MUONIUM KINETICS AND FREE RADICAL FORMATION IN SOLUTIONS OF FULLERENES

Sonja Kecman B.Sc., Physical-Chemistry University in Belgrade, 1998

THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

In the

Department of Chemistry

0 S. Kecman 2004

SIMON FRASER UNIVERSITY

May 2004

All rights reserved. This work may not be reproduced in whole or in part, by photocopy

or other means, without permission of the author.

APPROVAL

Name: Sonja Kecman

Degree: M.Sc.

Title of Thesis: Muonium Kinetics and Free Radical Formation in Solutions of Fullerenes.

Examining Committee:

Chair: Dr. G. W. Leach, Associate Professor

Date Approved:

Dr. P.W. Percival, Professor, Senior Supervisor

Dr. A.J. Bennet, Professor, Committee Member

Dr. S. Holdcroft, Professor, Committee Member

Dr. H.Z. Yu, Assistant Professor, Internal Examiner

Partial Copyright Licence

The author, whose copyright is declared on the title page of this work, has

granted to Simon Fraser University the right to lend this thesis, project or

extended essay to users of the Simon Fraser University Library, and to

make partial or single copies only for such users or in response to a

request from the library of any other university, or other educational

institution, on its own behalf or for one of its users.

The author has further agreed that permission for multiple copying of this

work for scholarly purposes may be granted by either the author or the

Dean of Graduate Studies.

It is understood that copying or publication of this work for financial gain

shall not be allowed without the author's written permission.

The original Partial Copyright Licence attesting to these terms, and signed

by this author, may be found in the original bound copy of this work,

retained in the Simon Fraser University Archive.

Bennett Library Simon Fraser University

Burnaby, BC, Canada

The purpose of this research was to study the kinetics of the reaction of muonium

with C60 in solution. The solubility of C60, which is poor in most organic solvents and

negligible in water, has been one of the greatest impediments to study reactions and

possible biological functions. The kinetics of the reaction of muonium with C60 in

solution was investigated by transverse field muon spin resonance (TF-pSR). Two

different methods were used to determine rate constants: muonium decay rates at low

magnetic field; and measurements of radical signal amplitude as a function of applied

magnetic field.

From measurements of muonium decay rates in dilute solutions of C60 in

cyclohexane, the rate constant for the reaction of muonium with C60 was found to be

2.0(3) x 10" M-I s-' at room temperature, in agreement with previous work. C60 is

thought to form a true solution in cyclohexane. However, in water C60 forms sols -

suspensions of C60 clusters.

Aqueous C60 samples were prepared by three different methods. The

hydrodynamic radius of C60 so1 clusters was determined by dynamic light scattering; it

was found to be in the range of 70 - 2 12 nm depending on the preparation method of the

C60 sols. The rate constant for the reaction of muonium with C60 sols prepared by the

Andrievsky method was determined to be 7.8(2) x lo9 M-I s-' at 25 "C and the activation

energy was found to be 15 kJ mol-I. The equivalent rate constant determined for C60 sols

prepared by the Deguchi method was found to be 2.5(1) x 101•‹ M-' s-I at 25 "C with an

activation energy of 20 kJ mol-'.

The rate constant for the reaction of muonium with C60 in decalin was extracted

from the magnetic field dependence of the C60Mu radical signal amplitude. The rate

constant determined by this method was found to be 5.5(7) x 101•‹ M-I s-I at 25 "C with an

activation energy of 18 kJ mol-I.

By comparing the experimental results with predictions it was concluded that the

reaction of muonium with C60 in solution is diffbsion limited.

iii

To my family,

"Za moju porodicu"

I would like to express my gratitude to Professor Paul Percival, my senior

supervisor, for his guidance and support over the years. He has taught me a great deal

about pSR techniques and science and different software. He has been a great mentor,

training discipline when needed and celebrating successes.

I would like to thank Dr. Jean Claude Brodovitch for his technical support, perfect

designs, discussions that were very instructive for me, and he was always there when I

needed him. I wish to thank all my co-workers in the SFU muoniurn group for their help

and discussions.

Also I would like to thank Dr. Barbara J. Frisken and Philip Patty for their help

and valuable discussion about dynamic light scattering.

Financial support from Dr. Percival's research grant and Department of

Chemistry is gratefully acknowledged.

Finally, I would like to thank my husband and my daughters for their patience and

support over the years.

TABLE OF CONTENTS

. . Approval .......................................................................................................................................... 11

... ........................................................................................................................................... Abstract 111

.......................................................................................................................... ~~knowledgements v

............................................................................................................................ Table of Contents vi ... ............................................................................................................................... List of Figures vlll

List of Tables ..................................................................................................................................xi . .

List of Abbreviations ..................................................................................................................... xi1

CHAPTER 1 . Introduction ............................................................................................................... 1

1 . 1 Motivation ............................................................................................................... 1

1.2 Muon and Muonium Properties ............................................................................... 2

CHAPTER 2 . Fullerenes in Solution ............................................................................................... 6

2.1 Fullerene Properties and Reactivity ........................................................................ 6

2.2 Fullerenes in Organic Solutions .............................................................................. 9

2.3 Aqueous Solutions of Fullerenes (Sols) ................................................................ 12

2.4 Preliminary pSR Studies of Fullerenes ................................................................. 14

CHAPTER 3 . Preparation and Characterization of Fullerene Solutions and Sols ......................... 17

3.1 Preparation of Fullerene Solutions and Sols ......................................................... 17

3.1.1 The method of Andrievsky and co-workers .................................................. 17

.............................................................. 3.1.2 The method of Wei and co-workers 19

....................................................... 3.1.3 The method of Deguchi and co-workers 19

3.2 UV Analysis of Fullerene Solutions and Sols ....................................................... 21

3.3 Dynamic Light Scattering Studies of Fullerene Sols ........................................ 23

vi

.................................................................................. CHAPTER 4 . pSR Theory and Techniques 26

.............................................................................................. 4.1 Muon Spin Rotation 26

.............................................................................................................. 4.2 Muonium 3 2

.............................................................................................. 4.3 Muoniated Radicals 3 5

4.4 .................................................................................. Transfer of Mu Polarization 36

........................................................... . CHAPTER 5 Experimental Methods and Instrumentation 39

....................................................................................... Introduction to TRIUMF 39

.................................................................................... Beam lines M 15 and M20 4 2

................................................................................................ pSR Spectrometers 43

Flow System .......................................................................................................... 43

Data Acquisition and Analysis .............................................................................. 45

CHAPTER 6 . Muonium Decay Rates ............................................................................................ 48

.......................................................................................................... 6.1 Introduction 4 8

6.2 Results and Discussion .......................................................................................... 50

6.2.1 Kinetics: C6() in organic solutions .................................................................. 50

6.2.2 Kinetics: C60 sols ........................................................................................... 52

6.3 Conclusions ........................................................................................................... 60

CHAPTER 7 . Free Radical Formation .......................................................................................... 61

.......................................................................................................... 7.1 Introduction 6 1

7.2 Results and Discussion .......................................................................................... 61

7.3 Conclusion ............................................................................................................. 66

................................................................................................................ CHAPTER 8 . Summary 6 7

REFERENCES .............................................................................................................................. 69

Figure 2.1.

Figure 2.2.

Figure 3.1.

Figure 3.2.

Figure 3.3.

Figure 3.4.

Figure 4.1.

Figure 4.2.

Figure 4.3.

Figure 4.4.

............................................................. Structure of the soccer ball Cm molecule 6

Cm structure with two products of muonium attack, the muoniated

.............................. radical C ~ U (left) and encapsulated muonium, Mu@Cm. 15

The sonochemistry equipment: a) cleaning bath, and b) probe

............................................................................................................... system. 18

The system for purging nitrogen to evaporate the THF. .................................... 20

4 The W spectrum of 7 x 10 M Cm in decalin. ................................................. 2 1

W spectra of aqueous sols: a) 80 pM Cm so1 by the Andrievsky

method, b) 56 pM Cm so1 by the Wei method and c) 38 pM Cm so1

..................................................................................... by the Deguchi method. 22

Decay of pion (3 represents the momentum vector, -+ represents

the particle spin or neutrino helicity vectors). ................................................... 26

Decay of the muon (3 represents the momentum vector, -+

.................................. represents the particle spin or neutrino helicity vectors). 27

Schematic diagram of a simple TF-pSR experiment. The muon is

shown entering the target area from the left. The magnetic field is

applied vertically (M is the incoming muon detector, E is the emitted

positron detector; the white block arrow represents the muon spin

and the black arrow the muon momentum). ...................................................... 29

a) Raw time histogram from a simple TF-pSR experiment. b) TF-

pSR asymmetry spectrum obtained from the raw time histogram (red

line fitted data, black vertical lines raw data). ................................................... 3 1

viii

Figure 4.5.

Figure 4.6.

Figure 5.1.

Figure 5.2.

Figure 5.3.

Figure 5.4.

Figure 6.1.

Figure 6.2.

Figure 6.3.

