules to the walls is also too slow at pres­sures above 50 torr to be important in these experi­ments.

A second method of determining the rate of vibra­tional energy transfer in Hel-Hel collisions is to study the relaxation rate in mixtures of Hel with argon. The argon suppresses sample heating effects by adding translation heat capacity and by pressure broadening the absorption lines. Since there is only one vibrational level involved in this system, we have

(PTobs)-I= (PTIICI-HCl)-IXHC1 + (PTHCI_A,)-IXAr

= kncI-HcIXHCI + kUCI-ArXAr.

Here PTHCI-Ar is the relaxation time for Hel infinitely dilute in argon. The results shown in Fig. 3 give PTHCI-HCI = 1.5±0.1 JIsec· atm or kIlCI-HCl = 870±80 sec-I. tore!. The value of the relaxation rate of HCI by the argon buffer gas used was found from experi­n~ents on seven mixtures with XHC1 between 3 X 10-;'

3000 HCI (v = I)

- DC 1 (v= I) , E ~ w

1000

FIG. 4. Kinetic diagram for laser-excited vibrational fluores­cence in RCI-DCI mixtures. RCI is vibrationally excited by a laser pulse. Vibrational energy is transferred rapidly from HCI to DCI (Fig. 5) by V->V energy transfer. Subsequently, DCl decays more slowly by V->T, R energy transfer (Fig. 6). The concentrations of excited species are proportional to the observed fluorescence intensity, but the optical transition rates make a negligible contribution to the observed kinetics.

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ENERGY TRANSFER IN HYDROGEN CHLORIDE 4075

and 5 X 10-4 to be 2> kHCl-Ar > 1 secl. torr-I shown by the intercept marked on Fig. 3 (see last section of Results). Combining results of pure HCI and HCl-Ar mixtures kHC1-HCl = 830±80 secl. torr-I is chosen.

Relaxation of RCI-DCI Mixtures

When a mixture of HCI and DCI is excited by the HCI laser, energy is transferred rapidly out of the HCl vibration largely by V-N transfer to DCI. The DCI vibration is then subsequently deactivated by energy transfer to translation and rotation in collisions with HCI and DCI molecules. The experiment is illustrated schematically in Fig. 4. In this system with two modes of vibrational excitation there are five possible re-laxation processes:

ke HCI(v= 1)+DCI(v=O)~HCI(v=O)+DCI(v= 1)

ke'

kll HCI(v= 1) +HCI(v=0)----72HCI(v=0) +~E

= 2886 em-I, (2) kl2

HCI(v= 1) +DCI(v=O)----7HCI(v=O) +DCl(v=O)

+~E=2886 em-I, (3) k21

DCI(v= 1)+HCI(v=O)----7DCI(v=O) +HCI(v=O)

+~E=2091 em-I, (4) k22

DCI(v= 1) +DCI(v=0)----72DCI(v=0) +~E

= 2091 em-I. (5)

In mixtures with argon there are two additional

Loser

o DCI ~

HCI

~

t (msec)

FIG. 5. Vibrational fluorescence from an Hel-Del-Ar mixture. The first and third traces from the top show the laser-excitation pulse. The bottom trace shows the rise in Hel fluorescence during the laser pulse followed by an exponential decay, r=57 }J.sec. The Del fluorescence, second trace, is the sum of a rising ex­ponential, r=57 }J.sec and a decaying exponential, r=470 }J.sec, of the same amplitude. XgCl =O.Ol1, X DCl =0.041, and X Ar = 0.948. p= 119.5 torr.

processes: kUf

HCI(v= 1) +Ar----7 HCI(v=O) +Ar+~E= 2886 em-I,

(6) k2M

DCI(v= 1) +Ar----7 DCl(v=O) +Ar+~E= 2091 em-I.

