Aerodynamical acceleration and rotational-vibrational temperatures in seeded supersonic molecular beams

Chemical

Physics

North-Holland

81 (1943)

Publishing

X9-183 Company

AERODYNAMICAL TEMPERATURES

ACCELERATION AND ROTATIONAL-VIBRATIONAL IN SEEDED SUPERSONIC iMOLECULAR BEAMS

Received9 June19X3: in finalforn~3 August19X3

The time-of-flight of heavy

molecules

(TOF) and

technique

light

seeding

was used gas.

IO study

We also

the acmdynamical

studied

lhe correlation

xcslcrrttion hcwccn

in resdcd the degree

nchicvrd. nnd rotational-vibrationttl remperatures ;IS mrssured using the laser-induced velocity slip (difference) between helium and hydrogen carrier gases and iodine and aniline free-jet expansion by TOF measurcmrnts and compared with rotationnl trmpsraturss

supersonic

molwulur

of nsrod~namic

hams

xc&ration

fluorcxxncc (LIF) technique. The heax? molsculcs \vzts determined in mcusured by LIF. The helium

translational tentperature was found IO br abnormally high and dependent on ~hr:hcsvy-molecule concentration. even ;II concentration as low as 400 ppm. in the case of iodine it was found that ths rotationul dcgrecs of frcsdom were equilibrated with the helium or hydrogen seeding gas translational and slip temperatures. although this temperature \\‘a?; mow than an order of magnitudr higher than theoretical predictions obtained for the pure-gas expansion. In aniline. the rotational tcmperaturs is found to be higher than the gas-dynamic temperature and rotational relaxation is incomplete. The hea\?-mol
1. Introduction Seeded supersonic beams [l-3] provide a source of collision-free molecules_ which are characterized by a narrow velocity distribution and by extremely low rotational, and sometimes vibrational energy 141. If the carrier gas is lighter than the seeding molecule, the latter is accelerated to high energies which in extreme cases can be as high as 37 eV [5]. Due to these properties. the seeded-supersonicbeam technique is used in a large variety of experiments. Two important classes of experiments are molecular spectroscopy in supersonic expansions [4] and high-energy molecule-molecule or molecule-surface scattering [6.7]. The focus of this paper is to quantify the correlation between the aerodynamic acceleration achieved in the superwhich is important to the highsonic expansion, energy experiments. and the rotational-vibrational temperatures which are important for various 0301-0104/S3/0000-0000/$03_00

8 1983 North-Holland

spectroscopic measurements in supersonic expansions_ In the pioneering work of Smalley et al. [S] on the laser-induced fluorescence (LIF) spectroscopy of NO, in seeded supersonic expansions_ it was found that helium as a carrier gas is superior to argon in terms of obtainable low rotational temperatures and since then He has been routinely used. On the other hand Amirav et al. [9] have demonstrated that for large and heavy molecules like anthraccne (C,,H,,). tetracene (C,,H,,). pmtacene (Cz2H,*). ovalene (&HI,) and iodine (I,). argon as a carrier gas is much superior to helium in terms of the gas flow required to obtain vibrationally-rotationally cold spectra of these molecules_ It was found that the order of cooling efficiency was Xe > Kr > Ar > Ne > He. The results were attributed to the velocity-slip effect [9] which was explained as follows: the initially higher thermal velocity of the light carrier gas. causes accelcr-

ation This

of the heavy and slower seeding accclcration

Ic~w-cncrgv collisions a~f IIN

hrgc

can cause efficient

n~oIwuIc.

trlc~c at rehttivcly slip” (velocity

The

diffcrcncc)

tiotlal tcntpcraturc the light

tcmpcraturc

lioiik.

is incoma “velocity

between

the heavy moleis cxhibitcd. The transla-

gas. is defined slip

cxpandcd

as the

tenipcraturc

ltiglicr lllilIl thr lranslaIii~nal ~::Is

and

of the heavy n~olcc~lc colliding

sccdcd

‘I“. This

pure carrier

“cooling”

accclcration

low pressures

cult and the light dilucnt with

~nolcculcs.

is the first csscntial step before

slip

is much

tcn~pcrature

T’ of the the same condi-

under

II w;h ilhSllllled Illal the rotational

tchipcrn-

turn ‘/‘,(

ti(ln;lI

is cSScnti;llly dctcrmincd by 1“ and rotarelaxation is efficient. According to this

~A~>lillliltilIll llllly ill \‘efy

prchsurc ciciitly. plcxc.r

X no/.zle H’lICK!iIS

Iligll PD

clusters ~h:rt limit

md

KlllleS (hacking

iliamctcr) will helium cool cl% iIrglN1 forms Villl dcr WilillS Clllllits cooling

What

(b)

is the quantitative role of the effect in determining the cxpansinn and upo~i wlinl paramelcrs does it

How justified

lational-rotational

is the assumption equilibrium

is

that trans-

closely

main-

taincd

in the supersonic expansion? In order to answer these questions and to study the correlation between the ilerodyni~mic itcc&r:llion and the molecular vibrational-rotational temperatures we have performed time-of-flight expcrimcnts in seeded supersonic molecular hcams of iondine (I_) and aniline (C,,H,H) seeding in hydrogcn. heiiunl and argon. The results of our TOF experiments are then compared to the cxperimental results of the LIF studies mentioned bcforc [9-l I].

as found

for NC), Iti].

2. Experimental

‘I’hc icbdine (I z ) tnolcculc was sxtensively studied in scctlcd srrpsrsonic beams by McCIellat)d ct al. [ IO]. ‘I’hc rlIlilIi1lllill alld \~il~ril1i1IIlill tclllperil1Ure tlependcncc on the noUle hi&king pressures wcrc rlctrrminrd for I7 different seeding &l!XS. Ha-c ilg;IiI~ il

H’:lh fountI

sfficirncy

was in

III;I!

lllc r01:11i011;1lcooling

the order

Ar > Nc > I>, > He.