Breit-Rabi diagram showing the energy levels of the muoniated spin

states as a function of the magnetic field. The arrows indicate the

allowed transitions in TF-pSR. In low fields, only two transitions

................................................................ donated by solid lines are resolvable. 34

Variation of radical signal polarization for the different reaction

rates. The solid curves represent theoretical predictions for the

precession frequencies v12 and V23. .................................................................... 38

Beam lines and experimental facilities at TRIUMF. (Figure taken

from http://www. triumf.ca/tourmap.html). ....................................................... 4 1

............... Schematic set up for the flow system used for the pSR experiments. 44

Schematic drawing for a glass cell used in the flow system. ............................. 45

Fourier power spectrum for positive muons in powdered CW at room

temperature, showing simultaneously the signal from muons in the

C&U radical (R12 and R34) and endohedral muonium (Mu@CW)

atoms (Mul2 and Mu,). ..................................................................................... 46

Muonium decay rate measured in solutions of CW in cyclohexane as

a h c t i o n of concentration at different temperatures: 50 OC (A), 25

"C (a) and 10 OC (+). ......................................................................................... 5 1

Muonium decay rate measured in Cm so1 samples prepared by the

Andrievsky method as a function of Cm concentration at three

........................................ temperatures (the lines are a guide for the eyes only) 52

Muonium decay rates measured for the reaction of muonium with

CW so1 as a h c t i o n of concentration: a) the results obtained from

the December 2002 'beam time, b) the results obtained from the

August 2002 beam time. .................................................................................... 54

Figure 6.4. Muonium decay rate measured in solutions of Cm so1 by the Wei

method as a fhction of the concentration at two temperatures (lines

............................................................................ are a guide for the eyes only). 57

Figure 6.5. Muonium decay rate for the C60 so1 prepared by the Deguchi method

as a function of concentration at three temperatures: a) the results

obtained at December 2002 beam time, b) the results obtained at

August 2002 beam time. .................................................................................... 59

Figure 7.1. Fourier transform TF-pSR spectra at 65 G: a) 3 mM Cm in decalin at

10 "C, b) 2.7 m M I2cm in decalin at 25 "C and c) 3 mM C60 in

decalin at 50 OC .................................................................................................. 62

Figure 7.2. Field dependence of muon polarization transferred from muonium to

radical precession frequencies at (a) 10 "C, (b) 25 "C and (c) 50 "C.

The solid curves show the corresponding theoretical predictions for

the precession frequencies vl2 and ~ 2 3 . .............................................................. 64

Figure 7.3. The Arrhenius plot of the rate constant for the reaction of Mu with

Cm in decalin ...................................................................................................... 65

LIST OF TABLES

Table 1 . 1 .

Table 1.2 .

Table 2- 1 .

Table 2.2 .

Table 2.3 .

Table 3.1.

Table 6.1.

Table 6.2.

Table 7.1.

........................................................... The basic properties of the positive muon 3

........................................................................ The basic properties of muonium 4

...................................................................... Selected physical properties of Cm 7

............................................... The solubility of C60 in organic solvents at 298 K 9

The average hydrodynamic diameters of hllerene particles formed in

various solvents .................................................................................................. 11

The hydrodynamic radius of Cm so1 samples as determined by

different methods at 25 "C ................................................................................. 24

Rate constants determined for the reaction of muonium with Cm so1

prepared by the Andrievsky method .................................................................. 53

Rate constants determined for the reaction of muonium with Cm so1

prepared by the Deguchi method ....................................................................... 58

The rate constant determined for the reaction of Mu with Cm in

decalin ................................................................................................................ 65

T W F

TEM

THF

UV-Vis

IR

DLS

NMR

ODMR

ESR

CLSR

TF-pSR

LIST OF ABBREVIATIONS

Tri University Meson Facility

transmission electron microscopy

tetrahydrofuran

ultra-violet visible spectroscopy

infia-red spectroscopy

dynamic light scattering

nuclear magnetic resonance

optically detected magnetic resonance

electron spin resonance

muon spin rotation

transverse field muon spin rotation

CHAPTER 1.

INTRODUCTION

1 .I Motivation

The purpose of this research was to study the kinetics of the reaction of muoniurn

with fullerene in various types of solution. Fullerenes represent an intriguing new class of

carbon materials, which has attracted the attention of chemists interested in exploring the

fundamental properties of these novel materials, both as molecular entities and as an

anchoring base or building blocks essential to the design of special carbon materials. The

increasing availability of fullerenes with reproducible quantity and lower cost has

encouraged more research and development effort targeted for potential technological

applications.

C60 is one of the important members of the fullerene family. Availability in high

degree of purity has promoted many studies on structure, properties and reactions.

However, the solubility of fullerenes, which is poor in most organic solvents and

negligible in water, has been one of the greatest impediments to studying reactions and

possible biological functions. CbO is an extremely hydrophobic molecule. Getting

fbllerenes to dissolve in water and polar solvents is challenging because of this

hydrophobicity.

The synthesis of water-soluble fullerene derivatives based on polymers

biologically compatible with living organisms is an important problem because their use

in ~harmacology and medicine is very promising [I] . For example it has been reported

that substituted fullerenes inhibit HIV-1 protease activity and may be involved in

photoinduced DNA scission [2-51. Furthermore photodynamic therapy on tumors is based

1

on photo-induced generation of active singlet oxygen from oxygen present in the tissue,

and cbO is known to efficiently generate singlet oxygen when exposed to visible light.

A variety of different experimental techniques including nuclear magnetic

resonance (NMR), optically detected magnetic resonance (ODMR), electron spin

resonance (ESR), UV-visible, IR and Raman spectroscopy, scanning tunnelling

microscopy (STM), transmission electron microscopy (TEM), dynamic light scattering

(DLS) and muon spin rotation (pSR) have been employed to study fullerenes and

fullerene solutions. However, investigation of fullerene solutions by pSR techniques is

the main part of my thesis. The chemistry is well understood for organic (true) solutions

of hllerenes. In the next chapter will be given details of the chemistry of organic

solutions of fullerenes. However, fbllerenes are difficult to dissolve and being

hydrophobic their solubility in water is even more of a problem. One approach has been

to generate fullerene sols (colloidal suspensions) using three different methods. The

questions I set out to answer in this thesis are: How does fullerene aggregation affect

chemical kinetics? And is the reaction between Mu and the sol clusters diffusion-

controlled? Characterizing the aqueous fullerene sols by UV analysis and dynamic light

scattering and exploring these solutions with muonium chemistry is going to help to

answer those questions.

1.2 Muon and Muonium Properties

The development of muonium chemistry can be traced back to the discovery in

1937 of the positive muon, the first unstable elementary particle observed [6 ] . Both

occurring muons and those produced at cyclotrons, such as TRIUMF, result

from the decay of positive pions (lifetime 26 ns) into muons and neutrinos, according to:

These particles are emitted with equal and opposite momentum in the rest frame

of the pion. As pions have zero spin and neutrinos are spin '/z polarized opposite to their

Table 1-1. The basic properties of the positive muon.

Positive muon P+

Spin

Charge + 1

Rest mass 0.1 13429 u

- 119 mass of proton

Magnetic moment 3.1 83 3 proton magnetic moment

Magnetogyric ratio 13.5534 kHz G-'

Mean lifetime 2.197 ps

momentum, the muons are emitted completely spin polarized as well. Muons exist

naturally in two charge states: the positive muon Clf, and the negative muon y. This thesis will be limited to the positive muon, which is a useful analogue of the proton. The

positive muon has the same charge and spin as the proton but only has one-ninth the

3

mass. The muon has the ability to combine with an electron to form a muonium atom,

which acts as a light isotope of hydrogen. The basic muon properties are presented in

Table 1 - 1 , and the basic properties of muonium are given in Table 1-2 [7-81.

Table 1-2. The basic properties of muonium.

Muonium p+e- = Mu

Mass 207.8 mass of electron

Reduced mass 0.9956 p~ (the reduced mass of 'H)

Bohr radius 0.5315 A

Ionization potential 0.9956 that of 'H

Magnetogyric ratio 1.394 MHz G-'

Hyperfine frequency 4463 MHz in vacuum

Mean lifetime Limited by that of p+

The chemistry of muonium is similar to that of hydrogen, while the shorter

lifetime allows unique effects to be studied. The detection method in pSR takes

advantage of the natural decay of the muon, with a mean lifetime of 2.2 ps, into a

positron and two neutrinos [9]:

If the muon is forced to precess by a magnetic field applied perpendicular to its

spin direction, this precession can be traced by the stream of positrons, which are

conveniently emitted preferentially along the muon spin direction. Details of the

techniques will be described later in chapter 4.

CHAPTER 2.

FULLERENES IN SOLUTION

2.1 Fullerene Properties and Reactivity

Since 1985 there have been many publications on fullerenes. The C60 molecule is

the archetypal member of the fullerene family. The closed cage, nearly spherical

molecule CsO and related fullerene molecules have attracted a great deal of interest

because of their unique structure and properties. C60 or "buckminsterfullerene", consists

of carbons in truncated icosahedral symmetry, familiarly known as the soccer ball

structure (with 12 pentagons and 20 hexagons) [I], figure 2.1.

