Ions colliding with molecules and
molecular clusters: fragmentation
and growth processes
Tao Chen
Abstract
In this work we will discuss fragmentation and molecular growth processes in
collisions of Polycyclic Aromatic Hydrocarbon (PAH) molecules, fullerenes,
or their clusters with atoms or atomic ions. Simple collision models as well
as molecular structure calculations are used to aid the interpretations of the
present and other experimental results. Fragmentation features at center-ofmass collision energies around 10 keV are dominated by interactions between
the fast ion/atom and the electron cloud in the molecules/clusters (electronic
stopping processes). This electronic excitation energy is rapidly distributed on
the vibrational degrees of freedom of the molecule or of the molecules in a
cluster and may result in fragmentation. Here, the fragmentation is statistical
and favors the lowest-energy dissociation channels which are losses of intact
molecules from clusters, H- and C2 H2 -losses from isolated PAHs, and C2 -loss
from fullerene monomers. We will also discuss the possibility of formation of
molecular H2 direct from native PAHs which reach high enough energies when
interacting with ions, electrons, or photons.
For the experiments at lower center of mass collision energies (∼ 100 eV)
a single atom may be knocked out in close atom-atom interaction. Such nonstatistical fragmentation are due to nuclear stopping processes and gives highly
reactive fragments which may form covalent bonds with other molecules in a
cluster on very short time scales (picoseconds). This process may be important
when considering the formation of new species. For collision between 12 keV
Ar2+ and clusters of pyrene (C16 H10 ) molecules, new molecules, e.g. C17 H+
10 ,
+
+
C30 H18 , C31 H19 , etc are detected. We also observe molecular fusion processes
for He and Ar ions colliding with clusters of C60 molecules. These and related
molecular fusion processes may play a key role for understanding molecular
growth processes under certain astrophysical conditions.
c
Tao
Chen, Stockholm University 2015
ISBN 978-91-7649-063-1
Printer: Holmbergs, Malmö 2015
Distributor: Department of Physics, Stockholm University
to Xiaoyu
List of Papers
The following papers, referred to in the text by their Roman numerals, are
included in this thesis.
PAPER I: Formations of Dumbbell C118 and C119 inside Clusters of C60
Molecules by Collision with alpha Particles
H. Zettergren, P. Rousseau, Y. Wang, F. Seitz, T. Chen, M.
Gatchell, J. D. Alexander, M. H. Stockett, J. Rangama, J. Y.
Chesnel, M. Capron, J. C. Poully, A. Domaracka, A. Méry, S.
Maclot, H. T. Schmidt, L. Adoui, M. Alcamí, A. G. G. M. Tielens, F. Martín, B. A. Huber, and H. Cederquist PHYSICAL REVIEW LETTERS, 110, 185501 (2013).
DOI: 10.1103/PhysRevLett.110.185501
PAPER II: Ions colliding with clusters of fullerenes-Decay pathways and
covalent bond formations
F. Seitz, H. Zettergren, P. Rousseau, Y. Wang, T. Chen, M.
Gatchell, J. D. Alexander, M. H. Stockett, J. Rangama, J. Y.
Chesnel, M. Capron, J. C. Poully, A. Domaracka, A. Méry, S.
Maclot, H. T. Schmidt, L. Adoui, M. Alcamí, A. G. G. M. Tielens, F. Martín, B. A. Huber, and H. Cederquist THE JOURNAL
OF CHEMICAL PHYSICS, 139, 034309 (2013).
DOI: 10.1063/1.4812790
PAPER III: Non-statistical fragmentation of PAHs and fullerenes in collisions with atoms
M. Gatchell, M. H. Stockett, Patrick Rousseau, T. Chen, K Kulyk, H. T. Schmidt, J. Y. Chesnel, A. Domaracka, A. Méry, S.
Maclot, L. Adoui, K. Støchkel, P. Hvelplund, Y. Wang, M. Alcamí, B. A. Huber, F. Martín, H. Zettergren, H. Cederquist INTERNATIONAL JOURNAL OF MASS SPECTROMETRY, 365366, 260, (2014).
DOI: 10.1016/j.ijms.2013.12.013
PAPER IV: Non-statistical fragmentation of large molecules
M. H. Stockett, H. Zettergren, L. Adoui, J. D. Alexander, U.
Bērziņš, T. Chen, M. Gatchell, N. Haag, B. A. Huber, P. Hvelplund,
A. Johansson, H. A. B. Johansson, K. Kulyk, S. Rosén, P. Rousseau,
K. Støchkel, H. T. Schmidt and H. Cederquist PHYSICAL REVIEW A, 89, 032701 (2014).
DOI: 10.1103/PhysRevA.89.032701
PAPER V: Absolute fragmentation cross sections in atom-molecule collisions: Scaling law for non-statistical fragmentation of polycyclic aromatic hydrocarbon molecules
T. Chen, M. Gatchell, M. H. Stockett, J. D. Alexander, Y. Zhang,
P. Rousseau, A. Domaracka, S.Maclot, R. Delaunay, L. Adoui,
B. A. Huber, T. Schlathölter, H. T. Schmidt, H. Cederquist and
H. Zettergren JOURNAL OF CHEMICAL PHYSICS, 140, 224306
(2014).
DOI: 10.1063/1.4881603
PAPER VI: Formation of H2 from internally heated Polycyclic Aromatic
Hydrocarbons: Excitation energy dependence
T. Chen, M. Gatchell, M. H. Stockett, R. Delaunay, A. Domaracka, P. Rousseau, L. Adoui, B. A. Huber, H. T. Schmidt,
H. Cederquist and H. Zettergren JOURNAL OF CHEMICAL
PHYSICS, 142, 144305 (2015).
DOI: 10.1063/1.4917021
PAPER VII: Molecular growth inside polycyclic aromatic hydrocarbon
clusters induced by ion collisions
R. Delaunay, M. Gatchell, P. Rousseau, A. Domaracka, S.Maclot,
Y. Wang, M. H. Stockett, T. Chen, L. Adoui, M. Alcamí, F.
Martín, H. Zettergren, H. Cederquist, and B. A. Huber JOURNAL OF PHYSICAL CHEMISTRY LETTERS, 6, 1536 (2015).
DOI: 10.1021/acs.jpclett.5b00405
Reprints were made with permission from the publishers.
Articles not included in this thesis are listed in Appendix.
Author’s contribution
For Paper I-IV, I have modeled the electronic and nuclear stopping processes
following collisions between atoms/ions and PAH/fullerene molecules/clusters.
I have also calculated the molecular structures and electron density distributions by using quantum chemical methods.
For Paper V, I have calculated the electronic and nuclear stopping energies
for various collision systems. I have derived a simple scaling law for estimating non-statistical fragmentation cross sections. I have also analyzed the
experimental data and produced the model data. I drafted the publication and
made all figures.
For Paper VI, I have calculated the dissociation energies for single Hemission, sequential H-emissions (H+H) and H2 -emission from several PAHs,
and transition barriers for H2 -emission from PAHs. I drafted the publication
and made all the figures.
For Paper VII, I have participated in the experimental study of the molecular growth process and contributed with calculations of energy transfers through
electronic stopping processes. I have participated in discussions of the results
and their interpretations.
This thesis is partly based on my licentiate thesis "Statistical and Nonstatistical fragmentation of large molecules in collisions with atoms".
Sammanfattning
I denna avhandling presenteras resultat rörande sönderfall- och tillväxtprocesser efter kollisioner mellan fulleren-molekyler, PAH-molekyler (polycykliska aromatiska kolväten) eller kluster av dessa, och atomer eller atomära
joner. Två olika experimentella uppställningar har använts, en för höga kollisionsenergier (> 10 keV i masscentrumsystemet) och en för låga kollisionsenergier (< 1 keV i masscentrumsystemet). De experimentella resultaten
diskuteras och tolkas med hjälp av en kollisionsmodell, molekylära strukturberäkningar och molekyldynamik-simuleringar.
Vi visar att vid höga kollisionsenergier (flera keV i masscentrumsystemet)
är den dominerande processen för energiöverföring växelverkan med molekylernas elektronmoln (elektronisk excitationer). Den energi som överförs
fördelas sedan statistiskt över alla inre frihetsgrader innan molekylen eller
klustret börjar kylas genom att skicka ut fotoner, elektroner, atomer eller molekyler. De energier som överförs ligger generellt långt över tröskelenergin för
molekylär dissociation vilket leder ett innehållsrikt masspektra med många
toppar. Med strukturberäkningar visar vi att dissociationsenergier för PAHmolekyler har ett svagt beroende på molekylernas storlek, åtminstone för de
vanligt förkommande fragmenteringsprocesserna. Dissociationsenergierna för
att en PAH-molekyl ska avge H eller H2 ligger på cirka 5 eV respektive 4
eV, men reaktionsbarriärer gör att den senare processen i praktiken är mycket
långsammare än den förra. Detta leder till att H2 -emission blir en viktig process först vid höga PAH-temperaturer (> 2200 K). Temperaturer i detta område
är vanliga i våra kollisioner med keV-joner/atomer, men nås inte exempelvis
när PAH-molekyler absorberar enskilda UV fotoner med energier lägre än 13.6
eV (jonisationsenergin för atomärt väte).
Icke-statistiska sönderfallsprocesser är processer i vilka enskilda kolatomer
slås ut från PAH-molekyler eller fullerener i Rutherford-liknande spridningsprocesser. Vi har observerat icke-statistiskt sönderfall i experiment där vi kolliderat PAH-/fulleren-molekyler med atomer vid låga (< 1 keV) kollisionsenergier. Vi har utvecklat enkla samband för att beräkna absoluta tvärsnitt för
icke-statistiskt sönderfall av molekyler.
I kollisioner mellan keV-joner och molekylära kluster spelar de snabba
icke-statistiska sönderfallsprocesserna en nyckelroll i bildandet av nya molekyler.
De fragment som skapas genom icke-statistiskt sönderfall är oftast mer reak-
tiva än de som bildas i statiska sönderfallsprocesser. Detta leder till att de
reaktiva fragment som skapas i kollisionerna kan bilda nya kovalenta bindningar med andra molekyler i klustren. Vi har utfört experiment där vi kolliderat olika atomära joner med kluster av C60 eller pyren (C16 H10 ). I fallet med
fulleren-kluster såg vi att den hantelformade C119 -molekylen bildades. Med
PAH-kluster skapades en rad nya molekyler med formen C16+m Hx , där m =
1-21.
Contents
Abstract
ii
List of Papers
iii
Author’s contribution
v
Sammanfattning
vii
1
Introduction
2
Experimental techniques
7
2.1 Collision induced dissociation experiments with PAH and fullerene
cations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
2.2 Ion-impact induced fragmentation and molecular growth in molecular clusters . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
3
Theoretical tools and models
3.1 Collision model . . . . . . . . .
3.1.1 Nuclear stopping . . . .
3.1.2 Electronic stopping . . .
3.2 Molecular structure calculations
4
5
1
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
13
13
13
17
18
Results & Discussion
4.1 Collisions with isolated PAH or fullerene molecules . . . . . .
4.1.1 Statistical fragmentation . . . . . . . . . . . . . . . .
4.1.2 Competition between statistical and non-statistical fragmentation . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Collisions with clusters of PAH or fullerene molecules . . . .
4.2.1 Molecular growth . . . . . . . . . . . . . . . . . . . .
21
21
21
Concluding remarks
37
Appendix: Additional publications
26
30
31
xxxix
Acknowledgements
References
xliii
xlv
1. Introduction
Polycyclic Aromatic Hydrocarbons (PAHs) contain only carbon and hydrogen
atoms (Cm Hn ). They typically have three or more fused benzene-like rings. An
example of a PAH molecule, pyrene is shown in Figure 1.1a. Pyrene (C16 H10 )
has a planar structure with four benzene-like rings fused together. PAHs are
ubiquitous and abundant on Earth and in Space. On Earth, it has been commonly found in combustion products of organic materials [59]. In space, many
observations suggest that PAHs are present in meteorites [44], in comets [38],
and in the interstellar medium (ISM) as the carriers of the strong infrared emission features from galactic and extragalactic objects [6, 65, 68, 69]. Another
related class of molecules are the fullerenes, which contain only carbon atoms,
and have hollow spherical structures. An example of a fullerene with 60 carbon
atoms (C60 ) is shown in Figure 1.1b. This molecule has been unambiguously
identified in space [10, 62, 79]. A recent study suggests that fullerenes could be
formed from PAHs in space by multistep dehydrogenation and fragmentation
processes [5].
