Anomalies in the reactions of helium(1+) with sulfur hexafluoride

Shengfu Yang, Scott M. Brereton, Martyn D. Wheeler, and Andrew M. Ellis ... William K. Lewis, Brian E. Applegate, Judit Sztáray, Bálint Sztáray, To...
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2128

J. Phys. Chem. 1993,97, 2128-2138

Anomalies in the Reactions of He+ with SFs Embedded in Large Helium-4 Clusters A. %heidemam,+B. Schilling, and J. Peter Toennies' Max-Planck-Institut j3r Stramungsforschung, Bunsenstrasse 10, 0-3400 Gattingen, Federal Republic of Germany Received: August 4, 1992; In Final Form: October 13, 1992

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The embedding of single SF6 molecules in large liquid 4He clusters (N 3 X lo3atoms) and their ion molecule reactions with He+ within the clusters are studied in a molecular beam apparatus equipped with a sensitive mass spectrometer. After passing the He cluster beam (stagnation conditions: PO = 80 bar, TO= 24 K) through a scattering chamber filled with SF6, the electron impact mass spectra reveal essentially only the ion fragments SF5+ and SF6+ in addition to the usual He cluster ion fragments. This contrasts with the well-known mass spectrum of a free 300 K beam of SF6molecules which shows all the expected ion fragments SF,+ (n = &5) and F+ but no SF6+. The anomalous suppression of smaller ion fragments and the electron impact energy threshold for SFs+and SF6+indicate that the primary excitation is creation of a positive hole in the liquid He. This hole migrates within the H e cluster until it arrives at the embedded SF6 molecule, leading to the reaction of He+ with SF6. The results are shown to be consistent with the presence of the SF6 molecules located inside and not at the surface of the He clusters. The unexpected appearance of SF6+ is attributed to an extremely rapid energy transfer rate ( 10l6K/s) of the nascent SF6+to the surrounding H e atoms, leading to its stabilization.

I. Introduction The experimental and theoretical study of small clusters consisting of between several and many thousands of atoms has been one of the most rapidly expanding areas of research in the molecular sciences.' With the exception of He and possibly H2,2 all of the clustersstudied so far are expected to be highly condensed in either a solid or partially liquid state. Since 4He has no triple point and solidifies only at pressures above 25 bar, He clusters are definitely liquid.3 Other unique properties of He derive from the existence of a superfluid phase which in the bulk sets in at T C 2.19 K. These unique properties include a vanishing macroscopic viscosity and a special heat transport mechanism known as second sound, which leads to a heat conductivity which is roughly a factor lo3greater than in copper. There is now some theoretical evidence that small 4He clusters may indeed be superfluid4 and will have similar unique properties. The experimental study of helium clusters was pioneered by BeckerS and Gspann.6 This early work is summarized in an excellent review.6 Recently our group has embarked on an experimentalprogram to study He cl~sters.~-I I The time of flight spectra of the neutral componentsdetected by mass spectrometry have revealed up to three different neutral components in the cluster beam.* These could be attributed to a pure atom component and two different cluster components. These initial studies have involved excitation and ionization of He clusters by electron bombardment and the observationof the ionic fragment^.^ In the process of ionization large amounts of energy are released and the new ionic system has properties significantly different from the neutral species. In an attempt to avoid these difficulties we have begun to study He clusters using more weakly interacting probes. These include electron beams at subthreshold impact energiesI0and atomic and molecular beams.!I These experiments and related work by Reis and Gspannl2 provide direct evidence that He clusters are able to capture a wide variety of atoms and molecules, including H2,13Ne,11J3Ar,1302,13N2,13 H20,8J4C02,'4 CH4,I4 and Cs,12 as well as the present study of SF6. From the mass spectrum of the He clusters with these attached molecules, there is now evidence that the captured atoms and molecules aggregate to form clusters which are either insideor at the surface of the He clusters.

' Present address: Department of Chemistry, University of Washington, Seattle, WA 98195. 0022-365419312097-2128$04.00/0

The aim of the present study was to investigate the electron impact ionization mechanismsand fragmentation patterns of the captured species to see if there are special matrix effects in He clusters. In particular the question that arises is whether they are ionized directly or indirectly via positive hole or exciton mechanisms in which one of the He atoms somewhere within the cluster is first excited. The results reported here point convincingly toward a positive hole mechanism and that the SF6 ion fragments result from reactions of He+ with SF6 within the 4He clusters. For this initial study, SF6 is an ideal choice for several reasons. Free SF6 molecules are known to fragment after electron bombardment to produce a wide range of ion fragments SF,+ with n = 0-5 and F+.I5-I7 As with most hexafluoridecompounds and many other halogenated molecules with high symmetry, the parent ion is not observed.18 In the case of the tetrahedral molecules,this observation has been attributed to the Jahn-Teller effect, which predicts that electronically degenerate states (in this case the molecular ions) will be unstable leading to a loss in symmetry.I9 A similar effect has been proposed already in 1966 for SF6,20although no detailed calculations have been performed as far as we are aware.21 The ionization of SF6 has also been extensively studied experimentally by photoelectron spectroscopy.22*23 In his monograph Berkowitz22has carefully summarized the available results of both electron bombardment and photoelectron studies up to 1979. From the data presented there we have constructed an energy level diagram shown in Figure 1. At the left we show the absorption bands, while at the right the thresholds for production of various fragments as measured either by electronbombardment or photoionization are indicated. The potential curves have been estimated by us from the available data and are only approximate. From the photoelectron spectra it was estimated that between 1.1 and 2.2 eV is released in the decay of SFs+ to SFs+ + F from the ground and electronically excited states, respectively.*' The electronimpact induced ion fragmentation of small clusters of SF6 produced by expanding a small concentration of SF6 in a rare gas has been investigatedby several An analysis of the fragmentation process of small clusters reveals that the neutral dimer fragments 100% to monomer ion fragments and that 98.6% of the neutral trimers are broken down to monomer ion fragments2sand only about 1.4%to dimer ion fragments. The mass spectra of beams with large SF6clusters reveal in addition Q 1993 American Chemical Society

Reactions of He+ with SF6 Embedded in 4He Clusters

The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2129 SCATTERING CHAMBER

DETECTOR

-SF;

26.9SeV

-

U

S6 1.50 m

c

Figure 2. Schematic diagram of the molecular beam apparatus showing the location of the nozzle (N), the skimmer (S),the chopper (C),and the detector. The captureexperiments reported here were made by adding SFs to the chamber in which the chopper is housed (rotor chamber).