Figure 2.1. Structure. of the soccer ball C60 molecule.

Fullerene molecules all have a closed caged structure consisting of a network of

hexagons and twelve pentagons, with all carbons being formally sp2-hybridized and

bonded to three other carbon atoms. In C60 all carbon atoms are symmetrically

equivalent, as proven by NMR observation of a single line in the 13c spectrum [lo].

Some physical properties of C60 are listed in Table 2-1 [ l 11.

Table 2-1. Selected physical properties of C60.

Average C-C distance

Mean diameter

Mass density

Molecular density

Binding energy per atom

Electron affinity

1 " ionization potential

2nd ionization potential

1.44 8,

6.83 8,

1.72 g cm"

1.44 x 1 o2 c m ~ ~

7.4 eV

2.65 eV

7.58 eV

11.5 eV

Fullerenes were first expected to be quite unreactive, due to the stabilization

energy gained from the delocalization of .x: electrons. However, one of the possible

resonance structures of C60 has a double bond in at least one pentagonal ring. Further

destabilization is introduced by the strained bond angles, as one of the C-C-C bond

angles at each carbon atom in C60 is lO8O rather than 120" required by perfect sp2

hybridization. Although the average bond length is 1.44 A, delocalisation is not complete,

as the actual bond lengths for the bonds of the intersection of hexagons are 1.40 and

1.45 A for the bonds of the intersection of pentagons and hexagons.

The heats of formation of fullerenes are also considerably less than those of

diamond and graphite. The combination of electronic properties with the high double-

bond character at the junction of two six-member rings provides fullerenes with

extraordinary ability to undergo addition reactions. Fullerenes easily accept and donate

electrons, and thus they are expected to display very rich electrochemistry. Up to six

electrons can be added to &, and under special experimental conditions up to seven

electrons may be removed from C60 to produce multiply charged cations.

Fullerenes have no other groups attached to double bonds and hence cannot

undergo substitution reactions. However, fullerenes can undergo a wide variety of

addition reactions forming: halofullerenes, fullerols, fullerene anions, fullerene hydrides,

organometallic derivatives, polymers and fullerenyl radicals [12]. On the other hand,

there are many unique problems associated with fullerene product formation and

characterization. Products generally have poor solubility in common organic solvents and

are unstable under standard analytical methods.

2.2 Fullerenes in Organic Solutions

Many studies have appeared suggesting applications of fullerenes as optical and

electronics materials, superconductors, sensors, building blocks for new materials, etc.

However, many of the potential applications are hindered because the fullerenes are not

soluble or are only sparingly soluble in many solvents. The solubility of C60 is known in

almost 150 solvents; some of the data are listed in Table 2-2 [13-151.

It is possible to increase the solubility of fullerenes in some organic solvents by

Table 2-2. The solubility of C60 in organic solvents at 298 K.

Solvent Solubility I mg ml-'

Decalin

Toluene

Benzene

n-Hexane

Cyclohexane

Ethanol

grafting fullerene molecules with polymer chains or by solubilization and encapsulation

of fullerenes by amphiphilic block copolymers. Most of these studies show that the

fullerenes and their derivatives are dispersed in polar media in the form of aggregates

[16-181. Aggregation of C60 in neat solvents has also been reported by Ying et a1 [19-201.

The formation and the stability of colloidal dispersions of fullerenes in polar organic

solvents have been studied mainly with dynamic light scattering (DLS) and static light

scattering (SLS). Electron microscopy showed that the particles are roughly spherical

[211.

DLS can be used to determine the hydrodynamic diameter dh, which can be used

to characterize the formation and behaviour of the fullerene dispersion under various

conditions. DLS measurements showed that the size of the fullerene particles is

determined immediately after mixing of a small volume fullerene solution with a larger

volume of a polar medium (acetonitrile) [22]. The process of particle formation is fast

and the equilibrium average size of the fullerene dispersion is established immediately.

However, concentrated dispersions can be prepared without significant change in the

particle size. On the other hand, addition of the nonsolvent in the same way into a true

C60 solution was found to leed to the formation of larger particles with broader size

distribution. Table 2-3 gives some average hydrodynamic diameters in various solvents.

DLS measurements show that C60 in pyridine forms polydispersive solutions with

a large range of particle size present. In contrast, the particles in C6/pyridine/water

solutions are completely monodispersive and show only a single particle size, which

remains in solution and does not change with time [23].

Table 2-3. The average hydrodynamic diameters of fullerene particles

formed in various solvents.

Solvent dh / nm Reference

BenzeneIAcetonitrile 207 f 30 [221

Toluene/Acetonitrile 210 f 30 P I

THF/Acetonitrile 226 k 20 [221

Toluene/Ethanol 490 P I

Benzonitrile 250 k 100 [211

Benzene 1.28 f 0.02 [19-201

Pyridine~Water 60 [231

UV-VIS spectroscopy has been used to study the concentration and the chemical

stability of fullerenes. Samples show no significant change and no systematic deviation in

the average size with time. The structure of the fullerene particles was studied by high-

resolution transmission electron microscopy (HRTEM); it showed regular ordering of the

fullerene molecules where the fullerene colloid particles are formed as a result of a

crystallization process.

2.3 Aqueous Solutions of Fullerenes (Sols)

Water-soluble forms of fullerenes have long been sought for application in

biological systems. Due to the inherent hydrophobicity of fullerenes, aqueous solutions

have been limited in the past to modified forms such as the formation of host-guest

inclusion complexes with y-cyclodextrin [24-251 and the formation of micelles containing

ionic sulfonate arms [26]. Recently, however, methods have become available for the

production of aqueous fullerene solutions without chemical modification. Such solutions

have been prepared by three groups: Andrievsky and co-workers [27-291, Wei et al. [30-

3 11 and Deguchi and co-workers [32].

The method of Andrievsky and co-workers involves sonication of a millimolar

concentration of fullerene in organic solution in the presence of water. After the organic

solvent is evaporated the fullerene remains in the aqueous phase as a sol.

The method of Wei and co-workers involves preparation of organic solutions of

the monoanion, which are then added drop-wise to water. The anion is oxidized to the

neutral fullerene by molecular oxygen to form the sol.

The method of Deguchi and co-workers involves the injection of a saturated

solution of fullerene in tetrahydrofuran (THF) into water; THF is then removed by

purging the mixture with nitrogen gas.

Andrievsky's method is based on the transfer of fullerene from the nonpolar

solvent to the polar one under ultrasonic treatment. The solutions generated under this

condition had a bright orange-brownish colour, with a concentration up to 2.2 x 10" M,

and UV-VIS spectra of these solutions contained the main bands characteristic of C60

(220 nm, 260 nm and 330 nm). The colloidal water solutions of C60 appeared to be

extremely stable upon storage in a dark cool place for several months [33]. Those

solutions have been studied using transmission electron microscopy (TEM). Such

solutions may combine some properties of a typical colloidal solution with those of a true

molecular solution. TEM data show these solutions to be molecular-colloidal systems,

containing both single fullerene molecules and their fractal clusters in a hydrated state.

Sphere-shaped aggregates consisted of primary spherical particles of size 7-72 nrn. A

model of the diffusion limited aggregation of clusters as a result of the attachment of

separate particles gives the relation between the number of particles in the cluster (N), its

radius (R) and its fractal dimensionality (df - 1.8) [34-351 and has the form:

where r is the radius of a particle forming the cluster. The smallest stable spherical

aggregate of C60 consists of 13 C60 molecules [27-281.

The method of Wei et al. produces a dark red-brown aqueous colloidal solution of

C60 with the concentration as high as 1.4 x 10'~ M, and which is very stable for at least

six months in the dark. Electrospray ionisation mass spectrometry (ESIMS) of the sol

showed that it is composed of species C6 i and (C60);. TEM showed that the sol particles

are non-crystalline and the size is in the range of 20-100 nm [30].

The method of Deguchi and co-workers produces stable aqueous dispersions of

fullerene. The solutions are yellow and clear with concentration as high as 1.0 x 10" M.

In the UV-VIS the peaks are broader and less intense than the peaks of the C60 so1

prepared with the Andrievsky method. The spectroscopic results suggest that C60 is not

dissolved in water molecularly, but dispersed as fine solid clusters. The average

hydrodynamic diameter of the individual clusters obtained by DLS was found to be 62.8

nrn. High-resolution transmission electron microscopy revealed the polycrystalline nature

of the clusters formed by this method. It was also found that the surface of the clusters is

negatively charged [32].

2.4 Preliminary pSR Studies of Fullerenes

The muon spin resonance (pSR) studies (transverse field muon spin resonance

TF-pSR, muon level crossing resonance pLCR and radio-frequency pSR) of fullerenes

began during the early period of activity in fullerene science.

When powder C60 is irradiated with positive muons two species can be detected

by the radio-frequency muon spin resonance technique [36] as depicted in figure 2.2:

*:* Endohedral muonium M u @ C ~ ~ is characterized by a muon hyperfine constant (A,),

similar to Mu in vacuum.

