1916
J. Phys. Chem. 1988, 92, 1916-1922
Acknowledgment. This study was supported by the Netherlands Foundation for Chemical Research (SON) with generous financial aid from the Netherlands Organisation for the Advancement of Pure Research (ZWO). With pleasure, the authors acknowledge the skilful and invaluable assistance of the Daresbury S R S staff. And, last but not least, without the help of several colleagues from
the Eindhoven University (F. W. H. Kampers, F. B. M. van Zon, and J. van Grondelle) and the Leiden State University (F. C. Mijlhoff, M. J. P. Botman and H. den Hartog), these experiments would not have been performed. Registry No. R h , 7440-16-6; TiO,, 13463-67-7: O,, 7782-44-7.
Electron Bombardment Fragmentation and Intramolecular Ion-Molecule Reactions of Size-Selected CPH, Clusters U. Buck,* Ch. Lauenstein, H. Meyer, and R. Sroka Max-Planck-Institut fur Stromungsforschung, Bunsenstrasse 10, D 3400 Gottingen, Federal Republic of Germany (Received: July 9, 1987)
Ethylene clusters that are generated in an adiabatic expansion with He are size selected by scattering from a He beam. By measurement of angular-dependent mass spectra and time-of-flight distributions at one monomer fragment mass ( m = 26 amu), the complete fragmentation pattern for electron impact ionization of clusters up to tetramers is obtained for electron energies of 100 eV. For ionization of the dimer aside from typical monomer fragment masses (25-28 amu) the results are dominated by ion-molecule reactions within the cluster leading to the dimer to fragment channels at m = 29, 41, and 5 5 amu. No product is observed at the parent mass 56 amu. For larger clusters the main fragmentation product is the C4H8,+ (56) ion which is stabilized by third-body collisions with the other partner molecules within the cluster. The scattering analysis is also used for deriving information on the cluster formation and density as a function of the concentration and stagnation pressure as well as on the energy transfer to the clusters during the collisions with He.
I. Introduction Interest in the properties and dynamics of atomic and molecular clusters has dramatically increased during recent years.] Part of this interest comes from the fact that clusters provide a bridge between molecular physics and the condensed phase. Experimental studies of neutral clusters frequently involve ionization, followed by analysis and detection of cluster ions in a mass spectrometer.2 Numerous experimental results have been published in which the measured ion distributions are attributed to properties of the neutral precursors. However, this is a very dangerous procedure, since significant fragmentation following the ionization process has been observed in many experiment^.^-'^ It is very difficult to get quantitative information about this fragmentation process, since, at present, there is no cluster source available that produces only one cluster size. Therefore the cluster size has to be labeled by an experimental method independent from the ionization process. This can either be done by spectroscopic or by a scattering p r o c e s ~ . l In ~ ~the ~ ~latter (1) See, for example the volumes of the journals: Ber. Bunsen-Ges. Phys. Chem. 1984,88. SurJ Sci. 1985,156. Z . Phys. D A t . Mol. Clusters 1986, 3.
(2) Mark, T.: Castleman, A. W., Jr. Adu. At. Mol. Phys. 1985, 20, 65. (3) Dehmer, P. M.; Pratt, S. T. J . Chem. Phys. 1982, 76, 843. (4) Worsnop, D. R.; Buelow, S. J.; Herschbach, D. R. J . Phys. Chem. 1984,88, 4506. (5) Birkhofer, H. P.; Haberland, H.; Winterer, M.: Worsnop, D. R. Ber. Bunsen-Ges. Phys. Chem. 1984, 88, 207. (6) Stephan, K.; Mark, T. D. Int. J . Mass Spectrom. Ion Phys. 1983,47, 195. (7) Echt, 0.;Kreisle, D.; Knapp, M.; Recknagel, E. Chem. Phys. Lett. 1984, 108, 401. (8) Echt, 0.; Dao, P. D.; Morgan, S.;Castleman, A. W., Jr. J . Chem. Phys. 1985,82, 4076. (9) Kamke, W.; Kamke, B.; Kiefl, H. U.; Hertel, I . V . J . Chem. Phys. 1986,84, 1325.
(10) Recknagel, E. Ber. Bunsen-Ges. Phys. Chem. 1984, 88, 201.