o

0

u

y

-1

, R

-

-2

-

m

[AI

Figure 1. Schematic diagram showing the threshold energies for ion fragments and the absorption bands of SFs. The potential curves shown are estimated from the threshold and fragment energies. The data on which the diagram is based are taken largely from the book by Berkowitz.** There is now some evidence that the first ionization potential leading to SFs+ is considerably lower than the value of 15.4 eV and more likely 13.60 i 0.1 eV.23

to the known fragmentation of the monomer the corresponding dimer fragments SFb.SF,+ with n = 0-5.27 Similar trends have been observed for fragments of larger clusters ( s F 6 ) s F n +with m = 2 and 3.27Under certain conditions cluster ions (SF6),,$Fs+ have been observed with m I40.27-29 In the expansion of mixtures of SF6 with a large excess of At (1:400),the ion cluster fragments (SFs-Ar,)+, (SF6.SFshn)+, and [(SF6)2-SFs.Arn]+all with attached SFs+ ions with 0 In S 10 are observed.27 In addition mass spectral peaks are found which are attributed to (Arn.SF6)+ and (Ar,*(SF6)2)+with n 1 3 (at electron impact energies UCl= 150eV).Z7 These peaks are assigned to Ar,+ ionsto which neutral SF6 molecules are attached. For n I2 a charge transfer to SF6 is energetically allowed leading to the breakup of SF6+to SFs+, and this has been put forth to explain why the SF6+ containing fragment is not observed in the smaller clusters with Ar. Using even a larger excess of Ar, Isenor and Qi30 found an anomalous fragmentation pattern with an increasein the ratio of the intensity of SF3+relative to SFs+with increasingtotal stagnation pressure (Eel = 55 eV). Ratios greater than 1 were observed at the highest pressure. The observation of the trapping and encagement of single molecules and atomsby small clustersother than He has previously been reported for a large number of species, mostly in small Ar clusters. The clusters are either in a solid state or, in the case of small clusters, in a highly mobile amorphous (“slushy”) state. The embedded molecules have been investigated with IR spe~troscopy,”~~~ optical absorption spectroscopyP3 electron impact mass spectro~copy,3~,~~ p h o t ~ i o n i z a t i o n , ~and ~ * ~laser ~ induced f l u ~ r e s c e n c e techniques ~~,~~ and electron40 and light scattering.41 The investigationshave led to a number of molecular dynamics ~ i m u l a t i o n s , 4and ~ ~the ~ agreement with experiment has been found to be quite satisfactory in a number of cases. Evidence has been put forward that the captured molecules may be on the surface or in the inside of the clusters. There have also been a number of studies of reactions in small clu~ters.~6 Much of the recent work on SF6 in or on Ar clusters has been carried out by Scoles and collaborators. From infrared spectroscopic studies they have been able to identify two different sites of SF6attached to Ar clusters produced in the coexpansion

of a dilute mixture of SF6 in Ar.31s47Modeling calculations indicate that the SF6 may be on the surface as well as inside the Ar cluster^.^*^^^ In very recent work the same group has also observed a few infrared lines of SF6 attached to He ~1uster.s.~~ Finally we point out that the ion-molecule reactions of He+ with SF6 were first studied in afterglow drift tube experiments by Fehsenfeld in 1971 The present paper starts with a brief description of the apparatus, The mass spectral data as a function of the SF6 pressure in the scattering chamber are then presented. Next the electron impact energy dependenceof the mass spectra is shown and discussed in terms of positive hole and exciton mechanisms. The paper closes with a discussion of a potential model for the reaction of He+ with SF6. A steric hindrance and a rapid energy transfer mechanism are proposed to explain the observation of SF6+and the other species not seen previously. 11. Apparatus

Figure 2 shows a schematic diagram of the apparatus.I3 The He cluster beam is produced by expanding He gas from a high pressure POof typically 20-80 bar and a low temperature To of between 4 and 30 K through a 5 pm thin walled orifice. The central portion is skimmed and then after a total flight distance of 1.4m the beam is ionized by electron impact in a homemade open cage spacecharge limited ionizer. The ions are mass selected by a homemade magnetic mass spectrometer and detected by an open eIectron multiplier (EM1 9642/3B). For characterization of the beam it was pulsed by the chopper disk in the scattering chamber and the time of flight distribution measured and compared with earlier results.6 For the capture experiments the SF6 was admitted into the scattering chamber. This has the advantage that the total SF6pressure and the interaction path length are well-defined. The length of the scattering chamber is 106 mm. In all experimentsthe SF6 gas was admitted at room temperature. The concentration of bound dimers is estimated from values listed for K r z in Stogryn and HirschfeldersI to be less than 10% at typical pressures of 1 (r mbar. The total equilibrium internal energy of the SF6 molecules is estimated to be 1 1 2 meV of which 74 meV is vibrational energy.52 Most of the experiments were performed at a helium source pressure of PO= 80 bar and a source temperature of TO= 24 K. Very recent experiments in which the clusters are deflected by embedding atoms from a directed secondary beam indicate that the He clusters produced under these conditions consist of = 3 x lo3 atoms,s3 in good agreement with earlier estimates.*

III. Experimental Results A. Mass Spectra. Figure 3 shows a direct comparison of the mass spectra of free SF6 molecules and of a He cluster beam with captured sF6. Also shown is a mass spectrum measured for a Ne cluster beam which has also picked up SF6 molecules. Ne clusters are expected to be solid, and this mass spectrum is shown for

2130

The Journal of Physical Chemistry, Vol. 97, No. 10, 1993

Scheidemann et al.

106 105

10' 103

102

IO'

a1

VI

$

f e d

IO' 105

IO'

R

;I, 10'

bl

0 10' I 05

100

150 200 250 300 Mass [a.m.u.]

350

600 450

Figure 4. Mass spectrum of He clusters which have passed through the scattering chamber with a higher SF6+ pressure of PSF,= 1 X lo4 mbar at T = 300 K. The He source and ionizer conditions are the same as in Figure 3.

IO' 103

10'

cl 10'0

50

20

LO

60

BO

100

Mass Ia.m.u.1

120

1LO

160

Figure 3. Comparison of mass spectra (a) of a pure SF6 beam, (b) of liquid He clusters which have first passed through the rotor chamber with P S F=~ 3 X 1od mbar at T = 300 K and have picked up on the average less than one SF6 molecule, and (c) of Ne clusters which have passed the rotor chamber with SF6 pressure of 4 X lo4 mbar and have picked up several sF6 molecules. The source conditions of the sF6 beam in (a) were PO= 3 bar and TO= 3 1 1 K. In (b) the He cluster beam source conditions were PO= 80 bar and TO= 24 K, using a nozzle diameter of d = 5 pm. In (c) the Ne cluster beam source conditions were PO = 100 bar, To = 77 K, and d = 5 pm. The electron impact energy was Vel = 65 eV and the electron current was lel = 4 mA in all experiments. Note especially theappearanceofan SFb+peakintheHecluster massspectrum. In (c) the mass spectrum is more similar to that of the free SF6 mokcules. Since the N e clusters are considered to be solid, this confirms that the spectrum in (b) is related to the liquid state of the He clusters.