*:* Exohedral muonium adduct C60Mu is also detected and has a much smaller value of

A,.

When the muonium attacks any double bond in C60 only one radical, the

muoniated radical MuC60, is formed due to the high symmetry of the molecule and

consequently analysis is much simplified. The radical peaks correspond to a hyperfine

coupling of 325 MHz, typical of organic radicals, while the muonium peaks give an A, of

4265 MHz.

Figure 2.2. C60 structure with two products of muonium attack, the muoniated

radical C60M~ (left) and encapsulated muonium, Mu@CM.

From a chemical point of view muonium is a light isotope of hydrogen, so C&h

is the analogue of the radical CmH, which was detected by ESR [37-381 only after the

muon hyperfie constant of C&U was published. The signs as well as the magnitudes of

the "C hyperfine constants were determined in "C&U by muon level crossing

resonance [39].

Ca in dilute solution of decalin has also been studied by RF-pSR but the

hyperfine constant Ap of C& in solution is significantly different from that in the

solid. The A, value of 330.9 + 0.2 MHz was found in dilute solution, 2% larger than for the powder [3 61.

Decalin was chosen as the solvent because of its high solvating ability for C60

compared to the other hydrocarbon solvents [40]. The A, of C60 in cyclohexane has not

been determined due to low solubility in this solvent.

Muonium decay rates were measured for micromolar solutions of in

cyclohexane and the rate constant was determined to be diffusion limited. The rate

constant in decalin is 0.3 times that in cyclohexane [41].

CHAPTER 3.

PREPARATION AND CHARACTERIZATION OF

FULLERENE SOLUTIONS AND SOLS

3.1 Preparation of Fullerene Solutions and Sols

C60 powder was purchased from either SES Research or Hoechst, and then

cleaned of any residual solvent by baking under vacuum overnight. C60/decalin solutions

(3.2 mM) were prepared by stirring overnight. The concentrations were verified by UV

analysis [21] [(h = 330 nm, & = 51000 M-' cm-') and (h = 536 nm, E = 855 M" cm-I)]. For

these samples, dissolved oxygen was removed by the freeze-pump-thaw method and the

samples were sealed in stainless steel cells.

C60 is not readily dissolved in water so special methods have been devised to

prepare aqueous solutions of C60 sol. TO prepare my C60 so1 samples I have used 3

different methods.

3.1 .I The method of Andrievsky and co-workers

C60 powder was dissolved in decalin by stirring overnight. A mixture of 20 ml of

deionized water and 5 ml of Cddecalin was treated by ultrasound, either cleaning bath or

probe system as shown in figure 3.1, for 3-12 hours. The orange-brownish solution was

filtered through 0.22 pm micro filters (pH = 6). The concentrations were verified by UV

analysis, where the extinction coefficient of C60 so1 at 220 nm (44000 M-' cm-I), 260 nrn

(40000 M-' cm-') and 330 nm (20000 M-' cm-') was used to determine the exact

concentration of C60 so1 for all studies:

transducer generator housing

wate water+detergent

replaceable CBOIdecal in tip

*

stainless - steel tank

water

Figure 3.1. The sonochemistry equipment: a) cleaning bath, and b) probe system.

1 I I 1 I I

transducers bonded to base

R- optional heater

For the pSR experiments, dissolved oxygen was removed from the samples by

repeated purging with argon and evacuation on a vacuum line. The samples were than

stored in glass bulbs in a dark place.

3.1.2 The method of Wei and co-workers

Degassed water (5 ml) was added to a suspension of C60 powder, zinc powder and

solid NaOH in 20 ml THF, in the absence of oxygen, stirring overnight. The C60 and zinc

was suspended in the interface between the upper layer of THF and the lower layer of

aqueous NaOH. After that the dark red-purple solution of C6( in THF was separated from

the colourless aqueous NaOH solution. The THF solution of C6 i was added dropwise to

undegassed water to give a dark red-brown aqueous colloidal solution. The oxidation

process is given by [30][3 11:

Diluted aqueous sol (pH = 5) was used as a sample for pSR experiments. Oxygen was

removed by the argon-vacuum method, and the samples were stored in glass bulbs in a

dark place.

3.1.3 The method of Deguchi and co-workers

A small amount of solid C60 and THF were placed in a glass vial with a screw cap

and stirred overnight under one atmosphere of argon at room temperature. After the

excess solid was filtered to give a saturated solution of C60/THF the UV analysis showed

that C6() is soluble in THF. This solution was injected into an equal amount of water, and

THF was removed by purging with gaseous nitrogen for at least 3-6 hours (figure 3.2). A

yellow and visually clear solution of C60 so1 was formed (pH = 5).

19

nitrogen SUPP'Y

bber sept

bubblers

9 joint

sample 9

Figure 3.2. The system for purging nitrogen to evaporate the THF.

3.2 UV Analysis of Fullerene Solutions and Sols

W-visible absorption spectra were recorded on a HP-8453 UVNIS

spectrophotometer (USA). All the measurements were done at room temperature.

The UV spectra of C60 in organic solvents are relatively easy to obtain. They

show sharp bands at 220 nm, 260 nm and 330 nm with E = 135000 M-' cm-', 175000 M-'

cm-I and 51000 M" cm-', respectively. Also, there are weak broad bands at 500 nm, 540

nm, 570 nm, 600 nm and 625 nm characteristic for C60 in most organic solvents; for

example, hexane, benzene, etc. The W spectrum of C60 in decalin shown in figure 3.3,

has broad bands at 330 nm and 536nm.

wavelength 1 nm

Figure 3.3. The UV spectrum of 7 x lo4 M C60 in decalin.

The aqueous solutions of C60 prepared by the previously reported methods were

different colours but showed characteristic bands at 220 nm, 260 nm and 330 nm with no

broad band in the 450 nm - 550 nm region (figure 3.4).

6

0 1 I I I I 300 400

wavelength I nm

Figure 3.4. UV spectra of aqueous sols: a) 80 @I C60 so1 by the Andrievsky method, b)

56 pM C60 so1 by the Wei method and c) 38 pM C60 so1 by the Deguchi

method.

Knowing the absorbance of C60 in decalin (536 nm) and its extinction coefficient

(855 M-' cm-' at 536 nm) [21] the concentration of C60, which was extracted from

aqueous solution, could be determined. The extinction coefficient of C60 in the aqueous

22

phase was determined to be 44000 M" cm" (220 nm), 40000 M-l cm" (260 nm) and

20000 M-' cm-' (330 nm).

3.3 Dynamic Light Scattering Studies of Fullerene Sols

Samples of C60 so1 were also investigated with dynamic light scattering (DLS) at

SFU Physics Department, with the assistance of Dr. B. Frisken and Philip Patty. Using

this method of analysis it is possible to determine the hydrodynamic radius of a solute

from the intensity of the scattered light. Random motion of particles in solution causes

fluctuations in the intensity of the scattered light [42-451. The apparatus used for the light

scattering experiments was an ALV DLSISLS-5000 (ALV-Laser GmbH, Langen

Germany). DLS measurements involve analysis of the time autocorrelation function of

the scattered light as performed by a digital correlator. The time autocorrelation function

of the scattered light intensity was usually measured at scattering angle 90" but for the

C60 solutions we used 55". The time autocorrelation function was converted to the

scattered electric field autocorrelation function via the Siegert relation. The field

autocorrelation function decays exponentially, with a decay rate given by equation:

where D is the Stokes-Einstein diffusion coefficient and q is the scattering wave vector

magnitude (at 55"). The Stokes-Einstein equation for the diffusion coefficient is:

where k is the Boltzmann constant, T the absolute temperature, R the particle radius and

q the viscosity of the solvent.

Measurements were performed on 1 pM - 192 yM C60 so1 samples at 3

temperatures (10 "C, 25 "C and 50 "C) and no significant change of the radius of C60 so1

with temperature was detected. The results of DLS determinations of hydrodynamic

radius from samples prepared for the pSR analysis are given in table 3.1.

Table 3.1. The hydrodynamic radius of C60 so1 samples as

determined by different methods at 25 "C.

Andrievsky 7-72 nm 80- 100 + 47 nm

Wei 20-100 nm 212 f 32 nm

Deguchi 62.8 nm 140f 30nm

The results in table 3.1 were obtained after storage in the dark for two weeks after

preparation. The hydrodynamic radius of freshly made samples is 23% higher than afier 2

weeks of storage in the dark. However, after shaking the sample the hydrodynamic radius

can vary f 5 nm. This is different than for DLS measurements of C60 in organic solvents,

where small shaking makes the C60 aggregation disappear.

The radius of C60 so1 can be used to determine the number of particles in the

cluster N [33-341. The number of particles in the cluster can be obtain from equation 3.4:

where R is the radius of C60 so1 (DLS) and r is the radius of the most stable cluster

[(C60)13] and df is the fractal dimensionality. The number of particles in the cluster was

found to be N = 2223 f 82 for the samples made by the Andrievsky method. The DLS

results were in good agreement with previously published papers on C60 sols [27-281.