Hz.

( ‘f,, = 6.3. 13.5 mJ I 12 K for iodine seeding in argon. IWCW and helium rcSprctively for I’D = 1.0 cm Torr (nozzlr backing prcssurc x ncrzzlc diillllW2r).) In addition. the Slope of the prcssurc dependence of the rotational temperature had the siuiw order, being in its iIbSOlllle value larger for thr light gusts than for the heavy gases. Recently.

(a)

velocity-slip temperatures dcpcnd?

[he

aniline

molecules

were

studied

[ 1 I]. In this case the rotational contours of the O-O band of the ‘R2--‘A, transition of aniline were nleasurrd by the LlF technique and were fitted by computer-simulated

rotational

contours

resulting

in the determination of the rotalional temperature 7’,, and its dependence on the carrier-gas identity

and pressure. The rotational temperatures were found to be much higher than the translational temperatures of the pure-gas expansion. The differences found are larger for helium and neon than for argon, In light of these experimentai findings two basic questions can be raised:

The experimental apparatus will bc described in more detail elsewhere [I 21. Briefly it is a molcculur-hcam apparatus with the following compoIICIIIS: (it) supersonic ulolccular-beam source based on a 6” (varian VHS 6) diffusion pump backed by a 650 litcr/min rotary pump (Sargent Welch). The noz~lc was an electron microscope aperture disc (Polaron “). 3 mm disk diameter x 0.25 mm disk width. Two platinum nozzles were used. with noLzle diameter of 30 pm and 100 pm. The nozzles were drilled in the disks with thin wall compared with the nozzle diameter. The nozzle was plugged on the nozzle house that contained the iodine or aniline.

and

which

could

bc heated

and

three-di-

mensionally controlled outside of the vacuum system. The supersonic expansion was skimmed by an electroplated thin nickel skimmer 113) “* with 0.5 mm opening (Beam Dynamics Inc.) and doubly differentially pumped (2” Varian HeS and 63 mm Alcatel trapped diffusion pump). The nozzle-skimmer separation was adjusted to be 9 mm where the beam intensity was optimized. Op” Polaron Equipment LIP.. 21 Crrrnhill CrescrnI. WaIford

WDl 8XG. UK. “” Commercially availablr from Bram Dynamics Inc.. 708 Easr 56th SI., Minneapolis. Minnesota55417. USA.

crating the apparatus at mnsinwm gas load (IS :ttm using 30 pm nozzle) resulted in 2.5 X 10 ’ Torr carrier-gas pressure in the expansion chamber. 8 X IO-’ Torr in the first differential pumping chmihrr. 4 X IO-” Tar in the second differential chatnbcr and 3 X lo-” Torr in the detection chnmher. Most of the experiments were performed with much lower gas flow and the various chanibcr pressures were correspondingly reduced. In the second differential pumping chamber the molrcular beam was chopped by ;I conventional titns-offlight chopper which was an aluminum disc 60 mm in diameter with two slits 1.0 nm wide. Chopping ttt 320 Hz resulted in 20 PS beam pulses. The be:trn wts further collimated by a slit of 1.2 nun width and entered into the detection chamber which tllitintitirted ultrahigh-vacuum condition (2 X IO-" Torr base pressure). by ;t trapped diffusion pump (Alcatel 100 mm). The detector was a UT1 1OOC quadrupole mtss spectrometer which was separated from tlte chopper by 503 nun. Using the commercial UT1 amplifier. the resolution was limited to = 28 ps. The signal w;1s later processed by a transient recorder (Biomation 610) and :I home-made signal averager. The signal-to-noise ratio was very good and the velocity distribution maximn could be determined with better than 1% precision. The main problem was to measure XCUratcly the time of flight in the quadrupole mass spectromter. This WIS dotIe either by extrtlpolittion of the ion energy to co. or by calculating it from its known length and ion energy. Dynamic correction to the ion energy was made by adding to it the nmlccular kinetic energy by iterative cttlculittion. The ovcrull WXUIY~C~ taking into ~count the mass spectrometer time of flight is better than 0.5 K.

3. Summary of esperinaeutalresults The velocity distributions of both the carrier gas ttnd the seeding molecules were nwasurrd for the following mixtures: Hz/I,. He/I?. Ar/I,. He/aniline. Ar/nniline. In each mixture the pressure dependence was studied and for the hrliutn mixtures the nozzle-diameter effect was also studied. The data were corrected for a different

time of flight in the qu:tdrupole mass spectrometer and on each time-of-flight distrihtttion function. three points \verc trmslated into velocities. The peak of the time of flight is vrry close to the peak of the wlocitv distribution. and the r’:_lll-width Ilalf-*iiasiri,u~ii-points of the time of flight arc the smw points in the vrlocitv distribution. The data wcrc analvzcd in terms of rhc fnllmving paramcters: (1) The peak velocities of’ I, and aniline were used to calculate the kin&c energy of the heave 11101ec111eE,. (2) The rrlutive velocity 1,“ bet\\-ccn the heavy tnolecule and light gas was used to calculate the slip temperature. The slip tenipmtturc T‘ is the tanpcritturc that th; heavy n~olrculr scnscs colliding \vith the light ittoI11s. itssumins both velocitv distributions are S functions centered :II the pcai of the real velocity distribution:

\vherr p is the reduced mw \\hich is close to the light atom mass and li is the Bohztnann constant. \vhich is the translational 0) GL-~lc or G._ll, teniprraturc \v:ts det&ninsd from rhs velocity distribution fwhm. In this c;tsc ;L is half of the atomic IllilSS:

Thr proccsscd data shot\ the follo\ving: (1) -4 ‘velocity slip w;1s clearly observed both for aniline and iodine carried in hydrogen and helium. The existence of this velocity slip is :I well-known and documented effect especially in the case of atomic seeded bmrns [l&171. With argon the slip XXX below our limit of derrcrion over it11 the pressure range. (2) The magnitude of the velocity slip was in the expected order. Hz/I, > He/l, > He/aniline. (3) The translational temperature T;t,_Hc of the carrier gas ~~1s found to be abnormally high. In certain cases almost an order of magnitude higher than the rheorrtical prediction and the sspcrimsntill Vtllur Of pure-gas expansion. (4) The translational temperatures T&_ i,c of the carrier gases were found IO depend on the

heavy-molecule concentration. (5) The slip temperature T’ was found to be insensitive to the heavy-molecule concentration. (6) The heavy-molecule kinetic energy increases linearly with the light carrier-gas pressure at low pressures and saturates at high pressure. The s;lturation value is sensitive to the large-molecule concentration. The velocity distribution function of the heavy molecule is found to be narrower than that of the light gns. (7) A comparison of data collected using two no~rr.lrs with 30 pm and 100 Toni diameter shows that both slip temperature and kinetic energy are constants for constant PD value where P is the noble backing pressure and D is the nozzle diameIer. (8) A comparison with the published data of the rotational temperature T, shows that in the case of iodine seeded in hydrogen and helium. the rotatirmal temperature is close to the sum of slip and translational temperatures and the measured trnnslationnl temperature is much higher than the theoretical prediction and experimental value of pure-gas expansion. This observation implies rotational-temperature equilibration with the gas-dynamic temperatures. However. in the case of aniline srcdrd in helium. the rotational temperature is still almost an order of magnitude higher than the measured translational temperatures and more than this compared with the slip temperature. In this case we must conclude that the rotational temperature is not in equilibrium with the translational temperature “-_ (9) A comparison of the results with the published rotational temperature using neon as a carrier gas suggests a criterion for the determination of the importance of atomic polarizability. In the ctise of iodine the rotational temperatures using neon as a carrier gas are closer to the argon results whereas in aniline they are closer to the rotational rcmperature of helium. The reIative masses are 1. 5. 10 whereas the relative poiarizabilities are 1, 2, 8 respectively. (10) The slope of the pressure dependence of

* Privaw communication of J.B. Fan with J. Jortner concerning LIF results in aniline-seeded beam [ 111.

the slip temperature T” is larger than the theoretical one of pure-gas expansion_ The pressure-dependence curves cross at PD values which are sensitive to the mass ratio. The crossing points are PD = 0.8 cm for He/aniline. and 16.6 cm Torr for He/iodine. The implication is that after the crossing pressure diameter value. very low temperatures can be achieved using helium carrier gas without the complication of van der Weals complex formation as compared to argon. (11) At low pressures. or at the early stage of expansion at high nozzle backing pressure. the intermolecular collisional temperatures are dctermined by the velocity-slip effect in the dilutemixture limit. Both vibrational relaxation and van der Waals complex formation can be effected from this effect. The higher slip velocities can increase Landau-Teller type of vibrational relaxation as compared with neglecting the velocity-slip effect and assuming equilibrated pure-gas expansion temperatures. On the other hand the velocity slip can prohibit thermodynamic conditions for van der Waals complex formation to a region where effective three-body collisions are infrequent and therefore largely decrease the degree of complex formation. (12) There is a possibility of measuring the molecular kinetic energy using the rotational temperature obtained from the laser-induced fluorescence thechnique provided that the rotational relaxation is efficient.

4. Iodine seeded in helium Fig. 1 shows typical time-of-flight curves that were used for the data analysis_ In this case the iodine-concentration effect is studied. Fig. 1A shows the TOF of both iodine and helium expanded through a 30 pm nozzle and 770 Torr of helium as the nozzle backing pressure. The nozzle temperature is 22°C which corresponds to = 0.3 Torr partial iodine pressure_ Fig. 1A demonstrates the following: (a) The two curves are completely separated due to a difference between the velocities of the iodine molecules and helium atoms in the supersonic beam. 30% of the time separation is due to

I

100

I

200

TIME

300

OF

Fig. 1. The iodine-concsnlration distribution

400

FLIGHT

40

600

twx)

effect on the kns-of-flighr

function

of both iodine 2nd helium. Nozzle diamster is 30 .um. Helium pressure is 770 Torr. The upper curve X was taken with nozzle temperature of E°C. The iowsr CUI-XY B was taken with nozzle rsmperature of 7YC. The iodine parks1 pressures are 0.3 and 12 Torr respectively.

the difference of the ion time of flight in the mass spectrometer and 70% of the time separation is due to the “velocity slip” between the iodine and helium. The velocity of helium is 1.6s X 10’ cm/s whereas the velocity of iodine is 1.37 x 10s cm/s_ The difference of 3.1 X lo4 cm/s corresponds to slip temperature of T" = 15.3 K. The pure-helium expansion Mach number is M = 14 and the trans-

