Statistical and Non-statistical frag-mentation of large molecules in col-lisions with atoms: Polycyclic Aromatic Hydrocarbons and Fullerenes

Statistical and Non-statistical fragmentation of large molecules in colli- sions with atoms – Polycyclic Aromatic Hydrocarbons and Fullerenes

Tao Chen

Statistical and Non-statistical frag- mentation of large molecules in col- lisions with atoms

Polycyclic Aromatic Hydrocarbons and Fullerenes

Tao Chen

Abstract

In this work, I present a study of the fragmentation of Polycyclic Aromatic Hydrocarbon (PAH) molecules and fullerenes following collisions with atoms or atomic ions. The study is partly based on experiments at two different cen- ter of mass energy regimes. At the higher collision energy (∼ 10 keV), the molecules are mainly excited through interactions between the fast ion/atom and the electron cloud (electronic stopping processes). The excitation energy is then rapidly distributed across the molecules’ vibrational degrees of free- dom. The lowest energy dissociation channels, H- and C

H

-loss from PAHs and C

-loss from fullerenes, are then statistically favoured. This type of decay is referred to as statistical fragmentation. For the lower center of mass collision energies (∼ 100 eV), single atoms may be knocked out in close atom-atom col- lisions. Such non-statistical fragmentation processes are very fast and they are due to nuclear stopping processes. I will show that non-statistical fragmenta- tion processes become dominant for isolated PAHs with more than about 50 carbon atoms in the 100 eV regime. Prompt atom knockout gives highly re- active fragments which may form covalent bonds with other molecules and atoms. Dumbbell shaped C

molecules are detected following collisions be- tween 22.5 keV He

or 12 keV Ar

ions and clusters of C

molecules. This molecular fusion process is most likely due to single atom knock out and C

+ C

collisions inside the fragmenting cluster. Knockout of single carbon atoms from PAHs could, e.g., be a first step in forming nitrogen containing PAHs - so called PANHs. The theoretical part of the work is carried out with the aid of Monte Carlo simulations. The energy loss due to nuclear stopping is cal- culated using two different potentials describing atom-atom interactions. The energy loss due to electronic stopping is calculated with the aid of friction co- efficients for atoms interacting with PAH or fullerene electron clouds. Based on such simulations I present a simple scaling formula for total non-statistical fragmentation cross sections for H+PAH and He+PAH collisions in the 50 eV to 10 keV enrgy range.

c

Tao Chen, Stockholm 2014 ISBN 978-91-7447-869-3

Printed in Sweden by US-AB, Stockholm 2014

Distributor: Department of Physics, Stockholm University

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 C

and C

inside Clusters of C

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. Tie- lens, F. Martín, B. A. Huber, and H. Cederquist PHYSICAL RE- VIEW 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. Tie- lens, 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 col- lisions with atoms

M. Gatchell, M. H. Stockett, Patrick Rousseau, T. Chen, K Ku- lyk, H. T. Schmidt, J. Y. Chesnel, A. Domaracka, A. Méry, S.

Maclot, L. Adoui, K. Støchkel, P. Hvelplund, Y. Wang, M. Al- camí, B. A. Huber, F. Martín, H. Zettergren, H. Cederquist IN- TERNATIONAL JOURNAL OF MASS SPECTROMETRY (2013).

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.

B¯erzin¸š, 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 RE- VIEW A, 89, 032701 (2014).

DOI: 10.1103/PhysRevA.89.032701

PAPER V: Absolute fragmentation cross sections in atom-molecule col- lisions: Scaling law for non-statistical PAHs fragmentations 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, submitted.

Reprints were made with permission from the publishers.

Author’s contribution

The work included in this thesis is the result of collaborative efforts by research groups at Stockholm University, the CIMAP laboratory in Caen, France, Uni- versidad Autónoma de Madrid, Spain, and Leiden Observatory, Netherlands.

My main contributions are theoretical work, namely Monte Carlo simulations of the interaction between PAH molecules and ions. I have also assisted in the interpretation of the experimental results. I calculated the cross sections for collision between 22.5 keV He

and C

clusters for paper I. For paper II, I calculated the typical electronic and nuclear stopping energies for col- lision between 12 keV Ar

or 22.5 keV He

and fullerene clusters [C

]

for n = 1-55. In paper III we discuss non-statistical fragmentation of PAHs and fullerenes in collisions with atoms. I have provided nuclear and electronic stopping calculations to investigate the carbon and hydrogen loss processes and the formation of large molecules (e.g. C

).

I also carried out part of the quantum chemical calculations of molecular structures and electron density distribution which I then used in my stopping calculations. For paper IV, I calculated molecular structures, electron densi- ties and cross sections of carbon/hydrogen losses for several PAH molecules.

The calculated knockout cross sections are consistent with our experimental

results. For paper V, I analysed the mass spectra and explained the differences

between low energy collisions (Stockholm University) and high energy colli-

sions (CIMAP laboratory, Caen) by the stopping model. Two different scatter-

ing potentials are used to treat the non-statistical fragmentation process. I have

developed a simple scaling law for estimating of non-statistical fragmentation

cross sections.