CHAPTER 4.

pSR THEORY AND TECHNIQUES

4.1 Muon Spin Rotation

1937 was marked by the discovery of the muon, although another 10 years were

required for positive proof. However, it was not until 1957 when chemists showed

interest, with the discovery of muonium, a bound state between a positive muon and an

electron. Muonium is commonly referred to as a pseudo-isotope of the hydrogen atom

W I .

Muons, p', are the decay products of pions (figure 4.1). Conservation of angular

momentum ensures that the muons can be produced with their spins polarised

longitudinally along the beam.

Figure 4.1. Decay of pion (a represents the momentum vector, + represents the

particle spin or neutrino helicity vectors).

The lifetime of the muon is 2.2 ps. When it decays it does so according to figure

4.2, where the positron, e+ is of particular interest. The positron is ejected preferentially

along the spin direction of the muon providing a suitable means of monitoring the muon

spin direction at its moment of decay [47].

In experiments the positrons are detected with efficiency 5, which is not constant

over the entire energy range due to absorption and scattering in the target and the counter

as well as the effect of an external magnetic field on the positron trajectories. The

observed probability distribution is expressed by:

where 5 is an average positron detection efficiency. The probability R of positron

emission at an angle 8 with respect to the spin direction is given by:

R(8) = 1 +Ao cos 8 (4.2)

where & is the asymmetry. If all the positrons were detected with the same efficiency,

the value of & would be 113 [8].

Figure 4.2. Decay of the muon. (3 represents the momentum vector, +

represents the particle spin or neutrino helicity vectors).

27

In most muon experiments the effective asymmetry is less than 113. The time

differential measurement of the asymmetric decay of spin-polarized positive muons

precessing in a transverse magnetic field forms the basis of the pSR technique [46-491.

The simplest and most familiar time-differential (TD-pSR) technique is transverse field

muon spin rotation (TF-pSR, sometimes also known as transverse field muon spin

resonance). In order to measure the magnetic interaction of the muon beam with the

sample and their time-dependent effects on the polarisation, the positron distribution has

to be measured as a h c t i o n of the elapsed muon lifetime in a time-differential fashion.

In time-differential pSR each muon (or bunch of muons) starts a clock, which designates

to in the experiment, and both time and direction of each positron decay product is

recorded. The signature of an event is constructed such that only one muon might be

present in the sample at any time and only one positron can be detected at any time. The

muon beam enters the sample area with spin polarization opposite to its momentum. The

transverse field technique means that the external magnetic field (depicted by H in figure

4.3) is applied perpendicularly to the direction of the muon polarization, causing the

muon spin to precess (rotate) at the Larmor frequency. A schematic representation of the

experimental apparatus is shown in figure 4.3.

Figure 4.3. Schematic diagram of a simple TF-pSR experiment. The muon is shown

entering the target area from the left. The magnetic field is applied vertically

(M is the incoming muon detector, E is the emitted positron detector; the

white block arrow represents the muon spin and the black block arrow the

muon momentum).

The first counter triggered is the muon counter (depicted by M in figure 4.3). As

the muon decays, a positron is emitted in the direction of the muon spin at the time of

decay. The positrons are detected by counters placed in the plane perpendicular to the

field (depicted by E in figure 4.3). Triggering of these detectors stops the time interval for

each muon. Depending on the statistics required for the experiment - 10' muons are counted in the spectrum, producing a time histogram such as in figure 4.4.a, which

ideally has the following form:

where No is the normalization, B is the background, z,, is the muon lifetime and A(t) is

the asymmetry spectrum or the time evolution of the muon polarization. Figure 4.4.b

shows a typical asymmetry spectrum. In this thesis most spectra are displayed as the

Fourier transform of the data in order to display the frequencies of each signal.

Time / p

Figure 4.4. a) Raw time histogram from a simple TF-pSR experiment.

b) TF-kSR asymmetry spectrum obtained from the raw time histogram (red

line fitted data, black vertical lines raw data).

4.2 Muonium

Muonium is a two spin-112 system and it is characterized by the spin

Harniltonian:

where a~ = 27c A,, A, is the isotropic hyperfie coupling constant between the muon and

electron, o, and q are the Zeeman angular frequencies of the electron and muon, S, and

I, are the z-axis components of the electron and muon spin operators. There are four spin

states, which are divided into one triplet state and one singlet state at zero magnetic field.

If a magnetic field is applied to muonium, the degeneracy of the triplet states is lifted.

The variation of the energy levels of the four spin states as a function of the strength of

the applied field can be best illustrated by use of the Breit-Rabi Diagram in figure 4.5.

The eigenstates are labelled according to their quantum numbers [8]:

where

There are four allowed transition frequencies in a transverse field experiment. Due to the

limitation of the timing resolution for conventional apparatus, only two transitions (1 1)

-+ 12), 2 ) -+ 13)) are observed in pSR spectroscopy at low magnetic field. At high

magnetic field the muon and electron spin are decoupled. There are only two transitions

( 1 1 + 12), 13) -+ 14)), denoted by R, which are allowed at high field. At moderate

fields the splitting of two frequencies (v12 and ~ 2 ~ ) can be used to determine the hyperfine

coupling according to:

V12 = w e -v , ) -Q

V23 =%(V,

i2 = X {[A: + (v, + v , ) ~ ] " ~ -A,)

where v, and v, are the electron and muon Larmor frequencies.

Figure 4.5. Breit-Rabi diagram showing the energy levels of the muonium spin states as a

function of the magnetic field. The arrows indicate the allowed transitions in

TF-pSR. In low fields, only two transitions donated by solid lines are

resolvable.

4.3 Muoniated Radicals

Radicals are molecular species which are paramagnetic due to an unpaired

electron. Most muoniated radicals contain, apart from the muon, a considerable number

of other magnetic nuclei, which are also coupled to the unpaired electron. The Spin

Hamiltonian for such a multi-spin system is:

where a, q and are the Zeeman angular frequencies, and A, and Ak are the

hyperfine coupling constants (hfcc) [8] in angular frequency units for the muon and the

nuclei k, respectively. For N nuclei with spin quantum number Sk the above Hamiltonian

leads to 4nkN(2sk+l) eigenstates. From quantum mechanics the selection rule for the

transitions between these states is AM = + 1 1501, where M = m,+ m, + Zk mk (mi is the magnetic quantum number of the particle i. The muon polarization thus oscillates

between many of these eigenstates and muon polarization is distributed over many

frequencies. In most organic radicals signals can only be observed at high field and

selection rules allow only for the muon spin flip. Therefore, only two transition

frequencies remain, v l 2 and ~ 3 4 , and their formulae simpli& to:

In the high field limit, v,id can be further approximated as vP. This method is not

possible for dilute solutions, because the relatively slow radical formation process leads

to incoherent spin precession.

4.4 Transfer of Mu Polarization

Calculations [51-531 predict significant transfer of muon polarization from the

muonium to the radical at low and intermediate magnetic fields. This strategy would not

be feasible for most muoniated organic radicals because other magnetic nuclei (usually

protons) cause splitting of spectral lines to such extent that the spectrum becomes

undetectable. Muonium adducts of fkllerenes have the advantage of being two spin

systems and the spectrum is similar to muonium itself, but with a much smaller hyperfine

interaction (Ap = 330 MHz for C6~Mu, compared to 4463 MHz for Mu). The two smallest

precession frequencies occur at:

When muonium polarization is transferred to the radical, the residual polarization at the

radical frequency is given by [52]:

and

where c and s are defined in equation 4.6,

'2323 = ( 0 2 3 ~ - %3R

'4323 = ( 0 4 3 ~ - %3R )

and where h is the reaction rate, M refers to muonium and R radical.

The amplitudes of the radical signal are predicted to depend on the reaction rate and the

various frequency differences, which vary with magnetic field. Some representative

predictions are plotted below, in figure 4.4.

Magnetic Field I G 0.3 r

0 50 100 150 200

Magnetic Field I G

Figure 4.6. Variation of radical signal polarization for different reaction rates. The

solid curves represent theoretical predictions for the precession

frequencies v 1 2 and V23.

CHAPTER 5.

EXPERIMENTAL METHODS AND INSTRUMENTATION

5.1 Introduction to TRIUMF

TRIUMF is Canada's Laboratory for Particle and Nuclear Physics. TRIUMF is

operated as a joint venture of several Canadian universities (University of British

Columbia, University of Alberta, Carleton University, Simon Fraser University,

University of Victoria, etc.) and is funded by the National Research Council of Canada.

The TRIUMF cyclotron accelerates negatively charged hydrogen ions over a wide

energy range fiom 60 MeV to 520 MeV. The extraction of a proton beam fiom the

cyclotron involves intercepting the .H beam with a thin carbon foil which strips off two

electrons while the much heavier proton passes through. A general map of TRIUMF

showing the various experimental areas is shown in figure 5.1.

At TRIUMF, the cyclotron currently feeds four main beam lines. The first beam

line (BLI) delivers beam to the meson experimental hall. The second beam line (BL4)

provides beam to experiments in the proton experimental hall. The third beam line

(BL2C) delivers low-energy beam for the production of radioisotopes. The fourth beam

line (BL2) extracts high intensity, high energy protons towards ISAC to produce

radioactive beams.