Iational temperature is T,',e_,tr = 4.6 K. much lower than the slip temperature. (b) The velocity distribution of helium is characterized by Z+‘/c’ = 0.X. After deconvolution of the instrumental response (gaussian drconvolution) we obtain Al;/I’= 0.24. This width is surprisingly large as compared \vith the pure-gas espmsion and corresponds to a :ranslational temperature of T,'lc_ I,c = 15.2 K which is 1nuc11 higher than the pure-gas expansion value. and is conlparable with the slip temperaturs. This effect can be ratinnaliz~d in tr‘rn13 of three CaUSeS: (1) Each iodine molecule is accelerated to kinetic energies of = 30000 cm-'. Even in a rslative concentration of lo-‘. each helium atom contributes 30 cm-’ in one or a few collisions \vith iodine. If the number of helium collisions Lvith iodine is small. it can broaden the helium velocity distribution by about the average snersy transferrrd to iodine. (2) Due to the csistence of the velocity-slip effect. helium also has high-energy collisions \vith iodine which heats the helium. (3) Molecular iodine has internal degrees of freedom which decrease the average heat-capacity ratio of the mixture. This effect can be very important for large polyatomic molecules which have a high vibrational heat capacity. (c) An interesting fact that should be noted is that in spite of the large width of the helium velocity distribution and the large velocity slip between the iodine and helium. the iodine velocity distribution function is narrow. In fact. after dsconvolution_ its Lvidth is JI,W/I*~= 0.09s which is lower by the numerical factor of 2-5 than that of helium. The same kind of behavior is also reported by Campargue 21 al. [16] for HZ/Se and He/Se misturrs. (d) The helium velocity is 1.6s x lo5 cm/s which is slightly lolver than the value derived from pure-gas expansion 1’= (5kT/n1)'~'~ = 1.75x IO5 cm/s_ This small difference is explained in terms of slightly increased average mass of the expanded gas from jrr = 4.00 to no = 4.10 due to the presence of 0.04% of the heavy iodine. In other words. the helium is slighti>- decelerated by the trace mnount .of iodine.

In order to study the iodine-concentration effect. the nozzle temperature was raised to 75°C and the iodine partial pressure to = I2 Torr. The results arc shown in fig. 1B. A comparison between figs. 1A and 1 B shows the following: (a) The peak velocities of helium and iodine are 1.54 x lo5 and 1.23 x lo5 cm/s correspondingly. 7‘hc difference is 3.1 X 10’ cm/s which corresponds to a slip temperature of T” = 15.3 K. This means that the velocity slip was not changed at all by the large change in iodine concentration. The explanation for this is bawd on the fact that the

ity from 1.68 X 10S cm/s to 1.54 X 10’ cm/s is despite a nozzle temperature increase that should increase pure-gas values from 1.75 X 10’ cm/s to 1.90 x lo5 cm/s. This increased aerodynamical deceleration was caused by the much higher concentration of iodine when the nozzle temperature was raised to 75°C. The data from the experiments with heliumiodine mixtures are summarized in fig. 2. Fig. 2 is a plot of the various gas-dynamical -temperatures versus the product of nozzle backing pressure and

nozzle diameter on a log-log scale.

dzgrec: of aerodynamic acceleration depends on the number of collisions with helium that each

iodine

molecule

experiences.

sions does not drprnd

This number

Four

different

temperatures

are plotted

in fig.

of colli-

on the iodine concrntration

in the limit of infinite iodine dilution_ (h) The time-of-flight distribution function and the drrived velocity distribution of helium has AL’/ I’= 0.37 and after cieconvolution AV/ V 5 0.35. this value is considerably larger than AV/V = 0.24 which corresponds to the more dilute iodine mixture expansion. The translational temperature is TL ,tr = 27.4 K which is larger than the slip temperature and much larger than the pure-gas expansion value. The increased translational temperature with increasing iodine concentration is due to the fact that the helium temperature depends both on the number of helium-helium collisions and helium-iodine collisions. The latter depends linearly on the iodine concentration. In fact the surprising thing is the smallness of the effect: 0.3 Torr of iodine was enough to increase The:,, from 4.6 K to 15.2 K whereas 12 Torr increased it only to 27.4 K. Taking into consideration that the nozzle temperature was raised by 17%. the temperature change is small compared with the iodineconcentration change. (c) As in figs. 1A and lB, again the iodine velocity distribution is much smaller than the helium velocity distribution where it is characterized by AV/Y= 0.124 compared with AV/V = 0.35 of helium. (d) Although the velocity difference between the iodine molecules and helium atoms was not changed, their absolute values have decreased to V = 1.54 x lo5 cm/s for helium and V = 1.23 X lo5 cm/s for iodine. The decrease of helium veloc-

20

IODINE

- HELIUM

l-

a B

, IO

0.5

loq,o

Fig.

(PD cm-tow

15

1

Gas-dynamical temperatures in helium-iodine expan‘sion versus PD product on a log-log scale. Temperaturesare in K. The upper curve is the rotational temperature TR [IO]. Just below is Ihe heliumtranslational temperature T,!,=_“=measured 2.

using 30 pm nozzle and 7S°C nozzle temperztture. The third curve which is above the lowest curve is the slip temperature TS. Eight poinrs drawn as solid circles were measured using a 30 pm nozzle diameter at 75’T. The three open circle points were measured using 100 pm nozzle at 22°C. The lowest curve is the pure-helium expansion temperature taken from ref. [IS].

