J . Phys. Chem. 1986, 90,2917-2922 electrodes or ring electrodes and have the desirable properties of these classes of electrodes; i.e., transient techniques can be readily applied with conventional instrumentation and studies undertaken in high-resistance media. This work reports the fabrication of linear gold microelectrodes by thin-film techniques. The construction principles described here are not restricted to gold; other electrode materials, such as a whole range of metals, graphite, or semiconductors, can also be used. The combination of computer simulation data and experimental data shows that linear microelectrodes with submicrometer thicknesses are characterized by an almost purely cylindrical diffusion field and that they are ideally suited to measure fast rate constants at convenient sweep rates. Comparable conditions are predicted for microcylinder
2917
electrodes with radii < 0.1 pm which are difficult to obtain from a practical point of view.
Acknowledgment. We thank J. W. Bixler, T. Mann, and D. R. MacFarlane for stimulating discussions, P. van den Bosch for his skilful assistance in the construction of the linear electrodes, D. Luscombe for technical assistance, and F. Rothery (CSIRO Belmont, Victoria) for the scanning electrode microscope work. The generous donation of gold metalloorganics by S . Pons, University of Utah, contributed to the research described in this paper and is gratefully acknowledged. This work was supported financially by the Australian Research Grants Scheme. Registry No. Au, 7440-57-5; TEAP, 2567-83-1; ferrocene, 102-54-5.
Dissociation Dynamics of Mass-Asymmetric Molecules in Impact on Solid Surfaces Z. Barict and R. B. Gerber* Department of Physical Chemistry and The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (Received: September 25, 1985)
The dissociation of heteronuclear molecules, induced by high-energy collisions with chemically inert surfaces, is studied by classical trajectories. Results for IBr and IC1 in collisions with an MgO surface are compared with previous calculations for 12. New qualitative effects are found in the case of IC1 due to the high mass asymmetry, shown in the energy dependence of the dissociation probability, and in the velocity and the angular distribution of the dissociation fragments. The new features (compared with 12) are interpreted in terms of two different possible pathways for dissociation, corresponding respectively to collisions where the light or the heavy atom strikes the surface first. The results provide considerable insight into the role of collider masses in the dynamics of dissociation upon impact on surfaces.
I. Introduction The development of sophisticated experimental techniues, such as molecular beam scattering, has transformed the field of gassolid interactions in recent years by providing detailed information at the microscopic level on the processes involved.' Molecular dissociation on surfaces is among the topics most intensively pursued by the beam scattering Many such reactions involve strong chemical binding forces between the surface and the dissociation fragments, resulting typically in sticking of the products to the surface, and leading to complicated dynamical behavior,I3-l9 the theoretical treatment of which is difficult. The most simple kind of dissociation processes are, however, those where the surface is chemically inert with regard to the incoming molecule and its fragments. In such cases the molecule is essentially crushed against the steeply repulsive potential wall of its interaction with the surface, bond cleavage thus being induced by the high energy of the collision. These processes, by their relative simplicity, may offer some of the best prospects at the present time for understanding surface reactions from a firstprinciples point of view. Recently, first molecular beam studies of such dissociation processes induced by collisions with surfaces were reported by Amirav and Kolodney20-21for I2 in impact on MgO(001) and sapphire. Corresponding theoretical studies of collision-induced dissociation were carried out for 12/Mg0(001) and for related systems, using both classical trajectory simulat i o n ~ ~and ' - ~high-energy ~ impulsive collision models.2e26 From the experimental and theoretical results, a detailed physical picture emerges as to the dynamical mechanism of the fragmentation process, and how the latter is reflected in various observable features. One interesting conclusion is that dissociation occurs via a rotational predissociation mechanism: Fragmentation occurs when rotational excitation upon impact on the surface yields a centrifugal repulsion between the atoms that is high enough to Permanent address: Institute of Physics of the University, P.O.B. 304, 41001 Zagreb, Yugoslavia.
0022-3654/86/2090-2917$01.50/0
overcome the b i n d i ~ ~ g . Another ~ ' , ~ ~ conclusion is that after molecular impact on the surface, a "hard" collision takes place between the fragments before the latter separate. This step in the dissociation process leads to interesting pronounced features in both the angular and the velocity distribution of the p r d ~ ~ t s . ~ ~ * ~
(1) For a recent review see: Barker, J. A,; Auerbach, D. J. Surf.Sci. Rep. 1984, 4, 1 .
(2) Balooch, M.; Cardillo, M. J.; Miller, R. D.; Stickney, R. E. Surf. Sci. 1974, 46, 358.