comparison. The electron impact energy and currents were Eel = 65 eV and IC,= 4 mA in all three experiments. The mass spectrum of pure SF6 shows the expected series of ion fragments and no SF6+since the signal at mass 146 amu @Fa+) is about 6 counts/s and within the noise level. Thus we estimate the ratio of the SF6+to the SF5+ signals to be less than 3 X 10-4. This agrees well with the upper limit from photoionization measurements reported by Dibeler and Walker in 1966.20 The He cluster mass spectrum shows the expected slow, nearly exponential drop-off in the intensities of Hen+ fragments, as observed previously.8 At small masses there is a large peak at m = 18 amu. This has been seen in earlier work and attributed to ionization of H20 which has been picked up by the clusters from the residual gas. The efficient capture of HzO has recently been directly confirmed in experiments related to the present study.14 A careful comparison of Figure 3b with the mass spectrum of pure He clusters reveals an increase in intensity at 127 and 146 amu corresponding to the ion fragments SF5+ and SFa+, respectively. The ratio of SF6+to SFs+ is about 8%. As far as we are aware, this is the first experiment revealing the existence of SF6+ as a stable molecular ion. For confirmation that this unexpected effect is indeed related to the unique properties of He clusters discussed in the Introduction, an analogous experiment was carried out with a Ne cluster beam. Under the stagnation conditions of PO = 100 bar and TO= 77 K,using a nozzle diameter of d = 5 pm, the expansion is expected to lead to large solid Ne clusters. This beam was also passed through the same scattering chamber with SF6 gas. The mass spectrum, of which only the low mass region is shown in

Figure 3c, reveals that the Ne clusters have picked up SF6 molecules. TheSF6 ion fragmentation pattern in this experiment is, however, similar to that of the free SF6molecules. Since the Ne clusters are solid, the SF6 molecules are expected to reside on the surface where they are directly exposed to the incident electrons and fragment nearly as if they were free. Finally it is interesting to compare the intensities of the SF5+ signals in the He and Ne cluster mass spectra. To obtain an SF5+ intensity in the Ne cluster mass spectrum which is of the same order of magnitude as that in the He cluster mass spectrum, the SF6 pressure in the scattering chamber had to be 2 ordersof magnitude greater than in the He cluster experiment. This suggests either a strongly enhanced ionization probability of SF6 attached to a He cluster compared to SF6attached to a Ne cluster or a much smaller capture cross section for the Ne clusters. With increasing SF6pressure we observe a large number of additional peaks in the Hecluster mass spectrum. Figure4 shows a spectrum extending up to m = 410 amu with the highest SF6 pressure that could be used without excessively attenuating the beam. Dimer fragment peaks appear at P S F1~ 1 X 10-5 mbar. Their masses correspond to SF&Fs+ and (SF&+. Then with further increasing pressure additional weak monomer peaks corresponding to SF4+and SF3+are found. Moreover a SF,+ peak is observed which is probably due to fragmentation of the dimers. The other peaks in Figure 4 correspond to almost all possible combinations of dimer fragments SF,+ ( n = 2-7), SF&F,,+ ( n = &7) and the trimer fragments (SF&SF,,+ (visible from n = 0 to n = 4). In none of the mass spectra was there any evidence for ion fragments with attached He atoms, e.g. (SF,,*He,,,)+. The dependence of the intensities of the major SF6 monomer and dimer peaks (SFs+, SF6+,SF&F6+, and (SF&+), on the density of SF6 gas in the scattering (rotor) chamber contains information about the capture cross section of He clusters for SF6molecules and the buildup of large clusters of SF6molecules. Our results about the capture cross sections will be published in a forthcoming paper.I4 B. Ionization Mecbmlsms. In previous work we have discussed the ionization behavior of "puren He clusters without captured SF6.9 If SF6 molecules are attached to a He cluster it appears to be more likely that a He atom is excited and/or ionized than that the SF6 molecule is ionizeddirectlyby an impactingelectron. The overall ionization cross section of a large He cluster should be proportionalto its geometrical cross section, whereas the cross section for direct ionization of a capturedmolecule is much smaller. Moreover it will be significantly reduced depending on the number

Reactions of He+ with sF6 Embedded in 4He Clusters

TABLE I: Electron Impact Thresholds for Helium Atom and SF6Molecule Beams Measured with the Present Apparatus and Compared to Literature Values22 franment ion Het SFJ+ SF4+ SF>+ SF2+ ~~~~

~~

ionization potential (eV) measured threshold (eV)'

The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2131

'4

*He atoms opure He cluster beam in He clusters

P'p

&,... SF;

SF, 1x10)

6.1

1

24.6' ~ - 1 5 . 4-18.1 ~ -19.4 -26.9 [24.6Id 16.9 19.1 21.7 27.1

In a liquid the ionization potential is expected to be lower than for free atoms because of the stabilization due to the interaction of the ion with the surrounding medium. This effect is smallest for He and is estimated to amount to only 0.15 eVS9 The free atom value has been listed. A value of 13.60i 0.1 eV instead of 15.4 eV has recently been determined.*' r All experimental values were corrected for a space charge shift which was determined from a comparison with the He threshold to be 17.4 eV. The errors are estimated to be i 1 .O eV. This value was used for normalizing the experimental determinations.

of He atoms between the impacting electron and the molecule. In liquid He, as will be discussed in detail later on, the created exciton and positive hole are both expected to be highly mobile. Thus they can wander about inside thecluster until the excitation becomes finally localized at the SF6 impurity with its lower ionization potential ( I = 15.3 eV for production of SFs+; see Figure 1). Surprisingly there is relatively littleevidence for either of these mechanisms from related studies of mixed solid clusters of heavier moleculessMO and up to now no unequivocal evidence for indirect ionization within He clusters. There is, however, considerable evidence that neat He clusters can be ionized at impact energies close to the first electronically excited state, i.e. below the ionizationthre~hold.~-~ This result has been interpreted as evidence for the importance of metastable excitonic states as an intermediate in the ionization process. The mass spectra of Figure 3b and Figure 4 provide important informationon theionizationmechanism. The fact that in Figure 4 only SF4+,SF3+,and, to a much lesser extent, SF2+fragments were observed and no smaller fragments suggests from the thresholds in Figure 1 that the ionization process occurred at an energy greater than about 20 eV and less than about 27 eV even though the electron impact energy was E,[ = 60 eV.61 For free SF6 molecules the cross section for production of SF+ has been measured to be comparable to that for SF4+at E,! z 60 eV in agreement with the massspectrum in Figure 3a.16J7 Thisstrongly suggests that indeed the ionization occurs indirectly via either excitons or positive holes. The threshold for electron impact electronic excitation of neat He clusters produced under similar He source conditions leading to creationof metastable excitonsin the clustershas been measured to be at 21.0 f 0.1 eV,lO which is about 1 eV greater than that for electronic excitation of free He atoms. This is consistent with the known surface barrier of liquid He surfaces for electrons. Thus the exciton energy is definitely in excess over that needed to produce SF3+which is estimated from the photoionization threshold to be between 18.3*3and 19.4 eVaZ2 For distinction between these two possibilities, mass selected ion currents were measured as a function of the electron impact energy. Table I summarizesthe results of threshold measurements made with pure He atom and SF6 molecule beams. Large deviations to higher energieswere observed between the measured thresholds and the literature values which were corrected for in Table I by calibrating with a He atom beam. The corrected thresholds agree with the expected values within the estimated errors with the possible exception of SF3+. Figure 5a shows the ionization curves of the major SF6fragments and compares them with the threshold measured for a room temperature He atom beam. It is seen that all the extrapolated values converge on the same ionization threshold as the He atom beam. The He atom beam threshold was used to calibrate the actual electron impact energy which was different by several electronvoltsfrom the actual accelerating voltage because of space charge effects. Thus these data indicate that positive holes and not excitons are largely