is the rotational temperature of iodine taken from McClelland et al. [lo]. below and very close is the translational temperature of helium T;,,_ ,,e derived from the width of the timeof-flight distribution function. The nozzle temperature was 75°C which resulted in an increased

helium translational temperature as in fig. 1 B. The lolvest curve is the theoretical curve of translational temperature for a pure-helium expansion [ 181. Above the lowest curve is the slip temperature Ts which crosses the theoretical curve at PD = 16 cm Torr. The data on the translational ternperature of helium when using the room-temperature nozzle with low partial iodine vapour pressure are close to the slip-temperature curve and are not shown for sake of clarity. The information from fig. 2 can be summarized as follows: (a) The slip temperature T’ and especially the helium translational temperatures T;,e_,,, are much higher than the pure-helium expansion temperature and they are close to the rotational temprrature. Therefore the large gap between the expected pure-gas expansion temperature and the rotational temperature is explained in terms of the velocityslip effect and the associate effect of increased translational temperature of helium. (b) The slope of the rotational temperature is - 1.17 + O.i)4. the slope of helium translational temperature is the same. - 1.17 f 0.08. The slope of the slip temperature is also the same as that of the rotational temperature - l-16 + 0.06. while the slope of the theoretical curve is - 0.8. The similarity of the slopes of the curves of TK_ T;,,_,,= and T’ can be considered as another proof for the important role of the velocity-slip effect on the iodine rotational temperature_ (c) Due to the difference in the slopes all the curves will cross the theoretical one at some PD value which is 16 cm Torr for T’ (7.3 atm for 30 pm nozzle). This means that at high enough PD values the velocity slip can be relatively unimportant_ On the other hand it plays a major role in the early stage of high-pressure expansions and when low PD values are used. (d) On the curve of the slip temperature. three points are measured using 100 pm nozzle diameter (open circles) and they are on the same line of PD dependence as those measured using 30 pm nozzle

diameter. According to this the velocity slip can be scaled in terms of PD as the translational tempemture is.

5. Iodine seeded

in hydrogen

Fig. 3 shovvs the experimental results of hydragen-iodine mixtures. The rotational temperatures [lo] and the measured slip temperatures are plotted on a log-log scnlr versus PI> (as in fig. 2). (a) The slip tcmpcrature is close to thE: rotational temperature. tional temperature temperature is 12.3 perature T,‘,,_ ,, is

At PD = 1.3 cm Torr the rotais 24.5 & 0.S K [lo]. the slip + 2 K. The translational tem13.2 1 3 K and the calculated

IODINE - !iYDROGEN

05-

00

00

05 log

IO i!‘Dcm

torr!

I5

pure-gas expansion temperature is 0.21 K [IO] which is two orders of magnitude lower than the other temperatures. Obviously. the velocity slip plays an important role on the increased iodine rotational temperature. (b) The slopes are - 1.14 f 0.02 for the rotational temperature. -0.97 f 0.05 for the slip temperature and 0.57 for the theoretical pure-diatomic expansion_ (c) The translational temperature T;12_,,3which is now shown in fig. 3 was larger than the siip temperature at low PD values, and crossed the T curve at PD = 5.3 cm Torr. It had a high negative slope of -1.30. The combinatior. of the translational T,‘,,_ ,, at low PD values and slip temperature at high& values well explains the relatively high rotational temperature. Fig. 4 shows the dependence of both the rotational temperature and the sum of both the slip temperature and the

log

(PD

cm.torr

)

Fig. 4. iodine-hydrogen mixlure: the Icmperature dependence on pressure. is shown on a log-log scale. The solid curve is rhe rotational temperature taken from ref. [lo]. The experimenral points arc Ihc sum of the slip temperature T’ and hydrogen Iemperulure T,‘,,_,,, measured using 30 pm nozzle diameter at 75OC. The pressure is multiplied by the nozzle diameter and is given in cm Torr.

hydrogen translational temperature. on the pressure on a log-log scale. The solid line is the rotational temperature taken from ref. [lo] and the experimental points are the sum of the slip temperature T” and hydrogen translational temperafit proves that the ture T,::- u,- The excellent velocity slip and its associate effect of hydrogen heating are responsible for the high rotational temperature

of iodine.

6. Aerodpamic acceleration helium and hydrogen

of

iodine

seeded

in

An important feature of the seeded-beam technique is the aerodynamical acceleration of the heavy molecule to a very high kinetic energy. This high kinetic energy is used in a variety of important high-energy-chemistry experiments [l-5-71. There are three ways of controlling the energy of a large molecule: (a) controlling the nozzle temperature and linearly the kinetic energy [15]. (b) using mixtures of accelerating gases with variable average mass, (c) using the velocity-slip effect in a controlled manner for scanning over the desired energy range [6]. The last method has the advantages of being the simplest to use and with the fastest response. However two disadvantages can be involved in this method: (1) non-linear energy-pressure dependence, (2) broad velocity distribution_ We have studied the kinetic-energy dependence of the iodine molecule seeded in helium and hydrogen on nozzle pressure. Fig. 5 shows the results. The kinetic energy of iodine (in eV) is plotted against the pressure (atm) using a 30 t.ttn nozzle diameter, and nozzle temperature is 75OC (solid circles). The open squares represent experimental results using a 100 urn nozzle diameter and 30°C nozzle temperature. The pressure scale of the 100 brn results was multiplied by a numerical factor of 10/3. The following conclusions emerge from fig. 5. (a) Iodine is easily accelerated to almost 10 eV close to room temperature using a 30 pm nozzle diameter and 6” diffusion pump. (b) The energy-pressure dependence is linear till 5 E,(max) and only then starts to saturate.

IODINE

- HYDROGEN

IODINE

-HELIUM

important in the case of hydrogen than in the CASE of helium. (d) The experimental results using 100 pm nozzle diameter and 30°C nozzle temperature (open squares) fall close to the curves. The pressure scale was multiplied by the nozzle diameter ratio. The fact that these points are very close to the 30 pm nozzle

diameter

curve

sugysts

that the degree

of

velocity slip and aerodynamical acceleration can be treated in the scale of PD as otlwr gas-dynamic31 properties.

7. Molecular kinetic-enere evaluation using rotational temperature obtained from laser spectroscopy

I

!

I

5

IO

15

I’,+

Fig.