(3) Becker, C. A.; Cowan, J. P.; Wharton, L.; Auerbach, D. J. J. Chem. Phys. 1977,67, 3394. (4) Sibener, S. J.; Lee, Y. T. Rarefied Gas Dynam. 1979, 11, 1417. (5) Bernasek, S. L. Ado. Chem. Phys. 1980, 41, 477. (6) Ceyer, S. T.; Somorjai, G. A. Annu. Rev. Phys. Chem. 1977, 28,477. (7) Salmeron, M.; Gale, R. J.; Somorjai, J. A. J . Chem. Phys. 1977, 67, 5324, 1979, 70, 2087. (8) Baldwin, D. A.; Murray, P. I.; Rabalais, J. W. Chem. Phys. Lett. 1981, 77, 403. (9) Comsa, G.; David, R. Surf. Sci. 1982, 117, 77. (IO) Brown, L. S.;Bernasek, S. L. J . Chem. Phys. 1985,82, 2110. (11) Robota, H. J.; Vielhaber, W.; Lin, M. C.; Segner, J.; Ertl, G.Surf. Sci. 1985, 155, 101. (12) McCreery, J. H.; Wolken, Jr., G. J . Chem. Phys. 1976, 64, 2845; Chem. Phys. Lett. 1976, 39, 478. (13) Gelb, A.; Cardillo, H. J. Surf. Sci. 1978, 75, 199. (14) Tantardini, G. F.; Simonetta, M. Surf. Sci. 1981, 105, 597. (15) Elkowitz, A. B.; McCreery, J. H.; Wolken, G.J. Chem. Phys. 1976, 17, 423. (16) Diebold, A.; Wolken, G. Surf. Sci. 1979, 82, 245. (17) Tully, J. Acc. Chem. Res. 1981, 14, 188. (18) Ron, S.; Shima, Y.; Baer, M. Chem. Phys. Lett. 1985, 116, 443. (19) Lee, C.-Y.; DePristo, A. E., a preprint. (20) Kolcdney, E.; Amirav, A. J . Chem. Phys. 1983, 79, 464. (21) Kolodney, E.; Amirav, A.; Elber, R.; Gerber, R. B. Chem. Phys. Lert. 1984, 111, 366. (22) Elber, R.; Gerber, R. B. Chem. Phys. Lett. 1983, 97, 4. (23) Elber, R.; Gerber, R. B. J . Chem. Phys. 1984, 88, 1571. (24) Gerber, R. B.; Elber, R. Chem. Phys. Lett. 1984, 107, 141. (25) Elber, R.; Gerber, R. B. Chem. Phys. 1985, 92, 363. (26) Elber, R.; Kouri, D. J.; Gerber, R. B. Chem. Phys., in press.
0 1986 American Chemical Society
2918
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986
Insight is thus available both on the dissociation mechanism and into its relation to observable features. However, the results obtained thus far were for homonuclear diatomics only. The purpose of the present study is to explore dissociation induced by high-energy collisions for systems of substantial mass asymmetry, and to examine whether this involves new features in the fragmentation mechanism and the observable quantities. Calculations using classical trajectories are carried out for models of IC1 and IBi in collision with an MgO surface, and the results are compared to those for 12/Mg0. The model systems are described in section 11. The results, focusing on the new effects found and on their physical interpretation, are presented in section 111. Concluding remarks are made in section IV. 11. The Model Systems
In the present study, the MgO target for the incoming molecule is modelled as a perfectly rigid, nonvibrating surface. Obviously this is a highly simplistic description of the actual physical system. Indeed, time-of-flight experiments on nondissociated I, molecules scattered from MgO(001) have shown that a very high fraction of the incident collision energy (order of 30%-40%) is transferred to the solid.21 Also, theoretical simulations for the same system have shown that upon high-energy impact (several electronvolts of collision energy) a shock-wave is created which travels into the solid, the latter being the dynamical mechanism of the energy transfer in this case.,’ Nevertheless, the rigid-surface model used in the present calculations is of major interest and relevance for the purpose of studying dissociation. It has been shown2’ that the dissociation probability in I2 collisions with MgO(001) is given to remarkable accuracy over the entire physically relevant range of energies (2-10 eV) by a rigid-surface calculation. Analysis of the detailed classical simulations (that include the motions of many solid atoms) throws light on the physical reason for this behavior.*’ Upon the very initial instant of impact, the surface s) as rigid, still behaves for an extremely brief interval in the sense that during this interval the shock wave has not yet been initiated, and no significant amount of the collision energy has as yet been transferred to the solid. However, already at that brief initial instant a large part of the collision energy has been transferred to internal molecular degrees of freedom (actually to rotation) and the fate of the molecule, as to whether it will dissociate or not, is already determined at this point. In essence, in this system the dissociation probabilities are determined by an instant so brief following impact that the solid may be treated as rigid during that time interval. It should be stressed that this behavior depends on parameters (masses, force constants) of both the molecule and the solid, and is by no means general. In the case of I2 collision with sapphire, for instance, the rigid surface model does yield the correct dissociation probabilities, since energy