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d , ' '

20 ' 22 ' 2b '

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Figure 5. Ion current for some SFb fragments and a H e atom atomic beam (To = 300 K)as a function of the electron impact energy on a linear (a) and a logarithmicscale (b). Theelectron energies have beencalibrated by setting the ionization threshold of He atoms to 24.6 eV. The good agreement of the cluster peaks with the He atom excitation curve at energies above the H e ionization threshold seen in (a) indicates that the molecules are indirectly ionized by positive holes produced in the He atoms of the cluster. The logarithmic plot of the same data in (b) shows that at low electron impact energies the SF6' and SFst curves deviate from the He atom curve. This is interpreted as evidence for an exciton ionization mechanism or direct ionization with a probability which is 10-3 smaller than the positive hole ionization mechanism.

responsible for the ionization. The ionization potential in a liquid is expected to be lower than for free atoms because of the stabilization due to the interaction of the ion with the surrounding medium. This effect is smallest for He and is estimated to amount to only 0.15 eV.9 Thus we expect to measure the same threshold for He atoms and He clusters within the experimental resolution. If we include the electron surface barrier, then the He cluster energy will be greater by only about 1 eV, which is within the experimental resolution. The same data as those plotted in Figure 5a are shown in Figure 5b in a log scale plot of the intensities. The extremely high sensitivityof our mass spectrometerdetector makes it possible to study the threshold region over 5 orders of magnitude in the intensity. The intensities of both SF6+ and SF5+ follow the ionization curves for the room temperature He atom beam and the cluster fragment Hez+down to its threshold. At lower impact energies there is a large discrepancy with a relatively greater intensity for both SF6 fragments. This increase can be explained either by direct ionization of SF6 inside the He cluster or, at least in the region between 21 eV and the He ionization threshold, by a mechanism in which the impacting electron produces a high Rydberg state He exciton directly which has enough energy to ionize SF6. The relative contribution to the ionization of the SF6 molecules from these mechanisms is, however, only about IO-). It is interesting to observe that the ratio of SF6+to SFs+ is nearly constant at about 7% above the ionization threshold and increases to about 10% in the region of possible exciton ionization. In interpreting these observations it is important to realize that the ionization of impurities by either the positive hole or exciton mechanism involves several elementary processes. These involve (1) creation of the excitation, (2) decay and attenuation of the excitation during its motion within the cluster, and finally (3) ionization of the impurity. These processes will be discussed in the next section.

Scheidemann et al.

2132 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993

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a rare gas atom, as illustrated here for an Ar cluster56

106

Ar,-M

al

+e

Ar+Ar,,.M

+ 2e

(1) followed by a rapid migration of the positive hole to the impurity molecule. After about 10-l2 s, electrostriction will take place and the energy releasedwill lead to fragm~ntation.~~ Two different ionization mechanisms have been discussed:56(a) direct charge transfer

-

Ar+Ar,,-M ArSM'Ar,, or (b) self-trapping followed by charge transfer

2m

iii

(2)

101

C I

1

bl

o

20 40 60

eo

x)o

120 ILO 160

Mass la.m.u.1

Figure 6. Comparison of mass spectra of He clusters with captured SFb at twodifferentelectron impactenergies. In (a) theelectronimpact energy is above the ionization threshold and the expected ionization of He,+ cluster fragments is seen in addition to the SF5+and SF6+fragments. In (b) thecharacteristic Hen+fragmentsareno longerseen and the remaining peaks are due to residual gas fragments as well as SF5+and SF6+. Note that the intensitiesin (b) are smaller by 3 orders of magnitude than those in (a). TheHes~urceconditionsandSF~gasprcssurearenearIy thesame as those in Figure 3.

Operating the electron beam in an impact energy region below the ionizationthreshold for HeopensupthepossibilityofobseMng theSF6fragments without significant from theHecluster fragments' Figure compares a spectrum measured at with a l9 eV (b), which is &low the ionization measured with Eel = 37 (a)9 which is above the ionizationthreshold. Thespectrum in (a) is similar to that shown in Figure 3 whereas in (b) the ClWely Spaced Hen+ ion fragments S e n in Figure 6b with a nearly regular are miming. The spacingof 14 amuare attributed to ionizationof captured residual gas mo1ecU1eS9presumably large hydrocarbon present in an oil diffusion pump evacuated vacuum system. The shaded area shows the signal increase after the addition of SF6 gas in the scattering chamber; again Only sF5+ and a amount of sF6+ are observed. This is consistent with the lower energy of the e x c i t ~ n . ~ ~ - ~ ~

IV.

Mscuapion

Probably the two most important observations emerging from these experiments are as follows: (1) The trapped SF6 molecules are largely ionized by positive holes at an effective energy of about 25 eV, whereas excitonic and direct ionization contribute only about 10-3 to the overall probability of ionization. (2) Since the hole mechanism predominates, the SF5+ and SFs+ ion fragments are in fact the products resulting from the reaction of He+ with the SF6molecules within or at the surface of the He clusters. In the following we discuss the positive hole ionization mechanism and the ion-molecule reaction dynamics and cage effect. A. The Positive Hole Ionization Mechmism. There is some evidence on the relative importance of the excitonic and hole ionization mechanism from previous work on small (& < 102 atoms) Ar clusters. The exciton mechanism has been postulated tolead tovibrational predissociationand theevaporation of several atoms from heavy rare gas ~1usters.s~ There is also evidence for ionizationof organic molecules in rare gas clusters by exciton^.^^.^^ Ionization of impurities by a hole mechanism has also been postulated to occur after an initial electron impact ionization of