Photons
Atoms
H ~ 5eV
Electrons
~7eV
Molecules
H2, C2H2 ~ 5eV
(a)
Photons
Electrons
~ 7eV
(b)
Molecules
C2 ~ 10eV
Figure 1.1: Internally heated molecules (a. pyrene, b. C60 ) may cool by emitting
photons, electrons, and/or molecules or atoms.
When internally heated, PAHs predominantly fragment by emitting Hatoms or C2 H2 -molecues which correspond to the lowest-energy dissociation
channels. It is much more difficult to remove a single C-atom which is re1
flected in the fact that the corresponding dissociation energy is much higher
than for H- or C2 H2 -loss. Similarly, the fullerenes have C2 -loss as their lowest dissociation channel while the removal of a single C-atom is much more
energetically unfavourable. The fullerenes have been extensively investigated
both experimentally and theoretically - see for examples [13, 31, 35, 72, 78].
Larsen et al performed a pioneering experiment on the fragmentation of C60
anions in 50 keV collisions with rare gas targets. There, they observed two different types of fragmentation processes: weak direct "knock-out" processes of
single C-atoms and strong delayed (statistical) fragmentation process, which
are dominated by C2 emission [35]. However, it is in general hard to distinguish the knock-out and statistical fragmentation processes for large and
complex molecules. Due to the three-dimensional hollow sphere structure, the
signature of a direct knock-out process namely the loss of a single C atom
is often disguised by secondary (statistical) fragmentation process and also
by additional knock-out processes. The latter are more likely for three than
for two-dimensional molecular structures. Attention has therefore be given
to PAH molecules, which have planar, simple and regular structures. A vast
number number of studies [15, 27, 29, 36, 47, 53, 58] have been performed on
excitation of PAHs by absorption of photons [24, 40], by interaction with energetic electrons [25], or atoms [9]. In a pioneering work, Postma et al studied
the fragmentation of the PAH molecule anthracene (C14 H10 ) in collisions with
protons and helium ions at keV energies. They introduced a method to calculate the molecular excitation due to electronic stopping, in which the electron
densities are obtained by means of Density Functional Theory (DFT). In both
their experiments and their model simulations it was found that the fragmentation increased with increasing projectile velocity [53]. Reitsma et al studied
the fragmentation of anthracene due to double ionization by 5 keV protons and
+
found clear experimental evidence for dominance of C3 H+
3 over C2 H2 in this
particular case [58]. However, Johansson et al found that C2 H2 -loss was the
lowest energy dissociation channel for singly charged anthracene molecules
[29]. Mishra et al were interested in the electron emission and electron transfer processes in proton-naphthalene collisions at velocities between 1.41 and
2.68 au. They found that electron capture cross sections decrease rapidly over
the corresponding energy range [47].
The study of PAHs and fullerenes is also a hot topic in astronomy. Recent investigations suggest that molecular hydrogen (H2 ) could be formed from
PAHs, in which the PAHs in some potential schemes may act as catalytic centers [2, 8, 12, 26, 45, 52, 64]. Figure 1.2 shows three possible routes leading to molecular hydrogen formation from a coronene molecule. In the first
case (Fig 1.2a.), a coronene molecule captures a hydrogen atom to form an
aliphatic carbon. This step is exothermic and the barrier for emitting a H2
2
+
+H
+H
PAH+H2
[PAH+H]
PAH
+
+Energy
+H
PAH
PAH
(b)
[PAH-H]+H2
[PAH+H]
+Energy
(a)
+
(c)
[PAH-H2]+H2
Figure 1.2: Three possible routes for the formation of H2 -molecules from PAH
molecules. The examples shown are for coronene C24 H12 . In processes a, and
b, the coronene molecule acts as a catalytic center absorbing one or two hydrogen atoms, respectively. In c, the H2 molecule is formed directly from pristine
coronene molecules (see the text for more details).
3
molecule from the aliphatic carbon is very low [34, 57]. In the second case
(Fig 1.2b.), the coronene with an aliphatic carbon can lead to the formation of
H2 without adding a second H-atom. This however, requires that a substantial
amount of energy is transferred to the system as the corresponding activation
barrier is high. There is another possible route, in which the H2 molecule
could be formed directly from a fully aromatic PAH as shown in Fig 1.2c. It
has been shown experimentally [74], that the last route is an inefficient process
for singly charged PAHs with low internal energy (i.e. close to the dissociation
threshold). In this work, we focus on the latter route and calculate dissociation and transition state energies for H- and H2 -emission from the naphthalene
(C10 H8 ), and the PAHs anthracene (C14 H10 ), pyrene (C16 H10 ) and coronene
(C24 H12 ). This work demonstrate that H- and H2 -formation from PAHs are
two competing process. For high energy collisions (center of mass energy
higher than 10 keV), the internal PAH temperatures typically exceed 2200 K
and H2 molecules may then be efficiently formed (see Paper VII for details).
We have also studied reaction within clusters of molecules. In all cases
these molecules are weakly (< 1 eV) bound to each other through weak (e.g.
van der Waals) forces. Two examples of clusters - pyrene and fullerene clusters
are shown in Figure 1.3. PAH and fullerene clusters have been suggested to be
omnipresent in nature [5, 7, 14, 18, 56, 68]. Many experiments and theoretical
works have dealt with clusters of PAHs and fullerenes [28, 30, 72, 78]. Holm
et al reported the first experimental study of keV ions interacting with clusters
of PAH molecules. They found that anthracene clusters easily fragment in the
collisions just like many other weakly bound clusters [28]. Johansson et al then
investigated the ionization and fragmentation of anthracene and coronene clusters with similar experimental techniques as Holm et al. They found that singly
charged and internally rather cold monomers are dominant products when PAH
clusters fragment due to collisions with keV ions [30]. In this work, we present
experimental evidence for the formation of so called dumbbell fullerene systems (see Paper I), and molecular growth of PAHs inside clusters (see Paper
VII), which are ignited by non-statistical knockout processes. The cluster environment is essential here as it helps to cool the fragments such that they have
time to react with neighbouring molecules in the cluster before they fragment
further.
This work focuses on fragmentation processes of PAHs or fullerenes following collision with energetic ions or atoms. In general there are two different fragmentation processes (see Paper IV for details): statistical fragmentation refer to processes in which there is time for a given excitation energy to
be distributed over all the internal degrees of freedom in the molecule before
fragmentation. Such processes favour the lowest-energy dissociation channels. The emissions of C2 molecules from fullerenes [35] are typical examples
4
(a)
(b)
Figure 1.3: Cluster of pyrene (a) and fullerene (b). The pyrene cluster contains
four pyrene molecule, and the fullerene cluster includes five C60 molecules. The
structures were optimized using the semi-empirical PM6 method as implemented
in Gaussian09 [23].
of statistical fragmentation processes. Examples of non-statistical fragmentation processes are processes in which atoms are knocked-out directly from
the molecule in head-on collision between atomic ions or atoms and individual atoms in the molecules. Such knockout processes are fast (femtosecond
timescales) and there is no time for the excitation energy to redistribute itself
over all the degrees of freedom of the molecule before the initial fragmentation step. Micelotta et al simulated the interaction between interstellar PAHs
and plasma shock waves from supernova explosions and concluded that nonstatistical fragmentation is an important destruction mechanism: interstellar
PAHs (number of carbon atom NC = 50) do not survive in shocks with velocities greater than 100 km s−1 and larger PAHs (NC = 200) are destroyed for
shocks with velocities ≥ 125 km s−1 [46]. Similar fragmentation processes
have been unambiguously observed in experiments at center of mass energies
from about 100 eV and up to about 1 keV for interaction between PAHs or
fullerenes and atoms, in which single atoms are lost from the molecules. This
leads to the formation of highly reactive fragments.
Statistical and non-statistical fragmentation processes often compete. After knockout, the molecule may still have high enough internal energy to decay
further in secondary statistical fragmentation steps. In general, the balance between processes in which energy is transferred to the electronic degrees of freedom (electronic stopping processes) and processes in which energy is transferred directly to the vibrational modes (nuclear stopping processes) affects the
balance between statistiscal and non-statistical fragmentation processes. Figure 1.4 shows the ratio between electronic and nuclear stopping as a function
5
of projectile energy for helium atoms colliding with anthracenes in solid phase
[80]. One can see from Figure 1.4 that nuclear stopping is more important for
ion energies lower than ∼ 2 keV, while the electronic stopping becomes more
important at higher energies (> 2 keV). In order to study both fragmentation
processes the present work covers the energy range from roughly 100 eV to
100 keV (gray area in Fig 1.4).
Energy loss (eV/nm)
103
102
Electronic
101
Nuclear
100
10-1 0
10
101
102
103
104
105
Projectile ion energy, eV
106
107
Figure 1.4: The nuclear and electronic stopping energies as functions of projectile ion energy in the case of helium atoms colliding with anthracene in the
solid phase [80]. The gray area indicates the energy range of main interest for
the present work.
The remainder of this thesis is organized as follows: In Chaper 2 the experimental technique is described for studies of PAH or fullerene monomer
cations and different noble gases at center of mass energies from about 100
eV to 1 keV. In the same chapter we describe the experimental technique used
for collision experiments with atomic projectiles with kinetic energies in the
range above 10 keV and neutral PAH or fullerene monomers or their clusters.
The theoretical calculations and the Monte Carlo simulations of electronic and
nuclear stopping processes are discussed in Chapter 3. The results on H2 formation, the simple scaling law for non-statistical fragmentation and molecular
growth processes are discussed in Chapter 4. Finally, concluding remarks and
an outlook are given in Chapter 5.
6
2. Experimental techniques
This section describes two complementary experimental setups for studies of
fragmentation and molecular growth processes in collisions between ion/atoms
and molecules or molecular clusters. The setup at Stockholm University is
utilized for low energy (< 1 keV) Collision Induced Dissociation (CID) experiments of molecular ions, where nuclear stopping is the dominant energy
transfer process in the collisions (see Figure 1.4). The setup in Caen, France,
is utilized for higher energy (> 10 keV) collisions. There, electronic stopping
is more important than nuclear stopping (see Figure 1.4).
2.1
Collision induced dissociation experiments with PAH
and fullerene cations
The experimental setup at Stockholm University is a part of the DESIREE facility [61, 67] and is designed for low energy collisions between molecular
ions/anions and neutral gases (atoms and molecules) and for studies of interactions with laser photons. A schematic of the experimental setup is shown in
Figure 2.1. The molecules under study are dissolved in a solution and brought
into gas phase by means of electrospray ionization [19, 76]. In this technique,
the needle of a syringe carrying the solution is kept at a high voltage (2-3 keV)
to create a strong electric field between the needle and a capillary serving as
a counter electrode. The syringe plunger is then pushed at a controllable rate
such that charged droplets are ejected from the top of the needle [50]. The temperature of the capillary may be adjusted for evaporation of unwanted solvent
molecules [77].
The so formed isolated molecules leave the capillary and enter a radiofrequency ion funnel [32, 33, 63]. The ion funnel focuses the ions into two
sets of octopoles [66] used to accumulate the ions in bunches (not used in the
present work), and to guide the ions to a quadropole mass filter [51].
The quadruploe mass filter is used to mass-to-charge select ions for the
primary projectile beams for the experiments. The mass-selected PAH cations
enter a quadrupole deflector before they leave the high-voltage platform, are
accelerated and enter the experimental beam line which is at ground potential. The accelerated ions are guided to the collision chamber by means of
7
Needle
Ion Funnel
8-pole Guide
Quadrupole
Gas Cell
Deflector
Acceleratio
MCP
Slits
Capillary
8-pole Trap
Mass Filter
Acceleration Lens
Deflectors
Electron Multiplier
Figure 2.1: Schematic of the experimental setup used for collision induced dissociation (CID) type experiments at Stockholm University. The molecular ions
are produced by means of electrospray ionization, collected by an ion funnel,
guided by two octopoles, mass-selected by a quadrople mass filter, and accelerated before entering the collision cell. There they collide with a target gas and
the so formed fragments are analyzed by means of electrostatic deflectors and a
micro-channel plate detector with a resistive anode (see text).
Normalized Rate
1
0.1
C14H10++He
C24H12++He
1
2
4
3
Pressure (mTorr)
5
6
Figure 2.2: Normalized count rates of the primary PAH+ -beams as functions of
gas cell pressure for different PAHs colliding with He at 110 eV center-of-mass
energy. The slope of the fitted lines yield the total fragmentation cross sections.
The pressure is measured by means of a capacitance manometer. Statistical errors
are smaller than the data points.