Contents

Abstract iv

List of Papers vii

Author’s contribution ix

1 Introduction 13

2 Experimental techniques 17

2.1 Low energy collisions . . . . 17

2.2 High energy collisions . . . . 19

3 Theoretical tools and models 23 3.1 Molecular structure calculations . . . . 23

3.2 Nuclear stopping . . . . 24

3.3 Electronic stopping . . . . 28

4 Results & Discussion 31 4.1 Collisions with monomer targets . . . . 31

4.1.1 PAHs . . . . 31

4.1.2 Fullerenes . . . . 33

4.2 Collisions with cluster targets . . . . 37

Summary & Outlook xli

References xliii

1. Introduction

Isolated, internally heated molecules may release their excess energies by emit- ting photons, electrons, atoms or molecules (see e.g. Paper IV). In collisions with e.g. atoms or atomic ions at sufficiently high velocities, the excess en- ergy usually has time to distribute across all internal degrees of freedom of the molecular system before it decays. This means that the lowest energy dissociation channels, which are H-loss or C

H

-loss from Polycyclic Aro- matic Hydrocarbon (PAH) molecules and C

-loss from fullerenes, dominate.

These processes are commonly referred to as statistical fragmentation. For large molecular systems with many degrees of freedom, the internal energy needs to be significantly higher than the dissociation energies to induce statis- tical fragmentation on the time scale of the experiment, which here is of the order tens of microseconds (∼ 10

seconds).

An example of a non-statistical fragmentation process is when a single car- bon atom is knocked out directly in a collision through Rutherford-like atom- atom scattering. This process has been detected earlier in 50 keV C

+ He/Ne collisions as a small contribution to the total fragmentation yields [1–3]. In these cases, the knockout takes place on the femtosecond timescale, which is substantially shorter than the typical vibrational timescales of picoseconds.

In this work, we study non-statistical fragmentation at center of mass ener- gies in the range between 50 eV and 1 keV. The experimental and theoretical results show that for large molecules colliding with light atoms (e.g. He), non- statistical fragmentation is the dominant process for the lower energies. The PAH molecules have been specifically chosen for this study since fragments from non-statistical fragmentation (single carbon loss) may be easily sepa- rated from statistical fragmentation processes in which two or more carbon atoms are lost. Other large molecules with more irregular structures do not show the same behavior which means that non-statistical processes are very difficult to isolate experimentally.

PAHs (C

H

) are organic compounds that typically contain three or more fused benzene-like rings and they often form planar structures (see Figure 1.1).

Fullerenes molecules (C

) consist of twelve all-carbon pentagons and zero or at

least two all-carbon hexagons, forming hollow sphere structures. In this work,

fullerenes with 60 carbon atoms (C

) are studied (see Figure 1.1). Both PAHs

and fullerenes have received considerable attention in environmental sciences

13

[4], medical research [5], material science [6] and astrophysics [7]. There are many observations which suggest that fullerenes and PAHs are present in space e.g. in the interstellar medium, in comets, and in meteorites [7, 8]. A vast number of experimental [9–11] and theoretical [1, 3, 12] investigations have been carried out to study the excitation of these molecules by absorption of one or several photons [13, 14], by the impact of energetic electrons [15], or atoms [16]. The studies have indeed revealed that the lowest dissociation pathways for PAHs and fullerenes correspond to losses of H-atoms or C

H

-molecules (at energies of 5-7 eV [17]) and C

-molecules (∼ 10 eV), respectively. Loss of a single carbon atom from these systems is associated with a dissociation energy of more than 15 eV [18] and is thus highly disfavoured in statistical fragmentation. The latter channel may therefore be used as a fingerprint for non-statistical fragmentation (knockout) processes.

Anthracene C14H10

Pyrene C16H10

Chrysene C18H12

Perylene C20H12

Benzo[ghi]Perylene C22H12

Coronene C24H12

Ovalene

C₃₂H₁₄ Circumpyrene

C₄₂H₁₆ Circumcoronene

C₅₄H₁₈ Fullerene C60

Figure 1.1: Examples of planar Polycyclic Aromatic Hydrocarbons (PAHs) and the three-dimensional (spherical) C

molecule.

Interestingly, ions in plasma shock waves from supernova explosions have

typical energies less than 1 keV and may interact with interstellar PAHs ex-

posed to such shocks [19]. In this work, we demonstrate that non-statistical

fragmentation is the dominant destruction mechanism for large PAHs at such

energies. Non-statistical fragmentation yields different, more reactive frag-

ments than statistical processes and may thus play an important role in the

formation of larger molecules through secondary reactions with other atoms or

molecules [20]. As shown in Paper I and Paper II, this phenomena has been

observed in loosely bound van der Waals clusters of C

molecules colliding

with 22.5 keV He

or 12 keV Ar

ions. We found that dumbbell shaped C

14

molecules are formed in this process when a single carbon atom is knocked out from a C

molecule and a highly reactive fragment C

is formed. The C

may then react with a neighboring C

molecule to form covalent bonds on pi- cosecond time scales [12]. For large molecules, knockout processes have only been observed in isolated C

molecules as small contributions to the fragmen- tation spectrum and only for negatively charged C

ions [1, 2]. We have used a new experimental setup to study non-statistical fragmentation processes in detail and specifically to study how their importance in relation to statistical fragmentation processes changes with the size of the molecular system.

The thesis is organized as follows: We describe the experimental tech- niques used for our studies of collisions between PAH or fullerene cations and different noble gases at center of mass energies from about 100 eV and up to about 1 keV in Chapter 2. In the same Chapter we also describe the method used to study collisions between atomic ions and neutral (PAH or fullerene) targets at energies of tens of keV and how we produce neutral molecular clus- ters. In Chapter 3, we give some details of the theoretical calculations and the Monte Carlo simulations. The experimental and theoretical results are dis- cussed in Chapter 4 where we present a simple scaling law for the total non- statistical fragmentation for PAH molecules of arbitrary size colliding with H or He in the center of mass energy range from a few tens of eV to 10 keV. We summarize the main conclusions along with an outlook in Chapter 5.

