Multifragmentation of molecules and clusters
( ) U. WERNER( 1 ), V. N. KONDRATYEV( 2 )( )and H. O. LUTZ( 1 ) ( 1) Fakult¨at f¨ur Physik, Universit¨at Bielefeld - D-33615 Bielefeld, Germany (
2
) Advanced Science Research Center, JAERI - Tokai, Naka, Ibaraki 319-11, Japan
(ricevuto il 21 Luglio 1997; approvato il 3 Novembre 1997)
Summary. — The multiple ionization and fragmentation of small polyatomic molecules and clusters, e.g. H2O, CH4, and C60by fast H
+
, He+
, and Oq+
ions were studied utilizing a position- and time-sensitive multiparticle detector which allows the coinci-dent measurement of the momenta of correlated fragments. Thereby, a kinematically complete image of the molecular break-up can be derived for each individual event. Of special interest are the “Coulomb explosion” processes, like H2O
!H + +H + +O q+ , where the measured dissociation energies and angular correlations show significant deviations from the pure Coulomb explosion model. For larger molecules and clusters, new phenomena may be expected. For example, using a classical molecular dynamics simulation, we have studied the break-up of hot Arn(
n100) clusters. For initial
tem-peratures around 500 K various analytical tools consistently indicate critical behaviour in the expansion phase.
PACS 34.50.Gb – Electronic excitation and ionization of molecules. PACS 36.40.Qv – Stability and fragmentation of clusters.
PACS 01.30.Cc – Conference proceedings.
1. – Introduction
The ion impact-induced multi-fragmentation of molecules and clusters is of fundamen-tal importance in various areas of science. In contrast to studies of the molecular break-up by impact of electrons or photons it has yet received comparatively little attention. In particular, experiments in which all fragment ions emitted after a particular collision are detected in coincidence, can not only provide valuable information about the charge state and potential energy surfaces of the intermediate multiply charged molecular ion, but also shed light on the excitation and fragmentation dynamics. Under certain con-ditions even information about the geometric structure of the fragmenting system may
(
)Paper presented at the 174. WE-Heraeus-Seminar “New Ideas on Clustering in Nuclear and
Atomic Physics”, Rauischholzhausen (Germany), 9-13 June 1997.
(
)On leave from: Institute for Nuclear Research, 47, Pr.Nauki, Kiev, 252028 Ukraine.
+U
CEM
+ E
e
(x,y,t)-Detector
Fig. 1. – Geometry of the fragmentation experiment. The point, shown by+, is the locus of the
Coulomb fragmentation. Projections of correlated fragment-ion paths are indicated.
be derived [1]. However, most work so far has concentrated on the observation of in-dividual reaction products without further attention to the correlated behaviour of the remaining fragments (cf., e.g., [2] and references therein). Exceptions can be found in dissociation studies of some diatomic molecules where the correlation of both fragments has been studied in detail (e.g., [3-5]) and in the Coulomb explosion imaging (CEI) of high energetic molecular ions (e.g., [1]) where all fragments from a particular explosion are detected in coincidence. In the work to be reported here, we use a similar approach to establish coincidences between low-energy fragments of a neutral molecule. A time- and position-sensitive multi-particle detector is used to establish coincidences between low-energy fragments of a neutral molecule. In the special case where all fragments from a particular molecular break-up are detected, the measured momentum vectors allow a kinematically complete analysis of the dissociation process. For larger aggregates (e.g., C60) such kinematically complete studies are not possible; however, in such cases our
de-tection system allows to establish correlations between different fragment sizes. 2. – Experimental set-up
Figure 1 shows the principle of the experiment for the Coulomb explosion of H2O.
Collimated beams of fast H+
, He+
, and highly charged O
q
+projectiles interact with a molecular gas target. The slow ions and electrons generated in the collision process are separated by a homogeneous electric field of 100–200 V/cm. Electrons are detected in a channeltron at one side of the interaction region; positive ions are accelerated towards the time- and position-sensitive multiparticle detector [6, 7] at the other side. After passing a field-free time-of-flight region the ions are post-accelerated to a few keV to increase the detection efficiency. For each positive fragment the position(
x
i
;y
i
)on the detector andthe time-of-flight
t
i
relative to the start electron are recorded. As a consequence of its crossed-wire structure the detector is capable to resolve particles which arrive “at the same time” on different wires. This “zero dead-time” feature is particularly useful for the study of the fragmentation of more complex molecules like CH4 or even C60, whereseveral correlated fragments with equal masses occur.