(7)

The time dependence of the HCI(v= 1) and DCI(v= 1) concentrations is determined by the rate constants of Eqs. (1)-(7). Each concentration is described by a sum of two exponential decaysl3:

[HCI (v = 1)] = A exp( - Alt) + B exp( - A2t) , (8)

[DCl( v= 1)] = C[ -exp( - Alt) +exp( - A2t)]. (9)

This is generally true for systems of this type when the excitation is sufficiently weak that v = 2 energy level populations and translational temperature changes are negligible. When the V----7V rates are larger than the V----7T, R rates, At! P and Ad p are given to order (AdAl) 2

and (A2/Al), respectively:

AI/P= (PTfast)-I;:~:{keX2+ke'Xl]

+f[kllXl+k12X2+kIMXM]

+ (1-f) [k2IX l+ k22X 2+ k2MX,f] , (10)

Adp= (PTslow )-I;:::::;,(jX2-1) 1 (ke'/ke)kllX12

+[ (ke' Ike) k12+k21]XlX2+k22X22

+ (ke' /ke)klMXlX~f+k2ilfX2XM). (11)

Here f=keX2(keX2+ke'Xl) , Xl=XHcl=mole fraction HCI, X 2=XDCl =mole fraction DCI, Xu=XAr=mole fraction Ar, and the rate constants are defined by Eqs. (1)-(7). The ratio ke'/ke=exp[ -h(VHCl-VDCl)/kT] is given by detailed balancing. The ratio A/ B is given to order (AdAI)2

A/ B;:::::;,[keXdke'Xl] 1 1 + 2[kllXI+k12X2+kwX,,1

- k2lX l- k22X 2- k2MX M ]/[keX 2+ke' Xl]), (12)

or when V----7V rates are much faster than V----7T, R rates A/B;:::::;,keXdke'Xl.

For the special case when keX2=ke'XI, the V----7V rates may be extracted accurately from measured Al and A2 to order (A2/Al) 2:

(Al-A2)/p;:::::;,keX 2+ke'Xl (keX2=ke'Xl). (13)

For the special case keX2»ke'Xl or (j-1)----70, Eqs. (10) and (11) may be simplified to

(PTfast)-I;:::::;,keX2+ke' XI+kllXl+k12X2+kufXM( f = 1),

(14)

(PTslow)-I;:::::;,k2lXl+k22X2+k2MX~lf (j = 1). (15)

These last two equations describe the relaxation times observed here for HCI-DCI mixtures to an accuracy of better than 2% and 5%, respectively.

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4076 H. - L. CHEN AND C. B. :\IOORE

TABLE 1. Vibrational relaxation rates in HCl-DCl mixtures.

(pTC.,,)-I ke (PT,low)'-I ( PTslow)calc-1

X HC1 X DC1 XAr (seci • torr-I) (seCI• torr-I) (seci • tore!) (seci • toreI)

0.0093 0.054 0.94 189±8 0.0109 0.041 0.95 145±6 0.0177 0.079 0.90 273±15 0.047 0.054 0.90 217±20 0.083 0.054 0.86 244±13 0.306 0.69 0 0.51 0.49 0 0.77 0.233 0

akDCI_HCI ~S7S±60 ,eel.torr-' and (kDCI-DCI+17kDCI-Ac) ~ 280±30 ~ec-1.torr-l are u~ed in EQ. (15) of text. Since allmixture:'i were about 5.4S:~ DCI anrl90% argon. kDCI-DCI j.:; not determined indeIlendently from kDCI-Ar. kHCI-HCI =830 sec-l·torr-l bused.

The experimentally measured relaxation times for eight HCl-DCl mixtures are shown in Table I. The most accurate determinations of the short relaxation time, AI-1=Tfaot, can be made from the HCI decay records (Fig. 5). The identical time is given by the increase in DCI fluorescence (Fig. 5). Fast relaxation times are not reported for mixtures without Ar since they were too short to be measured with P> SO torr. The slow relaxation time is determined from the decay of DCI fluorescence (Fig. 6). Application of Eq. (14) to the data gives the rate [ke+kI2J=(3.3±0.2)X103

sec1·torr-1• The rate kI2=kHCI-DCI is surely not greater

than kHCl-lICI (see Discussion) and thus 2.3X103< kc<3.4XI03 secl ·torI·-1• The fact that DCI fluor­escence is observed at all proves that he is not small. The slow relaxation rates observed depend sensitively upon the value of kI2=hDCI-HCl. This rate is determined with good accuracy to be 575±60 secl·torr-1. The value of hDCI-DCl determined from mixtures without argon is 215±60 secl. torr-I. The samples in argon all are about 17 parts argon to 1 part DCI and give the result hDCI-DCl+17 hDCI-Ar=280±30 sec1·torr-1

