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Reactions of muonium and positronium in solution Barnabas, Mary Vijayarani 1989

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R E A C T I O N S O F M U O N I U M A N D P O S I T R O N I U M IN S O L U T I O N by Mary Vijayarani Barnabas B. Sc. (Chemistry) Madras University, India, 1976 M. Sc. (Chemistry) Madras University, India, 1978 M. Phil. (Chemistry) Madras University, India. 1982 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S D E P A R T M E N T O F C H E M I S T R Y We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A Aug 1989 © Mary Vijayarani Barnabas (1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Chemistry The University of British Columbia 1956 Main Mall Vancouver, Canada Date: Abstract Positive muons are produced at TRIUMF as pion decay products and form muo-nium atoms in media such as water during their two microsecond lifetime. Muo-nium is a hydrogen-like atom with virtually the same Bohr radius and ionization energy as 1 H , 2 H and 3 H , but with a mass one-ninth that of a H . Its reactions toward solutes are studied by ^SR (the muon spin rotation technique) and the muonated free radicals it forms are studied by yLCK (muon level crossing reso-nance spectroscopy). In this thesis, rate constants for muonium reactions were determined for a range of solutes from simple amides to DNA bases. Their values ranged from <105 M " 1 ^ - 1 to >1010 M - 1 s - 1 . Kinetic isotope effects (relative to-'H) varied from 100 to 0.01 depending on the reaction-type. In the presence of added mi-celles the rates of some abstraction reactions were very greatly enhanced, whereas most addition reactions were unaffected by the micellar microenvironment. Muo-nium was seen by LCR spectroscopy to add at a diffusion-limited rate across thiocarbonyl groups, with muonium attached to the carbon and thus yielding thiyl radicals. Uracil and thymine were studied by both ySK and LCR and their relative addition probabilities at C(5) and C(6) were determined. Ortho-positronium (the atom consisting of an electron-positron pair with parallel spins) was studied by the positron annihilation lifetime technique for comparison with muonium in most of these same solutions. Its reactions are different, not 'adding' or 'abstracting' for instance, and it shows none of the properties of a hydrogen isotope. ii Table of Contents Abstract ii List of Tables ix List of Figures xii Acknowledgement xiii 1 Introduction 1 1.1 Muonium Chemistry 1 1.2 Positronium Chemistry 5 1.3 Micelles 6 1.4 Description of thesis content S 2 Background and Experimental 11 2.1 Production and decay of muons 11 2.2 Transverse field /xSR Measurements 13 2.2.1 Experimental set-up 14 2.2.2 Electronic logic 16 2.2.3 Data analysis 16 2.2.3.1 TF-/xSR : 5 to 100 mT 18 2.2.3.2 TF-MSR : 0.3 to 1.0 mT 20 2.2.3.3 TF-jxSR : 0.1 - 3 T 25 2.3 Longitudinal field pSR measurements . 29 i n 2.3.1 Time integrated LF measurements and LCR 29 2.3.2 Time differential LF measurements 36 2.4 Positronium Annihilation Lifetime measurements 38 2.5 Chemicals and sample solutions 42 3 Rate constants for Muonium reactions 44 3.1 Introduction v 44 3.2 Results 45 3.3 Discussion 56 3.3.1 Sensitivity of k^ to functional groups 56 3.3.2 Comparison of ILM with k// 61 3.3.3 Rate constants in micellar solution, ^-M(mic) • • • 63 3.4 Conclusion 68 4 Rate constants for Positronium reactions 70 4.1 Introduction 70 4.2 Results 71 4.3 Discussion 79 4.3.1 kp compared with kp(m;c) 79 4.3.2 Reactivity of o-Ps 80 4.3.3 Yield of Ps 81 4.3.4 kp compared with k^, k« and k e- ? 83 4.4 Conclusion 83 5 Muonated Thiyl Radicals Studied by T F - / i S R and / i L C R 86 5.1 Introduction 86 5.2 Results 87 iv 5.3 Discussion 96 5.3.1 Hyperfine coupling constants 96 5.3.2 LCR Parameters 98 5.3.2.1 LCR Amplitude 100 5.3.2.2 LCRLinewidth 101 5.3.2.3 LCR Position 103 5.3.3 Radical Yield 104 5.3.4 Relaxation effects 107 5.3.5 Effect of micelles 108 5.3.6 Rate constants 109 5.4 Conclusion 110 6 Muonated Radicals of Uracil and its Derivatives 112 6.1 Introduction 112 6.2 Results 113 6.3 Discussion 117 6.3.1 Hyperfine Parameters 118 6.3.2 LCR parameters and Radical Yield 121 6.3.3 Effect of pH . 