8
an einzel lens and deflector elements to enter a 4 cm long collision cell. The
absolute pressure of the target gas in the collision cell is measured with a capacitance manometer and the pressure may be adjusted in a controlled manner by a needle valve. The beam intensity for keV-ions entering the collision
cell is typically a few thousands of ions per second. The intact PAH cations
and fragment ions leaving the collision cell are mass-to-charge analyzed by
means of two sets of electrostatic deflectors and focused by means of an einzel
lens. The ions are then detected by a micro-channel plate (MCP) equipped
with a resistive anode for position information. The position information is
stored for each collision event together with the corresponding deflector and
lens settings. This may be used to achieve the necessary resolution in the mass
spectrum without using slits in front of the detector.
The beam attenuation method [71] was used to determine absolute fragmentation cross sections. The ion beam count rate is then measured as a function of the gas pressure in the cell. Figure 2.2 shows such trends for different
PAH cations colliding with He at 110 eV center of mass energies. The slopes
of the fitted lines in the lin-log plots give the corresponding total fragmentation
cross sections.
Liquid N2 < 100 K
He gas at ~ 1 mbar
PAH
Figure 2.3: Schematic of the the cluster aggregation source. An oven is mounted
inside a container filled with He buffer gas at a pressure of about 1 mbar. Liquid
nitrogen is used to cool the He gas to temperatures below 100 K such that weakly
bound clusters may be formed.
2.2
Ion-impact induced fragmentation and molecular growth
in molecular clusters
The experimental setup for high center of mass energy (> 10 keV) collisions is
located at the ARIBE facility in Caen, France [4, 16]. There, keV ion beams
9
MCP
-23 kV
e-
e-
e-
e- e
e-
-13 kV
-15.4 kV
-4 kV
2.145 kV
0V
-4 kV
0V
are produced in an Electron Cyclotron Resonance (ECR) ion source [42, 75]
and guided to interact with a beam of neutral molecules or molecular clusters
inside the extraction region of a linear time-of-flight mass spectrometer.
The neutral targets are produced in electrically heated ovens loaded with
commercially available molecular powders. There are separate ovens for producing neutral monomer and cluster beams. When the monomer oven is heated,
the molecules are evaporated and effuse into the interaction region through the
oven exit hole. The cluster source oven has a similar design as the monomer
oven but it is mounted inside a container filled with helium buffer gas where
the pressure is of the order of millibars (see Figure 2.3). The molecules effuse from the oven and enter the condensation region where the helium gas
is cooled down by liquid nitrogen to temperatures below 100 K. This leads
to formation of weakly bound neutral clusters with a broad (lognormal) size
distribution [28, 30]. The clusters are guided to the interaction region. The
cluster size distribution depends on the oven temperature, increasing the temperature (number density) gives larger clusters. The temperature depends on
the molecular species, e.g. 60 ◦ C and 250 ◦ C is typically set for producing
anthracene and coronene monomers, respectively. Production of clusters often
require higher temperatures.
Target collision
products
Weak magnetic field
Interaction region
~10-6 sec
Figure 2.4: Schematic of the time-of-flight mass spectrometer. A pulsed ion
beam enters the interaction region of the spectrometer. The charged collision
products are extracted and accelerated along the spectrometer axis shortly after
the beam pulse has left the interaction region. The ions hit a metal plate at the
end of the spectrometer. This produces secondary electrons which are guided by
a weak magnetic field towards a MCP detector.
A schematic of the mass spectrometry setup is shown in Figure 2.4. The
ion beam is chopped into ∼ 1µs long pulses before entering the interaction
region with a monomer or a cluster target. After the beam pulse has left the
10
interaction region, the charged collision products (intact and fragment ions) are
extracted by a pulsed homogeneous electric field. The ions are then accelerated
and enter a field free drift region. The acceleration system and the length of the
drift region are designed to let ions with the same mass to charge ratio arrive
at the same time at the end of the drift region regardless where they were
produced in the interaction region. After the drift free region, the ions are
further accelerated to increase the yield of secondary electrons emitted when
they hit the metal plate at the end of the spectrometer. A weak magnetic field is
then used to guide these electrons towards a MCP detector. The time difference
between the start of the extraction pulse and a hit on the MCP detector gives
the ion flight time. The metal plate combined with the weak magnetic field and
the MCP system gives a high detection efficiency, which allows for detection
of several charged fragments per collision event (coinicidence measurements).
11
12
3. Theoretical tools and models
This section describes the theoretical tools and models which have been used
to guide the interpretations of the experimental results. In Section 3.1 we
present a model for energy transfer processes when ions and atoms penetrate the molecular electron clouds and interact with the individual nuclei in
molecules or molecular clusters. In this model, we use a Monte Carlo technique where we calculate such electronic and nuclear stopping processes for
random ion/atom trajectories through or close to the molecules or clusters.
By performing a large set of trajectories we get information about the energy
transfer distributions. The collisional energy transfer is typically statistically
redistributed across all degrees of freedom before the system cool down by
emission of photons, electrons, atoms, or molecules. However, prompt (nonstatistical) atom knockout processes may also be important under certain circumstances (in low energy collisions with isolated molecules or high energy
collisions with clusters).
In Section 3.2 we describe the molecular structure calculations which was
used to investigate how the molecules and clusters respond to energy transfer
processes. These calculations give information about e.g. the lowest dissociation energy pathways and reaction barriers for the intact molecules and the reactivity of fragments from non-statistical fragmentation. They were also used
to produce collision model input parameters (nuclear coordinates and electron
densities).
3.1
Collision model
3.1.1
Nuclear stopping
Nuclear stopping, i.e. when the projectile lose some of its kinetic energy by
scattering on individual nuclei in the molecule, is the dominant energy loss
mechanism for low collision energies (see Figure 1.4). In a classical picture,
the energy lost by projectile atom with mass M1 , atomic number Z1 and a
target atom (M2 , Z2 ), is
Tnuc = Tmax sin2
φ
2
(3.1)
13
where
Tmax =
4M1 M2
E
(M1 + M2 )2
(3.2)
is the maximum energy transfer in head-on collisions and E is kinetic energy
of projectile in laboratory system. The scattering angle in the center of mass
system φ (see Figure 3.1) is related to the impact parameter p by [80]:


Z ∞

φ
pdr
q
sin = cos
 rmin 2

(r)
2
r 1 − VECM
− ( pr )2
(3.3)
where ECM is the center of mass collision energy, rmin is the closest distance
between the projectile and target atom during the collision. This distance of
closest approach can be found by solving the following equation
V (rmin )
p 2
1−
−
=0
ECM
rmin
(3.4)
Figure 3.1: Schematic showing the relation between the impact parameter (p)
and the scattering angle (φ ) in the center of mass (CoM) energy system for the
collision between two atoms (M1 and M2 ).
14
where V(r) is the interaction potential. In the present work, we use a
Coulomb potential multiplied by different types of screening functions, f(x),
V (r) =
Z1 Z2
f (x)
r
(3.5)
Lindhard [39] introduced screening function of the type
ks 1−s
x
(3.6)
s
where s is an integer and ks a constant determined by s. The variable x is the
ratio between the radial distance and the screening length (aLindhard )
q
2/3
2/3
r Z1 + Z2
r
=
(3.7)
x=
aLindhard
0.8853a0
fLindhard (x) =
where a0 is the Bohr radius. Lindhard applied an approximate method to evaluate φ (Eq. 3.3) and arrived at the following expression for s=2 and k2 =0.831
[35, 39]
π 2
p
φ
(3.8)
sin = 2 8 π0 2
2
p + 8 p0
The corresponding analytical solution is (see Paper V)
sin
φ
πp
= cos q
2
2 p2 + p2
(3.9)
0.831Z1 Z2 aLindhard
2ECM
(3.10)
0
where
p20 =
The present analytical solution (Eq. 3.9) and the approximate solution
(Eq. 3.8) give results in close agreement with each other. This is illustrated in
the left panel of Figure 3.2, which shows a comparison between the two expressions for 100 eV collisions (ECM =100 eV) between hydrogen (Z1 =1) and
carbon (Z2 =6). In the right panel of Fig. 3.2, we show a comparison between
the analytical expression for the Lindhard potential (Eq. 3.9) and the corresponding numerical results for the so called ZBL (Ziegler-Biersack-Littmark)
potential [80]. The latter is commonly used for ions or atoms interacting with
solids. The ZBL screening function is
fZBL (x) = 0.1818e−3.2x + 0.5099e−0.9423x +
0.2802e−0.4029x + 0.02817e−0.2016x
(3.11)
15
0.6
0.4
0.2
0.0
0
ZBL
Analytical
Lindhard
Analytical
ZBL/Analytical
sin(φ/2)
0.8
Lindhard/Analytical
1.0
1.000
0.996
0.992
0
1
2
4
3
5
1
4
2
3
Impact Parameter, p (a0 )
5
0
1.0
0.8
0.6
0.4
0.2
0
1
2
3
1
4
2
3
Impact parameter, p(a0 )
4
5
5
Figure 3.2: Comparison between Lindhard approximate expression and the
present analytical solution for the scattering angle φ as a function of impact
parameter (left), and comparison between scattering angles obtained with the
Lindhard (analytical solution) and the ZBL (numerical evaluation) potentials as
a function of impact parameter for collision between hydrogen and carbon (ECM
= 100 eV) (right). The insets show the ratios between the two curves.
where
x=
r
aZBL
=
r(Z10.23 + Z20.23 )
0.8853a0
(3.12)
and aZBL is the ZBL screening length. We find that the ZBL and Lindhard
potentials give rather similar results for light atoms (e.g. H or He) interacting
with hydrogen or carbon atoms in the 100 eV collisions energy range (see the
right panel of Figure 3.2). This allows us to use the analytical solution (Eq.
3.9) for the relation beween the impact parameter (p) and the scattering angle
(φ ) to get an analytical formula for single atom knockout out cross section per
atom in the molecule
σ = π p2 =
4π p20
p
π 2 arccos−2 ( Eth /Tmax ) − 4
(3.13)
where Eth is the threshold energy for knockout. Here, we use the results from
molecular dynamics simulations which show that the threshold energies for
knocking out a carbon or a hydrogen atom from a PAH molecule are close to
27 eV and 9 eV, respectively (see Paper V for details). In Figure 3.3 we show
the calculated cross sections for exceeding the thresholds for carbon knockout
H =9eV) in
(ECth =27 eV) in H+C, He+C collisions and hydrogen knockout (Eth
H+H and He+H collisions.
16
EthC=27 eV
3.0
H+C
He + C
Cross section, a02
2.5
2.0
1.5
EthH =9 eV
1.2
0.8
0.4
0.0
200
600
H+H
He + H
1000
1.0
0.5
0.0
2000 4000 6000 8000 10000
Kinetic energy, eV
2000 4000 6000 8000 10000
Kinetic energy, eV
Figure 3.3: Calculated absolute cross sections for H + C, He + C, H + H and He
+ H scattering above the threshold energy for knocking out a carbon (left panel)
or a hydrogen atom (right panel) from a PAH molecule.
3.1.2
Electronic stopping
The electronic excitation energies due to interactions with the PAH molecular
electron clouds are calculated by treating the valence electrons (all electrons
except the C 1s electrons) as a free electron gas. The energy lost by ion/atoms
traversing an electron gas depends on the electron density distribution along
the ion trajectories [21]. Here we assume that the electronic energy loss Te
is proportional to projectile velocity [70] and the electronic stopping power is
then given by
dTe
S=
= γ(rs )v
(3.14)
dR
where γ(rs ) is the so called friction coefficient, which is a function of the oneelectron radius rs
13
3
rs =
(3.15)
4πn0
where n0 is the valence electron density. The electron density is inhomogeneously distributed within the molecules and is calculated by means of molecular structure calculations (see Section 3.2). The friction coefficient is related
to the scattering phase shifts (δl ) through
γ(rs ) =
3 ∞
∑ (l + 1)sin2 (δl − δl+1 )
kF rs3 l=0
(3.16)
17
where kF is the magnitude of the Fermi wave vector. The friction coefficients
for various atoms and a few rs -values have been calculated by Puska and Nieminen [55]. We fit exponential functions to their results (see the examples in
Figure 3.4) to calculate the friction coefficients for any rs -value.
In the simulations, we calculate the electronic stopping power (Eq. 3.15)
for each point along random atom trajectories through the PAH molecular electron clouds, The stopping energy is then given by the stopping power multiplied by the step size. Simultaneously, we calculate the nuclear stopping energy as described in the preceding section. For each individual atom trajectory,
the sum of these two contributions gives the model total stopping energy.