-

(Ah-n )

5. Iodine seeded in hydrogen (upper curve) and hrlium

(lower

curve).

The

iodine

kinetic

energy

in eV versus

the

pressurein atm.

The nozzle diameter is 30 pm and its tempersture 75T. Se*:eral measuremenls (open squares) were psrformed using 100 pm nozzle diameter at 2Z°C. For these

measurements the nozzle backing pressure was multiplird by a numerical factor of 10/3.

(c) In the case of helium, the total kinetic-energy-pressure dependence can closely be represented as E, = 4.6 [l - exp( -0.47 P)] in units of eV (P is in atm). In the hydrogen-seeded beam. saturation is not achieved even at P = 18 atm and the pressure dependence deviates at high pressure from the simple formula that fits the helium-iodine mixture. The reason for this is probably that the hydrogen rotational degree of freedom is still relaxing [19]. In addition. even a small iodine concentration substantially increased the average mass. For example, the average mass of 10 Torr of iodine and 10 atm of hydrogen is 2.33 instead of 2.00 thus reducing 2 eV from the potential iodine kinetic energy. This increased average mass decreases linearly with the pressure and is twice as

An important issue is raised by the question --can one measure kinetic energy using the rotational temperature obtained from laser spectroscopy?* According to our finding the answer to this question is positive under certain conditions. (a) The mass ratio betlvern the heavy molecule and the light seeding gas should be large enough so that the rotational temperature xvi11 be determined by the velocity slip and not by inefficient rotational relaxation. (b) The healy molecule should be dilute enough to prevent carrier-gas heating above the slip tcmpcrature. (c) Although hydrogen can accelerate to higher energies. helium is preferred to hydrogen due to the absence of unknown degree of rotational relasation. Under

these conditions.

fulfilled

an iodine-helium mixture. kinetic energy is given by

whsre

M,

and

Jr,

are

the

the

in the case of

heavs-moleculr

hea\>-molecule

light-atom masses respectively. p mass of the sgtcm heavy rnolscule TX and TR are the nozzle and the perature respectively and X- is the

and

is the reduced plus light atom. rotational tem-

Boltzman constant_ In the case of hydrogen the numerical factor of 5 should br rrtplacrd by = 6.5 (7 for complctc rotational relasation). From this equation it is

.*

niixturcs. Our rclo the rohuional trmlreralurcs of Amirav cl al. Ill]. As in the iodine-helium experiment. we I~:I\T r0w illId nieilsurcd the slip lL’IIlpSIxtIi~C ‘I“ illld Ihe helium iransl:nion:rl Icniperaturc r{,_ ,,,.. Fig. 6 shows typical raw dala ( 11 = 100 1~111. ‘IN =

cxpcrinicnis suits

Will1 illllllIlC-llClilllll

wrc then compared

possibility of molecular kinetic-energy measurement using rotalional I~qxriIlurC is of considerable prilclical importance. (a) The rime-of-llighr method is ;I more general and accurate tcchniquc but for certain e.xprrimenls IIIZ use or :ln existing laser for an additional measurement can save the complicated molecular

l’lrc

henm chopper.

mass

speclron~etcr.

long

vacuum

chamber and transient recorder plus averager required for time-of-flight measurements. (b) In experiments where short-time puked nozzles are used. the velocity slip varies in the rise and fall of the gas pulse. The kinetic energy therefore is not uniform over the pulse duration. The non-uniformity of the kinetic energy precludes time-of-flight measurements if the synchronized chopper is far from the nozzle. This is due to an edge effect that can mask the central-pulse kinetic energy. A laser that probes the expansion near the nozzle avoids this problem.

8. Aniline seeded in helium In order to study polyalomic molecules,

the velocity-slip effect in we have performed TOF

PH.

&200TORR 0

I 100

I 200

I

I

1

I

300

400

500

600

TIME

OF FLIGHT

(ccssc)

Fig. 6. Time of flighI of aniline and helium in a seeded beam. (A) TOF distribution function both for aniline and helium. Helium backing pressure was 100 Torr. Nozzle diameter was 100 pm. Nozzle temperature was 22°C. (9) Helium TOF distribution function seeded with aniline and nozzle Ismperature SO’C. Noble diameter 100 pm. The helium pressures of 100, 200. and 800 Torr are indicaied in the figure.

::

v

b

log,,

ITI

used for rotational-temperature measurements was with 600 urn diameter [ll]. The nozzle temperature is 22°C which corresponds to an aniline partial vapour pressure of 0.4 Torr. From fig. 7 we conclude the following: (a) There exists a velocity slip between helium and aniline. Its magnitude is smaller than in iodine-helium mixture. as expected, and the crossing with the helium theoretical curve is at a lower value of PD = 0.8 cm Torr as compared with PD = 16.6 cm Torr in the case of iodine-helium mixture. (b) The helium translational temperature was measured to be considerably higher than the puregas expansion values. Its magnitude was found to depend on the aniline concentration in a non-linear way. (c) The rotational temperatures are much higher than any of the other temperatures alone or any combination of them. The difference is more than an order of magnitude. The large difference between the rotational temperature and the slip temperature or helium translational temperature implies that the rotational relaxation is incomplete. The conclusion of incom-

perature was measured using a 6 times larger nozzle diameter than in our measurements. This means that the relative aniline partial pressure was six times larger. Our study of the aniline partial pressure dependence teaches us that the effect can increase the helium translational temperature by about a factor of 1.7. (2) Pulsation of a large nozzle can be associated with imperfect gas-dynamic expansion_ At this point it is hard to quantify these effects. It seems to us that they are not enough to bridge the large gap between the rotational and our measured gas-dynamical temperatures. (d) The slopes of ail the temperature versus