transfer to the solid occurs essentially at the same instant as the excitation of the molecule.27 While the rigid-surface approximation yields the correct dissociation probabilities for I,/MgO, the results it gives for the angular and for the velocity distributions of the products are expected to be much less satisfactory.26 Nevertheless, we estimate, on the basis of a recent impulsive collision model,26that the main qualitative features of both the angular and the velocity spectrum of the fragments should be adequately described by the rigid-surface treatment. In conclusion, it should be physically justified (and, of course, profitable in terms of the simplicity of the calculations) to study heavy molecule dissociation in impact on MgO by using the rigid surface approximation. Another, less drastic approximation which will be employed here is to treat the MgO(001) as completely smooth. Recent calculations, using an impulsive collision model, have shown that high surface corrugation may significantly affect several features of the dissociation process, especially the angular distribution of the fragments.26 However, the size of the I, molecule is so large that the effective corrugation is likely to be very small in this case. (The molecular dimensions are larger than the MgO unit cell.) (27) Gerber, R. B.; Amirav, A,, to be published
BaEif and Gerber TABLE I: Potential Parameters for (Halogen Atom/MgO) halogen
I
c1 Br
ai,A-’
Ai, eV
3.460 3.912 3.595
2.950 3.260 2.520
TABLE 11: Potential Parameters for Inter-Halogen Molecules molecules I2
IC1 IBr
D,eV 1.5417 2.1520 1.8170
Pcq,
‘A
2.6666 2.132069 2.46898
P, A-‘ 1.8585 1.8591 1.8923
It is reasonable to assume that at the high impact energies relevant to collision-induced dissociation, only the repulsive part of the molecule-surface interaction is of importance. It has recently been proposed by Gadzuk and Hol10way~~ that mechanisms involving electron transfer from the surface could be important in some molecular dissociation processes, especially on metals and semiconductors. There is no apparent reason for us to suspect that such a mechanism could be significant for the systems studied here, ICI/MgO and IBr/MgO. (There is, in fact, some experimental evidence against such a mechanism in the case of 12/Mg0. In particular, excited iodine atom products could not be dete~ted.~’)We thus assume that nonadiabatic processes are negligible in these cases, and consider only the simplest and most likely mechanism, in which dissociation is due to impact on the steeply repulsive wall of the moleculesurface potential. Following the previous studies of 12/Mg0,2’-24we assume also for ICl/MgO and IBr/MgO investigated here a repulsive molecule/surface potential of the “surface dumb-bell” type29 Here z1, z2, and z are respectively the distances of atom 1, atom 2, and the molecular center-of-mass from the surface plane; p is the internuclear distance and 8 is the orientation angle between the molecular axis and the surface normal; V,(z,) is the repulsive interaction between atom i and the surface. To estimate these repulsive interactions, we use the fact that both Mgz+ and 02are Ne-like in their electronic structure. As an approximation for the repulsive potential between a halogen and Ne, we use the corresponding X/Ne interaction, where X is the rare gas near to that halogen in the periodic table. Finally, parametrizing the repulsive V,(z,)by Vl(z,)= AJe-a~ri
(2)
the values of A, and cyI were extracted from the repulsive (rare gas)/Ne potentials given in the l i t e r a t ~ r e . The ~ ~ parameter values used are listed in Table I. Obviously the potentials so obtained must be regarded as very crude, but the excellent agreement with experiment of the previous calculations for 12/Mg02’is encouraging in giving some credibility to the interactions used. Moreover, the results were found to be relatively insensitive to the potential parameters, as one might have intuitively expected for cases where the dissociation is due to the steeply repulsive part of the interaction. For the intramolecular potentials of IBr and IC1, Morse functions were used with parameters taken from Huber and Her~berg,~’ listed in Table 11.
All calculations were carried out for collisions with incidence normal to the surface. Since a flat surface model was used. the (28) Gadzuk, J. W.; Holloway, S . Chem. Phys. Left. 1985, J14, 314. Holloway, S.; Gadzuk, J. W. J . Chem. Phys. 1985, 82, 203. (29) Gerber, R. B.; Beard, L. H.; Kouri, D. J. J . Chem. Phys. 1981, 74, 4709. (30) Klein, M. L., Ed. Inert Gases: Potentials, Dynamics and Energy Transfer in Doped Crystals; Springer-Verlag: West Berlin, 1984. (31) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure: IV. Constants of Diatomic Molecules; Van Nostrand: New York, 1979.