121 6.3.4 Effect of micelles 122 6.4 Conclusion • 125 6.5 'Appendix to chapter 6': Assignment of LCR spectra of uracil . . 125 Summary 128 Bibliography 129 v Appendix: Collaborative work already published vi List of Tables 1.1 The physical properties of the muon and the muonium atom. . . 1 1.2 Some of the physical properties of Ps compared with Mu, 1 H , 2 H and 3 H 5 3.1 The summary of observed A and calculated ILM in aqueous solu-tions for the reaction of Mu with some amides and diamides in the presence and absence of micelles 46 3.2 The summary of observed A and calculated in aqueous solu-tions for the reaction of Mu with some thioamides in the presence and absence of micelles 48 3.3 The summary of observed A and calculated k ^ in aqueous solu-tions for the reaction of Mu with some related compounds (for comparison) in the presence and absence of micelles 50 3.4 The summary of observed A and calculated k ^ in aqueous solu-tions for the reaction of Mu with some carboxylic acids, at various pHs 51 3.5 The summary of observed A and calculated kA/ in aqueous solu-tions for the reaction of Mu with some amino acids in the presence and absence of micelles 52 3.6 The summary of observed A and calculated k\f for the reaction of Mu with some constituents of DNA and RNA in the presence and absence of micelles 53 vii 3.7 Rate constants for the reaction of Mu with selected compounds at natural pH and at pH = 1 55 3.8 Rate constants for the reaction of Mu compared with that of H. . 62 3.9 The enhancement factor i.e., ^M(mic)l^-M f ° r the compounds studied. 64 4.1 Lifetime values obtained for o-Ps with SHS micelles 71 4.2 The summary of observed o-Ps lifetime in aqueous solutions of some amides in the presence and absence of micelles 73 4.3 The summary of observed o-Ps lifetime in aqueous solutions of some diamides in the presence and absence of micelles 74 4.4 The summary of observed r 3 and I3 and kp (from Figs. 4.2 and 4.3) for the reaction of Ps with benzoquinone in different media. . 75 4.5 The summary of observed r 3 and I3 and calculated kp for the reaction of Ps with some benzoic acid derivatives in ethanol. . . . 78 4.6 The summary of observed T 3 and I3 for the reaction of Ps with nitrate in the presence and absence of SHS micelle 78 4.7 Upper limits to the positronium rate constants 82 4.8 Rate constants for the reaction of Ps compared with that of Mu, H, and e~q 84 5.1 Afj, values derived from the fitted frequencies of TF-/xSR measure-ments on TA and DMTFA 87 5.2 The Hyperfine parameters 89 5.3 LCR positions, linewidths, and amplitudes for the radicals formed with TA and DMTFA in solutions 92 5.4 LCR positions, linewidths, and amplitudes for the radicals formed with thioacetamide in solutions containing micelles. 93 viii 5.5 The rate constants for the reaction of Mu with some carbonyl or thiocarbonyl compounds 93 5.6 LCR linewidths, amplitudes and calculated relaxation parameters for the radicals formed with TA in water 102 5.7 The calculated LCR frequencies and HWHM for the three equiv-alent protons in TA for the transition K,mk to K,m A -l 103 6.1 LCR parameters and calculated PR values for the radicals formed in uracil and thymine in solutions 114 6.2 LCR parameters for the radicals formed with uracil (7.5 mM) in DTAB micelle (2.5 mM) in the presence and absence of benzene (7.5 mM) 117 6.3 Hyperfine coupling constants for uracil 120 6.4 A M values for muonated uracil radical calculated using BR and AH 127 ix List of Figures 1.1 Idealized picture of normal micelle 7 2.1 Schematic representation of time differential TF-//SR apparatus using backward muons 15 2.2 Logic diagram for TF-^SR 17 2.3 Time-evolution of /x+ spin in diamanetic states and in Mu. . . . 19 2.4 Time histogram showing the diamagnetic signal for target solution of (i) DMF at 10 mT and (ii) DMTFA at 8 mT 21 2.5 (a) Raw and (b) asymmetry //SR histograms at 0.8 mT for a target solution of 3 x 10 - 2 M thiourea in water 23 2.6 Plot of observed Mu - decay constants (\M) against solute con-centration [ribose] at room temperature 24 2.7 Breit - Rabi diagram for a two-spin-^ system 26 2.8 The power spectrum of the fast Fourier transform (FFT) in fre-quency space for 0.75 M thioacetamide in water at 2 different fields. 