• In spite of this rather large uncertainty, hD("[-D("[ is clearly

3320±200 20.6±1 20.5" 3330±200 18±2 17.7" 3240±200 3250±440 40±4 42" 3130±200 65±4 63"

320±30 324b

380±40 397h

470±90 +93h

Av 3250±200

bkDCI_HCI=S7S±60 sec-l·torr-[ and kf)CI_lJCI=215±60 sec-1·torr- l. ThevaluekDCI_DCI~2S0 (+.10, -90) ,ec I'[orr li"electecl.kHCI_HCI~ 830 sec-I. torr- J i~ used.

much smaller than both Il lI ('I __ II(:1 and llDCl-IIC'I. The results are summarized in Table [I.

Relaxation of Hel by Hz, H 20, and Rare Gases

Mixtures of Hel with normal Hz and with p"ra-Hz for X HC1 = 1.4XlO-3 gave kIlCi - ll ,= 170±30 sec1 •

torr-I. There was no detectable difference between ortho and para molecules.

A very rough study of the deactivation of Hel by water was carried out in order to assess its effect as an impurity in the other gases studied. Samples of HCI­Ar prepared with 1O-L I0-4 parts water were studied. Due to adsorption on surfaces, the actual water con­centration is uncertain, The result of several different sampling techniques defined /;;IICI-II,O = (5±3) X 10:' sec-I. torr-I. This total rate constant is for the sum of all possible V----+V and V----+T, R processes deactivating HCI.

The vibrational deactivation of Hel by collisions with rare gas atoms is about three orders of magnitude less effective than by HCI itself. Thus experiments must be carried out with XHC1 :::; 1O-~, Some impurities, especially H20, must be kept at concentrations much less than 1

TABLE II. Vibrational relaxation of hydrogen chloride.

System" k (secI·toreI) PT (J.Lsec·atm) a b U·2) pe

HCl-HCl 830±80 1.6 0.0042 12. 7X 10-5

DCl-DCl 25(),+30, -90 5.3 0.00128 3. 9X 10-5

DCl-HCl 575±60 2.3 0.0029 8. 9X 10-5

HCl-H2d 170±30 7.7 0.00029 9.4X10-6

HCH,Ie <2 >6 <10-5 <:lX10-7

HCI-H2O (5±3) X 105

a (Vibrati9nally excited molecule)- (colli~ion l)artner) rates are given for the first molecule infinitely dilute in the second.

h (1 =k/nV, where n =molecules/cubic centimeter and fJ b the average relative velocity.

C P =U/Ukin, where Ukin =33 1~. )Jote that these are much larger than for other diatomic::': PCO_CO~2XI0-10, JI=2143 cm--1 ; P02 -Ch=10- 8,

0.003 2 10-1

JI=1556 em-I; and PH2_IIz::::dO- 7. 11=4159 cm- I [:-;ee R. G. Gordon, \V. Klemperer, and ]. 1. Steinfeld, .\1lIl. Rev. Phy~. Chcm. 19, 215 (1968)

for revie\v J. d The ~ame rate i~ obsen"ed for bOLh normal and para hydrogen. e 1:1 =He, ~e, and AT.

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ENERGY TRANSFER IN HYDROGEN CHLORIDE 4077

ppm. At these low partial pressures of HCl and H 20 in strongly flamed sample vessels and fluorescence cells the adsorption of HCl on container surfaces created serious difficulty. Experiments have been carried out on mixtures of HCl with He, Ne, and Ar. Relaxation times were measured for a sample with X HCI initially about 10-3• The sample was successively diluted with the rare gas until X UCI < 10-4. The observed relaxation times tended to a limit as X HCI went to zero. These limits are between 1 and 2 sec10 torr-1 for He, N e, and Ar. However, with the present experimental setup it is not possible to conclude that these limits are equal to the desired relaxation rates. At this time, we may state with confidence only that kHCI-He, kHCI-Ne, and kHCI-Ar are less than 2 sec1otorr-l. They are at least 500 times smaller than kHCI-IICI.