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 2919
Dissociation Dynamics of Mass- Asymmetric Molecules
0
1
2
3
4
Ecoll
5
6
7
8
9
(ev)
Figure 1. Energy dependence of the dissociation probabilities for I*, IBr, and IC1 in collisions with MgO. The solid lines show the total dissoci-
ation probability p6;). The broken line shows the direction dissociation probability for IC1, which excludes final metastable states. collision dynamics was confined to a single plane perpendicular to the surface. The molecules were assumed to be initially in the ground vibrational and rotational state, v = 0, J = 0. The set of initial conditions used thus involved sampling over all molecular orientations (a set of 91 points was used), and over the phases of the zero-point vibration (a set of 12 values was employed). Hence, at each energy 1092 trajectories were computed to simulate the collisions. The sampling technique employed involved using regular sequences of initial value points, unlike the statistical choice in Monte Carlo procedures. The error in this scheme is due to the finite grid size of initial points, which leads to an error in averaging (integration) over initial conditions. Tests indicate that the number of trajectories used is adequate for yielding converged results for all properties of physical interest studied here (the dissociation probability and the angular and the velocity distribution a t each energy). 111. Results and Analysis Large mass asymmetry was found to induce pronounced effects in the structure of observable quantities when compared with the corresponding patterns in the case of 12/Mg0. These effects shed interesting light on the dynamic mechanism of the dissociation process. ( a ) Energy Dependence of the Dissociation Probability. The calculated dissociation probabilities for 12,ICl, and IBr/MgO as a function of the collision energy are as shown in Figure 1. Some of the calculated trajectories led to states of IX after the collision in which the vibrotational energy of the molecule is higher than the dissociation limit, but lower then the outer maximum of the effective potential between the atoms
05
%ib
5 Wbm)
+ L2/(2ppm2)
WL(Pm)
(4)
where pm is the (outer) maximum of the effective potential WL(p) = W(p) L 2 / ( 2 p p 2 ) of the scattered molecule, L is the final angular momentum, and p is the reduced molecular mass (evib = 0 corresponds to the dissociation limit). The above molecular states have of course an infinite lifetime in the classical framework, but correspond to metastable states quantum mechanically, the lifetime of which is determined by tunneling through the centrifugal barrier. Experimentally, such a collision product will enter the detector as a molecule if its lifetime T is greater than T ~its , flying time to the detector, and as separate atomic fragments if T~ > 7 . We denote by P$Y:s(E)the probability of direct dissociation, i.e., corresponding to collisions in which the fragments separate to arbitrarily large mutual distance also in the classical calculation. Pm)(E)will denote the probability of obtaining a metastable state as a product. Then
+
is the classical approximation to the total quantum mechanical
dissociation probability, including both direct and resonanceforming mechanisms. @::)(E) is also the prediction of the present calculation for the fragmentation probability measured in an experiment in which the flying time to the detector is extremely long. The solid lines in Figure 1 show @{:)(E) for collision energies E up to 9 eV for 12,IBr, and IC1. For 12/Mg0 the dissociation probability rises sharply in the threshold region, and continues to increase monotonically until a saturation behavior is approached at very high energies. The important new feature in the case of ICl/MgO is that after the rise of P$;js(E) an intermediate plateau, or saturation behavior, is obtained in the range between E = 3.5 eVand E = 4.5 eV, approximately. P$JS(E)then begins to rise again, approaching again a saturation behavior at very high energies. The same effect, but much more weak, is seen in the case of IBr, but for this system the intermediate plateau extends only over a range of about 0.2 eV in collision energy. An interpretation of this interesting effect is obtained by detailed analysis of the classical trajectories. As was previously pointed out in the case dissociation results in this system mainly from a cenof 1221,24 trifugal mechanism: Fragmentation occurs when the molecule strikes the surface at angles such that a very large torque for rotational excitation is administered, giving rise to a centrifugal repulsion strong enough to break the molecule apart. For a heteronuclear molecule IX, the outcome of the collision depends, however, on which end of the molecule had struck the surface. The classical trajectory results obtained for IC1 and IBr support the centrifugal dissociation mechanism in both cases and over the entire energy range studied. Important evidence is the fact that the trajectories resulting in dissociation seem all to correspond to molecular orientations at impact on the surface for which the rotational torque is very high, sufficient for (centrifugal) dissociation. At low energies just above threshold only a small range of molecular orientations, centered around the “maximum torque” orientation seem to result in dissociation (e.g., for 4.0-eV collisions of IC1 with MgO, only impact orientations pertaining to angles in the range (-35O, -45’) of the molecular axis with respect to the surface normal result in dissociation). As the collision energy increases, so does the range of orientations resulting in dissociation. No dissociation was found for perpendicular or near-perpendicular molecular impacts on the surface, the latter being the orientations most favorable for vibrational excitation. Whether the light or the heavy atom strikes the molecule first, the trajectories show that the centrifugal mechanism dominates over “direct” vibrational dissociation a t all energies considered. When the mass asymmetry is large, the molecular center-of-mass is located very near to the heavy atom. Collisions in which the much heavier (I) atom hits the