plete rotational

10. Aniline

pulsed

relaxation

is further supported

by

consideration of the rotational temperature using neon as a carrier gas. In the case of iodine, where we have proved that the velocity slip and heated carrier gas are responsible for the abnormally high rotational temperature. we can predict that using neon as a carrier gas results in rotational temperatures closer to argon than to helium. and indeed these are the experimental results of McLelland et al. [lo]. In the aniline-seeded beam it was found [l 11 that the rotational temperatures using neon or helium as a carrier gas were essentially the same and much higher than with argon. These results suggest that the velocity-slip effect does not play any major role in the increased rotational temperature. In this case we believe that the effective rotational cooling using argon as a carrier gas as compared with neon or helium is due to its much higher polarizability. The difference between the rotational temperature and gas-dynamic temperature can be somewhat reduced due to the following experimental aspects. (1) At the same PD values the rotational tem-

pressure curves are higher than that of the pure-gas expansion of -0.8. The slope of the rotational

temperature is - 0.93 [ll]. The slope of the helium translational temperature is -1.12 and the slope of the slip temperature is - 1.55. This reflects the fact that at high pressure the rotational temperature will converge to the helium theoretical curve and aniline will not interfere with the expansion process.

and iodine seeding

We have studied argon translational and iodine seeding

in argon

the velocity-slip effect and the temperature, both for aniline in argon. our results are nega-

tive in the sense that: (a) Velocity slip was not observed experimental

conditions

under the same

used with helium.

(b) Argon translational temperatures were very close to the pure-gas expansion value when seeded with iodine and only slightly above them when seeded with aniline using a roomtemperature 100 urn nozzle diameter_ The small increase in translational temperature can be explained in terms of relatively high vibrational heat capcity of the large polyatomic molecule_ Fig. 8 demonstrates the normal behaviour for iodine seeding in argon. Fig. 8A is a plot of the TOF distribution function of both iodine and argon using 100 urn nozzle diameter at room temperature and the argon backing pressure is 100 Torr. Fig. 8B is the same as fig. 8A except that the

2s 1

11. Application experiments

P -100 AI

and implication

to other

From the experimental results several conclusions emerge concerning experimental and throrstical aspects of other esprriments.

TORR

For hca\_v molecules. argon should be preferred as a carrier gas unless verv high helium flow can be tolerated or pulsed nozzles are used. This aspect is discussed in detail by Amirav et al. [9].

PA, = 1000

TORR

The velocity slip and its associate effect light-gas heating xvi11 prohibit complesarion

of of

heavy molecules. The complexation requires three-body collision but the local intermolecular temperature is much higher in the region lvhers three-body collision occurs. We predict that although hydrogen possesses higher polarizabiiitv than helium. complex formation of a heal? mole0

250

500

750

TIME

1000

1250

1500

OF FLIGHT(p,,,)

Fig. 8. Iodine seeded in argon: TOF distribulion funtions of both argon and iodine seeded from nozzle of 100 pm diamsrtr at 22OC. (A) With 100 Torr argon pressure, (B) with 1000 Torr argon pressure.

cule with hydrogen will require higher pressures than with helium. Seeding with a mixture of neon and hydrogen can enhance the hydrogen complex formation. Very low concentration of the hea\? molecule should be used if helium or h_vdrogen complex formation is desired. I I.5

argon backing pressure is 1000 Torr. We conclude that there is no velocity slip between argon and iodine, the small shift in the curves is pressure independent and within our experimental accuracy is 100% due to time-of-flight differences in the

mass spectrometer.

at-celerarion

When used for scanning the heax?-molecule kinetic energy. the velocity slip results in a linear dependence of the kinetic energy on pressure up to = 50% of the available kinetic energy_ The heavymolecule velocity distribution can be narrolver than that of the light gas. especially when a high degree of dilution is used. The degree of acceleration depends

on the value of the PD

product.

Secondly, the argon and iodine

TOF width are close. and the argon velocity distribution function fwhm is the same as the pure-gas expansion value even for only 100 Torr backing with the pressure, being 12.1 _C 1% as compared pure-gas

Aero~~rumCul

value of 11.6%.

I 1.3. Kineric-energy

mea.wrenieriIs

laser-imhrceci jhrorescence

Rotational laser-induced

using

xechiqlre

temperatures obtained using the fluorescence technique can serve for

the heavy-molecule kinetic-energy evaluation. In the limit of high-mass ratio of the heavy molecule to the carrier gas and very dilute mixtures. the calculated energy is accurate. otherwise the calculated energy can serve as a lower limit value. 11.5. MoJmcJiergrtic

light-gas stJpersoJlir Jmlecdur

he
Trace amount of heavy molecules can largely increase the width of the velocity distribution of hydrogen or helium. In this context even 100 ppm of heavy molecule are destructive_ When seeded beams are used the light-gas velocity distribution width is considerably higher than that of the pure gas.

11.6.

J!_aJJduu-Teller

Jm?chuJGsJ?zfor

il. 7. VihratioJJal reluxution

iJJduced by flJIorbitiJlg

resotmice

Rice and co-workers have found an abnormally large excited-state iodine vibrational relaxation at low collisional energies with helium and neon [21.22]. These results were explained by an orbiting resonance between the iodine and the low-energy colliding helium atom. According to our experimental results the collisional energies are more than an order of magnitude farger than the purehelium translational temperature which was used in the theoretical calculation of this effect. We suggest that according to our experimental results the collision temperature that should be used is the rotational temperature measured at these experiments_

L~ibrutioriui

rebsoriotr

II.??.