In the meson hall a proton beam passes through two production targets to provide

sources of muons and pions to a number of secondary beam channels before being

stopped in the beam dump. The first production target, lAT1, is 1 cm thick carbon or

beryllium and it can provide muodpion beams to three different channels: the M13

surface muon channel (low energy pions), the MI 1 good resolution pion channel (high

energy pions) and the M 15 high quality surface muon channel.

Figure 5.1. Beam lines and experimental facilities at TRIUMF.

(Figure taken from http://www.triumf.ca/tourmap.html)

The second target, lAT2, is 10 cm thick Beryllium and it can generate high

intensity muodpion beams to several channels: the M9 low energy pion (decay muon

channel) and the M20 surface muon channel.

5.2 Beam lines MI5 and M20

The experiments of this work were done at TRIUMF's M15 and M20 muon

channels [54]. Their main features will be described in this section.

There are three types of muon beam that are available for experiments, the

forward, backward and surface. The forward muon beam has the highest energy of the

three. This beam is rarely used due to the high stopping range and high degree of

contamination of pions, positrons and protons.

M15 is a dedicated surface p' channel. A surface muon beam usually has almost

100% polarization. Surface muons are produced from the decay of pions that are at the

surface of the production target. The stopping range of such muons is small (0.15 + 0.01 g ~ m - ~ ) , which corresponds to a penetration depth of about 0.2 rnrn in copper or 1.5 mrn

in water. This makes surface muons ideal for the study of gases, thin or rare solids, or

small quantities of liquid held in thin cells. There are disadvantages when surface muons

are used in experiment. Due to their low energy and momentum, there is significant beam

bending even in moderate transverse fields.

M9B is the backward muon beam line. The backward muon beam has

polarization of 60-100 %. The stopping range of these muons in matter is approximately

5 g ~ m - ~ . The backward beam is too energetic to be stopped properly in the sample cell.

This line was used for a high pressure vessel with a thick window details could be found

elsewhere [55].

5.3 pSR Spectrometers

The spectrometers are installed at the end of the beam line. They consist of a

magnet and an array of counters to detect incoming muons and decay positrons. For the

present experiments two magnets were employed, OMNI or LAMPF. They each consist

of a pair of Helmholtz coils and produce the low magnetic field needed for these

experiments.

5.4 Flow System

The general schematic design for the flow system set up is shown in figure 5.2.

The major parts consist of a temperature controller system, heating, nitrogen supply, the

sample supply, shroud covering a copper rod on which is mounted the glass sample cell

with a thin plastic window, plastic tubing, thermocouple, etc made by SFUMU (Simon

Fraser Muonium Chemistry Group). The flow system was used only for changing and

filling the sample cell; during the experiment the flow was stopped.

waste

P+ sample - supply thin win

vacuum

Figure 5.2. Schematic set up for the flow system used for the pSR experiments.

For experiments in this thesis a circulator (temperature bath) was used to control

the temperature of the sample by circulating fluid through insulated tubes between the

bath and a copper plate to which the sample was attached. The reason for using this

temperature control apparatus was to have the same temperature range, 10 "C to 50 "C, as

with the DLS apparatus. Because of an unavoidable temperature gradient between the

constant temperature bath and the glass sample cell (shown in figure 5.3), the real sample

temperature was measured by a thermocouple which was embedded in the glass sample

cell. It was found that the variation of temperature over the sample volume was less than

1 "C.

window holder \ \

j- sample out thermocouple--

(Kapton) I - sample in \ - liquid out -from circulator

Pfglass cell

Figure 5.3. Schematic drawing for a glass cell used in the flow system.

The sample cell used for another type of experiment was made of stainless steel.

The window of the sample cell was made from thin stainless steel foil so that surface

muons can pass through and stop in the sample. Samples were prepared on the vacuum

line in our laboratory and a freeze-pump-thaw method was applied for each sample

preparation. The cell was sealed after this procedure to ensure an oxygen free sample.

5.5 Data Acquisition and Analysis

At TRIUMF a common data acquisition system was used, called "MODAS",

based on CAMAC and Digital's VAX-VMS computers. However, for the last

experiments new data acquisition software based on the LINUX operating system was in

use. Depending on the statistics required for the experiment - 10' muons are counted in the spectrum, producing a time histogram (equation 4.3). Usually 4 histograms were

collected (10-20 million counts/per histogram in approximately 2-5 hours). The

appropriate theoretical expression was computer fitted to the experimental pSR spectra.

From TF-pSR signals it is useful to convert histograms to a frequency spectrum by

means of a fast Fourier transform (FFT). The Fourier transforms are useful for showing

the frequency spectrum for muon precession in complex spin systems such as organic

free radicals like C,j0M~@, as illustrated in figure 5.4. For the radical studies, frequency

values were extracted using a program written by a former member of the SFUMU group

WI-

50 100 150 200 250 Frequency (MHz)

Figure 5.4. Fourier power spectrum for positive muons in powdered C60 at room

temperature, showing simultaneously the signal from muons in the C 6 0 M ~

radical (R12 and R34) and endohedral muonium (Mu@C~~) atoms (Muln and

M~34).

Every pSR facility provides FFT algorithms as part of data analysis. There are

many variations and adaptations of these algorithms and there are many incompatible

opinions regarding the correct or optimal preparation of the time spectra before

transforming. Some notes on Fourier transforming TF-pSR data can be found elsewhere

[561.

Muonium decay rates were extracted from fits of pSR spectra using the

"MINUIT" program, based on a least-square minimization routine [57]. The program can

accommodate up to 30 variable parameters, any number of which may be fixed at any

time and restored at a later time. This program was used at TRIUMF during the

experiments.

CHAPTER 6.

MUONIUM DECAY RATES

6.1 Introduction

Investigations of the reaction of muonium with fullerene in solution by transverse

field muon spin rotation (TF-pSR) were done at TRIUMF where two types of

measurements were performed:

*:* Muonium decay rates in low magnetic field on dilute aqueous solutions of C60

sol and dilute organic solutions of C,jO in cyclohexane (described in this chapter).

4* Radical signal amplitude as a function of applied magnetic field on C60 in

decalin (described in chapter 7).

The rate of reaction between muonium and some reaction partner A,

Mu + A + products

can be written

--- - k , [A] [Mu] = ~ [ M U ] dt

where kM is the second order constant and h is the first order

concentration of A does not vary during an experiment, the decay

constant. Since the

kinetics are pseudo-

first order. kM can be determined from (A&) / [A] where h is the decay constant at

concentration [A] and ho is the residual decay constant for the pure solvent, i.e. with [A]

= 0.

In previous work [41] the muonium decay rate has been determined to be

diffbsion limited in dilute solutions of C60 in cyclohexane, with an activation energy of 6

kJ mol", for reaction:

and consequently the muonium decay rate Lxp could be directly related to rate constant

kM, by equation 6.4.

where is the decay rate in the pure solvent, included to incorporate any physical

effects.

To check apparatus and procedures, the same sample concentrations (2 and 4 pM

C60 in cyclohexane) and experiments as in [41] were repeated.

The muonium decay rate was measured for each C60 so1 sample prepared by

various methods as described earlier. The proposed mechanism for the reaction of Mu

with C60 clusters is given by:

From the formation of C~OMU the muonium relaxation (decay) rate k,, is directly related

to the rate constant kd by the equation:

hap = Lo + k,,[solI = 1 0 + (k,, N)[C,ol (6.6)

where sol = (C60),; [sol] = [C60] / N and N is the number of particles in the cluster

(chapter 3), is the muonium decay rate in pure water (solvent). The usual plot of decay

rate versus reactant concentration [C60] would give us (kWl/N) as the slope. However, the

aggregation number N is determined from the size of the sol particle with DLS, so the

rate constant kWl, which was obtained from equation 6.6 could be compared with the

previous results. The Arrhenius activation energy can be estimated from the variation of

kWl with temperature.

6.2 Results and Discussion

Muonium decay measurements were made in three different beam periods. The

results reported here were obtained with the new flow system.

6.2.1 Kinetics: CGO in organic solutions

Results for the muonium decay rate in two dilute C6dcyclohexane solutions and

pure cyclohexane at three temperatures are shown in figure 6.1.

The linearity of the plots implies a first order reaction rate and the rate constants are

2.0(4) x 10" M-I s-l, 2.3(5) x 10" M-' s-' and 3.9(4) x 10" M-' s-' for 10 "C, 25 "C and

50 "C respectively. The variation in kM, with temperature then provides the activation

energy, E, = 12(3) kT mol-', from the Arrhenius equation.

The results from this experiment were similar to the previous work [41]. Thus,

this implies that almost every encounter of muonium with C60 leads to reaction or that the

reaction rate is practically equal to the encounter rate. This is in agreement with the

previously finding that the reaction of muonium with CbO in cyclohexane is diffusion-

controlled [41].