15

16

2. Experimental techniques

The experiments are performed using two different experimental setups. One setup is located at Stockholm University as a part of the DESIREE-facility [21, 22] with instruments for various types of ion fragmentation and stability experiments. A single pass setup and a double electrostatic ion storage ring with a merging section for ion-ion collisions are central parts of this facility.

The single pass setup is utilized to produce PAH cations with various kinetic energies where we study prompt knockout processes in collisions with noble gases. The experiments for low energy collisions, which have center of mass energy less than 1 keV, are performed with this setup.

The second experimental setup is located at the ARIBE facility at the GANIL laboratory in Caen, France. Beams of atomic ions are produced in an Electron Cyclotron Resonance (ECR) ion source, and the neutral molecules/clusters of PAHs/fullerenes are prepared as a target to interact with the ion beams.

Here, the center of mass collision energies are orders of magnitude higher which leads to other fragmentation processes than at lower energies.

2.1 Low energy collisions

At Stockholm University, a CID (Collision Induced Dissociation) type exper- imental setup has been built up in order to study the details of fragmentation processes for low energy collisions between cations of molecule and various neutral gases. The electrospray ionization (ESI) technique (see Figure 2.1) is applied to ionize the molecules [23, 24]. The molecules are dissolved in ei- ther a suitable proton-donating acidic solution or in a solution that ionizes the molecules. The solution of choice is filled into a syringe and then pushed via a small, flexible glass tube to a needle. A high voltage (of 2-3 keV) applied to the needle creates a strong electric field between it and a capillary which serves as a counter-electrode causing charged droplets to be ejected from the solution at the tip of the needle [25]. The capillary is heated to ensure efficient evaporation of the remaining solvent molecules [26].

The ionized bare molecules exit the capillary and enter a radio-frequency

ion funnel [27–29]. This ion funnel collects the ions into a beam and is coupled

to two sets of octopoles [30]. The first one may be utilized to accumulate the

17

AcceleratioGas Cell Lens

Acceleration Lens Deflectors Cryogenic Ring

Electrode Trap

Capillary 8-pole Trap Mass Filter

MCP Ion Funnel 8-pole Guide

Electron Multiplier Quadrupole Deflector

Needle Slits

Figure 2.1: Schematic of the experimental setup at Stockholm University.

Molecular ions are produced by the electrospray technique and collected by an ion funnel. The ions are then guided at low energy by two octopole guides in series. The quadrupole mass filter selects the mass-to-charge ratio of the ions.

The mass-selected ions are typically accelerated to a few keV before entering the gas cell, where they collide with noble gases under single collision conditions.

After interaction the fragments are focused by a einzel lens and deflected accord- ing to their mass-to-charge ratio. A micro-channel plate (MCP) with a position sensitive resistive anode is used to detect intact and fragmented ions.

ions in bunches (not used in the current work), while the second one guides the ions to the next chamber.

A quadruploe mass filter [31] is used to select PAH cations according to their mass-to-charge ratios. The mass-selected ions are then travelling straight through a quadrupole deflector and then accelerated as they leave the high- voltage platform (on which the ion source and the rest of the equipment for low energy ion transport is mounted) to enter the experimental beam line at ground potential. An einzel lens and series of deflectors are used to guide the beam after acceleration to the collision chamber. The base pressure in the collision chamber is about 10

mbar. A typical ion beam intensity at the collision cell is a few thousand ions per second at a few keV. The ion beam is focused and enters a 4 cm long collision cell containing noble gas at a pressure which may be controlled with a needle valve and measured absolutely by means of a capacitance manometer. The fragments and intact PAH ions exiting the collision cell are deflected according to their mass-to-charge ratio.

A micro-channel plate (MCP) with a position sensitive resistive anode [32] is used to detect the ions. By recording the position of each individual event on the detector and the settings of the deflector voltages at that moment we may reconstruct a high resolution fragment spectrum although the slits in front of the detector are left wide open.

Absolute total fragmentation cross sections were determined from the at- tenuations of the primary ion beams as functions of the gas pressure in the cell.

The slope of this line in a lin-log plot gives the total cross section (see Figure

18

Pressure (mTorr)

1 2 3 4 5 6

C

H

+He C

H

+Ne

C

H

+Ar C

H

+Xe

N o rm al iz e d R at e

0.1 1

Pressure (mTorr)

1 2 3 4 5 6

C

H

+He C

H

+He C

H

+He

(a) (b)

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 (a) and for Pyrene cations colliding with four noble gases (b). The slope of the fitted lines in (a) and (b) yield the total fragmentation cross sections. The pressure is measured by means of a capacitance manometer. Statistical errors are smaller than the data points.

2.2). The slits in front of the detector could be set very narrow for the atten- uation measurements such that the hydrogen loss channels could be included in the total fragmentation cross sections. Alternatively they may be opened slightly such that only processes in which at least one heavy atom is lost from the molecule are included in the measured attenuation cross sections. Figure 2.2a shows the attenuation of several PAH cations in He at 110 eV center of mass energy, in which the slits are narrow, i.e. H-loss channels are included.