27 2.9 Schematic representation of time integrated LF-/xSR (LCR) ap-paratus using surface muons 30 2.10 Time integrated LF-^SR (LCR) Hardware configuration 32 2.11 (a) Breit-Rabi diagram for 3 spin | system and (b) LCR condition 33 2.12 LCR signal observed for CHMu proton in muonated cyclohexadi-enyl radical 34 2.13 Plot of experimental asymmetry against magnetic field 37 x 2.14 Decay scheme for 2 2 Na 38 2.15 Experimental set-up for PAL measurement 39 2.16 Positronium annihilation lifetime spectrum 41 2.17 Schematic arrangement of the closed cycle pumping used to de-oxygenate samples for LCR studies 43 3.1 The general structure of compounds listed in Tables 3.1 to 3.5 . . 47 3.2 The structure of some constituent molecules of RNA and DNA . 54 4.1 Plot of l / r 3 against micelle concentration for SHS micelles with [S] = 0 72 4.2 Plot of l / r 3 against concentration of benzoquinone in (a) water and (b) n-heptane 76 4.3 Plot of l / r 3 against concentration of benzoquinone in (a) 0.015 M SHS micelle and (b) 0.015 M a-cyclodextrin 77 5.1 The F F T of TF-//SR spectra of 0.4 M DMTFA in water at (a) 0.3 T, (b) 0.4 T and (c) 0.5 T 88 5.2 The LCR spectra of (a) 0.4 mM, (b) 12.5 mM and (c) 50 mM TA in water 90 5.3 The LCR spectra of (a) 0.1 mM and (b) 1 mM DMTFA in water. 91 5.4 The Ampl. /A 6 / plotted against [TA] 94 5.5 The linewidth plotted against [TA] 95 5.6 Radical yield, P^ plotted against [TA] 106 6.1 The LCR spectra of 7.5 mM uracil in water centered at (a) 1.68 T, (b) 1.82 T, and (c) 2.37 T 115 xi 6.2 The LCR spectra of 7.5 mM thymine in water centered at (a) 1.68 T, and (b) 2.37 T. . . 116 6.3 LCR's of 7.5 mM uracil in water at (a) pH = 1 and (b) pH = 10. 123 6.4 LCR spectra of 7.5 mM uracil in 2.5 mM DTAB micelles with and without benzene 124 6.5 C(5) and C(6) adducts formed by H atom addition to uracil and the Afj values 127 xii Acknowledgement The author wishes to take this opportunity to express her sincere thanks and appreciation to her research supervisor Dr. David C. Walker. It is such a great privilege having him as a teacher and an advisor. The author wishes to thank each member of her advisory committee: Dr. N. Basco, Dr. D. E. McGreer and Dr. M. C. L. Gerry for their help during this work. Special thanks are extended to the collaborators, especially to Dr. Krishnan Venkateswaran for his help during the early days of this work, and to Dr. J. M. Stadlbauer, Dr. B. W. Ng, Dr. R. F. Kiefl and Mr. Z. Wu for their assistance during this work. The author would like to thank members of /xSR group at TRIUMF, espe-cially K. Hoyle, J. Worden and C. Ballard, for their appreciable assistance. The author wishes to thank the electronic and mechanical shops at the Chemistry Department, UBC and at TRIUMF for their assistance. The author wishes to extend thanks to her family members Freddy, Sandy and Teddy, and to her parents Kanagammal and Arulraj for their constant en-couragement. Finally, the author would like to express her deepest feeling of appreciation to the Lord her God for His immense grace and mercy without which this thesis could not have been completed. xiii Chapter 1 Introduction 1.1 Muonium Chemistry Muonium, Mu, is the atom consisting of a positive muon (y+) and an electron. The muon was discovered [1] by Neddermeyer and Anderson in 1937 as the first unstable elementary particle. It occurs in two charge states, as /x+ and rest mass equal to one ninth the mass of a proton, or 207 times the mass of an electron, and with a lifetime of just over 2 /is. Mu is considered the simplest atom because both the muon and the electron are leptons[2]. Chemically, muonium is analogous to hydrogen and it can be regarded as the ultralight, radioactive isotope of hydrogen atoms. This is evident from the physical properties of the muon and muonium atom [3,4] given in Table 1.1. The Bohr radii and the ionization potentials of H and Mu are almost the same, Table 1.1: The physical properties of the muon and the muonium atom. Muon Spin | Mass mM = 206.77me = 0.1126mp Mean lifetime = 2.197 x 10 - 6 s Magnetic moment = 3.183//p = 4.835 xl0~ 3 / i e Muonium Bohr radius aA/u = 0.5317A= 1.0043 a# Ionization Energy 13.539 eV = 0.9957(H) Hyperfine oscillation period 2.24 x I O - 1 0 s 1 Chapter 1. Introduction 2 so Mu is a true isotope of H. Its collisions with