γ(rs )
10
10
0
-1
10
1
10
0
10
-1
10
-2
Hydrogen: 0.64e−(0.46 rs )
-2
10 0
Puska & Nieminen
1
2
3
rs , a 0
4
5
-3
6 10 0
Helium: 4.15e−(1.14 rs )
Puska & Nieminen
1
2
3
rs , a 0
4
5
6
Figure 3.4: The friction coefficient for hydrogen and helium as a function of
density parameter rs . The solid curves are exponential fitting functions, and the
red squares are data from Puska and Nieminen [55].
3.2
Molecular structure calculations
Molecular structures calculations are carried out using the Gaussian09 package
[23]. These give information about the dissociation energies and reaction barriers for the most important decay pathways, the coordinates of the optimized
molecules (input for the nuclear stopping model), and the valence electron
densities (input for the electronic stopping model).
In a typical calculation, the structure is optimized and the vibrational frequencies are then calculated. The latter is done to include the zero-point vibrational energy and to verify that the structure corresponds to a minimum
18
on the potential energy surface (all frequencies are real) or a transition state
(one imaginary frequencies). In these calculations, we have mainly used Density Functional Theory (B3LYP functional) and the 6-311++G(2d,p) basis set
[3, 37]. We have also used the computationally more demanding Complete
Basis Set (CBS-QB3) method [48, 49] for computing more accurate energies
(paper VI).
19
20
4. Results & Discussion
In Section 4.1, we will discuss the results on PAH- and fullerene-monomer
fragmentation in collisions with ions or atoms at low (about 100 eV) and high
(several keV) center of mass collision energies. In Section 4.2, we will discuss
results on molecular growth in clusters of PAHs and fullerenes.
4.1
4.1.1
Collisions with isolated PAH or fullerene molecules
Statistical fragmentation
Figure 4.1 shows the time-of-flight mass spectrum for collisions between 11.25
keV He+ ions and coronene. The two highest peaks in the spectrum correspond to intact singly and doubly charged coronene. These are associated with
rather low collisional energy transfers such that the intact, singly or doubly ionized molecule does not fragment on the experimental timescale of microseconds. The highest peak in the spectrum is attributed to single electron capture processes in large impact parameter collisions well outside the molecule
(see the picture to the upper left in Fig. 4.1). The so formed singly charged
coronene molecules are then produced cold enough to survive further fragmentation. The second highest peak is most likely due to somewhat closer nonpenetrating ion-coronene collisions leading to capture of two electrons or to
delayed thermionic emission processes [1] following single-electron capture.
To the far left in the spectrum there are peaks representing small hydrocarbon
fragments due to statistical fragmentation of coronene molecules which have
been more strongly heated in collisions where the ion trajectories pass directly
through the molecules (penetrating collisions). The insets in Fig. 4.1 show the
regions for losses of one or several (n) hydrogen atoms from intact singly and
doubly charged coronene. It can be seen clearly in Fig. 4.1 that even numbers
of H-losses are highly preferred, which is similar to what has been observed
earlier for PAH-fragmentation in collision with photons [43], electrons [17]
and keV ions [15, 36].
The nH-loss peaks must be associated with comparatively low internal energies such that the remaing large PAH fragments, [PAH+ - nH] remain sufficiently cold to survive the extraction phase in the time-of-flight spectrometer
(microsecond timescale). By analysis of simple mass spectra alone it is im21
He + + C24H12
Ionization+Fragmentation
Ionization
Intensity (arbitrary units)
C24H12 +
5 a.u.
n= 4
3
2
1
148.0 149.0 150.0
0
50
C24H122 +
n= 4
296
3
2
1
298
100
150
200
Atomic mass units per charge (u/e)
300
250
300
Figure 4.1: Mass-to-charge spectra for collisions between 11.25 keV He+ and
coronene (C24 H12 ). The two highest peaks correspond to singly and doubly ionized coronene without fragmentation on the experimental timescale of about ten
microseconds. The right and the left insets show the intensity distributions for
losses of different numbers, n, of H-atoms from the coronene cat- and dications.
Other peaks are due to fragmentation of the carbon-skeleton. The inset to the upper left shows the outer bound for one electron transfer from coronene to 11.25
keV He+ (blue surface) according to the classical over-the-barrier model by Forsberg et al [22]. The outer bound for ion trajectories transferring at least 5 eV to
the electron cloud of coronene is shown as a red surface.
22
possible to unambiguously determine whether the loss of two hydrogen atoms
are due to H2 emission or sequential H-emissions (H+H). To investigate this
further, the dissociation energies, barriers and energy transfers to the PAHs in
the collisions are required (see below).
Dissoc. energies
1+
2+
H
4.79 4.72
H2
4.19 4.17
H+H 8.68 8.66
Reaction barriers
1+
2+
H2
5.04 4.95
Units: eV
Figure 4.2: The lowest adiabatic dissociation energies and reaction barriers for
emission of H, H+H and H2 molecules from singly and doubly charged coronene.
The red circle represents the lowest dissociation energy channel, while the blue
circle indicates the initial positions of two hydrogen atoms that connect to the
lowest dissociation energy channels for (H+H)- and H2 . It is thus energetically
favourable to emit H2 from the same ring. It is also necessary to consider transition states and barriers when discussing the competition between H2 -loss and the
loss of single H-atoms (see text).
The DFT (B3LYP/6-311++G(2d,p)) calculation results for the lowest adiabatic dissociation energies and reaction barriers for H, H+H and H2 -losses
from singly and doubly charged coronene are shown in Figure 4.2. The lowest dissociation energies correspond to emission of H2 (∼4 eV), followed by
emission of H (∼5 eV) and H+H (∼9 eV). For H2 or H+H emission it is energetically favourable when both hydrogen atoms are from the same ring. This
seems to suggest that H2 -emission could be a dominant decay channel even
for modest internal excitation energies. However, the H2 -emission pathway
involves several transition states (see paper VI). The H- and (H+H)-emissions,
on the other hand, do not involve any barriers. As shown in Fig. 4.2, the lowest barrier for H2 -emission is comparable with the energy required for single
hydrogen dissociation. Therefore, these two processes could be competing in
different ways for different internal energies. Figure 4.3 shows that the dissociation energies and reaction barriers are rather independent of PAH size and
23
5
4
4
3
3
2
2
Energy (eV)
5
H-loss (diss. energy)
H2 -loss (diss. energy)
1
H-loss (diss. energy)
H2 -loss (diss. energy)
1
H2 -loss (reaction barrier)
0
C
+
10
H
14
+
10
H
C 16 PAH size
+
12
H
C 24
H2 -loss (reaction barrier)
0
+
C
2
2+
0
10
1
H
H
C 16
14
PAH size
2+
C2
Figure 4.3: The dissociation energies and reaction barriers for singly (left panel)
and doubly (right panel) charged PAHs.
24
H 12
4
charge state.
20
15
H(1.6 keV)+C10H8
He(11.25 keV)+C10H8
Diff. cross section dσ/dT (10−20 cm2 /K)
Diff. cross section dσ/dE (10−18 cm2 /eV)
50
40
30
20
10
0
10
8
6
4
2
0
10
8
6
4
2
0
100
80
60
40
20
0
0
He(11.25 keV)+C14H10
F(3 keV)+C14H10
He(11.25 keV)+C16H10
He(11.25 keV)+C24H12
H(1.6 keV)+C24H12
H(100 keV)+C24H12
20
40
60
80
Stopping energy, E (eV)
100
10
5
0
10
8
6
4
2
0
10
8
6
4
2
0
100
80
60
40
20
0
0
H(1.6 keV)+C10H8
He(11.25 keV)+C10H8
He(11.25 keV)+C14H10
F(3 keV)+C14H10
He(11.25 keV)+C16H10
He(11.25 keV)+C24H12
H(1.6 keV)+C24H12
H(100 keV)+C24H12
2000 4000 6000 8000 10000 12000
Internal temperature (K)
Figure 4.4: The model (see Paper V) results of the energy and temperature distributions for various collision systems.
Figure 4.4 shows calculated energy and temperature differential cross sections for different collision systems at different collision energies. We have
performed calculations for four different PAH targets and in each case we have
launched large numbers (200000) of ion trajectories with random orientations
of the molecules. In the left panels of Fig. 4.4 the energy distributions cover
the 5-100 eV range. For collisions with 11.25 keV He+ there is a distinct peak
at about 40 eV in all cases, which is due to the interaction between He and
carbon-carbon bonds in the PAH molecule (see Paper V). In the right panels of
Fig. 4.4, we have converted the horizontal axis to a temperature scale through
E = (3N − 6)kB T + Ed /2, where N is the number of atoms in the molecule, kB
is the Boltzmann constant, and Ed =5 eV is the dissociation energy of the PAH
molecule. As it has been shown in Paper VI, the temperature at which significant H2 could be emitted is about 2200 K (see paper VI for more details).
Clearly, most collisions yield internal temperatures exceeding that, suggesting that H2 indeed may be efficiently formed in the present keV-ion collisions.
This also means that the remaining large fragments ([PAH-2H]+ ) have high
internal energies. Therefore it is likely that they fragment further and that the
25
2H-loss peak in the mass spectrum does not directly reflect the importance of
H2 -loss even in cases where H2 is likely to be produced.
4.1.2
Competition between statistical and non-statistical fragmentation
+
In Figure 4.5, we show the mass spectra due to C14 H+
10 + He and He + C14 H10
collisions at center of mass energies of 110 eV and 11 keV, respectively. Results from Monte Carlo simulations of electronic and nuclear stopping processes are shown in the insets for the particular cases when the trajectories are
perpendicular to the molecular planes. Electronic stopping processes dominate the energy transfer to the molecule at the higher collision energy (see the
upper panel in Figure 4.5). Typical total internal energies are around 40 eV,
which is well above the lowest dissociation energies of about 5 eV for H- or
C2 H2 -loss. Many collisions will lead to statistical fragmentation processes in
the 11 keV case [17, 36]. This is consistent with the distribution of fragments
in the mass spectrum shown in the upper panel of Figure 4.5. The highest peak
is due to intact C14 H+
10 at a mass-to-charge ratio of 178. The smaller peaks
to the left are due to moderately heated systems which lose H- atom(s) and/or
C2 H2 molecule(s). The lighter fragments in the spectrum are due to more violent collisions where large amounts of energy are transferred (see Paper V for
details).
The fragment mass spectrum is different in the 110 eV case. Here the nuclear stopping dominates as can be seen in the inset. According to the molecular dynamic simulations by Postma et al. [54], only nuclear stopping above
about 27 eV will lead to prompt carbon knockout while 9 eV is sufficient for
knocking out of a H-atom (see Paper V for details). Our calculations show that
there are many collisions which lead to nuclear energy transfers above these
thresholds at 110 eV. On the average the masses of fragments are larger here
than in the cases of the higher energy collisions reflecting cooler anthtracene
molecules and fragments in the 110 eV case. The single carbon atom loss is
important at 110 eV which is a clear signature of a non-statistical fragmentation process. As shown in Paper V, the much higher dissociation energies for
C- or CHx -loss in relation to those for C2 H2 - or H- loss makes this channel
insignificant for statistical fragmentation processes.
The calculated non-statistical, statistical and total (statistical + non-statistical)
fragmentation cross sections using the ZBL potential and the total experimental cross sections for collisions between PAH cations and helium atoms with
center of mass energy 110 eV are shown in Figure 4.6. Martin et al [40] measured the internal energies of fragmenting anthracene cations and found that
about 10 eV is needed for statistical fragmentation on microsecond timescales,
26
Figure 4.5: Fragmentation mass-to-charge spectra for He + C14 H10 collisions at
11 keV (upper panel) and for C14 H+
10 + He at 110 eV center-of-mass energy collisions (lower panel). Insets show electronic and nuclear stopping contributions
to the molecular excitation energies.
27
which is relevant for their and the present experiments. These results are used
to calculate the total fragmentation cross section by assuming that trajectories associated with larger stopping energies (electronic plus nuclear) than 10
eV will lead to fragmentation of anthracene within microseconds. A subset of
these trajectories will lead to much larger nuclear energy transfers to individual
atoms in anthracene and lead to single-carbon knockout i.e. to non-statistical
fragmentation. The threshold energy for statistical fragmentation should scale
roughly with the number of atoms, N, in the PAH
Tthstat (N) =
3N − 6
× 10 eV
3 × 24 − 6
(4.1)
Here, the value 10 eV is the internal energy needed for fragmentation of anthracene, C14 H10 , on the microsecond timescale. This has been measured directly by Martin et al [41]. In eq. (4.1) we scale this result with the number
of degrees of freedom for an arbitrary PAH molecule containing N atoms. For
anthracene N = 24. The scaling relies on the fact that dissociation energies are
similar for PAHs of different sizes. This was shown to be the case for a range
of PAHs by Holm et al [27].