0022-3654/88/2092-1916$01.50/0
method the different kinematical behavior of the clusters in a scattering experiment is used to separate them from each other. By measuring the angular and velocity distribution of the scattered clusters, their intensity can be uniquely attributed to a certain cluster size independent from the subsequent detection process. In particular, this procedure allows the determination of the fragmentation during the ionization process if the intensity of certain clusters is detected at different masses. Applications to the fragmentation by electron impact ionization of the van der Waals clusters ArnI6 and (C02)n17and the stronger bonded (NH3),,l8clusters have been carried out. In the present contribution we present a detailed investigation of the fragmentation of ethylene clusters (C2H4),,. This is an especially complicated case, since already the monomer is fragmented upon ionization by electron bombardment. There has been great interest in these clusters in photoioni~ation’~ and infrared photodissociation20$21 processes. Some of the measurements indicate that the mass
(11) Geraedts, J.; Stoke, S.; Reuss, J. Z. Phys. A 1982, 304, 167. (12) Hopkins, J. B.; Powers, D. E.; Smalley, R. E. J . Chem. Phys. 1981, 85. 3739. (13) Gough, T. E.; Miller, R. E. Chem. Phys. Lett. 1982, 87, 280. (14) Bombach, R.; Honegger, E.; Leutwyler, S. Chem Phys. Lett. 1985, 118, 449. (15) Buck, U.; Meyer, H. Phys. Reo. Lett. 1984, 52, 109. (16) Buck, U.; Meyer, H. J . Chem. Phys. 1986, 84, 4854. (17) Buck, U.; Lauenstein, Ch.; Sroka, R.; Tolle, M. Z . Phys. D.:A t . , Mol. Clusters, to be published. ( 1 8) Lauenstein, Ch. Diplomarbeit, Universitat Gottingen, 1986. Buck, U.;Meyer, H.; Nelson, Jr., D.; Fraser, G.; Klemperer, W. J . Chem. Phys., in press. (19) Ceyer, S. T.; Tiedemann, P. W.; Ng, C. Y . ;Mahan, B. H.; Lee, Y. T. J . Chem. Phys. 1979, 70, 2138. (20) Cassasa, M. P.; Bomse, D. S.; Janda, K. C. J . Chem. Phys. 1981, 74, 5044. (21) Hoffbauer, M. A,; Liu, K.; Giese, C. F.; Gentry. W. R. J . Chem. Phys. 1983, 78, 5567. ~~
0 1988 American Chemical Society
Size-Selected C2H4 Clusters 2000
r
The Journal of Physical Chemistry, Vol. 92, No. 7, 1988 1917 TABLE I: Beam Data 10% C2H4in He
nozzle diam/pm press./ bar peak vel/m s-] (AO/U)100
55 4.0 1450 6.2
speed ratio
26.7
He 30 40.0 1823
2.7 62.1
los
E
lo'
3
VC~H / ,m/s Figure 1. Newton diagram for the scattering of (C,H,),, clusters with
He. The circles denote the positions of elastically scattered monomers, dimers, trimers, and tetramers. spectra are dominated by intramolecular ion-molecule react i o n ~ ' which ~ ~ ' are ~ ~well ~ ~studied for these systems by various mass spectrometric techniques.22 Some qualitative features of the scattering analysis of the cluster fragmentation were presented in the previous papers on the infrared photodissociation of C2H4 cluster^?^*^^ To deal with the larger number of fragment channels, a new technique is applied, the measurement of angular-dependent mass spectra. The results obtained in this way together with time-of-flight data at one monomer fragment mass give sufficient information to determine the complete fragmentation pattern for (C2HJn, where n = 2, 3, and 4. Qualitative information is obtained up to n = 7. The fragmentation behavior was found to be dominated by ion-molecule reactions within the cluster which lead to interesting reaction products. For the dimer the same reaction channels and intensity ratios are found as were measured previously in high-pressure mass spectrometry. The main reaction product for the larger clusters, however, is the C4H8+ion stabilized by third-body collisions with the other cluster molecules. In addition to these main results, the scattering analysis is also used to gain information on the beam composition of mixtures as a function of the C2H4 concentration and the stagnation pressure and to measure the amount of energy transfer to the (C2H4), clusters during the collisions with helium.
XI. Experimental Section A . Crossed-Beam Apparatus. The crossed-beam apparatus has been described elsewhere in detai1.25*26 Briefly, the two molecular beams are produced in two differentially pumped source chambers. To define beams with small angular divergence, the beams enter the scattering chamber through skimmers. They intersect each other at an angle of 90'. The angular dependence of the scattered intensity is measured by rotating the source assembly around the scattering center, while the detector position is kept fixed. The scattered particles pass through a time-of-flight (TOF) spectrometer with a mechanical pseudorandom chopper and a flight path length of 449.5mm. Finally, they are detected by an electron bombardment ionizer, a quadrupole mass filter, and a secondary electron multiplier. The data acquisition is carried out by using a minicomputer-controlled CAMAC interface. The detected ions are counted either time resolved to measure T O F spectra or angular resolved to determine the angular dependence of the scattered intensity. B. Scattering Analysis. As described in an earlier paper,16 the scattering analysis of cluster beams enables us to find unambiguously a correlation between detected cluster ions and their (22) Futrell, J. H.; Tiernan, T. 0. In Ion-Molecule-Reactions; Franklin, J. L., Ed.; Butterworths: London, 1972; Chapter 11, p 485. ( 2 3 ) Huisken, F.; Meyer, H.; Lauenstein, Ch.; Sroka, R.; Buck, U. J . Chem. Phys. 1986, 84, 1042. (24) Huisken, F.; Pertsch, T. J . Chem. Phys. 1987, 86, 106. ( 2 5 ) Buck, U.;Huisken, F.; Schleusener, J.; Schaefer, J. J . Chem. Phys. 1980, 72, 1812.