In the present configuration the experimental set-up is sensitive to all reaction chan-nels resulting in at least one electron and one or more positive ions. Thus relative
cross-0 20 40 60 80
Kinetic energy release [eV]
0.0 0.5 1.0
Intensity
2 A1 2 A12B22B14A22A22A22B12B2 CEFig. 2. – Total kinetic energy distribution of coincident H+
-H+
-O+
fragments from collisions of
H2Owith 250 keV He +
(—) and 92.4 keV O6+
(:::) [8]. The dashed curve (- - -) is the result of an ab
initio calculation taking into account the indicated molecular states of (H2O) 3+
which are labeled by their symmetries; the prediction of a point charge Coulomb explosion model (CE) is shown as — –.
sections for the production of selected ions (as e.g. CH+
n
or H+in collisions with CH4)
and special processes (e.g. CH 4 ! CH + 2 +2H +
) can be obtained. Furthermore, if all fragments of a particular break-up are detected a kinematically complete study of the molecular fragmentation is possible and information about the dynamics and the molecu-lar structure can be derived. In the following we will concentrate mainly on those reaction channels which are complete in this sense.
3. – Coulomb fragmentation of H2O and CH4
Among the numerous reaction channels occurring in ion-water collision processes, we will concentrate on complete fragmentations of the type
X
p
+ +H 2 O!H 2 O (q
+2)+ +X (p
,m
)+ +(q
+2,m
)e , x !H + +H + +Oq
+ whereq
+2,m
1.Experimentally these reactions are established as fourfold coincidences between an electron and three positive fragment ions. In collisions with 50–350 keV H+
and He+
we observed the reaction channelsH
+ + H + + O + andH + + H + + O 2+ [9]; in collisions with O6+ and O7+
even reactions with
q
=5occurred [8]. If the time-of-flight and the position onthe detector are recorded for each fragment from a particular process, the conditions for a kinematically complete experiment are fulfilled and the fragmentation dynamics may be analyzed in terms of three independent parameters which are derived from the measured velocity vectors. Besides the total kinetic energy of all fragments (kinetic energy release) we choose the angle
v
between the two Oq
+-H+
relative velocitiesv
OH, as well as the
angle
between the H+
-H+
relative velocityv
HHand the velocity of the O
q
+-ionv O[9].
0 10 20 30
Kinetic energy release [eV]
0 1000 2000
Intensity
CH2+ H2+ CH3+ H+ 0 10 20 30 40 50 0 10 20 30 CH+ H2+ H+ CH2+ H+ H+Fig. 3. – Total kinetic energy distribution of two and three (inset) coincident fragment ions from collisions of 742 keV O7+
on CH4.
Among these parameters the angle
gives a first insight into the fragmentation dy-namics: it may be used as an indicator whether the molecular bonds break simultaneously or in a stepwise fashion [10]. A break-up of both OH-bonds in a time short compared to the rotation and vibration periods of the system leads to a strong angular correlation between the corresponding velocities which shows up as a narrow peak in thecos
-distribution. In
case of a two-step process the ‘intact’ (OH)(
q
+1)+subsystem may rotate around its cen-ter of mass and the correlation would be lost resulting in an uniformcos
distribution.
In ion-water collisions studied so far the measuredcos
-spectra are compatible with the
assumption of a practically simultaneous bond-breaking in theH 2 O! H + +H + +O q+ fragmentation [9, 8].
A simultaneous break-up into positive fragment ions suggests the application of the simple Coulomb explosion (CE) model where the dynamics is governed by the strong mu-tual repulsion of the generated positive ions, and the kinetic energies and emission angles may be computed by assuming Coulomb forces acting between point charges as a first ap-proximation. In this picture (at least for the short collision times under consideration) the result of the calculation is independent of the details of the ionization process. Figure 2 shows the result of a simulation based on this model in comparison to the measured ki-netic energy release in collisions of 250 keV He+
and 92.4 keV O6+
with H2O. In contrast
to the Coulomb explosion of H2and D2which is well described by the CE model [5, 6, 11],
the agreement is comparatively poor in the case of H2O. The model overestimates the
500 1500 2500 3500 4500 5500
TOF [ns]
0 2000 4000 6000 8000 600keV Ar3+ 0 2000 4000 6000 8000 400keV Ar2+ 0 2000 4000 6000 8000Intensity
200keV Ar+ 0 2000 4000 6000 8000 200keV He+ 0 2000 4000 6000 8000 200keV H 2 + 0 2000 4000 6000 8000 10000 C60+ C60 2+ C603+ C604+ C605+ H20 + N2 + C583+ C56 3+ C+ C3 + C5 + C7+ C11 + C2 + C4 + C6+ C 8 + C+ C2+ C 3 + C4 + 200keV H+Fig. 4. – Time-of-flight (TOF) spectra of fragment ions produced in collisions of 200 keV
H + ;H + 2 ;He + and 200 keVqAr q+ ions with C60.
ions as given by the H2O vibrational ground state is smaller than that of the experimental
spectra. Furthermore, the shape of the energy spectrum shows a distinct dependence on the projectile type which is inconsistent with a point charge CE model. Whereas in case of H2 and D2only one potential curve describes the final
H +
+H +
products, there are in general many states of(H
2 O)
3+
which finally result inH + +H + +O + fragments with different characteristic energies.