other atoms or molecules and its chemical reactions can be studied with better sensitivity than deuterium or tritium. Mass dependent phenomena such as kinetic isotope effects and quantum mechanical tunnelling should be most evident when comparing reactions of Mu with the other H isotopes because of the mass ratios Mu:H:D:T « 1:9:18:27. Positive muons are available as energetic spin polarized beams at the sec-ondary channels of the beamlines of special accelerators (such as TRIUMF, Van-couver; KEK, Tokyo; PSI, Zurich and RAL, England). These facilities provide the opportunity of studying fi+ and Mu as chemical species. Garwin et o/[5] and Friedman et al[6] made the first experimental observations of the breakdown of the principle of parity invariance[7] in the decay of positive muons in 1957. Their methods are forerunners of the present day //SR (muon spin rotation) technique. The /zSR technique (details in Chapter 2) monitors the time evolution of muon spin polarization as a function of magnetic field. One of the identifiable chemical states accessible to /xSR is that of the free Mu atom[8]. Others include muons in diamagnetic environments and muonium incorporated in various free radicals. Furthermore, the yields and rates of reaction from these states are observed on the 10 - 9 to 10~5 s timescale - the period over which many fundamental physical and chemical interactions occur. Muons in diamagnetic states include free muons, solvated or trapped muons and any diamagnetic molecule incorporating the muon, such as MuH, MuOH, C 6 H 1 3 M U , and so on. These different states cannot be distinguished from each other by /JSR because 'chemical shifts' are currently beyond the frequency resolu-tion. However, Mu and muonium-radicals register at distinct muon spin rotation frequencies and are separately identifiable. Chapter 1. Introduction 3 Muonium is expected to undergo several types of well-known chemical reac-tions like abstraction, addition, electron transfer, spin exchange and combination, as shown in the following reactions: Abstraction Mu + (CH3)2CHOH —» MuH + (CH3)2COH (1.1) Addition Mu + H2CCHCGH5 —• MuCH2CHC6H5 (1.2) Electron transfer Mu + Fe3+—» Mu+(orn+) + Fe2+ (1.3) Spin exchange Mu(T) + Ni2+(i) —> Mu(i) + M' 2 + (T) (1.4) Combination Mu+OH—> MuOH (1.5) Rate constants for chemical reactions of Mu have been determined and compared with corresponding values for the reactions of H, and kinetic isotope effects rang-ing from 10 - 2 to 102 have been observed[9,4]. In reactions 1.1, 1.3 and 1.5 the muon ends up in a diamagnetic environment, either free or chemically bound in a molecule. In reaction 1.2 it becomes incorporated in a paramagnetic state, the muonated styrene radical and in 1.4 it does not change its chemical state. Muonated radicals can be considered in the same way as deuterium labelled radicals where comparison with the hyperfine coupling constants of hydrogen analogues showed deviations beyond the ratio of magnetic moments, and they Chapter 1. Introduction 4 have been explained by dynamic effects[10]. Corresponding effects are expected to be much larger, and opposite, for muonated radicals. In 1984, Abragam[ll] made use of the mixing effect of near degenerate levels known for years[12] in atomic spectroscopy and nuclear quadrupole resonance and proposed the use of the phenomenon to detect nuclear hyperfine splittings of paramagnetic ions in longitudinal field p;SR. The mixing of levels leads to reduction in muon spin polarization which can be observed using the technique 'muon level crossing resonance' (LCR). The principle of the LCR technique (de-tails in Chapter 2) consists of the transfer of spin polarization from / J + to the neighbouring nuclei through the occurrence of mutual spin flips, by matching the splitting of the spin-up and spin-down p,+ energy levels with the splitting of nuclear energy levels. Experimentally, the resonance or matching condition is detected by a decline of the /x+ polarization, registering as a change in the forward-to-backward positron decay rate at a certain longitudinal field. This change in the forward-backward count rate can be monitored either in a time-integral fashion, which yields the time averaged decay asymmetry (polarization), or