( 2 6 ) Andres, J.; Buck, U.; Huisken, F.; Schleusener. J., Torello, F. J . Chem. Phys. 1980, 73, 5620.
1 0 ' " " " " " " " " " " ' 2.5 5.0 7.5 10.0 lab. angle / deg.
12.5
Figure 2. Measured total scattered intensity of C,H4-He scattering for different concentrations of C2H4 in the primary beam. The stagnation pressure is 4.5 bar, and the signal is detected at 5 5 amu. The sharp rise of the intensity at 11.7', 7.8', and 5.9' correspond to dimer, trimer, and
tetramer contributions, respectively. neutral parents independent of the cluster size distribution in the molecular beam and the cluster fragmentation in the ion source. In principle, the kinematically different behavior of clusters with different masses in a collision process with a light target gas is exploited. Figure 1 shows the Newton diagram for the scattering of ethylene clusters from He. The circles define the center-of-mass angular range into which different clusters are scattered. In the laboratory system monomers are deflected up to 23.3' from the primary beam, whereas the maximum scattering angles for dimers, trimers, and tetramers are 11.7', 7.8', and 5.9', respectively. It was found that some of the clusters are scattered inelastically, which reduces the size of the Newton circles and therefore also the maximum angles slightly. To determine the fragmentation of C2H4 clusters, a 10% mixture of ethylene in He is expanded through a 55-pm nozzle. The target beam is a pure He beam expanded through a 30-pm nozzle. A summary of the bam data is given in Table I. In all experiments described in this paper the energy of the ionizing electrons is adjusted to 100 eV. 111. Results
A . Beam Composition. In a first series of experiments the influence of the ethylene concentration in He on the cluster formation is investigated. Mixtures with ethylene concentrations varying between 1% and 10% were used. Figure 2 shows the measured total scattered intensity as a function of the laboratory angle for various mixtures. All mixtures are expanded by using a source pressure of 4.5 bar and a 55-pm nozzle. Since ions of mass 5 5 amu are detected, only dimers and larger clusters contribute to the detected signal. Decreasing the deflection angle, we see the steps due to dimer, trimer, and tetramer scattering. Comparing the interisity at small angles with the dimer signal at angles larger then 8' or 9' we see that increasing the concentrations from 1% to 10% enhances the density of larger clusters dramatically. This can be seen as well in Figure 3; in this figure the pressure dependence of the intensity at 9' and 5' is shown for a 1% and a 10% mixture. The angles are chosen to represent the dimer and trimer contributions, respectively. From the slopes it is evident that clustering in a 10% mixture is much heavier than for the more diluted mixture. For a more quantitative analysis we have to remember that the scattered intensity Nnkof the cluster size n detected at mass k depends on the detection probability, the cluster density, and the
Buck et al.
1918 The Journal of Physical Chemistry, Vol. 92, No. 7, 1988
TABLE 11: Data for Lab-Cm Transformation and Trimer to Dimer Density Ratio for Different C2H4Concentrations Obtained at a 4.5-bar Stagnation Pressure"
704 m = 55 amu
mixture 1%
cos
0.45 g/m s-I, re1 vel 2512 u/m s-l, final cm vel 148 $)/m s-l, final lab vel 1679 ci2)/m s-l, final lab vel 1546 [J,") J ~ 2 ) ] / [ J 3 ( ' )J 3 ( 2 ) ] 0.73 A (see ( 5 ) ) 0.095 0.38 P3IP2 CK
+
+
2%
5%
10%
0.51 2480 145 1643 1495 0.68 0.088
0.63 2400 139 1547 1370 0.56 0.072 0.71
0.76 2305 132 1420 1219
0.50
0.50 0.065 0.87
"For the definition of these quantities see ( l ) , (2), (3), and (5). I
1
,
, ' "
0
,
I
1
,
2 4 Pressure / bar
6
Figure 3. Measured scattered intensity of the C,H4-He system for two different C2H4concentrations as a function of source pressure. The points obtained at 9O correspond to dimers; those taken at 5 O to trimers. 00'
laboratory cross section. The scattered intensity at the laboratory angle 0 and the final velocity uf isI6
(Jn(i)(uxm + o , ( 2 ) ( u(Jn(2)(w,uf) ) ) I (1)
3.