We find that the model and experimental total fragmentation cross sections
are similar for the PAHs considered here. We see from Figure 4.6 that the nonstatistical knockout cross section becomes more important for larger PAHs and
dominant for circumcoronene. The reason is that the statistical threshold enstat increases as a function of PAH size, while the non-statistical threshergy Tth
old energy essentially is size independent - the chemical bonds within the PAH
molecules have similar strengths for different PAH sizes.
From Figure 4.6, we see that the total cross sections are measured to be
significantly smaller than the geometrical cross sections. This means that
the PAHs are partially transparent to helium atoms with energies in the range
around 100 eV.
In Figure 4.7, we show fragmentation spectra for 9 keV C+
60 colliding with
He, Ne, Ar and Xe yielding center of mass energies of 50 eV, 245 eV, 473 eV
and 1388 eV, respectively. For the Ne, Ar and Xe targets we detect C+
59 ions
most likely stemming from prompt carbon knockout processes. In the case
of the He target it was not possible to separate a possible corresponding contribution from features due to other processes. The He atom could be either
scattered or captured to form endohedral He@C60 [11, 60, 73]. The scattering
process gives a broad shoulder on the low-energy side of the primary beam
peak. This shoulder extends to energy losses of about 200 eV, which corresponds to elastic scattering of He in the forward direction (see Paper III for
details). Interestingly, the single carbon loss peaks are much smaller for C60
(Figure 4.7) than for PAHs (lower panel of Figure 4.5). A reason for this could
28
6
Cross Section (10−15 cm2 )
5
4
3
Cm Hn + - destruction in He, ECM = 110 eV
Non-stat. fragmentation cross section (calc.)
Stat. fragmentation cross section (calc.)
Total (stat. + non-stat.) cross section (calc.)
Geometrical cross section
Total cross section (exp.)
d = 18.5 A
◦
2
1
0
Circumcoronene
10 20 30 40 + 50 60 70
No. of atoms in the Cm Hn molecule, m + n
80
Figure 4.6: Statistical, non-statistical, and total fragmentation cross sections
as calculated using the ZBL potential for PAH-cations colliding with He at 110
eV center of mass energy. Inset: Estimate of the geometrical cross section area
2
of a coronene molecule σ = 0.8π d4 , where the factor 0.8 is due to the random
orientation of the molecule in the collision [22].
29
be that PAHs are planar while fullerenes have truly three dimensional molecular structures.
Figure 4.7: Fragmentation spectra for 9 keV C+
60 (energy in the laboratory frame
of reference) in collisions with He, Ne, Ar and Xe. There are more fragments
for the heavier atoms where the center-of-mass energies are higher. The He may
be inserted in the fullerene cage to form endohedral He@C60 or scattered. Both
processes contributes to the shoulder to the left of the main peak. Inset: A zoomin with the expected C+
59 position indicated.
4.2
Collisions with clusters of PAH or fullerene molecules
We show a mass spectrum for 22.5 keV He2+ colliding with loosely bound
van der Waals clusters of C60 fullerenes in Figure 4.8. The total time-of-flight
spectrum, where C+
60 dominates is shown in the top panel of Figure 4.8. The
low-intensity peaks to the right of C+
60 are mainly due to intact [C60 ]n ions
(the intensity scales are different for the right and left panels of Figure 4.8).
The peaks close to nC /e = 120, where nC is the number of carbon atoms in the
fragment, are shown in an expanded scale in Figure 4.9 (first from left) with
positions corresponding to nC /e=119 and 118 etcetera. In the left top panel of
Figure 4.8 there are a few rather weak peaks due to the emission of one and
30
several C2 molecules from C60 monomer cations that have been left sufficiently
hot to fragment. This could occur after several steps of fragmentation of a
charged [C60 ]n -cluster leaving at the end one or several singly charged C60
molecules of which a few may fragment further.
We show single stop events, i.e. events where only one charged fragment
is detected, in the middle panel of Figure 4.8. The peaks in this panel are
attributed to the most distant electron transfer collisions where the clusters
become singly and doubly ionized. Here, only low amounts of energies are
transferred to the individual molecules and the fragmentation is weak.
In the lowest panels in Figure 4.8, we show product ions measured in coincidence with C+
60 ions. These events are mainly due to closer collisions and
multiple ionizations of [C60 ]n -clusters in which substantial amounts of energy
are transferred. A zoom-in on the peak in the lower right panel of Figure 4.9
reveals that there are peaks at nC /e = 118, 119 and 120. The latter, could be
due to weakly bound [C60 ]+
2 dimers from decays of larger clusters but may
also be due to C+
+
C
→
C+
60
120 covalent bond formation. As there are sub60
stantial barriers involved in the formation of C120 from two unperturbed C60
molecules it could be reasonable to assume that this peak instead could be due
to reactions where one of the C60 cages are damaged. This could be caused by
an incomplete knockout process where the C-atom does not actually leave the
fullerene. The peaks at nC /e = 119 and nC /e = 118 are most likely produced
+
+
in at low energy C+
59 /C58 + C60 reactions, in which covalently bound C119 and
+
C118 dumb-bell systems are formed as discussed in detail in Papers I and II.
4.2.1
Molecular growth
We show a zoom-in of the mass region around nC /e=120 in the spectrum due
to Ar2+ + [C60 ]n collisions in Figure 4.9. There are more peaks than in He2+
case. We have performed electronic and nuclear stopping calculations for 22.5
keV He2+ and 12 keV Ar2+ collisions on both fullerene monomers and clus+
ters. Highly reactive products (e.g. C+
59 , C58 , etc) are produced by prompt
knockout processes due to nuclear stopping processes for the collisions on
monomers and on clusters. The C59 and C58 produced in knockout collisions
with monomers inevitably also become strongly heated due to electronic stopping processes. They would therefore decay very quickly - on subpicosecond
time scales if they were isolated. In the clusters however, the electronic excitations of those individual molecules that are directly penetrated in the collision
may share its excitation energy with other (colder) molecules in the cluster. In
this way, fragments like C59 and C58 may stay intact long enough in order to
react with other (intact) molecules in the cluster (see inset in Figure 4.9, Paper
I and II). The knockout cross sections calculated using the nuclear stopping
31
Counts
8000
56
60
+
C60
Total spectrum
200
300
400
C118-120
+
7
+
+
C54
x50
C
+
8
2+
9
2+
+
9
2+
11 13
+
17
+
11
4000
+
x100
C54
C56
+
6
+
5
150
+
7
+
+
8
4
+
+
C58
100
+
3
2+
9
2+
11
2+
7
+
9
2+
13
2+
17
10
C60
+
11
0
70
+
+
50
+
2+
15
50 52 54 56 58
Coincidences
+
with C60
50
0
+
C118-120
2000
Counts
+
10
2+
50 52 54 56 58
Single stop events C60
100
2+
15
2+
7
6000
0
1800
1600
1400
1200
1000
800
600
400
200
0
150
+
3
250
200
4
+
700
300
He + [C60]n
+
6
5
C58
600
2+
+
+
56
500
+
Counts
52
Counts
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
48
C118-120
60
50
+
40
C58
30
+
C56
x20
Counts
Counts
28
20
52
54
56
58
28
48
52
56
10
60
200
300
400
500
600
0
700
Number of carbon atoms per charge (nC/e)
Figure 4.8: Mass to charge-spectra due to 22.5 keV He2+ + [C60 ]n collisions.
From top to bottom we show the total mass spectrum (all events including singleand multiple-stop events), single-stop events (only one ion registered per collision), and coincidences with only intact C+
60 ions (one or several). There are
different intensity scales for the parts of the spectra shown in the right and left
panels.
32
model with the screened Bohr potential (see Eq. 3.5 and 3.6 in Section 3.2)
are displayed in Figure 4.9. The cross sections are calculated assuming that
the threshold for knocking out a carbon from a C60 molecule is about 15 eV
(this was the value used for the analysis in Paper I. We have later found, however, that much larger energy transfers to the molecular system are needed to
break all bonds of a C-atom in a fullerene). In the He2+ case, single knockouts
are more likely than knockouts of two different C atoms. The situation is the
opposite in the case of Ar2+ where the projectile does not need to come as
close to an individual C atom in the molecule to knock it out as was the case
with He2+ . This is most likely the reason for the more extensive distribution
of peaks due to molecular fusion processes in the case of Ar2+ .
Ar2 + + [C60]n
He2 +
70
C119
2.0
Counts
60
C118
50
40
30
20
2.5
C118
C120
C116 C119
C114
C120
σm , 10−15 cm2
80
He2 + + [C60]n
Ar2 +
1.5
1.0
0.5
10
0
110 115 120
110 115 120
No. of carbons per charge, nc /e
0.0
54 55 56 57 58 59
Cm -fullerene size, m
Figure 4.9: Zoom-ins on mass-to-charge spectra due to 22.5 keV He2+ + [C60 ]n
(left panel) and 12 keV Ar2+ +[C60 ]n collisions (middle panel). The curves show
events recorded in coincidence with one or several C+
60 ions. The peaks are due
to bond forming reactions in which e.g. dumbbell shaped C119 molecules may be
formed (an example is shown in the inset in the left panel). The bond formation
process is most likely initiated by prompt knockouts of one or several carbon
atoms in a C60 molecule. The right panel shows calculated absolute cross sections
for producing Cm -fullerenes in direct knock-out processes.
In Figure 4.10 we show a few examples of typical reactions leading to formations of new molecular structures when pyrene clusters are hit by 12 keV
Ar2+ projectiles. In all three examples, the reactions are between one pyrene
fragment and one intact molecule according to our molecular dynamics simulations [20]. Within a few tens of femtoseconds, bonds are formed by the
interacting fragment and an intact pyrene molecule. The top row shows the
33
Figure 4.10: Snapshots from molecular dynamics simulations of 12 keV Ar+
[C16 H10 ]9 collisions (three different trajectories). The molecular growth processes are typically started by prompt atom knockouts or bond cleavages. The
highly reactive fragments then form covalent bonds with neighbouring molecules
in the clusters on the sub-picosecond timescales.
34
case where no atom has been knocked out, but instead a C-C bond has been
spilt open by the projectile. The dangling C atoms react with a neighboring
intact molecule before the system emits a C2 H2 molecule. The latter is typically one of the lowest energy decay pathways in PAH molecules, and here it
results in a fused C30 H+
18 molecule at mass 378 amu. The second row shows
the inclusion of a C-atom (from a knockout process), reaction with an intact
pyrene molecule and formation of a C17 H+
10 which undergoes a few isomerization steps during the 1 ps simulation time. In the last row of Fig. 4.10, C31 H+
19
is formed when a CH group has been knocked out from one pyrene molecule
which then forms bond with another molecule. A single bond is formed with
a neighboring pyrene where one ring in the merged product closes into a pentagon.
35
36
5. Concluding remarks
In this work, fragmentation and molecular growth processes following collisions between fullerene/PAH molecules or clusters and atoms or atomic ions
are presented. Experiments were performed with the aid of two complementary experimental setups for studies of collisions at high center of mass collision energies (> 10 keV) and for low center of mass collision energies (<
1 keV). The experimental results have been discussed in view of a collision
model, molecular structure calculations, and molecular dynamics simulations.
We show that high energy (keV energies in the center-of-mass system)
are dominated by heating of the molecular electron clouds (electronic stopping). The excess energy is then statistically distributed among all degrees
of freedom before the molecules or molecular clusters cool down by emiting
photons, electrons, atoms or molecules. The typical energy transfers are well
above the dissociation energy thresholds, which lead to rich fragment mass
spectra. Molecular structure calculations show that the dissociation energies
are rather independent of PAH size for the energetically most favourable decay pathawys. The dissociation energies for H-loss and H2 -loss are about 5 eV
and 4 eV, respectively. However, there are reaction barriers for H2 emission,
which significantly reduce the decay rate. As a consequence, H2 -emission is
only important for high internal PAH temperatures (> 2200 K). Such temperatures are typically reached in the present collisions with keV ions/atoms but
not upon e.g. single UV-photon absorption.
