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
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
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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 lo9M-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 ...... 32
4.3 Muoniated Radicals...... 35
4.4 Transfer of Mu Polarization ...... 36 CHAPTER 5. Experimental Methods and Instrumentation ...... 39
Introduction to TRIUMF ...... 39
Beam lines M 15 and M20 ...... 42
pSR Spectrometers ...... 43
Flow System ...... 43
Data Acquisition and Analysis ...... 45
CHAPTER 6 . Muonium Decay Rates...... 48
6.1 Introduction ...... 48
6.2 Results and Discussion ...... 50
6.2.1 Kinetics: C6()in organic solutions...... 50
6.2.2 Kinetics: C60sols ...... 52
6.3 Conclusions ...... 60
CHAPTER 7. Free Radical Formation ...... 61
7.1 Introduction ...... 61
7.2 Results and Discussion ...... 61
7.3 Conclusion ...... 66
CHAPTER 8. Summary ...... 67
REFERENCES ...... 69 Figure 2.1. Structure of the soccer ball Cm molecule...... 6
Figure 2.2. Cm structure with two products of muonium attack, the muoniated radical C~U(left) and encapsulated muonium, Mu@Cm...... 15
Figure 3.1. The sonochemistry equipment: a) cleaning bath, and b) probe
system...... 18
Figure 3.2. The system for purging nitrogen to evaporate the THF...... 20
Figure 3.3. The W spectrum of 7 x 10 4 M Cm in decalin...... 2 1
Figure 3.4. 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
Figure 4.1. Decay of pion (3represents the momentum vector, -+ represents
the particle spin or neutrino helicity vectors)...... 26
Figure 4.2. Decay of the muon (3 represents the momentum vector, -+
represents the particle spin or neutrino helicity vectors)...... 27
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 arrow the muon momentum)...... 29
Figure 4.4. 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. 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
Figure 4.6. Variation of radical signal polarization for the different reaction
rates. The solid curves represent theoretical predictions for the
precession frequencies v12 and V23...... 38
Figure 5.1. Beam lines and experimental facilities at TRIUMF. (Figure taken
from http://www. triumf.ca/tourmap.html)...... 4 1
Figure 5.2. Schematic set up for the flow system used for the pSR experiments...... 44
Figure 5.3. Schematic drawing for a glass cell used in the flow system...... 45
Figure 5.4. Fourier power spectrum for positive muons in powdered CWat room
temperature, showing simultaneously the signal from muons in the
C&U radical (R12and R34) and endohedral muonium (Mu@CW)
atoms (Mul2and Mu,)...... 46
Figure 6.1. Muonium decay rate measured in solutions of CWin cyclohexane as
a hction of concentration at different temperatures: 50 OC (A), 25
"C (a) and 10 OC (+)...... 5 1
Figure 6.2. 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
Figure 6.3. Muonium decay rates measured for the reaction of muonium with
CW so1 as a hction 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 mM I2cmin 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 ~23...... 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 . The basic properties of the positive muon ...... 3
Table 1.2 . The basic properties of muonium...... 4
Table 2- 1. Selected physical properties of Cm...... 7
Table 2.2 . The solubility of C60in organic solvents at 298 K ...... 9
Table 2.3 . The average hydrodynamic diameters of hllerene particles formed in various solvents...... 11
Table 3.1. The hydrodynamic radius of Cm so1 samples as determined by
different methods at 25 "C...... 24
Table 6.1. Rate constants determined for the reaction of muonium with Cm so1
prepared by the Andrievsky method...... 53
Table 6.2. Rate constants determined for the reaction of muonium with Cm so1
prepared by the Deguchi method...... 58
Table 7.1. The rate constant determined for the reaction of Mu with Cm in
decalin...... 65 LIST OF ABBREVIATIONS
TWF Tri University Meson Facility
TEM transmission electron microscopy
THF tetrahydrofuran
UV-Vis ultra-violet visible spectroscopy
IR infia-red spectroscopy
DLS dynamic light scattering
NMR nuclear magnetic resonance
ODMR optically detected magnetic resonance
ESR electron spin resonance
CLSR muon spin rotation
TF-pSR 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. CbOis 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 ~harmacologyand 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 cbOis 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 3.1 833 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 CsOand related fullerene molecules have attracted a great deal of interest because of their unique structure and properties. C60or "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 C60molecule. 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 13cspectrum [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 1.44 8,
Mean diameter 6.83 8,
Mass density 1.72 g cm"
Molecular density 1.44 x 1 o2 cm~~
Binding energy per atom 7.4 eV
Electron affinity 2.65 eV
1 " ionization potential 7.58 eV
2ndionization potential 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 C60in 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 PI
THF/Acetonitrile 226 k 20 [221
Toluene/Ethanol 490 PI
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 C6iand (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 Mu@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/decalinsolutions
(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: wate water+detergent
* stainless - steel tank optional R-heater 1 I I 1 I I
transducers bonded to base
transducer generator housing
replaceable CBOIdecal in tip
water
Figure 3.1. The sonochemistry equipment: a) cleaning bath, and b) probe system. 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 C6iwas added dropwise to undegassed water to give a dark red-brown aqueous colloidal solution. The oxidation process is given by [30][311:
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
9sample
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
1 I I 0 I I 300 400 wavelength I nm
Figure 3.4. UV spectra of aqueous sols: a) 80 @IC60 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
WI.
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 (arepresents 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 +Aocos 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. (3represents 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 hction 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 (v12and ~2~)can be used to determine the hyperfine coupling according to:
V12 =we-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, vl2 and ~34,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 = (023~- %3R
'4323 = (043~ - %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 IG 0.3 r
0 50 100 150 200 Magnetic Field IG
Figure 4.6. Variation of radical signal polarization for different reaction rates. The
solid curves represent theoretical predictions for the precession
frequencies v12 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 C60M~
radical (R12 and R34)and endohedral muonium (Mu@C~~)atoms (Mulnand
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,jOin 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] = ~[MU] dt where kM is the second order constant and h is the first order constant. Since the concentration of A does not vary during an experiment, the decay 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 Lxpcould 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~OMUthe muonium relaxation (decay) rate k,, is directly related to the rate constant kd by the equation:
hap = Lo + k,,[solI = 10+ (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 kWlwith 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: CGOin 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 CbOin 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 C60so1 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
AU~US~2002 7.5(7) x lo9 25
1.3(6) x 101•‹ 50
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(jOso1 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 RMuin water is the same as RMuin cyclohexane, it is possible to write the ratio of the two rate constants as
where T)~6~12is the viscosity of cyclohexane, q~20is 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 C6~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/NI M-IS-~ TI0C
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 12c60at 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' i1at
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 ~23. 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 (Caosol) has been studied by measuring muonium decay rates. The CaOso1 samples were prepared by three different methods. The hydrodynamic radius of CaOso1 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 lo9M-' 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 C60in 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
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