Process 1 and the self-trapping process (3), both leading toenergy release, have been invoked to explain the ionization and fragmentation of pure heavy rare gas clusters. The energy of several electronvolts released in step 2 or 3 is usually sufficient to break up the neutral ~1uster.s~ In step 3 this leads to predominantly Arz+ and some larger cluster ion fragments. When impurities are present, part of the energy will be dissipated in process 3 and thus, since the ionization potential of Ar2+ is less than that of Ar+ by about 2 eV, less energy is available for ionizing the molecule M. In either case the cluster is expected to be largely destroyed by the vibrational energy released from the Ar2+ clusters, and fragments much smaller than Ar,*M+ are thus observed.60 There are a number of important differences in the properties of H~ clusters compared to clusters which to be taken into in discussing the present results and how they relate to the above previous work. The biggest difference aside from the differences ofthe energy levels ofthe atoms is, of course, that He clusters are definitely liquid. Under the expansion conditions of the present experiments, the He clusters have about fi x 103 He atoms,S3 With the assumption that they are spherical, they are expected to have a mean radius of about 38 A53 and to be very cold with a temperature of about o,4 K.6,62 Thus they are considerably larger and much colder than the Ar clusters (NAr lo2,and TAr= 10 K) used in the earlier work mentioned above. As discussed in the I n t r ~ u c t i o nthere , is evidence from theory that He clusters are superfluid and may possess the other of superfluid He 11, unique Concerning the possible ionization mechanisms in He clusters, it is important to realize that the excitonic levels at >21 eV lie at much higher energies than in all other rare gases and that their energies are large enough to ionize all other species including very likely even Ne (IP = 21.56 eV). In contrast to the heavy condensed rare gases, excitons in bulk liquid superfluid He I1 have been shown to travel unattenuated over distances of about 1 cm.63,64There is some reason to believe that these excitons are simple excited atoms since there is a barrier preventing recombination to form He2* excimer molecules.1°,6s Because of the nature of the dispersion curve of the collective excitations of superfluid He 11, Landau has postulated that particles moving atvelocitiesless than60m/s willnot beabletoproduceelementary excitations and will therefore be able to move unhindered through the liquid.2366 Although no mechanism has so far been proposed to explain the high mobility of excitons, it is intriguing to speculate if the Landau mechanism may be involved. In this connection it is also important to realize that excitons behave much differently in liquid He than in most other media in that they form bubbles with radii of about 12.4 A at T = 0 K67 in times of the order of about 10-12 s6* after formation. These metastable excitonic bubbles have been postulated to play an important role in explaining certain observations made in mass spectral studies of Hecluster beams, mostly in the electron energy threshold r ~ g i o n . ~

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Reactions of He+ with SF6 Embedded in 4He Clusters

The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2133

TABLE II: Egtimates of Single Hop Times and Overall Average Hopping Numbers, Distances, and Times for Exciton and Positive Hole Transport in Liauid Helium I1 exciton hop 2 3s + 1 IS exciton hop 2 IS + 1 IS positive hole hop

22.55 30.35 86.7

30.6 22.7 1.95

1.85 X IO3 136 3.36 X 103 183 2.74X IO" 522

57 76 218

Reference 65.

For positive hole transport the Landau mechanism, discussed above in connection with excitons, cannot be postulated even in bulk He I1 because, at the low velocities involved, electrostriction will occur and destroy the cluster before the hole has had a chance to move. Subsequently after the released energy has been dissipated "snowballs" are created. These consist of a He ion surrounded by about 40-60 tightly bound Heatoms with anoverall radius of about 7 A.69 Thus in conventional ion mobility experiments in liquid He, it is the motion of snowballs which is, in fact, observed. Despite many attempts the Landau process has only once been observed for negative He ions, which are also believed to form snowballs, in liquid He I1 at high pressures of 25 bar and T I 0.5 K.70 We feel, however, that the most probable mechanism for transporting both excitons and positive holes is a hopping mechanism, which was first proposed and discussed in some detail by Atkins for positive holes in 1963.71 This mechanism was proposed to explain the initial precursor phase of ionization of clusters by Haberland59 and Polymeropoulos et We summarizehere Atkins' theory without specifyingwhether exciton or hole transport is involved, and we will refer to both merely as an excitation. Estimates based on both mechanisms are then summarized in Table 11. First we note that an excited atom can readily pass on its excitation to a neighbor by a resonance mechanism. Since the two particles are identical,their combined electronicwave function is either a symmetric or an antisymmetric combination of the product of the atomic wave functions. For the same reason the excitations cannot be localized on one or the other particle, and thus the excitation hops back and forth between the two. The hopping time is given by72

= h/L\E(R) (5) where hE is the energy difference between the symmetric and antisymmetric states for a given internuclear distance R. In the Franck-Condon limit of instantanous excitations, hE has to be evaluated at the average distance of two He atoms in the liquid, which is R = 3.16 A.73 In the liquid each He atom has six nearest neighbors,73and the hopping time is reduced accordingly T

T(1iquid He) = h / 6 M ( 3 . 1 6 A) (6) Since T is about 10-14 s and much smaller than the time needed for a He atom to be accelerated s), we expect hopping to occur many times before a recombination of two He atoms in the bound gerade-symmetry state can occur, leading to a localization of the excitation. Atkins estimated the total number of hops n by assuming a random walk for which the distance traveled is given on the average by l = n'l26 where 6 is the distance in one hop (6 = 3.16 A). The effective average velocity of the hopping excitation decreases with the number of hops as b = n ' I 2 6 / n r = 6 / n l / 2 7 . Atkins proposed that localization occurs as soon as b equals the local velocity of sound ul, which is a measure of the speed at which the system can propagate and respond to pressure disturbances. For liquid He, u l ( T 4 K ) = 240 m/s. Thus we can calculate the total number of hops R, averagedistance traveled E, and the total time by the following formulas

R = (6/U,T)*

L = 62/u,r

Table I1 summarizes the data for the hopping of excitons and positive holes in liquid He. The results of Table I1 indicate that the excitons will travel distances of about 150 A, whereas the positive hole has a range of 520 A. Since all three mechanisms have a range much greater than the cluster radius of 38 A, all three excitations can easily reach an impurity molecule near the center of the cluster. Of course we realize that these numbers can only be regarded as very rough estimates since they do not account for the broad smearing in positions of the He atoms resulting from the large zero point motion. Nor do they account for effects related to the large coherence of states in the superfluid component. As far as we are aware, such effects have not been discussed previously in the literature.74 Additional information is needed for estimating theefficiencies for ionization of an impurity by an exciton relative to ionization by a positive hole. At least three cross sections need to be considered. One is for the initial electron impact excitation, another involves the relativechance of finding an impurity. Finally we have to considerthe probabilityof ionization once the excitation arrives at the impurity. At 60 eV electron impact energy, the relative cross section for e x c i t a t i ~ nand ~ ~ ionization76 is

Obviously this effect alone cannot explain the observed 10-3 smaller probabilityfor exciton ionization. The other cross sections are more difficult to estimate. We note, however, that they will also favor the positive hole mechanism. The probability of ionization by the positive hole will depend on the size of the charge transfer cross sections. From low temperature studies of ion-molecule reactions we expect that these cross sections will tend to the Langevin limiting value77s78 which will be extremely large (2100Az) at T = 0.4 K. The analogous capture effect for exciton ionization resulting from the weaker long range potential will lead to a smaller enhancement of the exciton ionization cross section. The only available information comes from beam experiments at room temperature for which the ionization cross sections for higher Rydberg states of Ne are of the order of 20 A2.79 This is consistent with an estimate of 27 A2 for ionization by a beam of He (2 3S)metastable atoms.80 Finally we consider the chance of the different excitations finding the impurity molecule. If the values of in Table I1 are correct, then this probability should in any case be close to 1. If on the other hand they are, in fact, only an upper limit, which is more likely the case, then we might expect only the relative magnitude to be significant. In this case the positive hole mechanism will also be favored. Thus the hopping mechanism is also consistent with the observed much smaller probability of excitonic excitation. The ionization of impurities in the liquid cluster by the hole hopping mechanism will be further enhanced by the tendency of the positive hole to diffuse toward the center of the cluster where its overall interaction with the neutral He atoms will be greatest. For the same reason we expect the trapped molecules also to be located near the center. Moreover the long range induction interaction of the positive charge with the highly polarizable SF6 will add to this focusing effect. The observed apparent small "excitonic" contribution seen in the electron impact ionization curves could, in fact, also be due to direct ionization of some SF6 molecules at or near the Surface. Recall from Figure 1 that the electron impact threshold for

Scheidemann et al.