2.2 High energy collisions

The experiments for high center of mass energy (> 10 keV) collisions are performed in Caen, France [33, 34]. In these experiments, various keV ion beams are produced using an Electron Cyclotron Resonance (ECR) ion source [35, 36]. The ion beam is guided to the interaction region where it crosses with a beam of neutral molecules or clusters.

The neutral molecules or clusters are produced in separate electrically

heated cylindrically shaped ovens, in which commercially available molecular

powders are loaded. In order to bring the molecules into the gas phase, differ-

ent temperatures are used, e.g. a temperature of 60

C is applied for producing

monomer beam of anthracene and pyrene molecules, while 250

C is required

to produce a monomer beam of coronene molecules. The cluster source oven

19

is mounted inside a container filled with helium buffer gas on a pressure of the order of millibars (see Figure 2.3). Liquid nitrogen cools the helium gas down to temperatures below 100 K. The molecules effusing from the oven will form clusters when their internal temperatures are low enough and when the number densities are sufficiently high. For the latter reason the oven temperatures are often higher for production of clusters than for production of monomer targets of a given species.

C60

He gas at ~ 1 mbar

Liquid N2 < 100 K

Figure 2.3: Schematic of the C

cluster source oven and enclosure. The cluster source oven is mounted inside a container filled with He buffer gas at a pressure about 1 mbar. Liquid nitrogen is used to cool the He gas to temperatures below 100 K.

There is a beam chopper, which pulses the ion beams in ∼ 1µs long pulses

before they enter the interaction region. Intact target ions and their fragments

after the collisions are analyzed with respect to their mass-to-charge ratios

by means of a time-of-flight mass spectrometer (Figure 2.4). The time-of-

flight spectrometer consists of four regions. The ion beam interacts with tar-

get molecules in the extraction region, where the molecules are ionized and/or

fragmented after interaction. Ions are extracted by a pulsed homogeneous elec-

tric field. The extracted ions are then accelerated in the acceleration region, in

which the initial spatial spread of the ions is compensated. The acceleration

region together with the following field-free drift region make ions produced

at different positions in the extraction region arrive at the same time at the

end of drift region [37]. The ions are further accelerated after the field-free

drift region in order to increase the secondary electron yield for ions hitting

the metal plate. The electrons are guided by a weak magnetic field towards a

MCP detector, which is placed with its active front surface perpendicular to

the flight path of the ions. The signals from MCP detector are amplified and

discriminated and the time between extraction and detection for each hit on the

20

detector are recorded.

-4 kV Metal plate

2.145 kV -4 kV 0 V

Interaction region

e-e-e- e-

e-e-

Tar g et col lisi o n p ro ducts

~10 -

sec.

Weak magnetic field

Extraction Acceleration

Field-free drift

MCP 0 V

-13 kV -15.4 kV

Figure 2.4: Schematic of the time-of-flight mass spectrometer used at Caen. Ion beams with ∼ 1µs pulse length enter the interaction region. The product ions are accelerated and drift at constant velocity through the field-free region. Secondary electrons are produced when the ions hit the metal plate at high voltage (here -23 kV). The secondary electrons are guided by a weak magnetic field and detected by a MCP detector.

21

22

3. Theoretical tools and models

This section describes the theoretical tools and models which have been used in the present work. We will mainly deal with molecular excitation processes by considering electronic and nuclear stopping processes for atoms or ions passing through (or passing close to) isolated molecules or clusters. The mech- anisms behind this is that particles colliding with a molecule may lose some of its kinetic energy directly to the electron cloud and by scattering on individual nuclei in the molecule inducing vibrational motion. When a molecule interacts with energetic atoms/ions, photons, or electrons, its internal energy increases and this energy is typically statistically distributed on the molecule’s internal degrees of freedom before it relaxes. This relaxation may in general occur through radiative decay, thermionic emission of electrons, or/and by fragmen- tation. Here, we will discuss the importance of non-statistical fragmentation processes as function of the center of mass collision energy for light (H and He) and heavy (Ar and Xe) ions or atoms colliding with PAH molecules, fullerenes or their clusters. Such processes are believed to be important when plasma shock waves pass through stellar atmospheres, the interstellar medium etc [19].

Some of these environments are believed to contain PAHs and fullerenes. For the simulations we will use the Monte Carlo technique where we take all possi- ble orientations of the molecules and all contributing impact parameters (with respect to the center of the molecule) into account.

3.1 Molecular structure calculations

Molecular structures and electron density distributions are calculated by means of Density Functional Theory (DFT) methods. The calculations are carried out using the Gaussian09 package [38], the B3LYP functional [39, 40], and the 6- 31G(d) and the 6-311++G(2d,p) basis sets. The coordinates of the optimized molecule are used in the nuclear stopping calculations, and the molecular or- bital coefficients are used to calculate the valance electron densities for the electronic stopping calculations (see Paper V for details).