Figure 6.1. Muoniurn decay rate measured in solution of C6() in cyclohexane as a

function of concentration at different temperatures: 50 "C (A), 25 "C

(a) and 10 "C (+).

6.2.2 Kinetics: CW sols

Figure 6.2 shows results for the muonium decay rate measured at three different

temperatures for a solution of C60 so1 prepared by the Andrievsky method.

2 -,

Figure 6.2. Muonium decay rate measured in C60 so1 samples prepared by the

Andrievsky method as a function of C60 concentration at three

temperatures (the lines are a guide for the eyes only).

Comparison of figures 6.1 and 6.2 reveals markedly different values of ho for

solvents cyclohexane and water. The former is probably due to residual impurities

(alkenes and oxygen), while the value in water represents the residual effect of magnetic

field inhomogeneity and unresolved splitting between the muonium precession

fiequencies.

It is evident that the data deviates fiom linearity at the highest concentration

studied. The reason for this will be discussed later. However, for concentrations < 100

pM the linearity is consistent with a first order reaction (figure 6.3. a). Similar results

were obtained during the August 2002 beam time (figure 6.3. b).

The rate constants for the C60 so1 samples in different beam times and at the three

different temperatures are shown in table 6.1.

Table 6.1. Rate constants determined for the reaction of muonium with C60 so1

prepared by the Andrievsky method.

-

Beam time kWl/N / M-'s" T 1 "C

5.5(3) x 1o1O

October 200 1 7.2(4) x 10l0

8.6(5) x 10l0 --

6.9(2) x lo9 10

A U ~ U S ~ 2002 7.5(7) x lo9 25

1.3(6) x 1 01•‹ 5 0

7.2(1) x lo9

December 2002 7.8(2) x lo9

1 .O(3) x 10l0

Figure 6.3. Muonium decay rates measured for the reaction of muonium with C60

sol as a function of concentration: a) the results obtained from the

December 2002 -beam time, b) the results obtained from the August

2002 beam time.

Knowing the radius of C60 so1 and the number N = 2223 + 82 of particles in the cluster from DLS (chapter 3), the C60 so1 rate constants at 25 "C are ksol = 1.5(1) x 10'"

M-ls-', kml = 2.0(3) x 1013 M-'i' and kml = 1.9(2) x 1013 M-~s-' for October, August and

December beam time respectively.

The diffusion rate constant can be predicted by the Smoluchowski equation:

where R is a radius and L is the Avogadro constant. D is a diffusion coefficient which

can be calculated fiom

where k is the Boltzmann constant, T the absolute temperature, R the particle radius and

q is the viscosity of the solvent. Assuming that R,1 >> RMu and DM, >> Dsol, the rate

constant (ksol) for the C(jO so1 can then be simplified as (6.8):

k,,, = 4000xLR,,DMu (6.8)

The diffusion rate constant for C60 in cyclohexane can be expressed by eq. (6.9):

kc, = 4000~L(RMu + RC,)(DM, + Dc,) (6.9)

Assuming &60 >> RMu and DMu >> DC60, the rate constant k~~~ for reaction muoniurn

with C60 in cyclohexane is written as (6.10):

By combining equations (6.8 and 6.10) and the Stokes-Einstein equation (6.7)

assuming that RMu in water is the same as RMu in cyclohexane, it is possible to write the

ratio of the two rate constants as

where T ) ~ 6 ~ 1 2 is the viscosity of cyclohexane, q ~ 2 0 is the viscosity of water. By

substituting values into the right hand side of equation 6.1 1 the ratio of the rate constant

is predicted to be 95. Using the experimentally determined rate constant of the reaction

for muonium with C60 in cyclohexane (k60 = 2.3(5) x 1011 M-ls-') and C60 so1 (ksol =

2.0(3) x 1013 M"S-') the ratio was found to be 87 k 22. Since the ratios are in agreement

(within error) it is concluded that the results are consistent with a diffision controlled

reaction.

From the results displayed in Table 6.1, the Arrhenius activation energy may be

obtained using the Arrhenius equation (6.5), giving the activation energy Ea = 9(2) kJ

mol'', Ea = 16(3) kJ mol-I and Ea = l5(2) kJ mol-' for the October, August and December

beam times, respectively.

The results for muonium decay rates obtained from samples prepared by the Wei

Figure 6.4. Muoniurn decay rate measured in solutions of C 6 ~ so1 by the Wei

method as a function of concentration at two temperatures (lines are a

guide for the eyes only).

These results were obtained in the October 2001 beam time and are unreliable,

since it was observed later that oxygen may have leaked into the flow system.

The results for muonium decay rates measured using samples prepared by the

Deguchi method are shown in figure 6.5. The linearity of these plots implies a first order

reaction. The rate constants for the C60 so1 samples by the Deguchi method in different

beam times and at three different temperatures are listed in table 6.2. Again knowing the

radius of C60 so1 and the number of particles in the cluster (N = 3980 f 65) from DLS, the

rate constants can be calculated to be ksol = 3.4(1) x 1014 M-'s-' and 1.0(2) x 1014 M-'s-' at

room temperature. The activation energy is found to be E, = 28(3) kJ mol" and E, =

20(1) kT mol'lfor the August and December beam times, respectively.

Table 6.2. Rate constants determined for the reaction of muonium with C60 so1

prepared by the Deguchi method.

Beam time kwl/N I M - I S - ~ T I 0 C

4.0(6) x 10'' 10

August 2002 8.5(9) x 10l0 25

1.6(2) x 10' ' 50

l . l ( l ) x 1o1O

December 2002 2.5(1) x 10l0

4.1(2) x 10l0

Figure 6.5. Muonium decay rate for the C60 so1 prepared by the Deguchi method as a

function of concentration at three temperatures: a) the results obtained in the

December 2002 beam time, b) the results obtained in the August 2002 beam

time.

6.3 Conclusions

The results for the rate constant obtained by the muonium decay method were

inconsistent with each other. The explanation for the scattered results seems to lie in the

dependence of the reaction rate on the aggregation number N. The C60 sols were prepared

by three different methods so the aggregation number for each of those solutions was

different, as was shown in the chapter 3. The differences in the results from different

beam times can also be attributed to using freshly prepared solution so used "aged"

samples were used in the December 2002 beam, whose DLS measurements showed to be

monodisperse (sol particles with a narrow size distribution). The data accumulated in the

December 2002 beam time present a set of consistent and reliable results. Also there was

no leaking of oxygen (using the new flow system). However, in figure 6.2 the data does

not show the muonium decay rate as a linear function of C6() concentration. One reason

for this discrepancy may be the aggregation number N of C60 sol. For C60 so1 samples

with the highest concentration N = 80 + 47 and for lower concentration of C60 so1 samples the aggregation number was N = 100 + 47. For future work, I would recommend making "aged" samples of concentration 100-190 j&l and to perform more DLS or DWS

(Diffusion Wave Spectroscopy-multiple scattering for higher concentration samples) to

confirm R and N values and to confirm that concentrated solutions are monodisperse.

Muonium decay rates were measured for micromolar solutions of C60 in

cyclohexane and C60 so1 in water and the rate constants were determined to be diffusion

limited.

CHAPTER 7.

FREE RADICAL FORMATION

7.1 Introduction

Measurements were made of the signal amplitude of C60M~ as a function of

applied magnetic field for solutions of C60 in decalin and 12c60 in decalin. The purpose

was to extract the rate constant and the activation energy from a study of the fraction of

initial muon polarization transferred to a radical signal (chapter 4.4). The radical signal

amplitude is predicted to vary with applied magnetic field and reaction rate (figure 4.4).

7.2 Results and Discussion

A study of the variation in radical peak amplitudes with field was undertaken for

two samples: 2.7 mM 12c60 (12c enriched) in decalin and 3 mM C60 (natural abundance)

in decalin at three different temperatures. Radical peaks are broadened in the spectrum

from the sample with natural abundance due to the presence of a third spin, 13c [36].

Peak amplitudes were measured from the low field TF-pSR spectra of those two

samples in a field range of 3-150 G. TF-pSR spectra of natural abundance C60 at 50 OC

and 10 OC, and 12c60 at 25 OC are shown in figure 7.1. The spectra were collected at the

same field so the signal amplitudes can be compared. It can be seen that the intensity is

different for the natural abundance sample from the enriched sample and for the same

abundance sample at different temperatures.

0 20 40 60 80 100

Frequency (MHz)

Figure 7.1. Fourier transform TF-pSR spectra at 65 G: a) 3 rnM C60 in decalin at

10 "C, b) 2.7 mM 12c6() in decalin at 25 OC and c) 3 mM C60 in

decalin at 50 OC.

The rate can be derived fiom fitting the theoretical curve for the field dependence

of the radical amplitudes to the experimental one. From the best fits the reaction rates

were determined to be h = 1.0 x 10' s" at 10 "C; h = 1.5 x 10' s-I at 25 "C and h = 2.75

x 10' s-' at 50 "C. The rate constant k ~ , was then calculated fiom:

where h is the rate of reaction, k~~ is the second-order rate constant and [C60] the

concentration of C60 in decalin. The predicted and experimental values for the two

samples at three temperatures are shown in figure 7.2. The results are listed in table 7.1.