surface basically have the effect of reflecting the center-of-mass momentum at the steeply repulsive potential wall. The lighter atom mainly adjusts adiabatically to the motion of the heavy I, and only a small fraction of the collision energy is transferred to the I-X relative distance mode, which is pertinent to dissociation. The light atom, however, couples strongly to the relative I-X motion, and collisions in which X hits the surface convert more effectively the incident center-of-mass translational energy into internal energy, leading to dissociation. This is the simple physical picture that analysis of the trajectory motion portrays. For collisions energies up to about E = 4.5eV, only collisions in which the C1 end of the IC1 strikes the MgO surface can result in dissociation. In the range 2-4.5 eV Pfi,(E) thus first rises, then levels off where the pathway associated with C1 hitting the surface has reached its saturation value. At 4.5 eV, the collisions in which the I end strikes the surface begin to contribute to dissociation since then the transfer of even a relatively small fraction of the collision energy to the I-C1 mode suffices for breaking the bond. At very high energies, also the contribution of this pathway to dissociation must, of course, level off. In the case of IBr, the “intermediate plateau” effect is much weaker, obviously due to the smaller mass asymmetry. ( b ) Dynamics of Metastable Formation, and the Energy Variation ofP#jS. The probability of forming a metastable state of IC1 in the collision is given by the difference between @::)(E)
2920 The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 and %;,(E) for that molecule in Figure 1. P@”’’)(E) is largest in the vicinity of the threshold of dissociation, where it is of the order of IO%, then decreases with increasing collision energy, reaching a value of about 1% only, at about 4.5 eV. Then fim)(E)increases with energy reaching the magnitude of about 7% for the range falls of 6.5-6.7 eV collision energy. For higher energies pmS)(E) off as the energy increases. This behavior of P(ms)follows also from the “two pathways” picture for exciting the ICl: from the onset of dissociation at about 2.5 eV up to -4.5 eV collision energy, only the encounters where the CI end hits the surface are effective in inducing internal excitation. As the energy increases in this range, the collision increasingly leads to higer centrifugal energiesfollowing impact, hence the effective potential WL(p)is purely repulsive for the dominant angular momentum values, accounting for a reduced production of metastable states. Then, for E > 4.5 eV, as mentioned in subsection a above, the second pathway for internal excitation, where the I end hits the surface, becomes effective. At first, around the onset energy of this mechanism it produces angular momentum values L that are not extremely high, so a significant proportion of metastables is formed, by (4). The higher the collision energy becomes, the greater is the propensity for producing very high L values, giving rise to purely repulsive effective potentials WL(p).Hence the fall-off of fim)with increasing collision energy for E > 6.7 eV. Unlike the pronounced intermediate plateau effect in the energy dependence of P$$(E) for ICI, the energy variation of PAfis(E)only weakly reflects the two pathways mechanism for dissociation: P$is(E) increases steeply with E from threshold up to about 4.0 eV, then the slope of the E dependence decreases up to approximately 6.0 eV, but increases again for E > 6.0 eV. The partial flattening of the P#js(E) curve in the range of -4.0-6.0 eV collision energy is obviously the signature of the two pathways mechanism for this quantity. Comparison of P$jS(E) with f i z i ) ( E ) in Figure 1 shows that @$:)(E) exhibits a strange intermediate plateau effect because the contribution of P(ms)(E), which is much greater (especially in terms of its relative contribution to in the regime corresponding to the ”first pathway”, where the C1 strikes the surface. The physical interpretation as to why metastable formation is larger for the first pathway than for the second one is as follows: When the lighter atom strikes the surface, the I atom does not move throughout the impact. If the collision results in an angular momentum L such that a local maximum in W,(p) is obtained, the relative distance p of I and C1 is likely to be in the attractive well region of WL(p).However, when I strikes the surface, the CI atom adjusts its position adiabatically to some extent, leading to a p value that lies outside the maximum of WL(p)in the cases where such a maximum exists. Hence the probability of metastable formation for this type of collision is smaller. The above interpretation was reached by examining the values of p and of WL(p)during impact for trajectories leading to formation of metastables, and contrasting this with the results for trajectories leading either to direct dissociation or to a stable final state of ICI. (c) Kinetic Energy Distribution of the Dissociation Fragments. Figure 2a shows the histogrammed kinetic energy distributions of the C1 and the I dissociation products for IC1 impact on MgO at 4.5 eV collision energy. Figure 2b shows the energy distributions of the fragments for a collision at 11.0 eV. A striking feature of the results is that at the lower collision energy the C1 atom emerges as the more energetic product, while at the higher energy I is by far the more energetic fragment. In both cases the energy separation between the peaks of the I and the C1 energy distributions is quite a large fraction of the total collision energy: In the collision at 4.5 eV incidence energy, the most probable energy of a CI fragment is by about 2.4 eV greater than the most probable energy of an I fragment. At 11.O eV impact energy, the most probable energy of an I atom is about 8.0 eV, that of a C1 atom around 1.0 eV. To interpret the structure of the fragment energy distributions, and especially the great qualitative difference between parts a and b of Figure 2, it is instructive to recall the analysis given in previous
e:))
BaEi6 and Gerber
..p
40
204
L
r’ j
2
0
t., 0
’
: &.’