Non-statistical fragmentation refer to the process, in which a single carbon atom is knocked out directly from the molecule in Rutherford like atomatom scattering processes. The latter has been observed in experimental studies of collisions between PAH/fullerene molecules and atoms at low center of
mass collision energies (< 1 keV). In general this yields more reactive fragments than statistical fragmentation processes. For non-statistical fragmentation, simple scaling laws for estimates of absolute fragmentation cross sections
have been deduced.
For collision between keV ions and molecular clusters, prompt knockout
processes play a key role in the formation of new molecules. The highly reactive fragments may then form covalent bonds with neighbouring molecules in
the clusters. The experiments were carried out for collisions between various
atomic ions and clusters of fullerenes or pyrene molecules (C16 H10 ). In the
37
former case, exotic dumbbell shaped molecules (e.g. C119 ) are formed, while
broad size distributions with masses corresponding to C16+m Hx with m=1-21
may be formed with the PAH cluster target.
Isolated PAHs or fullerenes and their clusters are believed to be important
in various astrophysical environments [68, 69]. However, little is known about
how they e.g. are formed, destroyed or how they react when they are intact or
when they have been fragmented. It is also not known if molecular hydrogen,
H2 , may form directly from internally hot native PAHs. One study presented in
this thesis suggests that this may indeed be the case. More detailed information
about these intriguing aspects are of great interest for the future. This may
e.g. be obtained using the experimental setups at the novel DESIREE (Double
ElectroStatic Ion Ring Experiment) facility at SU. Possible future experiments
involve studies of molecular growth processes inside size selected clusters at
the standalone beam line for low energy (<100 eV) collisions (see Section
4.2), and studies of charge and energy transfer processes between anions and
cations of PAHs/fullerenes in DESIREE [61, 67]. In the latter case, different
ranges of initial internal ion temperatures may be selected by storing the ions
for different times before the collisions. By storing for long times the ions
will equilibrate thermally with the ring and its vacuum vessel which may be
operated down to about 12 K. From a theoretcial point of view, calculations of
the H2 rates from internally heated PAHs would help to gauge the significance
of such processes in astrophysical environments.
38
Appendix: Additional publications
Peer-reviewed articles
1. Ions interacting with planar aromatic molecules: Modeling electron
transfer reactions
B. O. Forsberg, J. D. Alexander, T. Chen, A. T. Pettersson, M. Gatchell,
H. Cederquist and H. Zettergren JOURNAL OF CHEMICAL PHYSICS,
138, 054306 (2013).
DOI: 10.1063/1.4790164
2. Ions colliding with polycyclic aromatic hydrocarbon clusters
M. Gatchell, H. Zettergren, F. Seitz, T. Chen, J. D. Alexander, M. H.
Stockett, H. T. Schmidt, A. Ławicki, J. Rangama, P. Rousseau, M. Capron,
S. Maclot, R. Maisonny, A. Domaracka, L. Adoui, A. Méry, J. Y. Chesnel, B. Manil, B. A. Huber, and H. Cederquist PHYSICA SCRIPTA,
T156, 014062, (2013).
DOI: 10.1088/0031-8949/2013/T156/014062
3. First storage of ion beams in the Double Electrostatic Ion-Ring Experiment: DESIREE
H. T. Schmidt, R. D. Thomas, M. Gatchell, S. Rosén, P. Reinhed, P.
Löfgren, L. Brännholm, M. Blom, M. Björkhage, E. BäckstrÃűm, J.
D. Alexander, S. Leontein, D. Hanstorp, H. Zettergren, L. Liljeby, A.
Källberg, A. Simonsson, F. Hellberg, S. Mannervik, M. Larsson, W. D.
Geppert, K. G. Rensfelt, H. Danared, A. Paál, M. Masuda, P. Halldén, G.
Andler, M. H. Stockett, T. Chen, G. Källersjö, J. Weimer, K. Hansen, H.
Hartman and H. Cederquist REVIEW OF SCIENTIFIC INSTRUMENTS,
84, 055115 (2013).
DOI: 10.1063/1.4807702
+
+
+
4. Formation dynamics of fullerene dimers C118
, C119
, and C120
Y. Wang, H. Zettergren, P. Rousseau, T. Chen, M. Gatchell, M. H.
Stockett, A. Domaracka, L. Adoui, B. A. Huber, H. Cederquist, M. Alcamí and F. Martín PHYSICAL REVIEW A, 89, 062708, (2014).
DOI: 10.1103/PhysRevA.89.062708
5. Ions colliding with mixed clusters of C60 and coronene: Fragmentation and bond formation
M. Gatchell, P. Rousseau, A. Domaracka, M. H. Stockett, T. Chen, H.
T. Schmidt, J. Y. Chesnel, A. Méry, S. Maclot, L. Adoui, B. A. Huber,
H. Zettergren and H. Cederquist PHYSICAL REVIEW A, 90, 022713,
(2014).
DOI: 10.1103/PhysRevA.90.022713
6. Fragmentation of anthracene C14 H10 , acridine C13 H9 N and phenazine
C12 H8 N2 ions in collisions with atoms
M. H. Stockett, M. Gatchell, J. D. Alexander, U. Bērziņš, T. Chen, K.
Farid, A. Johansson, K. Kulyk, P. Rousseau, K. Støchkel, L. Adoui, P.
Hvelplund, B. A. Huber, H. T. Schmidt, H. Zettergren and H. Cederquist.
PHYSICAL CHEMISTRY CHEMICAL PHYSICS, 16, 21980, (2014).
DOI: 10.1039/C4CP03293D
Peer-reviewed conference contributions
1. Bond formation in C+
59 -C60 collisions
H. Zettergren, P. Rousseau, Y. Wang, F. Seitz, T. Chen, M. Gatchell, J.
D. Alexander, M. H. Stockett, J. Rangama, J. Y. Chesnel, M. Capron, J.
C. Poully, A. Domaracka, A. Méry, S. Maclot, H. T. Schmidt, L. Adoui,
M. Alcamí, A. G. G. M. Tielens, F. Martín, B. A. Huber, and H. Cederquist JOURNAL OF PHYSICS CONFERENCE SERIES, 488, 012028
(2014).
DOI: 10.1088/1742-6596/488/1/012028
2. Modeling electron and energy transfer processes in collisions between ions and Polycyclic Aromatic Hydrocarbon molecules
T. Chen, J. D. Alexander, B. O. Forsberg, A. T. Pettersson, M. Gatchell,
H. Cederquist and H. Zettergren JOURNAL OF PHYSICS CONFERENCE SERIES, 488, 102015 (2014).
DOI: 10.1088/1742-6596/488/10/102015
3. Commissioning of the DESIREE storage rings - a new facility for
cold ion-ion collisions
M. Gatchell, H. T. Schmidt, R. D. Thomas, S. Rosén, P. Reinhed, P.
Löfgren, L. Brännholm, M. Blom, M. Björkhage, E. BäckstrÃűm, J.
D. Alexander, S. Leontein, D. Hanstorp, H. Zettergren, L. Liljeby, A.
Källberg, A. Simonsson, F. Hellberg, S. Mannervik, M. Larsson, W. D.
Geppert, K. G. Rensfelt, H. Danared, A. Paál, M. Masuda, P. Halldén, G.
Andler, M. H. Stockett, T. Chen, G. Källersjö, J. Weimer, K. Hansen,
H. Hartman and H. Cederquist EPJ WEB OF CONFERENCES, 488,
012040, (2014).
DOI: 10.1088/1742-6596/488/1/012040
4. First results from the Double ElectroStatic Ion-Ring ExpEriment,
DESIREE
M. Gatchell, H. T. Schmidt, J. D. Alexander, G. Andler, M. Björkhage,
M. Blom, L. Brännholm, E. BäckstrÃűm, T. Chen, W. D. Geppert, P.
Halldén, D. Hanstorp, F. Hellberg, A. Källberg, M. Larsson, S. Leontein,
L. Liljeby, P. Löfgren, S. Mannervik, A. Paál, P. Reinhed, K. G. Rensfelt, S. Rosén, F. Seitz, A. Simonsson, M. H. Stockett, R. D. Thomas,
H. Zettergren, and H. Cederquist EPJ WEB OF CONFERENCES, 488,
092003, (2014).
DOI: 10.1088/1742-6596/488/9/092003
5. DESIREE: Physics with cold stored ion beams
R. D. Thomas, H. T. Schmidt, M. Gatchell, S. Rosén, P. Reinhed, P.
Löfgren, L. Brännholm, M. Blom, M. Björkhage, E. BäckstrÃűm, J.
D. Alexander, S. Leontein, D. Hanstorp, H. Zettergren, L. Liljeby, A.
Källberg, A. Simonsson, F. Hellberg, S. Mannervik, M. Larsson, W. D.
Geppert, K. G. Rensfelt, H. Danared, A. Paál, M. Masuda, P. Halldén, G.
Andler, M. H. Stockett, T. Chen, G. Källersjö, J. Weimer, K. Hansen, H.
Hartman and H. Cederquist EPJ WEB OF CONFERENCES, 84, 01004,
(2015).
DOI: 10.1051/epjconf/20158401004
Acknowledgements
This work was accomplished with the help of many people, without them my
journey would have been a lot more difficult. I would therefore like to thank
the following people:
Henrik Cederquist, my main supervisor and the leader of the group. He
helped create an excellent environment for conducting my research. His guidance has helped develop the DESIREE and ISLab projects, and introduce me
to the wider scientific community via external collaborations as well as enabling me to participate in conferences, etc. All of these led to fruitful results
and helped me grow in many different ways.
Henning Zettergren, my co-advisor and life teacher. I have learned from
him not only how to do research, search literature, give talks, publish articles,
but also how to behave like a father, husband and how to defend myself against
pollen.
Henning Schmidt, as my co-advisor and principle of study, he gave me
the opportunity to teach, which not only improved my teaching skills but also
helped my family improve the financial problems in the beginning when I had
utbildningsbidrag for three people in the family.
Wolf Geppert, as the director of the AstroBiology Centre (ABC), he organized many memorable events, which helped me to know all the aspects about
astrobiology and to expand my horizons. I feel very happy and pround to be
part of the ABC.
John Alexander, my previous roommate, I had the pleasure of collaborating
with him on several projects. He is not only an encyclopedia but also my
english and swedish teacher. He is a nice person in all dimensions, and I like
to chat with him about everything.
Fabian Seitz, another previous roommate with whom I had a lot of interesting conversations. He knows a lot of things about Sweden, sometimes I feel
that he knows more than most Swedes. Thanks to Fabian I took part in my first
triathlon (10 km run) and tasted my first feuerzangenbowle.
Michael Gatchell and Mark Stockett for providing the experimental data
and explaining the experimental setup. As english native speakers, their help
in correcting my papers, thesis, etc is very much appreciated. Special thanks
to Mark, it is always fun to talk with him, he brings a lot of positive energy
to the group. I like his presentation style and I consider him one of the best
speaker I ever met.
Tor Kjellsson and Viktoria Larsson, my trainer and the organizer of many
activities. Thanks to them I now have good health. I took part in lots of memorable events with them: the 1.6×4 relay, AlbaNova bench press competition,
climbing classes, 12 km runs around lappis and the lake near AlbaNova, etc.
Michael Wolf, Emma Anderson, and Sifiso Nkambule - my current roommates. I appreciate the relaxed and creative atmosphere they make; it is the
most joyful time chatting with them everyday.
Muhammad Umair, thanks for providing lots of useful information, and
the supertasty pakistani-flavor pies and cakes.
There are many others who have contributed to various aspects of my PhD,
e. g. Elisabet Oppenheimer, Petra Nodler, Wolf Geppert, Albert Siegbahn, PerErik Tegnér, Sven Mannervik ... but due to limited space, I have to draw the
line here.
Deepest thanks to my mother and mother-in-law, they dedicate themself
to help my family. It was a huge challenge for them to travel 7000 km to a
completely different culture at their age. I am so proud to have parents like
them.
Finally, I would like to thank my significant other Xiaoyu Li who has been
taking care of the other part of my life day by day, year by year. Her willingness to come to Sweden to help me further my education is very much appreciated. Her constant supports and encouragements has helped me through both
my PhD and adapting to Sweden. I can not imagine what my life would be
without her. Since coming to Sweden, she has also given me the greatest gift
of my son Ethan. His presence always lightens my day...
Thanks again to all the people who helped me to complete this work, and
who made my life easier and happier.
Tao Chen
March, 2015 Stockholm
References
[1] J. U. A NDERSEN , E. B ONDERUP, AND K. H ANSEN. Thermionic emission from clusters. Journal of
Physics B, Atomic, Molecular and Optical Physics, 35,R1, 2002.