23

3.2 Nuclear stopping

For the interaction between a projectile atom with mass M

, atomic number Z

and a target atom (M

, Z

), see Figure 3.1, the energy lost by the projectile in this process is described by [1]

T

= T

sin

φ

2 (3.1)

where T

is the maximum energy transfer for head-on collisions, and is given by

T

= 4M

M

(M

+ M

)

E (3.2)

E is kinetic energy of projectile in laboratory system. The scattering angle in the center of mass system φ is related to the impact parameter p by [41]:

sin φ 2 = cos





 Z

rmin

pdr r

q 1 −

CM

− (

)







(3.3)

where E

is the center of mass energy of the collision system, r

is the distance of closest approach between the projectile and target atom, its value can be found from the following equation

1 − V (r

) E

−

 p r



= 0 (3.4)

V(r) is the interaction potential − for example the Bohr potential:

V (r) = Z

Z

r f (x) (3.5)

where f (x) is the screening function. In 1968, Lindhard [42] introduced power- law screening functions

f

(x) = k

s x

(3.6)

where s is an integer, k

a constant determined by s and x is

x = r

a

= r q

Z

+ Z

0.8853a

(3.7)

Here a

is the screening length, a

is the Bohr radius. Lindhard

applied an approximate method to evaluate φ (Eq. 3.3) for such potentials. For

24

Figure 3.1: The schematic drawing showing the collision between two atoms.

the case s = 2, k

= 0.831, an approximate solution to Eq. 3.2 can be written [1, 42]

sin φ 2 =

π 8

p

p

+

p

(3.8)

As described in Paper V of this thesis the corresponding analytical solution is

sin φ

2 = cos π p 2

q p

+ p

(3.9)

where

p

= 0.831Z

Z

a

2E

(3.10) Figure 3.2 shows the comparison between Lindhard approximate result and the present analytical solution of the scattering angle φ for the case E

= 0.1 keV, Z

= 1, and Z

= 6 as a function of the impact parameter. For comparison we also study the Ziegler-Biersack-Littmark (ZBL) potential [41], which is commonly used for studies of ions or atoms interacting with solids

f

(x) = 0.1818e

+ 0.5099e

+

0.2802e

+ 0.02817e

(3.11)

25

Figure 3.2: The comparison between Lindhard approximate expression and the present analytical solution for the scattering angle φ as a function of impact pa- rameter.

where

x = r

a

= r(Z

+ Z

)

0.8853a

(3.12)

and a

is the ZBL screening length. The integral in Eq 3.3 is evaluated numerically in the case of the ZBL potential.

Figure 3.3 shows a comparison between the results obtained with the Lind- hard (analytical solution) and the ZBL potentials for E

= 100 eV, Z

= 1, and Z

= 6 as a function of the impact parameter.

Due to nuclear stopping processes, one or several atoms may be imme- diately knocked out when an atom collides with a molecule. This process is non-statistical as the time scale for the knockout is on the order of femtosec- onds while the typical vibrational time scales are much longer - picoseconds.

Thus there is no time to distribute the energy transferred to one (or several) individual atoms in the molecule to vibrational energy in the whole system be- fore the fragmentation occurs. By using the analytical solution for the relation between impact parameter, p, and scattering angle for the Lindard potential (with s=2, and k

=0.831) we get the following analytical formula for the sin- gle atom knock out cross section per atom (in the molecule)

26

Figure 3.3: A 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 (E

= 100 eV).

Figure 3.4: Calculated absolute cross sections for H + C, He + C, H + H and He + H scattering. T

is the threshold for knocking out a carbon from a PAH molecule, and T

is the threshold for knocking out a hydrogen from a PAH molecule.

27

σ = π p

= 4π p

π

arccos

( p

E

/T

) − 4 (3.13) where E

is the threshold energy for knockout. Molecular dynamics simula- tions 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). Figure 3.4 shows the cross section calculated by using Eq. 3.13 for H + C, He + C, H + H and He + H scattering. For carbon knockout, the cross section increases with increasing collision energy and reaches maxima at 140 and 370 eV for collisions with He and H, respectively.

3.3 Electronic stopping

The electronic excitation energies deposited by the atoms in a molecule are determined by treating the non-localised electrons in PAHs as free electron gases. The energy lost by ions traveling through an electron gas depends on the electron density distribution along the ion trajectories [43]. This density is inhomogeneously distributed within the molecules, and is characterized by the standard one-electron radius:

r

=

 3

4πn



(3.14) where n

is the valence electron density (see Chapter 3.1). Here we assume that the electronic energy loss T

is proportional to projectile velocity [44].

Then, the electronic stopping power is given by S = dT

dR = γ(r

)v (3.15)

where γ(r

) is the so called friction coefficient, which is a function of r

and related to the phase shifts δ

by

γ (r

) = 3 k

r

∞

∑

l=0

(l + 1)sin

(δ

− δ

) (3.16) where k

is the magnitude of the Fermi wave vector. Puska and Nieminen [45]

calculated the friction coefficient for various atoms and r

. Their results are well described by means of exponential functions as can be seen in Figure 3.5.

Alternatively, a power law fitting function may be used.

28

Figure 3.5: The friction coefficient of hydrogen and helium as a function of density parameter r

. The solid curves are exponential fitting functions, and the red squares are data from Puska and Nieminen [45].

29

30

4. Results & Discussion

We have performed several experiments in order to investigate the excitation, ionization, and fragmentation properties of PAHs and fullerenes and their clus- ters. We will discuss the results for PAH and fullerene monomer targets sepa- rately in Section 4.1 and the results for the cluster targets in Section 4.2.