2134 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993

ionization of SF6 is 15.4 eV or less.17J4 If a significant fraction of the SF6 molecules were located on the surface, it is hard to understand why the fragmentation is so different than that observed for pure or nearly pure SF6 molecules. At the surface the attached SF6molecules would be exposed to directly ionizing collisions. The fragmentation pattern and ionization mechanism should thus have additional features in common with the free molecules. As we have shown in Figure 3, the fragmentation pattern of SF6attached to large Ne clusters is very similar to that of free SF6. These Ne clusters are thought to be solid, and the SF6fragmentation signals are attributed to molecules attached mainly to the surface. If we assume the SF6 molecules to be inside the cluster, then the appearance of a weak SF2+signal with a threshold energyof 26.95 eV22is, in fact, consistent with neither excitationmechanism. Most likely, however, SF2+is not produced by direct ionization of monomer SF6 on the surface but more likely of a small concentration of centrally embedded SF6 dimers or trimers for which the threshold for formationof SF2+is expected to be lower. This is suggested by the observation that SF2+ is only apparent when ion fragments of larger clusters are also observed. Accepting then that the SFs molecules are inside the cluster, it is easy to argue, as discussed above, that they are probably close to the middle. There the sum of the strongly R-dependent long range van der Waals interactions with the surrounding He atoms will be greatest.*' Moreover the appearance of dimer and larger aggregates with increasing SF6pressure suggeststhat when several SF6 molecules are present, they are, in fact, clustered together within the He clusters. If they are present as widely separated molecules, it is hard to imagine a mechanism which would bring the fragments together to form the observed dimer ion and larger ion fragments once the cluster has disintegrated. Since He has a dielectric constant of nearly 1 (e = 1.055 at 2-4 K), the long range van der Waals forcesare essentiallyunaffected by the intervening He atoms, and thus the individualSF6 molecules entering the cluster will, after they have come to rest, attract each other and conglomerate. The time for passage from the scattering region to the detector of 1 t 3 s is much more than sufficient for the individual SF6 molecules to diffuse toward each other over distances of the order of hundreds of angstroms. The times for diffusion leading to this recombination are estimated in Appendix B. B. Ion-Molecule Reaction Dynamics. Next we discuss the other important result of this experimental study, which is the unexpected observation of the SF6+ parent molecule ion. To explain this observation we have set up the potential energy diagram shown in Figure 7 which essentially presents two cuts through the potential hypersurface for the first three steps of the reaction sequence He+

- + - +

+ HeSF,

He+-SF6

He

He

(SF,')*

-

(SF,')* (SF,')*

He+.SF, (charge transfer I) (9)

(SF,')'

(charge transfer 11) (10)

SF,+ + F +

-

-

1-2 eV KE

(1 l a )

SF4+ 2F + KE

+

(1lb)

+ 3F + KE

(1 IC)

SF3'

where KE = kinetic energy. The first step (q7) involves a charge transfer of the mobile positive hole to one of the He atoms adjacent to an embedded SF6 molecule. This is followed by a charge transfer to the SF6 molecule leading to one of several different electronically excited states of SF6+.23These fragment subsequently by the three energetically

! !

! ! ,

! ! 5

Charpa tranafer 11

Chorpe I transfer I

! 21.6 aV

I

! I ! I

i

i

Ij

i

A

i:!

I

Y

'

I Charpa transfer I I

I

H@;Sd/ Distance Ha- S [ A

I

~

,

\SFs !!lev *-I

~

!

I I I

t -2

Distance F-S [AI

L3.v

-

Figure 7. Schematic diagram showing two cuts through the potential hypersurface for the reaction He+ + SF6 SF5+ F He KE. The left hand side shows the potentials involving the He+ and He species, whereas the right hand side shows the potentials involving the F bond in SFb and SF6+. The energy scale is only qualitative. For simplicity we have left out the excited-state potential curves of (SFs+)* since they are not known. The reaction energies are taken from Figure 1, and the well depths are based on the following sources. The H&F6 van der Waals potential has been measured:* and the well parameters are t = 5.4 X lo-) eV and R, = 4.22 A. The He+SF6 and He-SF6+ potential parameters have been estimated from calculations of the corresponding He+-Xe, and He-Cs+ potentials to be c = 0.280 eV and R, = 3.00 A83 and t = 0.163 eV and R, = 3.62 A4: respectively. The FSF5 potential parameters are c = 3.95 eV85 and R, = 1.56 A.

+ + +

allowed channels (eqs 1l a d ) . SF4+and SF3+have been observed in flowing afterglow measurements of He+ in SF6 gas.50 These latter channels (eqs 11band 1IC)are not shown in Figure 7 since the corresponding potential curves are not known. Their Occurrence in the afterglow experiments implies, however, that the energy released in the step eq 10leads to electronic excitation of the SF6+complex,as suggested by photoelectron experiment^.^^ Equations 9-1 1 and Figure 7 thus appear to provide a consistent scheme within which we can seek an explanation for the appearance of SF6+in He clusters. We note that SFb+is not seen in the above mentioned analogousgas-phase afterglowexperiments corresponding to eqs 9-11.50 This strongly suggests that its appearance is due to some type of matrix or cage effect. Basically two fundamentally different mechanisms have to be considered. One possibility is a cage effect in which one SFs+-F bond breaks up first. The fragments are then sloweddown after some collisions and are recaptured before the entire cluster disintegrates. In Appendix A we use a simple model for estimating if the F and SF5+ fragments can get rid of their kinetic energy before they leave the cluster. The result is that our clusters are far too small for this mechanism to operate. Of course our simple estimates may be in error because of collective interactions which could increase the energy-transfer efficiency. In this eventuality then the SF5+ molecular ion and the F atom could be trapped inside the cluster and conceivably recombine by diffusing toward each other. Of course the cluster will, because of the energy released by electrostriction,be strongly disturbed. For purposes of a simple estimate we neglect this disturbing effect and assume that a pressure wave travels to the surface where it produces a rarefaction wave which then travels back to the center. If we assume both waves to propagate at the