[2] C. W. BAUSCHLICHER J R . The Reaction of Polycyclic Aromatic Hydrocarbon Cations with Hydrogen Atoms, The Astrophysical Implications. The Astrophysical Journal, 509,L125–L127, 1998.
[3] A. D. B ECKE. The Journal of Chemical Physics, 98,5648, 1993.
[4] T. B ERGEN , X. B IQUARD , A. B RENAC , F. C HANDEZON , B. A. H UBER , D. JALABERT,
H. L EBIUS , M. M AUREL , E. M ONNAND , J. O PITZ , A. P ESNELLE , B. P RAS , C. R ISTORI , AND
J. C. ROCCO. Multiply charged cluster ion crossed-beam apparatus, Multi-ionization of clusters by
ion impact. Review of Scientific Instruments, 70,3244–3253, 1999.
[5] O. B ERNÉ AND A. G. G. M. T IELENS. Formation of buckminsterfullerene (C60 ) in interstellar
space. Proceedings of the National Academy of Sciences, 109,401–406, 2012.
[6] C. B OERSMA , J. B REGMAN , AND L. J. A LLAMANDOLA. Properties of Polycyclic Aromatic Hydrocarbons in the Northwest Photon Dominated Region of NGC 7023. I. PAH Size, Charge, Composition,
and Structure Distribution. The Astrophysical Journal, 795,110, 2014.
[7] P. B OISSEL , C. J OBLIN , AND P. P ERNOT. Singular value decomposition, A tool to separate elementary contributions in ISOCAM spectral maps. Astronomy & Astrophysics, 373,L5–L8, 2001.
[8] L. B OSCHMAN , G. R EITSMA , S. C AZAUX , T. S CHLATHÖLTER , R. H OEKSTRA , M. S PAANS , AND
O. G ONZÁLEZ -M AGAñA. Hydrogenation of PAH cations, a first step towards H2 formation. The
Astrophysical Journal Letters, 761,L33, 2012.
[9] K. A. CALDWELL, D. E. GIBLIN, AND M. L. GROSS. High-energy collisions of fullerene radical cations with target gases, capture of the target gas and charge stripping of C60.bul.+, C70.bul.+,
and C84.bul.+. Journal of the American Chemical Society, 114,3743–3756, 1992.
[10] J. C AMI , J. B ERNARD -S ALAS , E. P EETERS , AND S. E. M ALEK. Detection of C60 and C70 in a
Young Planetary Nebula. Science, 329,1180–1182, 2010.
[11] E. E. B. CAMPBELL, R. EHLICH, A. HIELSCHER, J. M. A. FRAZAO, AND I. V. HERTEL.
Collision energy dependence of He and Ne capture by C+
60 . Zeitschrift für Physik D Atoms, Molecules
and Clusters, 23,1–2, 1992.
[12] P. C ASSAM -C HENAÏ , F. PAUZAT, AND Y. E LLINGER. Is Stripping of Polycyclic Aromatic Hydrocarbons a Route to Molecular Hydrogen? AIP Conference Proceedings, 312,543, 1994.
[13] H. C EDERQUIST, J. J ENSEN , H. T. S CHMIDT, H. Z ETTERGREN , S. T OMITA , B. A. H UBER , AND
B. M ANIL. Barriers for asymmetric fission of multiply charged C-60 fullerenes. Physical Review A,
67,062719, 2003.
[14] D. C ESARSKY, J. L EQUEUX , C. RYTER , AND M. G ERIN. ISO observations of the reflection nebula
Ced 201, evolution of carbonaceous dust. Astronomy & Astrophysics, 354,L87–L91, 2000.
[15] J. P. C HAMPEAUX , P. M ORETTO -C APELLE , P. C AFARELLI , C. D EVILLE , M. S ENCE , AND
R. C ASTA. Is the dissociation of coronene in stellar winds a source of molecular hydrogen? application to the HD 44179 nebula. Monthly Notices of the Royal Astronomical Society, 441,1479–1487,
2014.
[16] F. CHANDEZON, B. HUBER, AND C. RISTORI. A new-regime Wiley-McLaren time-of-flight
mass-spectrometer. Review of Scientific Instruments, 65,3344–3353, 1994.
[17] S. D ENIFL , B. S ONNWEBER , J. M ACK , L. T. S COTT, P. S CHEIER , K. B ECKER , AND T. D. M ARK.
Appearance energies of singly, doubly, and triply charged coronene and corannulene ions produced
by electron impact. International Journal of Mass Spectrometry, 249,353–358, 2006.
[18] F. X. D ESERT, F. B OULANGER , AND J. L. P UGET. Interstellar dust models for extinction and
emission. Astronomy & Astrophysics, 237,215–236, 1990.
[19] M. DOLE, L. L. MACK, AND R. L. HINES. Molecular Beams of Macroions. The Journal of
Chemical Physics, 49,2240, 1968.
[20] M. E LSTNER , D. P OREZAG , G. J UNGNICKEL , J. E LSNER , M. H AUGK , T H . F RAUENHEIM ,
S. S UHAI , AND G. S EIFERT. Self-consistent-charge density-functional tight-binding method for
simulations of complex materials properties. Physical Review B, 58,7260, 1998.
[21] T. L. FERRELL AND R. H. RITCHIE. Energy losses by slow ions and atoms to electronic excitation in solids. Physical Review B, 16,115–123, 1977.
[22] B. O. F ORSBERG , J. D. A LEXANDER , T. C HEN , A. T. P ETTERSSON , M. G ATCHELL , H. C ED ERQUIST, AND H. Z ETTERGREN . Ions interacting with planar aromatic molecules, Modeling electron
transfer reactions. The Journal of Chemical Physics, 138,054306, 2013.
[23] M. J. F RISCH , G. W. T RUCKS , H. B. S CHLEGEL , G. E. S CUSERIA , M. A. ROBB , J. R. C HEESE MAN , G. S CALMANI , V. BARONE , B. M ENNUCCI , G. A. P ETERSSON , H. NAKATSUJI , M. C AR ICATO , X. L I , H. P. H RATCHIAN , A. F. I ZMAYLOV, J. B LOINO , G. Z HENG , J. L. S ONNEN BERG , M. H ADA , M. E HARA , K. T OYOTA , R. F UKUDA , J. H ASEGAWA , M. I SHIDA , T. NAKA JIMA , Y. H ONDA , O. K ITAO , H. NAKAI , T. V REVEN , J. A. M ONTGOMERY, J R ., J. E. P ERALTA ,
F. O GLIARO , M. B EARPARK , J. J. H EYD , E. B ROTHERS , K. N. K UDIN , V. N. S TAROVEROV,
R. KOBAYASHI , J. N ORMAND , K. R AGHAVACHARI , A. R ENDELL , J. C. B URANT, S. S. I YEN GAR , J. T OMASI , M. C OSSI , N. R EGA , J. M. M ILLAM , M. K LENE , J. E. K NOX , J. B. C ROSS ,
V. BAKKEN , C. A DAMO , J. JARAMILLO , R. G OMPERTS , R. E. S TRATMANN , O. YAZYEV, A. J.
AUSTIN , R. C AMMI , C. P OMELLI , J. W. O CHTERSKI , R. L. M ARTIN , K. M OROKUMA , V. G. Z A KRZEWSKI , G. A. VOTH , P. S ALVADOR , J. J. DANNENBERG , S. DAPPRICH , A. D. DANIELS , Ö.
FARKAS , J. B. F ORESMAN , J. V. O RTIZ , J. C IOSLOWSKI , AND D. J. F OX. Gaussian 09 Revision,
D.01, 2009.
[24] K. H ANSEN AND O. E CHT. Thermionic emission and fragmentation of C60 . Physical Review Letters,
78,2337–2340, 1997.
[25] D. H ATHIRAMANI , K. A ICHELE , W. A RNOLD , K. H UBER , E. S ALZBORN , AND P. S CHEIER.
Electron-impact induced fragmentation of fullerene ions. Physical Review Letters, 85,3604–3607,
2000.
[26] M. H IRAMA , T. T OKOSUMI , T. I SHIDA , AND J. A IHARA. Possible molecular hydrogen formation
mediated by the inner and outer carbon atoms of typical PAH cations. Chemical Physics, 305,307,
2004.
[27] A. I. S. H OLM , H. A. B. J OHANSSON , H. C EDERQUIST, AND H. Z ETTERGREN. Dissociation
and multiple ionization energies for five polycyclic aromatic hydrocarbon molecules. The Journal of
Chemical Physics, 134,044301, 2011.
[28] A. I. S. H OLM , H. Z ETTERGREN , H. A. B. J OHANSSON , F. S EITZ , S. ROSÉN , A. Ł AWICKI ,
J. R ANGAMA , P. ROUSSEAU , M. C APRON , R. M AISONNY, L. A DOUI , A. M ÉRY, B. M ANIL ,
AND C EDERQUIST H. H UBER , B. A. Ions Colliding with Cold Polycyclic Aromatic Hydrocarbon
Clusters. Physical Review Letters, 105,213401, 2010.
[29] H. A. B. J OHANSSON , H. Z ETTERGREN , A. I. S. H OLM , N. H AAG , S. B. N IELSEN , J. A. W YER ,
M. B. S. K IRKETERP, K. S TØCHKEL , P. H VELPLUND , AND C EDERQUIST H. S CHMIDT, H. T.
Unimolecular dissociation of anthracene and acridine cations, The importance of isomerization barriers for the C2 H2 loss and HCN loss channels. The Journal of Chemical Physics, 135,084304, 2011.
[30] H. A. B. J OHANSSON , H. Z ETTERGREN , F. H OLM , A. I. S. S EITZ , H. T. S CHMIDT, P. ROUSSEAU ,
A. Ł AWICKI , M. C APRON , A. D OMARACKA , E. L ATTOUF, S. M ACLOT, R. M AISONNY,
B. M ANIL , J. Y. C HESNEL , L. A DOUI , B. A. H UBER , AND H. C EDERQUIST. Ionization and fragmentation of polycyclic aromatic hydrocarbon clusters in collisions with keV ions. Physical Review
A, 84,043201, 2011.
[31] J. O. J OHANSSON , G. G. H ENDERSON , F. R EMACLE , AND E. E. B. C AMPBELL. Angularresolved Photoelectron Spectroscopy of Superatom Orbitals of Fullerenes. Physical Review Letters,
108,173401, 2012.
[32] R. R. J ULIAN , S. R. M ABBETT, AND M. F. JARROLD. Ion funnels for the masses, Experiments
and simulations with a simplified ion funnel. Journal of the American Society for Mass Spectrometry,
16,1708–1712, 2005.
[33] R. T. K ELLY, A. V. T OLMACHEV, J. S. PAGE , K. TANG , AND R. D. S MITH. The ion funnel, theory,
implementations, and applications. Mass Spectrometry Reviews, 29,294–312, 2010.
[34] B. K LÆRKE , Y. T OKER , D. B. R AHBEK , L. H ORNEKÆR , AND L. H. A NDERSEN. Formation and
stability of hydrogenated PAHs in the gas phase. Astronomy & Astrophysics, 549,A84, 2013.
[35] M. C. L ARSEN , P. H VELPLUND , M. O. L ARSSON , AND H. S HEN. Fragmentation of fast positive
and negative C-60 ions in collisions with rare gas atoms. The European Physical Journal D, 5,283–
289, 1999.
[36] A. Ł AWICKI , A. I. S. H OLM , P. ROUSSEAU , M. C APRON , R. M AISONNY, S. M ACLOT, F. S EITZ ,
H. A. B. J OHANSSON , S. ROSEN , H. T. S CHMIDT, H. Z ETTERGREN , B. M ANIL , L. A DOUI ,
H. C EDERQUIST, AND B. A. H UBER. Multiple ionization and fragmentation of isolated pyrene and
coronene molecules in collision with ions. Physical Review A, 83, 2011.
[37] C. T. LEE, W. T. YANG, AND R. G. PARR. Development of the Colle-Salvetti correlation-energy
formula into a functional of the electron density. Physical Review B, 37,785–789, 1988.
[38] A. L I. PAHs in Comets, An Overview. ESO Astrophysics Symposia, pages 161–175, 2009.
[39] J. LINDHARD, V. NIELSEN, AND M. SCHARFF. Approximation method in classical scattering by screened Coulomb fields. Matematisk-fysiske meddelelser udgivet af det Kongelige danske
videnskabernes selskab, 36,3, 1968.
[40] S. M ARTIN , J. B ERNARD , R. B REDY, B. C ONCINA , C. J OBLIN , M. J I , C. O RTEGA , AND L. C HEN.