4.1 Collisions with monomer targets

4.1.1 PAHs

Figure 4.1 shows the mass spectra due to C

H

+ He and He

+ C

H

col- lisions at center of mass energies of 110 eV and 11 keV, respectively. The cor- responding simulation results for face-on atom trajectories through anthracene molecule are shown in the insets. For high energy collisions (upper panel, Figure 4.1), electronic stopping is the most prominent energy loss mechanism and thus dominates the total stopping energy [46]. The electrons are excited locally along the ion trajectories on the sub femtosecond timescales of the col- lision and in most cases there is time to redistribute this internal energy on the vibrational degrees of freedom of the molecule before fragmentation. As the internal energy is typically 40 eV, i.e. well above the lowest dissociation energy channels of about 5 eV (loss of H or C

H

) a large fraction of the collisions will lead to statistical fragmentation processes in the 11 keV case [10, 47]. This is consistent with the distribution of fragments in the mass spec- trum shown in the upper panel of Figure 4.1. The highest peak on the right hand side is due to intact singly charged monomer anthracene (m/q=178). The peaks immediately to the left of the main peak are due to moderately heated systems for which sequential losses of H-atoms and/or C

H

-molecules are the dominant decay pathways. The smaller fragments are due to more violent collisions in which larger amounts of energy are deposited (see Paper V for details).

For low energy collisions (110 eV), the fragment mass spectrum is dif-

ferent. As shown in the insets in the lower panel of Figure 4.1, the nuclear

stopping dominates the energy loss in this collision energy regime. Accord-

ing to the molecular dynamic simulations by Postma et al. [18], only nuclear

stopping above about 27 eV will lead to prompt carbon knockout or 9 eV for

31

hydrogen knockout (see Paper V for details). The stopping calculation shows that a substantial fraction of the trajectories lead to nuclear energy transfers exceeding these threshold at 110 eV center of mass energy. This explains why the fragment distribution in the mass spectrum is shifted towards larger masses, suggesting that the anthracene molecule on the average are much colder than for the high energy collisions. Here, the single carbon atom losses peak is prominent, which is a clear signature of a non-statistical fragmentation pro- cess. As shown in Paper V, the reasoning here is that the much higher disso- ciation energies of C- or CH

-loss compared to C

H

- or H- loss makes this channel negligibly weak whenever statistical fragmentation dominates.

Figure 4.1: Comparison of mass spectra due to C

H

+ He at 110 eV (upper panel) and He

+ C

H

at 11 keV (lower panel). The 2D insets show from left to right: electronic, nuclear and total calculated stopping energies.

The calculated non-statistical, statistical and total (statistical + non-statistical)

fragmentation cross sections using the ZBL potential and the total experimen-

tal cross sections for collisions between PAH cations and helium atoms with

center of mass energy 110 eV are shown in Figure 4.2. Direct measurements

by Martin et al [13] of the internal energies of fragmenting anthracene cations

shows that about 10 eV is needed for statistical fragmentation on the present

experimental time scale (microseconds). These results are used to calculate the

32

total fragmentation cross section by saying that all trajectories giving larger stopping energies (electronic plus nuclear) than 10 eV will lead to fragmen- tation of anthracene on the experimental time scale. A subset of these trajec- tories will lead to much larger nuclear energy transfers to individual atoms in anthracene and these trajectories will contribute to the knockout cross section.

Here we assume that the threshold energy for statistical fragmentation depends on the number of atoms, N, in the molecule as

T

(N) = 3N − 6

3 × 24 − 6 × 10 eV (4.1)

This scaling relies on the assumption that the lowest dissociation energies (H- and C

H

-loss) are similar for different PAHs (see Paper V).

As shown on Figure 4.2, the model and experimental total fragmentation cross sections are consistent with each other, and in this intermediate PAH size region about half of the total fragmentation cross sections are due to single atom knockouts. For large PAHs, non-statistical fragmentation dominates the total cross section, since the statistical threshold energy T

increases as a function of PAH size, while the non-statistical threshold energy is size inde- pendent.

The geometrical cross sections are estimated in the way shown in Figure 4.2 for coronene. As it has been discussed in Paper V that the total cross sections are significantly smaller than the geometrical cross sections, which means that the PAHs are partially transparent to helium atoms with energies around 100 eV and only trajectories close to the individual nuclei will lead to fragmentation on the experimental timescale.

4.1.2 Fullerenes

Figure 4.3 shows parts of the fragmentation spectra for C

colliding with He, Ne, Ar and Xe at a fixed C

laboratory energy of 9 keV. The center of mass energies are 50 eV, 245 eV, 473 eV and 1388 eV for He, Ne, Ar and Xe, respectively. For Ne, Ar and Xe we do observe small C

peaks due to prompt knock-out, while no clear such peak could be separated in the He case. The reason is most likely that the He atom is either scattered or captured to form endohedral He@C

[49–51]. The scattering process gives a broad shoulder on the low-energy side of the primary beam peak. This shoulder extends to a position corresponding to the energy loss for elastic scattering of He in the forward direction which is 200 eV.

Figure 4.4 shows the mass spectra for 6, 7, 8, 9 and 10 keV C

colliding

with helium gas (at center of mass energies of 33, 39, 44, 50 and 55 eV, respec-

tively). As it can be seen in Figure 4.3, no clear single carbon loss peak could

33

10 20 30 40 50 60 70 80 No. of atoms in the C m H n + molecule, m + n

0 1 2 3 4 5 6

Cr os s S ec tio n (1 0

15 cm 2 )

Circumcoronene C _m H _n ⁺ - destruction in He, E _CM = 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

Figure 4.2: The statistical, non-statistical and total (statistical + non-statistical) cross sections calculated using ZBL potential for collision between PAH cations and helium atoms with a center of mass energy of 110 eV. The inset shows how the geometrical cross section is estimated for collisions with the coronene molecule σ = 0.8π

, where the factor 0.8 is due to the random orientation of the molecule in the collision [48].

34

Figure 4.3: Mass spectra for 9 keV C

colliding with He, Ne, Ar and Xe. There are more fragments for heavier atom because it has higher center-of-mass energy.