These data are plotted in figure 7.3. The best fit to the Arrhenius equation gives

an activation energy of E, = 18(2) kJ mol-'. This is similar to the activation energies

determined from the Mu decay experiments (chapter 6) and is typical for diffusion

processes in water.

The experimental results can be compared with a prediction obtained by

correcting the rate constant for Mu + C6() in cyclohexane according with the difference in

viscosity between decalin and cyclohexane (rate constant in decalin is 0.35 times that in

cyclohexane [41]). The theoretical prediction for the reaction of muonium with C60 in

decalin were (1.8 x 10" M-'s-') which gives a muoniurn decay rate of 5.8 x 10' i1 at

25 "C.

0 50 100 150 200

Magnetic Field 1 G

Figure 7.2. Field dependence of muon polarization transferred from muoniurn to

the radical precession frequencies at (a) 10 "C, (b) 25 "C and (c) 50

"C. The solid curves show the corresponding theoretical predictions

for the precession frequencies vlz and ~ 2 3 .

Table 7.1. The rate constant determined for the reaction of Mu with C60 in decalin

Figure 7.3. The Arrhenius plot of the rate constant for reaction of Mu with C60 in

decalin.

7.3 Conclusion

The results of the previous study [41] show that the rate constant obtained from

the kinetics studies is in agreement with results based on the radical amplitude variation

with field. The results obtained from this experiment show that the rate constant k ~ ,

obtained from the radical product experiment is only one-tenth of that obtained from the

muonium decay rates in cyclohexane. The rate constant for the reaction of muonium with

C60 in decalin was predicted to be 0.3 times that in the reaction of muonium with C60 in

cyclohexane on the basis of solvent viscosity. The reason for this discrepancy might be

due to the different aggregation number and fractal dimensionality of the C60 in organic

solutions.

CHAPTER 8.

SUMMARY

Transverse field muon spin resonance TF-pSR was employed in this kinetics

study of the reaction of muonium with C(jO in solution. Two different methods were used:

muonium decay rates in low magnetic field; and measurements of radical signal

amplitude as a function of applied magnetic field.

A study of the kinetics by muonium decay rates was performed, using dilute

solutions of C60 in cyclohexane. The rate constant was obtained to be 2 x 10" M'' s-' at

room temperature, where this result is similar to a previous result.

The reaction of muonium with Cm in aqueous solutions (Cao sol) has been studied

by measuring muonium decay rates. The CaO so1 samples were prepared by three different

methods. The hydrodynamic radius of CaO so1 samples was determined by dynamic light

scattering. It was found to be in the range of 70 - 212 nm depending on the preparation

method of the C60 so1 samples. The rate constant for the reaction of muonium with C6() so1

samples prepared by the Andrievsky method was obtained to be 7 x lo9 M-' s-' at 25 "C.

For this reaction the best fit to the Arrhenius equation gives an activation energy of 15 kJ

mol-'. The rate constant for the reaction of muonium with Cso sol samples prepared by the

Deguchi method was obtained to be 2 x 10" M-' s" at 25 "C. From the result of the rate

constant at three different temperatures for this reaction the activation energy was found

to be 20 kJ mole'.

The rate constant for the reaction of muonium with CaO in dilute solution of

decalin was obtained from measurements of radical signal amplitude as a function of

applied field and it was determined to be 5 x 10" M-' s-' at 25 "C. The activation energy

of this reaction was found to be 18 W mol-'. The rate constant of muonium with C60 in

decalin obtained from the radical signal amplitude as a function of applied magnetic field

was 3 times smaller than the predicted value for this reaction. The reason for this

discrepancy might be due to the different aggregation number and fractal dimensionality

of the C60 in organic solutions.

There have been difficulties in obtaining the stable solutions of C60 in organic

solvents, as well as to determine the suitable solvent, which has delayed progress in this

field. Also, there have been difficulties to obtain stable aqueous C60 samples because of

the C60 aggregation. So to better understand aggregation of the Cso in solutions there

should be performed more Dynamic Light Scattering, Static Light Scattering, Diffusion

Wave Spectroscopy and Transmission Electron Microscopy. In spite of these problems

the kinetic results show that the reaction of muonium with C60 in organic solvent and C60

in water is diffusion limited. The obtained values of the rate constants for the reactions of

muonium with the C60 in organic solutions were also in agreement with the previous

result.

REFERENCES

K. M. Kadish and R. S. Ruoff, Fullerenes: Chemistry, Physics and Technology

(Wiley-Interscience, New York, 2000).

T. Da Ros and M. Prato, Chem. Commun. (1999) 663.

Y. Tabata and Y. Ikada, Pure Appl. Chem. 71 (1999) 2047.

E. Nakarnura, H. Tokuyama, S. Yamago, T. Shiraki and Y. Sugiura, Bull. Chem.

Soc. Jpn. 69 (1996) 2143.

T. Wharton, V. U. Kini, R. A. Mortis and L. J. Wilson, ~etrahedron Letters 42

(2001) 5159.

S. H. Neddermeyer and C. D. Anderson, Phys. Rev. 54 (1938) 88.

A. Schenck, Muon Spin Rotation Spectroscopy: Principles and Applications in

Solid State Physics (Adam Hilger Ltd, Bristol and Boston, 1985).

E. Roduner, The Positive Muon as a Probe in Free Radical Chemistry; Lecture

Notes in Chemistry Vol. 49 (Springer, Heidelberg, 1988).

A. Schenck, Nuclear and Particle Physics at Intermediate Energies (Plenum

Press, New York, 1975).

M. S. Dresselhaus, G. Dresselhaus and P. C. Eklund, Science of Fullerenes and

Carbon Nanotubes (Academic Press, Toronto, 1996).

R. Taylor, The Chemistry of Fullerenes (World Scientific, London, 1995).

A. Graja, Fullerene Science and Technology 8 (2000) 187.

P. Boulas, W. Kutner, T. M. Jones and K. M. Kadish, J. Phys. Chem. 98 (1994)

1282.

N. Sivararnan, T. G. Srinivasan and P. R. V. Rao, J. Chem. Inf. Comput. Sci. 41

(2001) 1067.

Y. Marcus, A. L. Smith, M. V. Korobov, A. L. Mirakyan, N. V. Avramenko and

E. B. Stukalin, J. Phys. Chem. B. 105 (2001) 2499.

R. V. Bensasson, E. Bienvenue, M. Dellinger, S. Leach and P. Seta, J. Phys.

Chem. 98 (1994) 3492.

T. Rudalevige, A. H. Francis and R. Zand, J. Phys. Chem A. 102 (1998) 9797.

H. N. Ghosh, A. V. Sapre and J. P. Mittal, J. Phys. Chem. 100 (1996) 9439.

Q. Ying, J. Marecek and B.'Chu, Chem. Phys. Lett. 219 (1994) 214.

Q. Ying, J. Marecek and B. Chu, J. Chem. Phys. 101 (1994) 2665.

S. Nath, H. Pal, D. K. Palit, A. V. Sapre and J. P. Mittal, J. Phys. Chem. B. 102

(1998) 10158.

R. G. Alargova, S. Deguchi and K. Tsujii, J. Am. Chem. Soc. 123 (2001) 10460.

A. Mrzel, A. Mertelj, A. Omerzu, M. Copic and D. Mihailovic. J. Phys. Chem. B.

103 (1999) 11256.

K. I. Priyadarsini, H. Mohan and J. P. Mittal, Fullerene Science and Technology 3

(1 995) 479.

T. Andersson, K. Nilsson, M. Sundahl, G. Westman and 0. Wennerstrom, J.

Chem. Soc. Chem. Cornrnun. (1992) 604.

U. S. Jeng, T. L. Lin, C. S. Tsao, C. H. Lee, T. Canteenwala, L. Wang, L. Chiang

and C. Han, J. Phys. Chem. B 103 (1999) 1059.

G. V. Andrievsky, M. V. Kosevich, 0. M. Vovk, V. S. Shelkovsky and L. A.

Vashchenko, J. Chem. Soc., Chem. Cornmun. (1995) 1281.

G. V. Andrievsky, V. K. Klochkov, E. Karyakina and N. Mchedlov-Petrossyan,

Chem. Phys. Lett. 300 (1999) 392.

R. S. Ruoff and K. M. Kadish, Fullerenes: Recent Advances in the Chemistry and

Physics of Fullerenes and Related Materials (The Electrochemical Society Inc.,

Pittsburg, 1995).

X. Wei, M. Wu, L. Qi and Z. Xu, J. Chem. Soc., Perkin Trans. 2 (1997) 1389.

X. Wei, Z. Suo, K. Zhou, Z. Xu, W. Zhang, P. Wang, H. Shen and X. Li, J. Chem.

Soc., Perkin Trans. 2 (1999) 121.

S. Deguchi, R. G. Alargovaand K. Tsujii, Langmuir 17 (2001) 6013.

G. V. Andrievsky, V. K. Klochkov, A. B. Bordyuh an