Especially for the trimer ( n = 3) to dimer ( n = 2) ratio this expression can easily be evaluated. The ratio of the fragmentation probabilities is known from experiment (see section 1II.C). From the time-of-flight spectra we know the average energy transfer and therefore the final velocities so that J,,(l) and Jn(') can be calculated. The actual values used in the calculation are given in Table 11. Then only the experimental quantities N3k and N2k remain. The measurement of the total differential cross sections taken at mass k = 55 amu in the region of the plateaus for the dimers ( 8 . 5 - 9 . 5 " ) and trimer ( 5 - 6 O ) provide the input data for these quantities (see Figure 2). Thus the ratio of the trimer to the dimer density is given by
It contains the Jacobian for the transformation from the center-of-mass (cm) to the laboratory (lab) system (uf and uf are the final velocities in the cm and lab system and a is the angle between them) and two additional velocity factors, the relative velocity g, which is introduced to express the incident flux in terms of the density, and the reciprocal of the final lab velocity u i l , which accounts for the velocity-dependent detection probability of the detector.27 Whereas the detection probability, given by the product of ionization cross section C,, and the decay probability fnk, is a function of the electron energy only, both the density p and the laboratory cross section u depend on the concentration. This is because the most probable velocity in a seeded beam is a function of the concentration. Thus the collision energy and also the factor fl) are influenced. Since two cm angles contribute to one lab angle, we must add the two contributions. Since neither the ionization cross section C, nor the scattering cross sections are known as a function of cluster size, we use an approximation for deriving information on the cluster density p,. We express the cross sections in terms of the cross section for monomers as follows: u,, = n2i3u,C, = n2/-'C. Furthermore. we will neglect the angular dependence of u,. This seems to be justified because at the probed laboratory angles only cm angles larger than 80" contribute and in this angular range the cross section is nearly constant and proportional to the square of the hard repulsive wall of the interaction potential. To account for the transformation, we calculate the Jacobian factor for a most probable energy transfer, which is determined by analyzing TOF spectra. With these approximations we get for p n relative to the dimer density 4 / 3 f ~ ,~~, , ~ ( C ) , u f{)(
E
N',k(@rUf)
Wtuf)) +
{(.TJ*)(Uf))
(J2(')(uf)
)I
+ (J,"'(Cf)))
(27) Buck, U.; Meyer, H.; Schinke, R.; Diercksen, G. H. F. J . Chem. ~ 1986, 84, 4976.
p3
- = A
I(5.5")
- J(9O)
I(9")
P2
(4)
with
Values for A and p 3 / p 2 are also given in Table 11. It is quite obvious from the results that even for very dilute mixtures the contribution of trimers compared to the dimers measured at a 4.5-bar stagnation pressure is still about 30%. The pressure dependence of p 3 / p 2 is plotted in Figure 4. In this case the data are taken from the measurements at 9' and 5" shown in Figure 3. The measurements at 5" and 10% ethylene contain also a small fraction of tetramers, which were corrected for in the analysis. Within the experimental error the results are in agreement with those of Table 11. It is apparent that the pressure dependence is quite different for the two concentrations. At low pressures the densities do not differ very much for the two mixtures. This might reflect the equilibrium densities of ethylene clusters at room temperature. At pressures larger than 2 bar, dimers and trimers are formed in the expansion. In this range the ratio of their densities is well reproduced by a power law
(3) h
1 60
Figure 4. Measured density ratio for ethylene trimers to dimers as a function of source pressure. The results are based on the data of Figure
K is an angular-dependent constant and J ( ' )is given by
Pz
I
LO
Pressure/ bar
x
Nflk(wf) = K(~)~(~)c(~)~,~((u,(I)(B,E)
1
20
p
P,/P2
a
PO'?
The Journal of Physical Chemistry, Vol. 92, No. 7, 1988 1919
Size-Selected C2H4Clusters 10
lo
u r 5
** c
t
C,H,-He Trlmer 0=177'
5 1
E
1
= o
$
lo
a \
5
4 % . 0
2
10
Q c
s 5
0 0.1 0.2
0.3 0.4
0.5
0.6
Nighttime / ms Figure 5. Measured time-of-flightdistributions of C2H,-He scattering for 8 = 9.5O taken at three different masses. The dashed lines denote the contribution of the different cluster sizes: dimers at m = 55 and 41 amu; monomers and dimers at m = 26 amu. The arrows mark the
-70.0 -50.0
-30.0
-10.0
10.0
Energy transfer / meV Figure 7. Measured energy loss spectra for (C,H,),-He scattering in the cm system. The spectra are derived from the data of Figures 5 and 6 . The collision energy is 98, 104, and 107 meV for the monomer, dimer, and trimer, respectively.