The He may be captured, forming the endohedral He@C

or it may be scattered.

35

be isolated. This is different from the PAH cases discussed in the previous section where prominent single carbon loss peaks could be isolated easily. It is most likely because of the differences in geometries between the planar PAHs and the three-dimensional fullerene cages. When a helium atom penetrates a fullerene, it is likely to induce secondary knockout processes either with the scattered He or with carbon fragments. Further, the electronic interactions will be stronger as the He projectiles often will interact with a much thicker elec- tron gas for simple geometrical reasons. In such cases, the internal energies of the fullerenes will often be higher than for the PAHs. The inset in Figure 4.4 shows the C

- and 2×C

-loss peaks, which are the dominant statistical de- cay processes [10, 13, 14]. The endohedral He@C

and scattering features mentioned above have been observed for the lower collision energies. The mixing of the statistical fragmentation and endohedral effects are energy de- pendent, as shown on Figure 4.4, the endohedral complex formation increases with decreasing collision energies, as do the scattering effects (see Paper III for details).

Figure 4.4: Mass spectra for 6/7/8/9/10 keV C

colliding with He.

36

4.2 Collisions with cluster targets

The mass spectra for collision between 22.5 keV He

and van der Waals clusters of C

fullerenes is shown in Figure 4.5. In the top panel we show the total time-of-flight spectrum, where the most prominent peak corresponds to C

ions. The much weaker peaks on the right hand side of C

(note the different intensity scales of the left and right panels) are mostly singly and doubly ionized intact [C

]

. The peak in region of n

/e = 120 is zoomed-in on Figure 4.6 (first from left), where the C

and C

molecules are detected.

On the left side of Figure 4.5 there are a few rather weak (these peaks are much stronger than the intact cluster peaks) peaks due to the emission of one and several C

molecules from statistically driven fragmentation processes.

The middle panel of Figure 4.5 shows single stop events, i.e. only one charged fragment is detected. The peaks in this panel are attributed to the most distant electron transfer collisions where the clusters are singly and doubly ionized. Thus, low amounts of energy are deposited in nuclear and electronic stopping processes.

The spectrum of product ions detected in coincidence with one or several C

ions is shown in the lowest panels of Figure 4.5. There are no clusters larger than the dimer; these stem from closer collisions leading to multiple ionization and high energy deposition. A zoom-in of the broad "dimer peak" is shown in the left panel of Figure 4.6, which reveals that it contains three com- ponents corresponding to 118, 119 and 120 carbon atoms per atomic unit of charge. The peak at n

/e = 120 could be due to weakly bound [C

]

dimers, which are formed after decay of larger clusters but may also be the result of C

+ C

→ C

covalent bond formation. In the latter case, this could pos- sibly be due to damaged C

fullerenes where a C-atom has been displaced from its original position but has not left the molecular cage. Such a "frac- tured" molecule is expected to be much more reactive than an undamaged C

molecule. The peaks at n

/e = 119 and n

/e = 118 are most likely produced in at low energy C

/C

+ C

reactions, in which covalently bound C

and C

dumb-bell systems are formed as it has been discussed in detail in Papers I and II.

The middle panel of Figure 4.6 shows the mass spectrum around the dimer region for collisions between 12 keV Ar

and fullerene clusters. In this case more peaks are observed than the case with He

collisions discussed above.

In order to understand the physics behind this, electronic and nuclear stopping energy calculations have been performed for 22.5 keV He

and 12 keV Ar

collisions with fullerene monomers and clusters. The calculations show that

for high energy collisions, most of the kinetic energy lost by the projectile

along its trajectories are due to electronic stopping. Highly reactive products

37

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

28 48 52 56 60 200 300 400 500 600 700

0 50 100 150 200 250 300

0 50 100 150

200 300 400 500 600 700 0 10 20 30 40 50 60 70 0

2000 4000 6000 8000

28 48 52 56 60 0

200 400 600 800 1000 1200 1400 1600 1800

C

C

C ou nt s

Total spectrum C

3

17²⁺

15²⁺

11²⁺

9²⁺

C

11

10

9

8

7²⁺

13²⁺

5

7

6

4

C ou nt s

He

+ [C

]

3

7²⁺

17²⁺

15²⁺

13²⁺

11²⁺

9²⁺

11

10

9

8

7

6

5

4

C ou nt s

C

Number of carbon atoms per charge (n

/e)

C ou nt s

C

x50

x100 C

C

C

C

C ou nt s

Single stop events

C

C

C

C ou nt s

Coincidences with C

x20

52 54 56 58 50 52 54 56 58 50 52 54 56 58

C

Figure 4.5: Mass-to-charge spectra for collisions between 22.5 keV He

ions and [C

]

. From top to bottom: Total spectrum, single stop spectrum (only one ion detected per collision event), and coincidence spectrum (events recorded in coincidence with one or several C

ions). Note the differences in intensity scales for the monomer region (left panels) and the cluster region (right panels).