as a function of elapsed / / + lifetime, i.e., in a time-differential fashion. The former is convenient because it allows use of the high fi+ stopping rates available at TRIUMF. The LCR technique has some advantages over the conventional transverse field /xSR. Firstly, in transverse field measurements the muon polarization is lost when the Mu precursor lifetime exceeds ~10 - 1 0s, whereas the LCR (longitudinal field, time integrated) measurements allow the observation of radicals even when a Mu precursor has a lifetime of a microsecond, provided the transition frequency ur, is high enough to produce a significant LCR signal in the remaining muon lifetime. Secondly, the coupling constants of nuclei other than the muon are Chapter 1. Introduction 5 obtained which allows a complete characterization of the system under study. 1.2 Positronium Chemistry Positronium, Ps (e+e~), forms in most materials at the end of some 3+ tracks, simply by the capture of an electron by the positron as it approaches thermal energy. When the positron associates with an electron in a bound quantum state it may appear as a singlet ground state (para-Ps, with antiparallel spins) or as a triplet ground state (ortho-Ps, with parallel spins). They have the same energy, but quite different lifetimes[13]. Para-Ps has a self-annihilation lifetime of 1.25 x 10 - 1 0 s and it decays by two-photon emission; whereas the intrinsic lifetime of ortho-Ps is considerably longer, 1.4 x 10 - 7 s, and its self-annihilation occurs through three-photon emission. Ortho and paxa Ps are formed in the ratio of 3:1. Table 1.2 shows that Ps cannot be considered as an isotope of H or of Mu. Table 1.2: Some of the physical properties of Ps compared with Mu, 1 H , 2 H and 3 H . Atom Mass Reduced mass Ionization potential Bohr radius /m e /eV A 3 H 2.993 0.9998 13.603 0.5291 2 H 1.998 0.9997 13.601 0.5293 J H . 1.000 0.9995 13.599 0.5294 Mu 0.1131 0.9952 13.541 0.5317 Ps 0.00109 0.5000 6.8 — In Ps there is no nucleus because the two particles of which it is composed are of equal mass. As a result, they both form orbitals about the centre of mass and Chapter 1. Introduction 6 its ionization energy half. Its rate of diffusion in water is comparable to that of Mu and H[14], however, and its chemical reactivity is well worth contrasting with them. 1.3 Micelles Surfactants are amphiphilic compounds (with a hydrocarbon chain and a polar head group) which form micelles in solution. The fundamental characteristic of micelle forming monomers is due to the presence of both polar and non-polar moieties in the same molecule. The classification of surfactants as non-ionic, an-ionic, cationic and zwitterionic depends on the nature of the head group. Ionic surfactants are always associated with ion atmospheres containing the counter ions. The hydrophobic part can contain unsaturation centres, aromatic portions, and can consist of two or more chains of various length. Those used here con-tained only unreactive saturated hydrocarbon chains. When surfactant molecules are dissolved in water they can achieve self-aggregation from the solvent by segregation of their hydrophobic part. The aggregate products are known as normal micelles. The micelle will consist of a hydrocarbon core with the polar head group at the surface (see figure 1.1). On the other hand, when surfactant molecules are dissolved in non-polar solvents, the aggregate products are known as reversed micelles. The reversed micelles have their polar head groups centered in the interior of the aggregate, with their hydrocarbon chains at the surface surrounded by the bulk non-polar solvent. The mechanism responsible for micellization is well documented[15]. There is a relatively small range of concentrations separating the limit below which no mi-celles are detected and the limit above which all the additional surfactant forms Chapter 1. Introduction 7 Figure 1.1: Idealized picture of normal micelle Chapter 1. Introduction 8 micelles. This range of surfactant concentration at which micelles first become detectable is defined as the critcal micelle concentration (CMC). Mu reactions in micelles have been studied here for the following reasons: (i) Mu acts as a light isotope of hydrogen, and it allows for the