positions of elastic scattering.
masses m = 41 and 5 5 amu the pure spectrum is detected. The positions of elastically scattered dimers are marked by arrows in the spectra. The two peaks correspond to forward and backward scattering, respectively (see Figure 1). In both spectra the maximum intensity is shifted relative to the elastic position, indicating an appreciable collisional energy transfer. At mass 26 amu the monomer contributions appear. The measurements at 0 = 6O contain, in addition, contributions of the trimer. Again we find a distinct shift of the maximum position of the scattered intensity compared to the expected position of elastically scattered particles, indicating inelastic collisions. To get a quantitative ::;;'; picture of the energy transfer, the measured TOF distributions ~ , 0 are compared with simulated distributions which contain all the information on the averaging processes of the apparatus and the 0.1 0.2 0.3 0.4 0.5 0.6 transformation from the center-of-mass (cm) to the laboratory Nighttime / ms (lab) system. These distributions are calculated for a number of Figure 6. Measured time-of-flight distributions of C2H4-Hescattering possible energy transfer AE by a Monte Carlo procedure, using for 8 = 6.0' taken at m = 55 and 44 amu (dimers and trimers) and m as input information the measured angular and velocity spreads = 26 amu (monomers, dimer, and trimers). The dashed lines denote the of the two beams and the transmission function of the time-ofcorresponding contributions of these clusters. The arrows mark the flight a n a l y ~ e r . ~Then ' the calculated distributions are fitted to positions of elastic scattering. the measured spectra, the only adjustable parameters being the amplitudes which are proportional to effective cross sections. The giving values of q2= 2.1 for the 10% mixture and a32 = 1.3 for fitted curves for each cluster size are shown in Figures 5 and 6 the 1% mixture. The individual values of the exponent a for the by dashed lines. The information which can be extracted from dimer to monomer ratio p 2 / p I and the trimer to monomer ratio these data is as follows: p 3 / p , are cyzI = 2.4 and a3,= 4.5 for the 10% mixture and cyzl (1) We get directly the contributions of different clusters n, = 1.4 and a3]= 2.7 for the 1% mixture. Only in the limit of very detected at the same mass k (see section IV). dilute mixtures is the slope similar to the one found for the trimer (2) In the simulation process, different energy transfers AE have formation in the adiabatic expansion of pure rare g a s e ~ . ~ *It* ~ ~ to be assumed to fit the data. This gives indirect information on is noted that for an expansion through a 55-gm-diameter nozzle the binding energy of the investigated cluster, since it is very the pressure has to be lowered below 2.5 bar in order to have a improbable that energy transfer above the dissociation threshold beam with a trimer contribution of less than 20%. occurs. We find for the dimer a limit of AE = 50 f 5 meV. This B. Energy Transfer. The measured time-of-flight spectra of value sets a lower limit for the bonding energy of the dimer in the scattered (C,H4), clusters not only give information on the good agreement with recent ab initio c a l ~ u l a t i o n s . ~ ~ ~ ~ ' cluster distribution but also on the possible energy transfer of the (3) From the AE and the corresponding effective cross sections cluster due to the collision with He. Time-of-flight spectra have also the average energy transfer can be derived, which amounts been measured at lab scattering angles of 9.5' and 6' and three to 30 meV for the dimer. To get better insight, the data have different masses m = 26, 41, and 5 5 amu and the beam conditions to be presented in the cm system. Therefore, the effective cross listed in Table I. The results are displayed in Figures 5 and 6. sections are formally transformed into the cm system and the According to the Newton diagram of Figure 1 the spectra obtained energy-loss space (AE)and, then, averaged over the experimental at 9 . 5 O contain only dimer or monomer contributions. Thus at distribution function in the cm system which is also known from the Monte Carlo c a l c ~ l a t i o n . The ~ ~ result for selected cm angles,
1
4
'
(28) Buck, U.; Meyer, H. Surf. Sci. 1986, 156, 275. (29) Buck, U.; Meyer, H.; Pauly, H. In Flow of Real Fluids;Meier, G. E. A., Obermeier, F., Eds.; Lecture Notes in Physics 235; Springer: Heidelberg, West Germany, 1985; p 70.
(30) van der Avoird, A.; Wormer, P. E. S.;Mulder, F.; Berns, R. M. Top. Curr. Chem. 1980, 93, 1. (31) Suzuki, R.; Iguchi, K. J . Chem. Phys. 1982, 77, 4594.
Buck et al.