DISCUSSION

Recent shock tube measurements3 ,4 have established the vibrational relaxation rates in pure HCl and DCl between 7000K and 20000K (Fig. 7). The only previ­ously reported vibrational relaxation data at room temperature is a spectrophone study l4 which reports PT> 10-2 secoatm for both HCl and DCl. These times are nearly four orders of magnitude greater than those measured in shock tubes at 7000 K and thus the spec­trophone and shock tube results may not reasonably be connected. By contrast the shock tube results may be extrapolated quite smoothly to the relaxation times given here. It seems probable that the spectrophone measurements suffered seriously from the fact that the vibrational relaxation was several orders of magnitude faster than expected or measurable.

Shock tube measurements have also given the estimate4 that between 1200 and 20000K PTHCI-Ar~ 4,5 PTHCI-HCI. Our room temperature result is that PTHCI-Ar?::400 PTHCI-HCI. In view of the extreme sensi­tivity to impurities, it seems wise to consider both the shock tube and laser results as lower limits on the value of PTHCI-Ar. Anlauf et al,1 has estimated the rate of vibrational relaxation of HCl bv H2 from the decay of chemically produced vibration~l excitation. The 'col-

o Empty Cell

DCI

~

t (msec)

FIG. 6. DCI fluorescence decay for sample in Fig. 5.

2

10-3

8

6

:;:-4

.c 0 .c 0

It 2

10-4

8

6

4

• HCI-HCI aDCI-DCI • DCI-Hel

FIG. 7. Probability of vibrational deactivation in hydrogen chloride per kinetic collision vs r--1I3. Linear extrapolation of shock tube data between 1000 and 20000 K gives P a factor of 16±6 smaller than observed for room temperature. This devia­tion from linearity is already quite noticeable in the shock tube data between 1000 and 700oK. PncHICl is for vibrational de­a.ctivation of DCI by an HCI collision partner. _0_0_, interpola­han by P(T)=A r--1I6 exp[(!hp+.)/kT exp[i3r--1/3]. ---, arbitrary but equally possible interpolation.

lision probability of 2X 10-3 deduced is over two orders of magnitude larger than observed here and indicates that another species in the chemically reacting system may be responsible for the observed deactivation.

The nonlinear dependence of log P on T-l/3 noted by Breshears and Bird3 is dramatically confirmed by the room temperature measurements (Fig. 7). It seems unlikely now that a maximum in PTHCI-HCI exists near 8oooK. A linear extrapolation of the data between 1000 and 20000K to room temperature gives a proba­bility 16±6 times smaller than observed for both HCl and DCl. This large enhancement of probability at low temperatures is predicted by approximate theories15

whenever hp»kT or whenever there is an attractive interaction potential well depth, f?::kT. A widely used formula,!' inadequateh' tested for a s\'stem such as HCI, gives ' ,

peT) =AT-l!6 exp[(thp+f)/kTJ exp[f3T-l/3].

Figure 7 for HCI shows the interpolation between shock tube and infrared data using this expression with (thp+f) = 1600 CriC l

. Thus the degree of curvature observed cannot be considered as a gross departure from SSH-type theories.1:;.16 However, it must also be pointed out that the approximations used to arrive at the formula above are not valid for HCI at 296°K and

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4078 H.-L. CHEN AND C. B. MOORE

I n

m

FIG. 8. Collision models for vibration-to-rotation energy trans­fer in hydrogen chloride. Deactivation of excited DCl by an HCl collision partner is illustrated. In Model I the velocity of impact of the vibrating D atom with the collision partner is predominantly D atom (vibrator) rotation. Energy is transferred to rotation of the vibrator and no rate change on isotropic sub­stitution of collision partner H by D is expected. In Model II impact velocity is taken to be entirely rotation of the collision partner H atom and reduction of this velocity by substitution of D would decrease the probability by a large amount. Energy is transferred into collision partner rotation. Model III is a compromise between I and II. Experiment indicates that Model I plays the dominant role for HCI-HCI and DCl-DCl collisions.

thus the formula does not serve as a reliable interpola­tion method.