38

(e.g. C

, C

, etc) are produced by prompt knockout processes due to nuclear stopping. These products may survive on picosecond timescales in spite of large electronic stopping energies due to rapid energy redistribution amongst all the molecules in the cluster. This allows for secondary reactions inside the clusters where the product reacts with a neighbouring C

to form covalently bound systems (see Paper I and II). The knockout cross sections calculated us- ing the nuclear stopping model with the screened Bohr potential (see Eq. 3.5 and 3.6 in Section 3.2) are shown in the right panel of Figure 4.6. The cross sections are calculated assuming that the threshold for knocking out a carbon from a C

molecule is about 15 eV (this was the value used for the analysis in Paper I but later it has been realized that much larger energy transfers are needed for knockout due to bond-stretching effects), and the molecular struc- ture is optimized at B3LYP/6-31G(d) level. In the He

case, single knockouts are more likely than double knockouts due to its lower mass and smaller energy transfer. In contrast, collisions with Ar

projectiles are more likely to result in double knockouts and other products because of its higher mass. Thus, the richer distribution for Ar

than He

reflects the higher tendency to form additional somewhat smaller highly reactive fragments in collision with Ar

projectiles.

110 115 120

No. of carbons per charge, n 20 30 40 50 60 70 80 10 0 _c /e

Counts ^C

C

C

He ^{2 +} + [C 60 ] _n

110 115 120

C

C

C

C

C

Ar ^{2 +} + [C 60 ] _n

54 55 56 57 58 59 C _m -fullerene size, m 0.0

0.5 1.0 1.5 2.0 2.5

σ m , 1 0

15 cm 2

He

Ar

Figure 4.6: Parts of the mass-to-charge spectra due to 22.5 keV He

+ [C

]

(left panel) and 12 keV Ar

+[C

]

collisions (middle panel). The curves show events recorded in coincidence with one or several C

ions. The right panel shows the absolute cross sections for producing C

-fullerenes in direct knock- out processes.

In order to further investigate the bond formation processes, molecular dy-

39

Figure 4.7: A snapshot from our molecular dynamics simulations showing the formation of a C

molecule in a collision between an α-particle and a [C

]

cluster. The bond formation process is ignited by the prompt knockout of one of the carbon atoms in a C

molecule (see text).

namics simulations for binary C

+ C

collisions inside fragmenting clus- ters were performed as a part of a collaborative effort with colleagues at the Universidad Autónoma de Madrid (UAM) in Madrid, Spain. The simulation package DL_POLY [52] are used in the microcanonical (NVE) ensemble. The carbon-carbon interactions are described by Tersoff potential (see Paper IV and ref. [53]). Figure 4.7 shows snapshots obtained from a simulation of a collision between He

(α-particle) and [C

]

cluster. One can see from this figure that a covalently bound dumbbell C

system is rapidly formed on the picosecond timescale in a fragmenting cluster of C

. The center of mass col- lision energies and temperatures of the system are varied in these simulations (performed at UAM) to study bond formation between molecules. Compared to the formation of C

in C

+ C

collisions, which requires 60 eV collision energy, the formation of C

from C

+ C

requires only less than 1 eV. This means that the C

systems may be formed rather efficiently inside the cluster as we have measured kinetic energies of the emitted molecules ranging up to a few eV (see Paper I and Paper III). In addition, quantum chemical calculations performed at UAM (Paper I and ref. [53]) shows that adiabatic dissociation energies for C

and C

are 5.4 eV and 1.0 eV, respectively. Thus, C

is more likely to survive until experimental detection since it is inherently more stable than C

.

40

Summary & Outlook

In this work, collisions between ions/atoms and isolated C

or PAH molecules and clusters have been studied. Both high (> 10 keV) and low (< 1 keV) center of mass energies were investigated. Two fragmentation processes have been identified: statistical fragmentation and prompt knockout (non-statistical) fragmentation. Analysis of the mass spectra of PAHs following collisions in these two different energy ranges showed that for high energy collisions large amount of H-/C

H

-loss could be detected, which correspond to statisti- cal fragmentation. For low energy collisions, a clear CH

-loss peak could be observed, which is due to the non-statistical, prompt, knockout process.

These two processes have been investigated by combining molecular struc- ture calculations and well-established models for atom-atom interactions, in which the nuclear and electronic energy transfers for PAH + He/H collisions in the 0.05-10 keV center of mass energy range were calculated. It was shown that nuclear stopping dominates at low collision energies (< 1 keV) and that a substantial fraction of the total PAH destruction cross section is due to non- statistical atom knockout processes, in agreement with recent experimental results. At higher collision energies, electronic stopping dominates and this leads to statistical fragmentation processes for isolated PAHs.

Prompt knockout processes have also been observed for C

colliding with Ne, Ar or Xe. However, single atom losses are extremely rare as the three dimensional cage structure leads to multiple scattering effects. For collisions between ions and clusters of fullerenes, the formation of larger molecules have been detected. In these collisions, highly reactive products (e.g. C

, C

, etc) are produced by prompt knockout processes due to nuclear stopping. These products may survive on picosecond timescales, allowing for secondary re- actions inside the clusters where they react with neighbouring C

to form covalently bound systems. This phenomena has also been studied by means of molecular dynamics simulations.

H- and 2H/H

-losses have been observed in most of the PAH mass spectra,

but they have not been analyzed in detail. This will be one of the main topics

of my near-future research efforts and will require additional measurements

of PAH fragmentation. I have argued here that non-statistical fragmentation

is a very effective process at low collision energies and that it leads to very

reactive fragments. These fragments are often thermodynamically stable in

their ground states but they are of course produced with substantial internal

energies. An interesting question is if they may relax without loosing addi-

tional heavy atoms or if they do fragment by additional heavy atom emission

on longer time scales. Such effects may be studied by trapping such fragment

ions in the storage rings of DESIREE. I also plan to study the stabilities of

biomolecule in solution following collisions with atoms and following laser

excitation.

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