3
4
i I
2
I
4
6
0
Ib
Fragment energy ( e V )
Figure 2. Energy distribution of dissociation fragments in IC1 collisions with an MgO surface. The distribution is given in terms of the histo-
grammed number of trajectories corresponding to the final fragment energies: (a) for 4.5 eV collision energy; (b) for 11.O eV collision energy. studies for the kinetic energy distribution of I fragments in I, dissociation on Mg0.22923+25 The distribution obtained from the classical trajectory simulations in this case shows that the difference between the incidence energy and the binding energy is unequally distributed between the two fragments: The energy distribution shows two maxima corresponding to the formation of a fast and a slow product atom in each typical collision. Examination of the computed trajectories,, yielded the following interpretation: Collisions leading to dissociation involve molecular orientations that are far from being parallel to the surface. One atom then strikes the surface while the second atom is still outside the range of the strong repulsive interaction with the surface. As the first atom is arrested by the wall the second I atom keeps moving toward the surface and, inevitably, a “hard” collision between the two atoms takes place, governed by the steeply repulsive part of the interaction between them.,, The dynamics of collision-induced dissociation at surfaces thus inherently involves a double collision mechanism: First one of the atoms strikes the surface, then the second atom keeps moving and collides with thefirst. Only then do the fragments scatter apart. It turns out that in the hard collision between the two atoms, the second atom transfers energy to the first one by compressing it harder against the walls. Therefore, the atom that had struck the surfacefirst always emerges as the more energetic one.,, It turns out that the same mechanism holds also in the case of heteronuclear molecules. Consider first the results of Figure 2a, which are for collisions at 4.5 eV. By the discussion of subsection a above, the collisions that lead to dissociation at the (relatively low) energy are such that the lighter atom strikes the surface first. By the above “double collision” mechanism the C1 will then gain energy from the I atom as the latter ”collides” with the former and compresses it toward the surface potential wall. Indeed the C1 is seen to be the more energetic product in Figure 2a. The results of Figure 2b are for the high collision energy of 1 1.O eV. Both “I-first” and “CI-first” impacts can contribute to the dissociation in this case, as noted in subsection a. However, it turns out that the collisions in which the I hits the surface dominate the energy distribution (although also “Cl-first” collisions contribute to dissociation), and I thus emerges as the more energetic product-see in detail in Figure 2b. To clearly see the origins of the dominance of the I-first collisions collisions in determining the energy distribution of the products, it is useful to consider the results shown in Figure 3. The energy distributions of the fragments produced by I-first collisions and by C1-first collisions are shown separately in parts and and b of Figure 3, respectively. It is clearly seen that the atom which strikes first emerges in both cases as the more energetic product. However in the C1-first case the difference between the energy distributions of the I and the CI is not very large, while the I-first collisions gives dramatically different final energy distributions for the two atoms, I emerging
Dissociation Dynamics of Mass-Asymmetric Molecules 801
"I -first"
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 2921
( a) collisions
V
.-01
z
( b)
+
"CI- first" collisions i90'5 Bi 5 180")
z
0
100,
6
I i., I
0
Figure 3. Energy distribution of dissociation fragments in IC1 collisions with an MgO surface, for I first and C1 first impacts separately. The results are for incidence energy of 11.0 eV. Bi denotes the molecular orientation angle with regard to the surface at the instant of impact. For Oo IBi I 90' the I atom strikes the surface; for 90° IBi I 180' CI is the tom that hits.
4
j \/CI
0
Fragment energy (ev)
2
rI
c
CI
-0
80
8
IO
Fragment energy ( e V ) Figure 4. Fragment energy distributions in IBr impact on MgO. The results are for collision energies of 11.0 eV. The distributionsare shown as histogrammed numbers of trajectories leading to various values of final fragment energy.