The isotope effects on the rates of vibrational relax­ation in hydrogen chloride give unambiguous informa­tion on the dynamics of the vibrationallv inelastic collisions. Bre;hears and Bird3 have argu~d from a comparison of the high temperature HCI and DCl data with simple V~T15 and V~R2 theories that vibra­tional energy is transferred into rotation in hydrogen chloride. This conclusion rests primarily on the fact that V--T theory predicts that Pncl-Hcl«PDCI-OCI,

while V~R theory predicts, in agreement with the data, Pncl-HcI:2:PDcl-OCI. The direction of predicted isotope effects and their rough orders of magnitude result in a general way from the assumption of either a translation coupling model, V~T, with the appropriate velocities and reduced masses or a rotational model, V~R, with its very different velocities and masses. Intermediate models, V~R, T, will give intermediate predictions. As long as the probability of energy transfer in in­dividual collisions remains small the isotope effects for each model will not be changed in direction or grossly in magnitude by eliminating the severe mathematical approximations employed to obtain simple scattering solutions. The probability for HCl-HCI deactivation is greater than that for DCl-DCI inspite of the fact that the HCI vibrational quantum is 1.38 times larger. The

result can be understood onh' when the mass of the deactivating degree of freedo'rn increases bv nearly a factor of 2 from HCI to DCI (thus dec;easing 'the velocity of impact by v'2). At room temperature PHCI-HCI/ P oc I-OC I is predicted to be roughly 2X 10-3

for V~T transfer (,uOCI-ocl-,uncI-HcI = 18.5/18) and about five for V--R transfer (,uDCI-OCI/ ,unCI-HCI = 2/1).

A theory taking simultaneous account of the oscil­lator's rotational degree of freedom and the translational degree of freedom has been developed by Nikitin and co-workers.17 The appropriate combination of vibration and translation is deduced by assuming the angular dependence of the intermolecular potential to be given by the shape of the molecular equielectron density curves. The reduced masses in this calculation are largely from the rotational degree of freedom since ,uDCI-OCI* / ,uHCI-HCl* = 6.2/3.5 is nearly equal to two, the value for pure rotational motion. Even for this small contribution to the deactivation bv translation PHCI-HCI/ POCI-DCI is calculated to be 0.i2. Thus, the fact that the experimental ratio PHCI-I1CI/ POCI-DCI

is greater than one allows us to conclude that the vibrational energy is transferred almost entirely into some combination of the rotational degrees of freedom of the vibrationally excited molecule and its collision partner.

Energy transfer in isotopically mixed collisions gives information on the relative contribution of the rotation of the vibrationally excited molecule and of the col­lision partner to the velocity of impact. Figure 8 gives three different collision models. We shall compare the expectations for each of these V--R collision models with the experimental result that PHCI-HCI:2:POCI-llCI>

POCI-DCI. The actual relaxation is undoubtedly achieved by a distribution of collisions represented by these models and by intermediate collision geometries. In Model I the hydrogen atom of the collision partner does not participate in the collision at all; thus, PDCI_HCIT = P OCI- OC / and also PHCI_HCI

1 = PUCI_OCI1

.

In model II the entire rotational velocity is assumed to be that of the collision partner; the rotational velocity of the vibrator molecule does not contribute to the impact. For this model PDCI_IlCP»PHCI_HCIIl since the rotational velocit\· is that of HCI, ,uu= 1, for both cases but for Del the vibrational frequency is much lower. Similarh" PHCI_OClII«PHCI_IlCIII. As with all V~R models' PIICI_HCIII:2:PDCI_OCIII. Approximate V~R calculations [Eq. (9), Ref. 2J give PDCI_HCIII~ 30 PHCI_HCIII ~ 200 PDCI_OClII ~ 2 X 10

4 PHCI_OCl

II•

In :\1odel rrf the predictions are intermediate: POCI_HCITII> Prx'I_DCI1Il and P nc I_HCII II > PIICI_OCI

III.