To account for the most dominant reaction channels we used the MOLPRO code [12,13] for an ab initio multi-configuration self-consistent field computation (MCSCF) of the nine lowest molecular states of the intermediate(H
2 O)
(
q
+2)+ions. For each of the obtained potential surfaces the resulting total kinetic energy and angular distributions were cal-culated by Monte Carlo techniques assuming a Franck-Condon transition from the H2O
ground state to the particular dissociating(H 2
O) (
q
+2)+state. The position of the max-imum of each distribution is marked in fig. 2. Note that most of these states result in energies which are lower than the energy predicted by the CE model. A major prob-lem for a quantitative comparison with the experimental data are the unknown transition strengths for the individual states. Since a multi-parameter fit to the data gave ambiguous
T = 2in t = .10 t = 2.41 t = 5.83 t =17.33 T = 4in t = .10 t = 2.41 t = 5.83 t =17.33 T = 7in t = .10 t = 1.44 t = 4.86 t = 9.54 Fig. 5. – Time evolution of hot Ar300clusters at three different initial temperatures
Tin(in units of
119 K).
results we assumed a transition strength proportional to1
=E
2i
(withE
i
the excitation en-ergy of the corresponding intermediate(H2 O)
3+
state), a scaling behaviour which is well known, e.g., in inner shell ionization. Figure 2 shows the weighted sum of the nine energy distributions convoluted with the response function of the detector. A comparison of the measured energy spectra to the MCSCF prediction shows reasonable agreement. The best agreement is achieved in collisions with highly charged ions: according to the clas-sical over-barrier model excited states are expected to be less important in such “gentle” collisions which is in agreement with the experimental finding.
Fig. 6. – The inclusive reduced variance 2 =M 2 M 0 =M 2
1 as a function of the initial temperature Tin(=119K)for three cluster sizes:n=100(solid curve),n=300(short dashed),n=500(long
dashed).Mkis thek-th moment of the fragment mass distribution.
Even more complicated is the situation for CH4. In collisions with 742 keV O 7+
com-plete Coulomb fragmentations in two (CH
+ 3 +H + andCH + 2 +H + 2 ), three (CH + 2 +2H + andCH + +H + +H + 2 ), and five (C
q
+ +4H
+) fragments were observed. Whereas the CE model allows at least a qualitative explanation of the measured kinetic energies for the processCH 4 !C 2+ +4H +
, it has conceptual problems to explain the fragmentation into two or three fragments (fig. 3). Therefore, the assumption of point charges is unsuitable for an understanding of the occurrence of channels likeCH
4 !CH + 2 +H + 2 . Furthermore, there are hints that stepwise fragmentation processes may play a role in some reaction channels. Quantum chemical studies of these problems are at a very early stage.
4. – Fragmentation of larger aggregates
Clearly, a kinematically complete study of multi-fragmentation of much larger aggre-gates is not possible; too many fragments had to be detected, with correspondingly low de-tection efficiency for the complete ensemble. Nevertheless, interesting information can be gleaned even in such complex situations. For example, we have investigated the Coulomb fragmentation of C60 under impact of various energetic ions. A simple mass spectrum
is displayed in fig. 4, showing dominant contributions of small fragments to the charged fragment spectrum. An inspection of the correlations reveals that in case of Ar2+
impact the parent C60cluster is apparently smashed into many small pieces (although the energy
loss is mainly electronic [14]), while for H+
and He+
impact correlated small fragments are considerably less abundant. This indicates that electron-phonon coupling efficiently transfers the deposited electronic energy into the fragmentation channels.
Interestingly, the mass spectrum of fig. 4 indicates that in collisions with Ar
q
+the small and medium sized fragments follow a power law distribution,
N
/A
,
with
ranging up to 1.9 depending on the impacting ion and its energy. This behaviour suggests to search for critical behaviour in the dynamical phase of cluster fragmentation. Choosing hot Ar
n
at various initial temperatures as parent clusters, we have studied such processes in more detail [15, 16] using a molecular dynamics simulation. Various analytical tools, as the av-erage fragment mass distribution, Campi and intermittency analysis of the correlation and fluctuation properties, consistently indicate critical behaviour during the expansion process. As an example, fig. 5 shows the time evolution of Ar300clusters at three
differ-ent initial temperatures (in units of 119 K). At low
T
in, the cluster dissipates its energyby single atom evaporation; at high
T
in, strong fragmentation “explodes” the cluster andresults in mainly small fragments. At a temperature around
T
in=4, the cluster
under-goes critical evolution characterized by large fluctuations; the fragment mass distribution follows a power law with an exponent
of about2
:
2. This indication of critical behaviour iscorroborated by the Campi scatter plot, the reduced variance
2and the scaled factorial
moments. For example, the inclusive reduced variance
2(fig. 6) displays a distinct peak
at
T
i
3:
5; the maximum is the more pronounced, the larger the cluster (i.e., the smallerthe statistical fluctuations).
The authors wish to thank Prof. R. MORGENSTERNand his group for their support during the measurements with the O
q
+-ions at the ECR ion-source at the KVI in Gronin-gen as well as for many stimulating discussions. This work was supported by the Deutsche Forschungsgemeinschaft (DFG). One of us (VNK) gratefully acknowledges the financial support from the Alexander von Humboldt-Stiftung.
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