Reactions of He+ with SF6 Embedded in 4He Clusters

speed of sound (ul = 240 m/s), we get for a cluster of radius 38 A a total time of 3.2 X 10-11 s. This time has to be compared with the time needed for SF5+to recapture the F atom. These times have been estimated in Appendix B. In Table I11 we see that the times needed for recombination over distances of 40 A lie between 6 X and 3 X 10-8 s, depending on the assumed value of the helium viscosity. Thus this mechanism is ruled out also from simple considerations based on the times available. The only other possibility is that the observation of SF6+ can be explained solely in terms of the cold and dense He environment which provides an unusually efficient heat bath able to remove the excitation energy from the nascent SF6+before it can undergo unimoleculardecay, i.e. within a time period equal toa vibrational period which is typically 10-12 s. Evidence for such a mechanism also comes from the observed dependence of the intensity of (SF6),,+ fragments with SF6 gas pressure in a related study of larger SF6 clusters in He ~1usters.I~ As pointed out in section IIIB, a free (SF6),,cluster has a propensity to fragment to (SF6)2+ while losing one or more F atoms. For the case of SF6 in large He clusters the fragmentation is not observed; rather we find strong evidence that the (SF6),,+signals are directly related to the neutral (SF6),,cluster concentration. This independent result supports the idea that quench processes in He clusters are rapid and efficient enough to stabilize nascent molecular cluster ions. A lower limit for the rate of energy transfer from the excited SF6+ion to the surrounding He atoms can be obtained if we neglect, for simplicity, the kinetic energy of the neutralized He atom after the initial ionization of the sF6 molecule. This means that we also neglect the recoil energy imparted to the nearest F atom in the SF6molecule by the rebounding He atom. Thus we are left with the internal energy of the nascent free SF6+molecule in its lowest 1tl, state.23 This is known from the measured energy of SFs+after electron impact of free SF6 molecules which indicates that the recoil energy of the F atom from SFs+lies between 1 and 2 eV.21 As a lower limit we consider that only 1 eV of internal energy needs to be removed from the SF6+ ion within a typical vibrational time period of 10-l2 s. This corresponds to an extraordinarily rapid cooling rate of about 10'6 K/s. An alternative estimate of the lifetime of the excited SF6+molecule has been made assuming an equilibrium between the internal vibrational degrees of freedom of SF6+ and a unimolecular decay according to RRK theory. Such an estimate is described in Appendix C and leads to a rough lower limit on the cooling rate of 6 X 1014K/s. Also in Appendix C the mean number of collisions for relaxation is estimated to be 40. Unfortunately very little is known about vibrational relaxation times of simplemolecules in simple liquids with which to compare this result.86 Probably the most reliable results come from laser picosecond spectroscopy involving fairly large organic molecules such as CH3CC13 and CH3CH20H where relaxation times of (5-20) X 10-12 s are observed.87 A more direct comparison is provided by a recent molecular dynamics study of simple bimolecular reactions in rare gas solutions by Bergsma, Reimers, Wilson, and Hynes88 They find that large amounts of translational and rotational energy (15 kcal/mol) can be dissipated in the heavy rare gases in approximately 0.2 X 10-12s. In He these processes take longer, and the time for vibrational relaxation is about 10 ps. Thus the available evidence suggests vibrational energy relaxation rates which are slower than what is observed. There are also a number of molecular dynamics simulations of relaxation in clusters of the heavy rare gases. For example Amar and Bernea9 find times of several picoseconds for the relaxation of the excited Br2 bond in Br~Ar70clusters after photoexcitation. A more direct comparison is provided by molecular dynamics simulations of the decay in the internal vibrational energy of the Xe2 dimer ion in an Xe13+cluster ion. For this case Soler, Saenz, Garcia, and Echtgl find cooling rates

The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2135

IONI ZAT ION PROCESSES

8

ELECTRON IONIZES A He ATOM

HOLE MIGRATES TO SFa II

"~*-'-?''

COMPLETE FRAGMENTATION OF He CLUSTERS

Figure 8. Sequence of processes leading to the production of SFs+ ions from single SF6 molecules embedded in He clusters. The SFt, molecule is first "gently" ionized by a positive hole. The internal vibrational energy in the SF6+ ion which ordinately leads to its complete destruction is carried away by the evaporating H e atoms so that it is stabilized and can be seen in the mass spectrum.

of 6 X 1013K/s. Here again the observed rates in He clusters are at least 1 order of magnitude larger. We conclude this section by presenting in Figure 8 a simple schematic diagram summarizing the processes which lead to the formation of SF6+ ions after the initial ionization of one of the He atoms in the cluster has taken place. After the hole has migrated to the SF6 impurity at the center of the cluster, a complicated sequence of events is triggered. Within a time of about 10-12sthe SF6+ion is stabilized, and after about s the cluster begins to fly apart leaving behind the SF6+(or SFf+)ion.

V. Conclusions We have shown that SF6 molecules can easily be attached to large liquid He clusters with about fi = 3 X 103 He atoms. The observation of large signals in the mass spectra corresponding to single SF6 molecules points to an efficient ionization mechanism. The electron impact ionization threshold of the SF6mass spectral peaks is observed to be about 25 eV, equal to that of He atoms and much larger than the ionization threshold of free SF6 molecules. Both theseobservationssuggestthat theSF6 molecules are not ionized directly by the impacting electrons but rather indirectly by positive holes in the liquid helium which diffuse about within the cluster until they ultimately ionize the SF6 impurities. This "gentle" ionization mechanism is also confirmed by the fact that fragments smaller than SFs+ are not observed, although they are found for free molecules at the corresponding electron impact energies of 65 eV. Probably the most surprising observation, however, is the presence of a sizable SF6+signal in the helium cluster mass spectrum. This contrasts strikingly with the ionization of free SF6 molecules, where apparently all the

Scheidemann et al.

2136 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993

nascent highly excited SF6+ molecular ions decay within less than a collision period to SF5+and F atoms with energies of the order of 1-2 eV and are, therefore, not observed either in photoionization or in electron impact mass spectra. This is, as far as we are aware, the first observation of free SF6' ions. We have attempted to explain the formation of sF6+ Using a Simple classical model to simulate the interactions within the helium clusters. According to this model once SF6+has fragmented to SF5+and F, it is very unlikely that the energetic fragments can be stopped and can recombine inside a He cluster of lo3-lo4 atoms. Consequently we conclude that SF6+must be the result of an extremely rapid quench process within the helium clusters which prevents unimoleculardecay from occurring. All of these observations are consistent with the SF6 molecules located not at the surface of the cluster but deep within the cluster, most likely near its center. Indeed there is now considerable experimental']-I4 and theoreticaI*l~~ evidence that He clusters are good solvents of many molecules. Being weakly binding physical solvents, however, they do not apparently prevent the solvated species from coagulating. Even though we do not yet understand all of the details of the elementary processes involved in the rapid energy dissipation of the highly excited SF6+,this and other evidence indicate that very rapid energy quench rates occur in large liquid He clusters. If we neglect the energy of 7-9 eV of the He atoms released after the initial charge transfer and consider only the 1 eV needed to stabilize the SF6+ ion, we arrive at extremely fast energy dissipation rates of 1016K/s. At the present time there appear to be few results in the literature with which to compare this result. The closest theoretical result is a molecular dynamics simulation91 of the dissipation of the vibrational energy of a Xe2+ dimer within Xe13+which gives a rate of 6 X lOI3 K/s. In the He clusters the dissipation rate thus appears to be about 2 orders of magnitude greater. In conclusion these first studies of chemical processes in He clusters demonstrate that they provide a very cold inert liquid matrix environment with unusual properties. One of these is the short lifetime of about 3 X lo-" s between the initial localization of the diffusing positive hole and when the cluster fragments, which provides a welldefmed time window. Only processes which are faster than this time interval are therefore observed. In this way rapid processes not seen previously have become apparent. In the present experimentsthis made it possible to obtain the first direct experimental evidence for a rapid positive hole transport mechanism within the clusters. The other feature is the rapid vibrational quenching of molecules trapped within the liquid He matrix, as discussed above. This mechanism opens up the possibility in futureexperimentsof carryingout novel experiments on chemical reactions occurring within the clusters. The rapid quench mechanism could conceivably lead to a freezing out of thevibrationallyhot reaction intermediates. For exampleit might be possible to initiate simple bimolecular reactionsbetween species A and B which have agglomerated near the center of the clusters by, for example, laser photodissociation. If the reagents have intimate contact, we expect that the reaction can be initiated despite the rapid quenching. On the other hand, highly excited reaction intermediatesmay well be quenched down to their lowest energy states. In this way they could be detected for examplevia mass spectrometry. If such experiments are succespful they would not only serve to identify the intermediates but also make them accessible to spectroscopic study. Such experiments are in planning. Acknowledgment. This article is dedicated to Dudley Herschbach on his 60th birthday jubilee. It is a great pleasure for J.P.T. to recall 35 years of joint adventures with molecular beams with many happy encounters. We thank U. Henne, E. L.Knuth, M. Lewerenz, R.Frikhtenich, and Ch. Ottinger for carefully reading the manuscript.