The relations between POCI_HCIIII and PHCI_HCIIlI

and between Pllcl_DeP I and POCI_DCPI cannot be deduced from qualitative arguments. Simple V~R theory gives

PDCI_I1CIIII~3 PJl('I_II(,11"~1S POC1_OCI1Il

~25 PHCI_OClII1 •

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ENERGY TRANSFER IN HYDROGEN CHLORIDE 4079

The experimental result PHCI-HCI~POCI-HCI is com­pletely incompatible with Model II which predicts PHCI-HCIII«POCI-HCP. Since POCI-HCI> POCI-OCI, Model I is clearly not adequate for POCI-HCI. However, the contribution of Model III collisions necessary to give POCI-HCI~2 P oc I-OC I indicated by the quanti­tative theoretical estimates is about 25%. If this estimate is roughly correct, then PHCI-OCI will be smaller than PHC I-HCI by approximately 25%. If a significant fraction of the relative velocity of impact is due to rotation of the collision partner, then PHCI-OCI will be significantly less than PHCI-HCI. Thus we con­clude from the isotopic data, firstly, that the vibrational degree of freedom is coupled to rotational degrees of freedom and not to translation, and secondly, that the rotational velocity of the vibrating molecule itself plays the dominating role. Thus, barring a strong rotation-translation coupling late in the collision, the vibrational energy is transferred most to the rotation of the vibrator molecule, some to rotation of the collision partner and very little to translation.

For the deactivation of vibration ally excited HCI by H2 the rotational degree of freedom of the collision partner appears to be unimportant. It is unlikely that n-H2 and P-H2 with their very different rotational level spacings would exhibit the same relaxation rate to within the 20% uncertainty limits if much energy were transferred into rotation. This apparent lack of transfer is not surprising when one considers the nearly spherical potential of the H2 molecule, the wide spacing of energy levels, and the lack of a close coin­cidence of H2 rotational level spacings with the HCI vibrational frequency.18

The observed probabilities of vibrational relaxation of HCI by H2 and by rare gases are very much less than for relaxation by HCI itself. The increased collision velocities in HCl-H2 and HCI-He mixtures compared to those in pure HCI are expected to augment the energy transfer probabilities. The most reasonable explanation of the observed decrease seems to be that the HCI-HCI interaction potential is considerably stronger than the HCI-H2 and HCl-rare gas po­tentials.

Many qualitative features of the observed rates may reasonably be explained in terms of the hydrogen­bonding interaction between two hydrogen chloride molecules. This interaction gives a deep potential well19 with a strong angle and vibrational coordinate dependence for the orientation of Model I but not for Models II and III. For collisions of the Model I type there will be a large acceleration of rotational velocity, a strong coupling of vibrational and rotational co­ordinates, and consequently a large probability of energy transfer. This explains the dominance of Model I collisions deduced from isotopic rate changes in hydrogen chloride. The small size of the H atom relative to the CI atom may also contribute to the relative importance of Model I through a simple steric effect.

The much smaller probabilities in collisions with rare gases and H2 follows from the lack of H-bonding in these systems. Finally, the acceleration effect of the deep well contributes to the observed curvature of P vs T-I/3 illustrated in Fig. 7.

CONCLUSION

Vibrational relaxation in HCI proceeds by energy transfer into rotation. A considerable fraction, perhaps almost all, of the energy is coupled into the rotation of the vibrationally-excited (Fig. 8, Model I) molecule. The room temperature relaxation probabilities are at least one order of magnitude faster than estimated by linear extrapolation of the high temperature data on a T-I/3 plot. The hydrogen bonding interaction between two hydrogen chloride molecules provides a plausible explanation of these results and of the result that vibrational relaxation of HCI by H2 and by rare gases is very much less efficient than by HCI. The lack of an observed difference between the relaxation of HCI by n-H2 and P-H2 indicates that the rotational motion of H2 is not important in the energy transfer.