as much faster in all collisions of this type. The behavior seen in Figure 3a,b can be interpreted as follows: Before the collision with the surface, the two atoms bound in the molecule have the same velocity. The energy of the I atom is thus much greater than that of the C1. (At the 11.0-eV collisions, the I carries 8.62 eV, the C1 only 2.38 eV.) In the collisions where the I strikes the surface, the total energy of the atom does not change much during the process, because of the much lighter mass of the C1 which hits the I in the atom-atom encounter that follows the impact on the surface. Hence the sharp energy distribution of Figure 3a. In the collisions where C1 hits first the surface, the energy of this atom is much altered by the subsequent impact of the I on the C1, but the atomatom collision then results in a very broad energy distribution shown in Figure 3b. The much sharper energy distribution of Figure 3a dominates the total result. The total result for the case of Figure 2b is thus that when both types of collision are included, I will be found the more energetic fragment. Finally, in Figure 4 we show the energy distribution of the fragments for IBr impact on MgO at the high collision energy of 11.O eV. Both types of collision, Br-first and I-first, contribute at this energy to dissociation. However, by the above discussion, it is the I-first collision that should dominate the energy distribution, and I should therefore emerge as the more energetic fragment. This is indeed confirmed by the results of Figure 4. ( d ) Angular Distributions of the Dissociation Fragments. Figure 5a shows the histogrammed angular distributions of C1 and I fragments following a 4.5-eV collision of IC1 with MgO. The corresponding distributions for impact at 11.O eV are given in Figure 5b. The lower energy results show a broad distribution for the I fragment but with a maximum at the specular direction (the calculations are for normal incidence). The C1 emerges in appreciably nonspecular directions, the strongest peak being at
15
30
45
60
75
1
90
Scattering angle (deg.) Figure 5. Fragment angular distributions for IC1 impact on MgO: (a) for incidence energy of 4.5 eV; (b) for incidence energy of 11.0 eV. The
distributions are shown as histogrammed numbers of trajectories. about 15O, otherwise the angular spectrum of scattered C1 atoms is more confined than that of the I fragment. At the high collision energy, both the Cl and the I distribution are more.strongly peaked. The CI shows a highly nonspecular intensity peak at 40°, while the maximum of the I distribution has a maximum only slightly shifted from the specular direction. (This small shift is, however, real and not a consequence of insufficient trajectory statistic.) In providing an interpretation for the qualitative features of these results, it is instructive to consider the analysis of earlier calculationzz~23~z5 for the angular distribution of fragments in collision-induced dissociation of I2 on MgO. In this case, the main features of the I atom angular distribution for impact at high energies (7 eV) were a dip in the intensity in the specular direction, and a pronounced nonspecular intensity spike.22 It has been suggested on the basis of the trajectory calculations,2zand supported by analytical results from an impulsive collision approxi m a t i ~ n ?that, ~ at least at high incidence energies, the nonspecular spike is a rainbow. The shape of the angular intensity distribution, including the rainbow peak, was conveniently interpreted in terms of the double-collision picture of the dynamics, already referred to in the previous subsection:22After the first atom hits the surface the second atom undergoes a hard collision with the first. This hard collision between the two atoms before they separate causes both the dissociation rainbow and the specular dip. The first atom is deflected from the specular direction by the collision, its final direction (sensitive only to the interatomic potential and the collision energy) being that of the rainbow. The interatomic collision occurred as the second atom was still moving toward the surface. It is scattered sideways by the encounter, its final angle being strongly dependent on the angle between the 1-1 axis and the surface when the collision occurred, which corresponds to a very broad spectrum of possible final angles. Consider now the results of Figure 5a. As pointed out previously, at the relatively low energy of this case, only C1-first collisions can lead to dissociation. The interatomic collision is then of a CI beginning to emerge from the surface plane with an I atom incoming toward the surface. By the above analysis, the C1 will be deflected by the encounter with the I into an appreciably nonspecular direction. (The angle is higher, the higher the collision energy.) The I is scattered into a wide range of final possible angles depending on the orientation of C1-I at the collision instant with respect to the surface. The large mass asymmetry results, however, in smaller momentum changes for the I atom than for the C1, and gives a strong propensity for specular (normal) scattering of the I. All these considerations are in agreement with Figure 5a. In the case of Figure 5b both C1-first and I-first collisions contribute to dissociation. The propensity of the I fragment to nonspecular scattering is, as before, a consequence of the much larger inertia of this atom. The C1 nonspecular peak is shifted to a much higher angle, since the high collision energy results in larger momentum
2922
J. Phys. Chem. 1986, 90, 2922-2928 80 7
0
15
,
30
45
1
60
I
75
90
Scattering angle (deg.) Figure 6. Fragment angular distribution for IBr impact on MgO. Results are shown for incidence energy of 11 .O eV. The distributions are presented as histogrammed numbers of trajectories.
transfer to the CI in the interatomic collision step. The broad angular background in the CI distribution, not present in Figure 5a, is due to the I-first collisions, which by the previous discussion result in a wide final angle spectrum for the second atom (such collisions do not contribute to dissociation in the low-energy case). The nonspecular spike in Figure 5b, as in 5a, is due to the C1-first collision, and more specifically, to the deflection of the CI by I as the first atom emerges from the surface. An additional support for this physical interpretation comes from the results for IBr in 1 1.O-eV impact on the surface, shown in Figure 6. The much smaller mass asymmetry in this case results in a behavior intermediate between that previously found for 12,22and the above results for ICI. Due to its lighter mass, momentum transfer to Br in the interatomic collision step is higher than to I. The Br nonspecular peak thus occurs at somewhat higher angles. However, the Br is sufficiently near to I in mass to deflect the I considerably in the mutual collisions, and hence both the dip in the specular scattering intensity and the highly nonspecular peak found for this atom in Figure 6, as in the case of 12:2 and which did not arise for the very mass asymmetric ICI.