Fast Radiative Cooling of Anthracene Observed in a Compact Electrostatic Storage Ring. Physical
Review Letters, 110,063003, 2013.
[41] S. M ARTIN , L. C HEN , R. B RÉDY, G. M ONTAGUE , C. O RTEGA , T. S CHLATHÖLTER , G. R EITSMA ,
AND J. B ERNARD . Statistical fragmentation of doubly charged anthracene induced by fluorine-beam
impact at 3 keV. Physical Review A, 85,052715, 2012.
[42] L. M AUNOURY, R. L EROY, T. B EEN , G. G AUBERT, L. G UILLAUME , D. L ECLERC , A. L EPOUTRE ,
V. M OUTON , J. Y. PACQUET, J. M. R AMILLON , R. V ICQUELIN , AND GANIL I ON P RODUCT G RP.
LIMBE, A new facility for low energy beams. Review of Scientific Instruments, 73,561–563, 2002.
[43] P. M. M AYER , V. B LANCHET, AND C. J OBLIN. Threshold photoelectron study of naphthalene,
anthracene, pyrene, 1,2-dihydronaphthalene, and 9,10-dihydroanthracene. The Journal of Chemical
Physics, 134,244312, 2011.
[44] D. S. M C K AY, E. K. G IBSON , K. L. T HOMAS -K EPRTA , H. VALI , C. S. ROMANEK , S. J.
C LEMETT, D. F. C HILLIER , C. R. M AECHLING , AND R. N. Z ARE. Search for Past Life on Mars,
Possible Relic Biogenic Activity in Martian Meteorite ALH84001. Science, 273,924–930, 1996.
[45] V. M ENNELLA , L. H ORNEKÆR , J. T HROWER , AND ACCOLLA M. The Catalytic Role of Coronene
for Molecular Hydrogen Formation. The Astrophysical Journal, 745,L2, 2012.
[46] E. R. M ICELOTTA , A. P. J ONES , AND A. G. G. M. T IELENS. Polycyclic aromatic hydrocarbon
processing in interstellar shocks. Astronomy & Astrophysics, 510, 2010.
[47] P. M. M ISHRA , J. R AJPUT, C. P. S AFVAN , S. V IG , AND U. K ADHANE. Electron emission and electron transfer processes in proton-naphthalene collisions at intermediate velocities. Physical Review
A, 88, 2013.
[48] J. A. M ONTGOMERY J R ., M. J. F RISCH , J. W. O CHTERSKI , AND G. A. P ETERSSON. A complete
basis set model chemistry. VI. Use of density functional geometries and frequencies. The Journal of
Chemical Physics, 110,2822–2827, 1999.
[49] J. A. M ONTGOMERY J R ., M. J. F RISCH , J. W. O CHTERSKI , AND G. A. P ETERSSON. A complete
basis set model chemistry. VII. Use of the minimum population localization method. The Journal of
Chemical Physics, 112,6532–6542, 2000.
[50] J. S. PAGE , R. T. K ELLY, K. TANG , AND R. D. S MITH. Ionization and transmission efficiency in
an electrospray ionization-mass spectrometry interface. Journal of the American Society for Mass
Spectrometry, 18,1582–1590, 2007.
[51] W. PAUL, H. P. REINHARD, AND U. VONZAHN. Das elektrische Massenfilter als Massenspektrometer und Isotopentrenner. Zeitschrift für Physik, 152,143–182, 1958.
[52] F. PAUZAT AND Y. E LLINGER. The 3.2±3.5 µm region revisited - II. A theoretical study of the
effects of hydrogenation on some model PAHs. Monthly Notices of the Royal Astronomical Society,
324,355–366, 2001.
[53] J. P OSTMA , S. BARI , R. H OEKSTRA , A. G. G. M. T IELENS , AND T. S CHLATHÖLTER. Ionization
and Fragmentation of Anthracene upon Interaction with keV Protons and α Particles. The Astrophysical Journal, 708,435–444, 2010.
[54] J. P OSTMA , R. H OEKSTRA , A. G. G. M. T IELENS , AND T. S CHLATHÖLTER. The Astrophysical
Journal, 783,61, 2014.
[55] M. J. PUSKA AND R. M. NIEMINEN. Atoms embedded in an electron gas, Phase shifts and
cross-sections. Physical Review B, 27,6121–6128, 1983.
[56] M. R APACIOLI , C. J OBLIN , AND B OISSEL P. Spectroscopy of polycyclic aromatic hydrocarbons
and very small grains in photodissociation regions. Astronomy & Astrophysics, 429,193–204, 2005.
[57] E. R AULS AND H ORNEKÆR L. Catalyzed Routes to Molecular Hydrogen Formation and Hydrogen
Addition Reactions on Neutral Polycyclic Aromatic Hydrocarbons under Interstellar Conditions. The
Astrophysical Journal, 679,531, 2008.
[58] G. R EITSMA , H. Z ETTERGREN , S. M ARTIN , R. B REDY, L. C HEN , J. B ERNARD , R. H OEKSTRA ,
AND T. S CHLATHÖLTER . Activation energies for fragmentation channels of anthracene dicationsexperiment and theory. Journal of Physics B, Atomic, Molecular and Optical Physics, 45,215201,
2012.
[59] H. R ICHTER AND J. B. H OWARD. Formation of polycyclic aromatic hydrocarbons and their growth
to soot - a review of chemical reaction pathways. Progress in Energy and Combustion Science,
26,565–608, 2000.
[60] M. M. ROSS AND J. H. CALLAHAN. Formation and characterization of carbon mol.-helium
(C60 He+). The Journal of Physical Chemistry, 95,5720–5723, 1991.
[61] H. T. S CHMIDT, R. D. T HOMAS , M. G ATCHELL , S. ROSÉN , P. R EINHED , P. L OFGREN ,
L. B RANNHOLM , M. B LOM , M. B JORKHAGE , E. BACKSTROM , J. D. A LEXANDER , S. L EON TEIN , D. H ANSTORP, H. Z ETTERGREN , L. L ILJEBY, A. K ALLBERG , A. S IMONSSON , F. H ELL BERG , S. M ANNERVIK , M. L ARSSON , W. D. G EPPERT, K. G. R ENSFELT, H. DANARED ,
A. PAAL , M. M ASUDA , P. H ALLDEN , G. A NDLER , M. H. S TOCKETT, T. C HEN , G. K ALLERSJO ,
J. W EIMER , K. H ANSEN , H. H ARTMAN , AND H. C EDERQUIST. First storage of ion beams in the
Double Electrostatic Ion-Ring Experiment, DESIREE. Review of Scientific Instruments, 84,055115,
2013.
[62] K. S ELLGREN , M. W. W ERNER , J. G. I NGALLS , J. D. T. S MITH , T. M. C ARLETON , AND
C. J OBLIN. C60 in Reflection Nebulae. The Astrophysical Journal Letters, 722,L54–L57, 2010.
[63] S. A. S HAFFER , A. T OLMACHEV, D. C. P RIOR , G. A. A NDERSON , H. R. U DSETH , AND R. D.
S MITH. Characterization of an improved electrodynamic ion funnel interface for electrospray ionization mass spectrometry. Analytical Chemistry, 71,2957–2964, 1999.
[64] A. L. S KOV, J. D. T HROWER , AND L. H ORNEKÆR. Polycyclic aromatic hydrocarbons catalysts for
molecular hydrogen formation. Faraday Discussions, 168,223, 2014.
[65] J. D. T. S MITH , B. T. D RAINE , D. A. DALE , J. M OUSTAKAS , R. C. K ENNICUTT J R ., G. H ELOU ,
L. A RMUS , S HETH K. ROUSSEL , H., G. J. B ENDO , B. A. B UCKALEW, D. C ALZETTI , C. W.
E NGELBRACHT, K. D. G ORDON , D. J. H OLLENBACH , A. L I , S. M ALHOTRA , E. J. M URPHY, AND
F. WALTER. The Mid-Infrared Spectrum of Star-forming Galaxies, Global Properties of Polycyclic
Aromatic Hydrocarbon Emission. The Astrophysical Journal, 656,770–791, 2007.
[66] I. M. TABAN , L. A. M C D ONNELL , A. ROMPP, I. C ERJAK , AND R. M. A. H EEREN. SIMION
analysis of a high performance linear accumulation octopole with enhanced ejection capabilities.
International Journal of Mass Spectrometry, 244,135–143, 2005.
[67] R. D. T HOMAS , H. T. S CHMIDT, G. A NDLER , M. B JORKHAGE , M. B LOM , L. B RANNHOLM ,
E. BACKSTROM , H. DANARED , S. DAS , N. H AAG , P. H ALLDEN , F. H ELLBERG , A. I. S. H OLM ,
H. A. B. J OHANSSON , A. K ALLBERG , G. K ALLERSJO , M. L ARSSON , S. L EONTEIN , L. L IL JEBY, P. L OFGREN , B. M ALM , S. M ANNERVIK , M. M ASUDA , D. M ISRA , A. O RBAN , A. PAAL ,
P. R EINHED , K.-G. R ENSFELT, S. ROSÉN , K. S CHMIDT, F. S EITZ , A. S IMONSSON , J. W EIMER ,
H. Z ETTERGREN , AND H. C EDERQUIST. The double electrostatic ion ring experiment, A unique
cryogenic electrostatic storage ring for merged ion-beams studies. Review of Scientific Instruments,
82,065112, 2011.
[68] A. G. G. M. T IELENS. Interstellar polycyclic aromatic hydrocarbon molecules. Annual Review of
Astronomy and Astrophysics, 46,289–337, 2008.
[69] A. G. G. M. T IELENS. The molecular universe. Reviews of Modern Physics, 85,1021, 2013.
[70] B. A. TRUBNIKO AND Y. N. YAVLINSK. Energy Loss of Slow Protons in Metals. Soviet Physics
JETP-USSR, 21,167, 1965.
[71] M. V UJOVIC , M. M ATIC , B. C OBIC , AND Y U . S. G ORDEEV. Attenuation method for fast ion
beams, metastable state population and cross section measurements. Journal of Physics B, Atomic
and Molecular Physics, 5,2085–2097, 1972.
[72] Y. WANG , H. Z ETTERGREN , P. ROUSSEAU , T. C HEN , M. G ATCHELL , M. H. S TOCKETT, A. D O MARACKA , L. A DOUI , B. A. H UBER , H. C EDERQUIST, A LCAMÍ M., AND F. M ARTÍN . Physical
Review A, 89,062708, 2014.
[73] T. WEISKE, J. HRUSAK, D. K. BOHME, AND H. SCHWARZ. Formation of endohedral carboncluster noble-gas compounds with high-energy bimolecular reactions, C60Hen+ (n=1,2). Chemical
Physics Letters, 186,459–462, 1991.
[74] B. W EST, F. U SELI -BACCHITTA , H. S ABBAH , V. B LANCHET, A. B ODI , P. M. M AYER , AND
+
C. J OBLIN. Photodissociation of Pyrene Cations, Structure and Energetics from C16 H+
10 to C14 and
Almost Everything in Between. The Journal of Chemical Physics, 118,7824–7831, 2014.
[75] B. E. W OLF. Handbook of ion surces.
[76] M. YAMASHITA AND J. B. FENN. Electrospray ion source. Another variation on the free-jet
theme. The Journal of Physical Chemistry, 88,4451–4459, 1984.
[77] J. Z ELENY. Physical Review, 10,1, 1917.
[78] H. Z ETTERGREN , P. ROUSSEAU , Y. WANG , F. S EITZ , T. C HEN , M. G ATCHELL , J. D. A LEXAN DER , M. H. S TOCKETT, J. R ANGAMA , J. Y. C HESNEL , M. C APRON , J. C. P OULLY, A. D O MARACKA , A. M ÉRY, S. M ACLOT, H. T. S CHMIDT, L. A DOUI , M. A LCAMÍ , A. G. G. M.
T IELENS , F. M ARTÍN , B. A. H UBER , AND H. C EDERQUIST. Formations of Dumbbell C118 and
C119 inside Clusters of C60 Molecules by Collision with alpha Particles. Physical Review Letters,
110,185501, 2013.
[79] Y. Z HANG AND S. K WOK. Detection of C60 in the Protoplanetary Nebula IRAS 01005+7910. The
Astrophysical Journal, 730,126, 2011.
[80] J. F. Z IEGLER , J. P. B IERSACK , AND M. D. Z IEGLER. SRIM - The Stopping and Range of Ions in
Matter. 2008.