A realistic theoretical treatment of the relaxation of HCI is not yet available. A good expression for the intermolecular potential, including hydrogen bonding, and for its variation with rotational angles and vibra­tional coordinates is first needed. Next, the collision dynamics of the system must be solved for the coupling of energy from vibration simultaneously into the rotation of both collision partners and into translation. The theory of Nikitinl7 seems the best proposed to date for handling simultaneously energy transfer into translation and rotation. However, generalization to include the rotation of the collision partner and to include the hydrogen bonding potential remains to be done.

ACKNOWLEDGMENTS

We wish to thank C. Koch for his high resolution mass spectroscopy measurements of impurity levels and E. Lim for assistance in analysis of the data. We are grateful to the Advanced Research Projects Agency of the Department of Defense (monitored bv the U. S. Army Research Office-Durham, Box eM, Duke Station, Durham, North Carolina 27706, under Con­tract No. DAHC04 68 C 0044) and to the National Science Foundation for financial support. We also thank J. R. Airey, D. W. Breshears, A. M. Chaikin, E. E. Nikitin, and J. C. Polanyi for preprints and help­ful discussions of their work.

* Present address: Department of Chemistry, Catholic Univer­sity of America, Washington, D.C.

t Alfred P. Sloan Foundation Fellow and John Simon Guggen­heim Memorial Foundation Fellow.

1 T. L. Cottrell, R. C. Dobbie, J. McLain, and A. W. Read, Trans. Faraday Soc. 60, 241 (1964).

2 C. B. Moore, J. Chern. Phys. 43, 2979 (1965).

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4080 H.-L. CHEN AND C. B. MOORE

3 W. D. Breshears and P. F. Bird, J. Chern. Phys. 50, 333 (1969) .

4 C. T. Bowman and D. J. Seery, J. Chern. Phys. 50, 1904 (1969) .

5 W. D. Breshears and P. F. Bird, J. Chern. Phys. 51, 3660 (1969).

6 H.-L. Chen, J. C. Stephenson, and C. B. Moore, Chern. Phys. Letters 2, 593 (1968).

7 K. G. Anlauf, P. J. Kuntz, D. H. Maylotte, P. D. Pacey, and J. C. Polanyi, Discussions Faraday Soc., 44, 183 (1967).

8 J. R. Airey, IEEE J. Quantum Electron. 3, 208 (1967). We are grateful to Dr. Airey for detailed discussions of this laser.

9 J. R. Airey, J. Chern. Phys. 52, 156 (1970). 10 A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation

and Excited Atoms (Cambridge U. P., London, 1934), p. 99. AVD=[2(2R In2)1I2/cJpo(T/M)1/2.

11 W. S. Benedict, R. Herman, G. E. Moore, and S. Silverman, Can. J. Phys. 34, 830 and 850 (1956).

12 H. Babrov, G. Ameer, and W. Benesch, J. Chern. Phys. 33, 145 (1960).

13 C. B. Moore, Fluorescence, edited by G. G. Guilbault (Dekker, New York, 1967), p. 133. Exact expressions for AI, A2, A, B, and C may be found here.

14 M. G. Ferguson and A. W. Read, Trans. Faraday Soc. 63, 61 (1967).

16 D. Rapp and T. Kassal, Chern. Rev. 69, 61 (1969), Eq. (222).

16 (a) R. N. Schwartz, Z. I. Slawsky, and K. F. Herzfeld, J. Chern. Phys. 20, 1591 (1952); (b) K. F. Herzfeld and T. A.

THE JOURNAL OF CHEMICAL PHYSICS

Litovitz, Absorption and Dispersion of Ultrasonic Waves (Aca­demic, New York, 1959).

17 G. A. Kapralova, E. E. Nikitin, and A. M. Chaikin, Chern. Phys. Letters 2,581 (1968), and E. E. Nikitin, Teor. Experim. Khim. Akad. Nauk Ukr. SSR 3,185 (1967).