1920 The Journal of Physical Chemistry, Vol. 92, No. 7, 1988
TABLE III: Peak Areas S, of Angular-DependentMass Spectra for Different Lab Angles, Corresponding to Dimer, Trimer, and Tetramer Scattering in Arbitrary Units k 0 25 26 21 28 29 39 40 41 42 53 55 56 9.5 6.0 5.0
35 62 90
250 41 I 650
310 664 1060
520 1067 1540
22 138 325
101 255
40 485 1100
85
35
60
8 150 3 50
290 885
fragmented neutral dimers. As the scattering angle is decreased, new ions appear. At 4" and 5" larger ion signals are found at 41 and 56 amu, and at '3 a small signal at 69 amu is visible. On the other hand, the relative intensities change with decreasing scattering angle as well. At 8.5" the relative intensities of the monomer ions still reflect the monomer fragmentation pattern. At smaller angles, the ion signals at 27 and 29 amu increase, indicating contributions from larger clusters. For a more quantitative analysis the peaks are fitted by Gaussian distributions to determine the peak areas. The results are listed in Table 111.
IV. Fragmentation Analysis Due to the fragmentation of the clusters as a consequence of the ionization process, different neutral clusters can contribute to a specific ion signal. We therefore write the peak area S k of the angular-dependent mass spectra as s k ( e ) = Kunkln(e) '
;
i? ._ w 2 C : / 2 0 s 0
(6)
n
4
5'
20
40
60
80
Mass / amu Figure 8. Measured angular dependent mass spectra of (C2H4),clusters. The numbers denote the maximum cluster size which contributes to the spectrum according to the Newton diagram of Figure I .
which mainly correspond to the maximum intensity, is shown in Figure 7 . In general, the energy transfer does not depend very much on the deflection angle in the range between 60' and 180'. If we compare the cluster scattering, the maximum of the transferred energy increases slightly from 25 meV for the monomer, to over 36 meV for the dimer, to 38 meV for the trimer. C . Angular-Dependent Mass Spectra. As is well-known, organic molecules show severe fragmentation as a consequence of the ionization process. Therefore, in the case of van der Waals clusters formed by organic molecules, it is very difficult to derive data for the different fragmentation channels. For this purpose it is suitable to measure mass spectra at different scattering angles. These mass spectra are useful, first to find all different fragmentation channels and second to have comparable signals for normalizing TOF spectra detected at different ion masses. To discriminate against the large background signal on specific ion masses, the target beam is chopped, while a phase-sensitive detector is used to distinguish the scattered cluster intensity from the background. This requires the chopping of the target gas beam with a frequency much higher than the quadrupole mass filter. In our experiment the beam is chopped at 60 H z while the quadrupole is scanned at a rate of about 40 s per mass unit. The analog output signal of the phase-sensitive detector (lock-in amplitude: Ithaco Dyndiac 39/A) is digitized and further processed by using the minicomputer. The electron energy of the ionizer was kept constant at E, = 100 eV. Typical mass spectra for the scattering of ethylene clusters from He at different laboratory angles are shown in Figure 8. Also given is the maximum cluster size that contributes to each spectrum. At 8.5O only monomers and dimers contribute. Whereas large signals are found at ion masses that correspond to fragments of monomers, 25,26, 27, and 28 amu, smaller signals are found at 29, 41, and 55 amu which must be attributed to (32) Buck, U.; Meyer, H.; Schinke, R.; Tolle, M Chem Phys. 1986, 104, 345
where I, describes the total intensity of a neutral cluster of size n scattered into the angle 8. This quantity also contains the overall ionization cross section C, which we assume to be independent of the final fragmentation. The decay probability is given by f n k with the normalization condition
2
fnk
kSnm
= 1 and
fnk
= 0 for k
> nm
(7)
in which m is the monomer mass. Since the intensities Z, are unknown, the set of equations given by (6) is not sufficient to determine the fnk. We therefore measure one T O F spectrum at an ion mass k to which also monomers contribute. By use of the different kinematics for different neutral clusters, this TOF spectrum can be reproduced by fitting velocity distribution functions to the experimental spectrum, giving rise to the contributions Fnkof different clusters. The contribution of cluster X , to the ion Xk+is given by Xnk = Fnk/(x,,F&). From these fits the relative contribution of a species X, to the timeof-flight spectrum detected at mass k , is given by
Inserting this into (6) we get N Sk
=
mn=k
[fnk/fnk~l{~nko~kd
(9)
N defines the maximum size of a cluster contributing to a spectrum. From this set of equations the unknown quantitiesfflk/fnko can be calculated. Using the normalization condition (7) we finally find the fragmentation probabilities for k,: (10)
To start the procedure, the monomer fragmentation is determined with the data measured at an angle larger than 12". For this angular range only scattered monomers contribute to the signal and (9) reduces to:
With (7) the probabilities fnk can be determined. Using these values, we can apply (9) to mass spectra measured at angles to which only dimers and monomers contribute. The TOF spectrum shown in Figure 5 was used to determine the quantities X2,26S26
The Journal of Physical Chemistry, Vol. 92, No. 7, 1988 1921
Size-Selected C2H4 Clusters
TABLE I V Absolute and Relative Contributions of Clusters to Mass k = 26 amu ~
~~
x~926
9
1
2
9.5 6.0 5.0
0.75 0.45 0.33
0.25 0.30 0.19
xn,26s26
3 0.25 0.24
4
1
2
3
4
0.25
188 215 215
63 143 124
119 156
163
TABLE V Fragmentation Probabilities fnk for C2H4Clusters k
n
25
26
27
28
29
39
1
5 0 1 1
26 13 8 6
27 25 10 15
42 46 14 18
5 6 6
7 4
2 3 4
41
3
9 25 19
I
I
CZH4- He
1 ?'