SF6qF6

$1 10 20 30 40 50

1=0 1.8 X 10-" 3.0 X 10-Io

1.5 X 4.8 X le9 1.2 x 10-8

7

4.4 X 9.1 X 2.3 X 2.1 X 1.2 x

SF5+-F 7He

7-0

lo-'

9.4 X 7.5 X 1O-Il 2.5 X 10-Io

1V

6.0X 1@Io

10-II

10-5

1.1x

10-9

7 = ))He 1.3 X 4.5 X 10-10 5.0 X 2.8 X 10-8

1.1

x 10-7

Appendix A

We examine here !he possibility that the F atom and the SF5+ ion, which fly apart with a relative kinetic energy of about 1 eV after the breakup of the excited SF6+complex, lose their energy after a sufficient number of collisions with the He environment and become thermalized. For simplicity we assume that the He cluster consists of a gas of hard shell atoms and that the He atoms are initially at rest. Moreover only central collisionsare assumed, and the entire chain of collisions is restricted to one dimension. Finally the condition for thermalizationis that the averageenergy of the particles falls off to the thermal energy k ~ T oof the surroundingHe environment, where the temperature is estimated to be TO= 0.4 K.6,62 This implies that the F atoms interact with the surrounding medium before the cluster is heated and disintegrates (see section IVB). The energy of E H 1 eV is distributed between SF5+ and F according to their relative masses:

For the energy transfer of a moving particle 1 colliding centrally with another stationary particle 2, we use the simple Baule formula: m , / E , = 4 m , m 2 / ( m ,+ m2)2 (A3 Thus a F atom colliding with a He atom loses 57.5% of its energy, whereas SF5+can impart only 11.8% of its energy to a He atom by one collision. The number of collisions that are needed to thermalize the particles is given by

nF = -

In (1 - 0.575)

I.(%) k~,To

(A3)

respectively. Fortunately n~ and SF,+ are only slowly varying functions of the initial energies and the He cluster temperature TO.The resulting collision numbers are n~ = 11.8 and SF,+ = 65.6. From these numbers we can estimate a lower limit for the He cluster size that is necessary to allow so many collisions. If weassume theHeclusters tobesphericaldropletswith thedensity and interatomicdistance of liquid helium, the radius of thecluster is given by

where N is the number of atoms in the cluster, mHc is the mass of one He atom, and ~ L is Hthe ~densityof liquid He. The average interatomic distance is given by and thus we get a simple relation between the number of atomic layers between the center of the cluster and its surface, namely,

Reactions of He+ with SF6 Embedded in 4He Clusters

n = r/d"c-Hc = (3/4r)1/3N1/3 (A71 Assuming that the SFs+and F particles start in the center of the cluster and neglecting in a crude approximation the number of atoms that have to be evaporated in front of the moving particles in order to take up the kinetic energy, the number of He atoms between the center and the surface of the cluster should be at least equal to the number of collisions. From eq A7 we obtain a minimum cluster size of

N = 1 x io5 (AS) which is more than 1 order of magnitude larger than the average size of our clusters which we estimate to be N = 3 X 103.53The above model is of course oversimplified. In fact most collisions will be noncentral and lead to a smaller energy transfer, so that even larger He clusters would be required to thermalize the SF6 fragments. Appendix B Recombinntion Times within a Large Helium Cluster In Table 111the time for two SF6molecules at rest at a distance of ROto come together under the influence of their mutual long range attraction V(R)toa distance R = 4 A has been calculated. The form of the potential used was V(R)= -Cf,R4, where c6 was assumed to be equal to the c6 value for Xe-Xe, which was taken from ref 92 as c6 = 340 au. The viscosity of the He environment was set to 7 = 0 to model a superfluid behavior of the He cluster, and in a second calculation the viscosity was set to 7 = 3.5 X 10-6 kg/(m*s), the value for normal liquid He at T = 2.4 K. In another calculation we evaluated the recombination times for the system SFs+-F to find out if the products of the fragmentation of SFs+ have a chance to recombine if they were stopped within a He cluster. Here the form of the potential used was V(R) = -C@. Cd is given by the dipole polarizability a d of the F atom as C4= I / z e2ad,where e is the elementary charge and ad = 0.56 A3 was taken from ref 93. Appendix C Calculation of the Cooling Rates of an Excited SF6+Molecule in a Helium Cluster Assuming an RRK Unimolecular Decay We assume that two competing unimolecular reactions of (SF6+)* occur within the cluster

Accordingly

with the solution

Moreover we note that the experimental results (see Figure 3) indicate that

We first estimate k l from RRK theory

For Y we take as an effective frequency the average of the V I , v2, and v3 frequencies of SF6 leading to Y = 820 cm-I. From the F

The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2137 atom recoil we know that E - Eo assume EON 0.3 eV to get

1 eV and, moreover, we

k, = 6 X lO"s-' This is a lower limit since we neglect the channel degeneracy factor of 6. From eq C4 we calculate k, = 6 X 10" s-' This corresponds to a relaxation time of 72 = 1.6 X 10" s, and the rate of energy relaxation is thus given by

AE _ 72

104K

(1.6X

lo-" s)

=6X

lof4K/s

The collision number z has also been estimated from the speed of sound ul of liquid helium at T = 0 K.

z = nru,

(C6)

Assuming a density of liquid He of n = 2.2 X ~ m and - ~an average collision cross section of 45 X 10-'6 cm2 we get

z 2.3 X lo1,s-' implying a collision number of 40 for vibrational deexcitation of (SF6+)* in a liquid He cluster. This number is much smaller than average vibrational deexcitation rates in liquids. References and Notes

.

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