18 In the case of vibrational deactivation of CO by ortho- and para-H2, Millikan has found that p-H2 is about twice as efficient as o-H2 at room temperature. Here there is a good energy match between the J=2---->6 transition of p-H2 and the vibrational frequency of CO. R. C. Millikan and L. A. Osburg, J. Chern. Phys. 41, 1196 (1964); R. C. Millikan and E. Switkes, "Vibrational Relaxation of CO by normal and para-H2: High Temperature Results," J. Chern. Phys. (to be published).

19 Considerable spectroscopic information exists on HCI dimers, (HClh. D. H. Rank, P. Sitaram, W. A. Glickman, and T. A. Wiggins, J. Chern. Phys. 39, 2673 (1963) report a spectral feature in the gas phase due to (HClh with a AHf = -2.1 kcal/mole. Similar features were observed for HCl-Ar and HCI-Xe with AH = -1.1 and -1.6 kcal/mole, respectively. Spectra of HCI dimers have been observed by many authors in solid matrices such as Xe. [See works listed by A. J. Barnes, H. E. Hallum, and G. F. Scrimshaw, Trans. Faraday Soc. 65, 3150 (1969).J The strong vibrational coordinate dependence of the interaction is illustrated by HCI vibrational frequency shifts on the order of 50 cm-1 between monomer and dimer. The appearance of a hydrogen bond stretching vibration near 190 cm-I has been reported by B. Katz, A. Ron, and O. Schnepp, J. Chern. Phys. 47, 5303 (1967).

VOLUME 54, NUMBER 9 1 MAY 1971

Vibration ~ Vibration Energy Transfer in Hydrogen Chloride Mixtures

HAO-LIN CHEN* AND C. BRADLEY MOOREt

Department of Chemistry, University of California, Berkeley, California 94720

(Received 10 July 1970)

Laser-excited vibrational fluorescence experiments on HCI mixtures have given cross sections for vibra­tion---->vibration energy transfer from HCI to other molecules: O'HCI-HBr= (2.1±0.2) X 10-17 cm2, O'HC1~N2 = (4.2±0.4) X 10-19 cm2, O'HCI~HI = (3.5±0.5) X to-18 cm2, O'HCI~CO = (1.3±0.15) X 10-18 cm2, O'HCI~DCI = (1.66±0.1) X 10-18 cm2, O'HCI~CH4= (3.7±0.3) X 10-17 cm2, and O'D2~HCI (transfer from D2 to HCl) = (2.1±0.2) X 10-17 cm2. The cross sections are considerably larger than for other diatomic-diatomic systems and decrease comparatively slowly with increasing energy difference between the vibrational levels. This behavior may result from strong "chemical" intermolecular forces, from energy transfer to rotation, and from the large amplitude of hydrogen atom stretching vibrations. The lack of a smooth correlation be­tween cross section and energy difference illustrates the importance of the nature of the collision partners.

INTRODUCTION

In the preceding paperl laser measurements of energy transfer from vibration into translation and rotation (V~T, R) in HCI have been described. In this paper measurements of vibration-to-vibration (V~V) energy transfer from HCI to other hydrogen halides and to several other simple molecules are presented. V~V energy transfer among the hydrogen halides is par­ticularly interesting in view of the importance of molecular rotation and of strong attractive forces in collisions between hydrogen chloride molecules. ' It us usually true that V~V energy transfer rates are much faster than V~T, R rates.2 This is because much smaller amounts of vibrational energy may be given to translation and rotation in V-~V processes than in

V~T, R processes. HCI is not an exception to this generalization.

Rapid V~V energy transfer processes often dominate the relaxation of chemically produced nonequilibrium vibrational distributions. Inverted vibrational distri­butions are proquced in HCl by many chemical re­actions.3 •4 The initial distributions may be rapidly re­laxed by near-resonant processes such as

2 HCI(v= l)~HCI(v= 2)+HCI(v=0) +AE= 103 cm-1

(1)

In lasers this relaxation very seriously lowers the optical gain from a total inversion to a partial inversion regime." A second type of V~V energy transfer scheme allows small traces of impurities to speed up the V~T,

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