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<p><font color="white" size="6"><b>Theory of Cluster Dynamics</b></font><font size="5"><br>
</font><font size="6">
</font><font size="5">The Toulouse - Erlangen Collaboration</font></p>
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<a href="intro.html">1. What are clusters? </a>
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<div style="width:220px;float:left;text-align:center;font-weight:900;font-size:12px;">
<a href="dynamics.html"> 2. Why study cluster dynamics?</a>
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<a href="ourdynamics/our_dynamics.html"> 3. How we deal with cluster dynamics </a>
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Why study cluster dynamics ?
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<br>
Cluster dynamics represents a fast developing area of cluster
physics. The field covers various phenomena with impact both
on fundamental cluster research and on potential applications, for
example in cluster engineering. We show in the following a few
emblematic examples of the field. <br>
<br>
Clusters are made of electrons and ions. Both are charged particles
which can then be excited by an electromagnetic field. A favorite and
fashionable tool of investigation of cluster dynamics is thus provided
by lasers. The latter deliver to the system electromagnetic
pulses whose characteristics can be tailored
almost at will both in terms of deposited energy and time profile. Some
experiments are also performed by means of collisions between clusters
and highly charged projectiles, as delivered by heavy-ion sources
and facilities. <br> <br>
In both cases (lasers, ions), electrons and ions
strongly couple to the delivered
electromagnetic field, but at different time scales. Indeed, electrons
are light particles which thus react and evolve at short time scales,
typically the fs (10<sup>-15</sup>s). In turn, the much heavier ions
(several thousand times heavier than electrons) evolve on a much longer time scale of
order 100-1000 fs. Of course these time
scales are not fully independent of each other, through the natural
coupling between electrons and ions, and the actual relation
between these two time scales somewhat depends on the deposited energy.<br>
Let us illustrate the two coupled electron and ion dynamics on a few
examples. <br>
<br>
Metal clusters couple especially well to an electromagnetic
perturbation because their electrons are only moderately bound to the
ionic cores. They thus react strongly, for instance to a
laser excitation. The response, called "optical response" (because the emitted light
is to a large extent visible), is the
fingerprint of this coupling. <br><br>
The optical response
is caused by the collective oscillations of the cluster electrons
following an excitation by the electromagnetic pulse. The electron
cloud, elastically bound to the ionic cores, oscillates around
them, once displaced from its original position, and radiates
visible light. This collective response provides a signature of the
underlying structure of the irradiated cluster. The "color" of
the irradiated cluster, for example, significantly depends on the size
of the cluster. We thus have here an example where electron dynamics
provides a direct means of investigation of
structure properties. The case is illustrated on Figure 1 where the
frequency (the color) of the optical response of mixed gold and silver
clusters (embedded in an inert glass) is plotted as a function of
cluster size. One can see that the cluster color significantly depends
on size. It means that such golden inclusions in a glass (of course of
various sizes) would deliver a variety of colors, as it was already
well-known by ancient artcrafters (see in the cluster <a
href="intro.html">introduction</a> page).<br>
<br>
<table style="width: 100%; text-align: left;" border="0" cellpadding="2"
cellspacing="2">
<tbody>
<tr>
<td style="vertical-align: top;"><img
alt="silver optical response" src="images/opt2.jpg"
style="width: 620px;"></td>
<td style="vertical-align: middle;">Fig.1: Optical response of mixed
gold and silver clusters, embedded in inert glass, as a function of
size (<a href="javascript:lade(1)">details</a>).
</td>
</tr>
</tbody>
</table>
<br>
<br>
The optical response is a rather simple process, involving mostly electrons
(although ions may also interfere, for example when temperatures
are involved). Another interesting case is provided by cluster fission
where ionic motion then plays a key role. When sufficiently charged
(for example after a laser irradiation and escape of several electrons)
a metal cluster may become unstable with respect to fission, exactly as
massive atomic nuclei. It then becomes preferable for the
system to break into two smaller clusters, the fission fragments. In
such processes electrons play a relatively passive role (once the
system is properly charged) and tend to follow the ions during the fission
process. Fission is furthermore characterized by a potential barrier
over which the system has to pass in order to evolve from one
piece to two. This is illustrated in Figure 2 where the
fission barrier of a small metal cluster is shown, together with the different shapes
taken by the system at different deformations (from the smallest: 1
piece, to the largest: 2 pieces). Figure 3 presents an example of
fission dynamics for another cluster.<br>
<br>
<table style="width: 100%; text-align: left;" border="0" cellpadding="2"
cellspacing="2">
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<td style="vertical-align: middle;"><img alt="K12++ fission"
src="images/fission2.jpg" style="width: 420px;"><br>
</td>
<td style="vertical-align: middle;">Fig.2: Potential energy of K<sub>12</sub><sup>++</sup>
as a function of the extension of the cluster (<a
href="javascript:lade(2)">details</a>).<br>
<br>
Fig.3: Movie of the fission of Na<sub>14</sub>, induced by a laser
irradiation (<a href="javascript:lade(3)">details</a>).<br>
<object data="images/film_fission.mpg" type="video/mpeg" width="300" height="300">
<param name="src" value="film_fission.mpg">
<object data="images/film_fission.mpg" type="video/mpeg" width="300" height="300">
<param name="src" value="film_fission.mpg">
<br><i>
Your browser is unable to open the video. You need a suitable MPEG plugin to watch
it inside this window.
</i>
</object>
</td>
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</table>
<br>
<br>
A most interesting situation is attained when both electron and
ion dynamics explicitely couple to produce elaborate dynamical
scenarios. This is illustrated on the third example we want to present
here. We consider the case of embedded silver clusters, the shape of
which can be tailored, as one can see on Figure 2. Metal clusters
possess a specific frequency at which they couple to light (the optical
response frequency seen above). If one shines a cluster with a laser
precisely tuned at that frequency, one will so much excite the
cluster that it will emit several electrons. This is a typical resonant
behavior as is well known in any oscillating system. <!--Think for example to
the case of noise associated to mechanical vibrations in a car or the
search of a TV or a radio channel by tuning reception to the right
frequency of the electromagnetic signal.--> <br> <br>
In this case <!-- the case of irradiated
clusters-->, if several electrons are stripped during the exposure to the
laser, the cluster may become highly charged and will consequently
expand because of the net charge acquired, as in fission. But full
ionic expansion is hindered here by the fact that the cluster is
included in a matrix. The final result is a somewhat expanded cluster.
This expansion can be further analyzed by irradiating again the cluster
and recording its optical response (pump and probe experiment). As seen above the optical response
provides a signature of the cluster size. A variation in the optical
response thus indicates a structure modification. This is exactly what
one can see on Figure 4. The peak is at the same time broadened and
shifted to a higher wavelength. Moreover the optical response depends
on the laser polarization, reflecting a non-spherical shape of the
cluster. The laser and its preferred coupling to the cluster has thus
allowed to tailor the system shape. This allows to envision
potential applications in laser assisted tailoring of materials at the
nanometer scale. <br>
&nbsp;<br>
<table style="width: 100%; text-align: left;" border="0" cellpadding="1"
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<td style="vertical-align: middle;" width="100"><img alt="Ag burning"
src="images/burning2.jpg" width="600" ><br>
</td>
<td style="vertical-align: middle;" width="100">Fig.4: Optical response of
silver clusters embedded in an inert glass (<a href="javascript:lade(4)">details</a>).<br>
</td>
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