40
m=26amu
v=;"
\
42
1
53
55
56
2
2 9 6
19 19
"ir ,l:;; .-.
c 04
e 8109
2.5
LL
7.5
12.5
Lab. angle / deg. Figure 9. Measured angular distribution of scattered (C2H4),,clusters. The arrows mark the maximum scattering angle and the contribution of various cluster species to the scattered signal.
02
-I-
0 28
L1
56
Mass I amu
Figure 10. Measured fragmentation probabilities for (C2H4),clusters
obtained for electron bombardment ionization at the electron energy of E, = 100 eV.
and x1,26&6. The mass chosen for comparison is ko = 26 amu. The fit of the spectrum yields the values x],26and x2,26. The result is listed in Table IV. From Table I11 we get the corresponding peak areas from the measurement at 9.5O. This allows us to determine all f2,k values using (9). Finally, a more pictorial way of understanding the fragmentation analysis will be mentioned. Using the quantity x1,26determined from the T O F spectrum at 9.5O and mass 26 amu it is possible to adjust the mass spectrum at monomer angle (1 2') to the spectrum measured at dimer angle (9.5'). This is practicable because x1,26gives the contribution of the monomer to the peak at mass 26 amu at the dimer angle and the fragmentation of the monomer is obviously independent of the scattering process. Substracting this obtained spectrum from the mass spectrum at 9.5" results in a spectrum that shows only contributions of the fragmented dimer. The summation of the peak areas yields the total amount of dimers and the single areas divided by the total area all f2,k values. In a similar way the fragmentation of trimers is determined. In this case the TOF spectrum measured at 8 = 6' is used (see Figure 6). The estimated values for Xi.26, i = 1, 2, and 3, are also presented in Table IV. For the tetramers T O F spectra were not available so that in this case the x,,26value were taken from extrapolation of total differential cross section at 8 = 5O as shown in Figure 9. The final results for all the available fragmentation probabilities are given in Table V. With increasing cluster size the number of possible fragmentation channels increases dramatically. All the same, the number of dominant ions formed in the ionization process is relatively small. Apart from the monomer ions corresponding to masses 26, 27, and 28 amu, trimers and tetramers show a strong preference to form ions with masses 41 and 56 amu which seem to be especially stable. Dimers appear at masses 29,41, and 55 amu but not at all at mass 56 amu. These results are visualized in Figure 10. V. Discussion A . Dimer Fragmentation. In a very simple picture we can assume that only one ethylene unit is ionized, which produces the
monomer fragmentation pattern resulting in highly excited ionic molecules. This internal energy is redistributed and results in the evaporation of the second neutral ethylene unit. This mechanism explains the neutral dimer contributions to the monomer masses. In comparison with the monomer fragmentation we find nearly the same decay probabilities. The small contributions to mass 41 and mass 55 can be understood in terms of an internal ionmolecule reaction. In this reaction a highly excited intermediate complex C4Hs is f ~ r m e d : ' ~ . ~ ~ C2H4'
+ C2H4
+
(CdHg')'
(12)
Rearrangement of the positive charge and the remaining electron from the p orbital leads very probably to a 1-butene ion structure, H3C-CH2-CH+-CH2.19.33 This complex decays by removing a CH, radical or an H atom,22leaving us with the C4H7+( 5 5 ) and C3HSf (41) ions (C4Hs')
-
-
C3H5'
+ CH3
C4H7++ H
(13)
Since the C H 3 unit can remove more energy from the complex than a single atom, we expect to find the C3H5+ion more stable in accordance with the experimental value and also in agreement with mass spectrometric studies.34 This reaction pathway also explains why the parent ion C4Hs' is not found in the dimer fragmentation. The observation of the C2HSf (29) ion can be traced back to the H atom transfer reaction" C2H4'
+ C2H4
-+
C2H5+ + C2H3
(14)
which is endothermic by 0.78 eV. The detection of this product is further evidence that the ions formed by electron impact ion(33) Le Breton, P. R.; Williamson, A. D.; Beauchamp, J . L.; Huntress, W. T . J . Chem. Phys. 1975, 62, 1623. (34) Anderson, D. R.; Bierbaum, V. M.; Depuy, C. H.; Grabowski, J. J. I n t . J . Mass Specrrom. Ion Phys. 1983, 52, 6 5 .