Rotatiorral

reia_wtioJJ

irl seeded

.stJpersoJJic

heun1s

The vibrational temperature of the diatomic iodine molecule was found to be above the rotational temperature [lo]. The terminal vibrational temperature is determined by the vibrational-relaxation cross section and not by the ultimate translational temperature. Therefore the existence of velocity slip and heated light gas in seeded beams of iodine with helium and hydrogen, will result in higher-energy collisions than are predicted using pure-gas expansion equations_ In this respect it is worthwhile to note that the velocity-slip effect is maximized near the nozzle throat [20] where both the collision rate and temperature are highest. This effect can largely increase the role of the Landau-Teller mechanism in vibrational relaxation. In contrast to what was claimed by McClelland et al. [IO], we say that since in their experiments iodine was mixed with both helium in majority and other molecules, the vibrational relaxation induced by the helium is largely increased over that found in pure helium-iodine mixture. mainly due to increased helium translational temperature. Our experimental results suggest the increased importance of the Landau-Teller mechanism for vibrational relaxation.

Rotational temperatures and relaxation in supersonic free-jet expansions have long been studied, both in pure-gas expansions 123-251 and in seeded supersonic expansions [25-271. Quah has developed a theoretical model for relating relaxation rates and cross sections for rotational and vibrational energ to terminal values of lagging internal temperatures in seeded supersonic expansions 1281. From our results it implies that in experiments where a light carrier gas and heavymolecule seeded beams are studied, the velocity-slip effect and light-gas translational temperature heating are of considerable importance. Quah has used in his model T& as the “equilibrium temperature of the gas jet as predicted by the isentropic relations for y = 1.67”. We believe that this treatment will result in largely reduced rotational relaxation cross sections and T, rrqshould be replaced by the real atom-molecule’ intermolecular gas-dynamic temperature.

Acknowledgement

We are very grateful to Hanan Horwitz for skillful technical assistance_ We wish to thank the staff of the mechanical workshop for their expert

technical assistance in constructing the experimrntal apparatus. Finally we are very grateful to Professor J. Jortner. Professor U. Even and Dr. 0. Cheshnovski for stimulating and valuable discussions. This research was supported in part by the Israel Academy of Sciences Basic Research Foundation and by the Applied Industrial Research in Israeli Universities Foundation.

References [l] T.A. Milne and F.T. Greene. Advan. High-Temp. Chem. Z (I 969) 107. 121 J.B. Anderson. R.P. Andres and J.B. Fenn. Advan. Chem. Phys. 10 (1963) 275. [3) H. Pauly and J.P. Toennies. in: Methods of experimrmal physics. Vol. 7A. eds. B. Bederson and W. Fife (Academic Press. New York. 1968) p. 227. [4] D.H. Levy. L. Wharton and R.E. Smalley. in: Chemical and biochemical applications of lasers. Vol. 2. rd. C.B. Moore (Academic Press. New York. 1977) p_ 1. 15) R. Campargue and A. Lebehot. in: Rarefied gas dynamics. Vol. 9 (Academic Press. New York. 1974) p. CII-1. [6] M.S. Connolly. E.F. Greene. C. Gupm. P. Xlnrzuk. T-H. Morton. C. Parks and G. Staker. J. Phys. Chem. 85 (19s:) 235. [7] G. Prada-Silva. D. Loppler. B.L. Halpem. G.L. Hailer and J.B. Fenn. Surface Sci. 83 (1979) 453. IS] R.E. Smalley, L. Wharton and D.H. Levy. J. Chcm. Phys. 63 (1975) 4977. [9] A. Amirav. U. Even and J. Jortner. Chem. Phys. 51 (1960) 31.

GM. XicClelland. K.L. Saenger. J.J. Valemini and D.R. Hcrschbach. J. Phyr. Chum. RI (1979) 947. .A. Amirav. U. E\*en. J. Jortner. F.W. Birss and D.A. Rnmsay. Can. J. Phys. 61 (1953) 27s. E. Kolodnsy and A. Amirav. 10 be puhlishsd. W.R. Grrnrry ilnd CF. G&e. Rev. Sci. lnstr. 46 (19753 104. R. Cnmparguc and J-P. Brcmn. Enlropie 41 (1971) IS. S. Ahuaf. J.B. Anderson. R.P. Arrdrcrs. J.B. Fenn rend D.R. Xliller. in: Rarilied _g~s dynamics. Vol. 5 (1967) p. 1317. R. Campargue. A Lchehol. J.C. Lcmonnisr and D. Mxstrs. in: Knrlfled gas dynamics. cd. _ S S. Fisher (.ALL\A. New York. 1951). J-E. Scotr. Enrropie 30 (1969) 1. J.P. Tocnnis and K. Winkslmann. J. Chsm. Phys. bb (1977) 3965. R. Gsllngher and J.B. Fsnn. J. Chsm. Phys. 60 (1971~ 3492. K. Nanbu. Phys. Fiuid 72 (1979) 99s. J. Tusa. 51. Sulkes and S.X. Rice. J. Chem. PhFs. 70 (1979) 3136. hi. Sulkes. J. Tusa and S.A. Rice. J. Chcm. Phys. 71(19SO) 5733. R-J. Gallagher and J.B. Fcnn. J. Chem. Phys. 60 (1971) 3487. S. Yamauki. 51. Tski and Y. Fujiiani. J. Chcm. Ph\s. 71 (19Sl) 4476. A. Amirav. U. Even. J. Jormer and L. Klcinman. J. Chem. Phys. 73 (19SO) -8217. U. Borkenhqen. H. Mzdthan 2nd J.P. Toenni?~. J. Chsm. Phys. 63 (1975) 3173. K. Koura. Phy. Fluids X(19Sl) Jol. C.G.\l. Quah. Chem. Phys. LsIrsrs 63 (1979) 111.