IV. Concluding Remarks The results reported in this article contribute in two ways to the study and understanding of molecular dissociation induced by impulsive collisions with surfaces. First, the calculations carried out predict several new and quite pronounced effects specific to molecules of high mass asymmetry. These effects should be conveniently observable, and their pronounced structures could be very useful in the experimental characterization of the collision-induced dissociation process. We stress in particular the intermediate plateau effect in the energy dependence of the
dissociation probability, the qualitative difference in the fragment energy distributions at high and at low energy (the lighter atom emerges as more energetic for relatively low energy impacts, while the heavier atom is the more energetic product for high collision energies), the difference between the angular distributions of the light and of the heavy fragments (the light atom peaks at highly nonspecular directions for normal incidence collisions; the heavy atom is mostly specularly scattered). However, in addition to the prediction of new features as a topic for future experimental investigation, the results obtained here also contribute to the consolidation and extension of the proposed physical mechanism for the dissociation dynamics. This physical mechanism, developed previously for mass-symmetric colliders, stressed the following two aspects. First, dissociation occurs mainly via a centrifugal mechanism (more precisely, whether dissociation occurs or not is determined by the rotational torque the molecule acquires upon impact). Second, following the initial impact of the molecule on the surface, the two atoms undergo a hard mutual collision before they separate. This double collision mechanism is most useful for understanding the angular and the velocity distributions of the fragments. Basically, the present study shows that the above mechanistic aspects apply also to heteronuclear colliders. The main refinement necessary in this case is to allow for two pathways for dissociation, initially depending on which of the two atoms strikes the surface first. The slope of the dissociation probability vs. energy in the case of ICl/MgO showed how the two pathways can occur independently, and in a sense be resolved by a simple experiment. The present study neglected energy transfer to the solid. Arguments were given for the supposition that in the specific cases of IC1 and IBr/MgO such a model may be reliable for the dissociation probabilities (even quantitatively), and should give at least qualitatively correct results for the main features of the angular and velocity distributions. However, for other systems the effects of energy transfer to the solid may be very large for all quantities of interest. Calculations for such systems, including the effects of solid vibrations, should be an important subsequent step.
Acknowledgment. We thank Drs. A. Amirav and E. Kolodney for helpful discussions. This research was supported by the US.-Israel Binational Science Foundation (Grant No. 3210). The Fritz Haber Center at the Hebrew University is supported by the Minerva Gesellschaft fur die Forschung, mbH, Munchen, BRD. Registry No. MgO, 1309-48-4; IBr, 7789-33-5; IC1, 7790-99-0.
Ag Atom Agglomeration in Monomeric and Oligomeric Olefinic Matrices. 1 Mark P. Andrewst and Geoffrey A. Ozin* Lash Miller Chemical Laboratories, University of Toronto, Toronto, Ontario, Canada M5S 1Al (Received: October 17, 1985; In Final Form: January 24, 1986) Attention is directed to the interaction of silver atoms (Ag) and low nuclearity silver clusters (Ag,) with mono- and oligoolefinic matrices. The study serves as a prelude to that involving the correspondingliquid-phase reactions including those with polyolefins (part 2). In this paper, model studies of the reactivity of Ag atoms toward ethylene, propylene, and 1-butene revealed an order of thermal stability for the products (assayed by observance of the intense characteristic charge-transfer band around 590 nm) of silver(ethylene), < silver(propylene), < silver(1-butene),. The above order of thermal stability did not carry over to higher molecular weight olefins. Squalene, a C,,H,, triterpene, was selected as a low molecular weight analogue of polyisoprene for use as a hybrid matrix. Although silver atoms, dimers, and higher nuclearity species could be isolated in this matrix, there was no evidence of a product showing a visible charge-transfer band. EPR spectroscopy of this same system showed Ag atoms to be distributed between alkene (pseudocomplex) and alkane sites.
Introduction Silver Atoms and Clusters in Weakly Interacting Supports. Explorations of methane and short-chain alkanes as "weakly Present address: AT&T Bell Laboratories, Murray Hill, NJ.
0022-3654/86/2090-2922$01.50/0
interacting" supports for stabilizing metal atoms and aggregates have been the subject of earlier work from our laboratory.' It (1) Klotzbucher, W.; Mitchell, S . A,; Ozin, G.A. Inorg. G e m . 1977, 16, 3062. See also ref 6 .
0 1986 American Chemical Society