1922 The Journal of Physical Chemistry, Vol. 92, No. 7, 1988
ization are highly vibrationally excited. Another explanation of the appearance of the C4H7+ion would be the ionization scheme of the monomer mentioned above; here the released hydrogen atom would carry so much energy that the formed C2H3+ ion is so cold that its internal energy is not enough to evaporate one C2H4 unit. This mechanism is unlikely since in the monomer fragmentation pattern C2H3+and C2H2+are formed with nearly equal probability, and the removal of two H atoms should stabilize the complex more efficient than one H atom. Since in the experiment no ions could be detected on mass 54 (C4H6+),this explanation is very unlikely. B . Fragmentation of Larger Clusters. For trimers and tetramers we find again large probabilities to form monomer ions. The relative values still reflect the probabilities of the monomer fragmentation pattern. A preference of C2H4' is found and nearly the same probability to form C2H3+ and, to a lesser extent, CzH2+. The formed fragments will most likely undergo H atom transfer reactions of the type shown in (14). This mechanism accounts for the decrease in the formation of C2H2+and the appearance of C2H5+. The prominent fragment ions, however, are C3H5+(41) and C4H8+(56). As in the case of dimers, C3H5+and C4H7+are the products of an ion-molecule reaction within the cluster (see (1 3)). In contrast to the dimer fragmentation, we find also C4H8+ fragments, which indicates again that during the ionization process a highly excited complex is formed (see (1 2)). This complex is now stabilized by removing one C2H4 unit (trimer) or two units (tetramer): In contrast to mass spectroscopic investigations of these ionmolecule reactionsZ2a large product intensity C4H8+is found. Similar results have only been obtained in studies in which a buffer gas is used in the ionization region.34 This stabilized complex can also be considered to be the initial compound for the internal ion-molecule reaction leading to C3H5+and C4H7+as was described earlier. The small decrease in the formation of these ions from tetramers compared with trimers might be due to the fact that the initial complex (C4Hs+)formed from tetramers is less internally excited than the same complex resulting from trimer ionization. It is also noted that the contributions which appear at 39 amu (C3H3+)and 53 amu (C4H5+)are typical fragments of the 1-butene parent ion.35
Buck et al.
For larger clusters, n 1. 5 , the contributions to C4H8+increase dramatically. Although fragmentation probabilities have not been determined for these species, the qualitative behavior can be observed by looking at the angular-dependent mass spectra of Figure 8. Because for these clusters the collisional stabilization due to the evaporation of k(C2H4), k 1 3, is even more effective, the complex C4H8+is internally cold. Consequently, the contributions to C3H5+and C4H7+decrease. In addition, the trend to form fewer monomer fragment ions continues. At angles smaller than 3.5O, to which clusters larger than n = 5 contribute, also ions of mass 69 amu are detected. These ions result from an intermediate complex (C6HI2+)*which has been stabilized by the evaporation of at least three C2H4units. Caused by similar internal reactions as for the dimer the ion C2H4C,H,+ (69) is formed. The intensity, however, is much smaller than that of the dominating C4H8+ion. For the largest detected cluster, the heptamer, this implies the evaporation of at least five C,H, molecules. We conclude that the fragmentation of (C2H4), clusters is dominated by ion-molecule reactions of a single ionized C2H4+ molecule within the cluster. For the dimer, the monomer fragmentation pattern gives the largest contribution together with reaction products at mass 29,41, and 55 amu. The parent dimer ion (CZH4)2+is not observed. The fragments of the larger clusters mainly result from a long-lived, highly excited complex (CZH4),+ which has to be stabilized by evaporation of C2H4 units. For clusters containing less than eight C2H4 molecules, this stabilization results in C4H8+ions. Depending on the efficiency of the stabilization and thus the internal temperature of this complex, internal ion-molecule reactions take place, leading to different product ions with a preference for C3H5+(41). The Occurrence of ion-molecule reactions within clusters have been observed previously in analyzing mass spectra of cluster^.'^^^^^^^ However, the present study is the first observation of these reactions with size-selected neutral clusters which are not disturbed by fragmentation problems. Registry No. C2H4,74-85-1.
(35) Aquilanti, V.; Galli, A.; Giardini-Guidoni, A.; Volpi, G. Trans. Faraday SOC.1967, 63, 926. (36) Garvey, J. F.; Bernstein, R. B. J . Phys. Chem. 1986, 90, 3577. (37) Ding, A.; Cassidy, R. A.; Futrell, J. H.; Cordis, L. J . Phys. Chem. 1987, 91, 2562.