exploration of processes that cannot be followed for H (because H atom reactions cannot be studied in micelles due to reactions of H with the surfactant molecules themselves with a rate constant of ~107 M - 1.s _ 1)[l6]. (ii) Muonium relaxation studies in pure hydrocarbons are difficult to carry out (due to the short lifetime of Mu with respect to reaction with impurities) so that producing muonium in water while making it react with a solute in a hydrocarbon core, offers wide scope, (iii) Micelles are used in chemical and biochemical situations as models, or mimics, of membranes. They create the sort of phase-separations that exist in living cells where membranes have a controlling influence on many physiological processes. The study of Ps reactions in micellar systems is undertaken for comparison purposes. 1.4 Description of thesis content Motivation for this study of Mu and Ps reactions in aqueous and micelle solutions come from the unsolved reaction mechanisms of biological reactions involving H. Chapter 2 gives details of the different techniques involved. Chapter 3 describes the reactions of Mu with some simple compounds of bio-logical importance in aqueous and dilute micelle solutions. Rate constants for Mu reaction with these solutes in water (k^) are determined and are compared with corresponding k# data, when available, to get information about kinetic isotope Chapter 1. Introduction 9 effects. The rate constants in micelle solutions (kM{mic)) are used to calculate an 'enhancement factor'. In order to try to understand the criteria for this micellar enhancement for the Mu reaction with 2-propanol in micelle[17], a number of simple compounds with different functional groups undergoing different types of reactions were selected and compared in aqueous and micellar solutions. Some representative reactions were studied at pH = 1 in order to evaluate the effect of pH on different types of reactions. Rate constants for most of the H atom reactions were reported[18] at pH = 1, which may or may not be the same at pH ~ 7 where physiological processes in living systems mostly occur. It is appropri-ate to study these reactions at pH = 7, but due to the experimental constraints (requiring a high concentration of H + in the medium which combines with e~g to form H atom) H atom reactions invariably have to be studied at pH = 1. By fiSK it is possible to study Mu reactions at any pH. Chapter 4 gives the results and discussion of Ps reactions. Some solutes were selected for comparison with Mu reactions and others for comparison with solvated electrons. Chapter 5 deals with characterization of muonated free radicals using the con-ventional method (TF-/iSR) and the new method (//LCR) developed recently. Thiocarbonyl compounds were selected for this study because of their deviation in rate constant at pH = 1 and at 7. Also, sulfur containing compounds are im-portant in pharmaceutical chemistry due to their radiation protection property. Thiyl radicals are observed (by /xLCR) in solution for the first time: radicals which have not been seen by ESR. They are highly reactive, and the relaxation processes involved are discussed. Chapter 6 gives the /xSR LCR study of a representative biochemical, namely uracil. The muonated radicals formed were compared with the corresponding Chapter 1. Introduction 10 hydrogen adducts and reasons for a change in the radical yields are discussed. In addition to the above mentioned work, the author was involved in other projects which are included in this thesis as 'collaborative work1 in an appendix. Much of this has now been published. Chapter 2 Background and Experimental 2.1 Production and decay of muons Cosmic radiations that reach the surface of the earth are mainly in the form of high energy light nuclei. When these light nuclei, mainly protons, collide with molecules in the upper atmosphere they interact with their nuclei resulting in the production of new particles. The positive pion is one such particle which decays to a positive muon and a neutrino. This combination of cosmic bombardment and atmospheric conversion is simulated at meson facilities to produce beams of pions and muons. At TRIUMF, the pions are generated by bombarding (for instance) a 9Be target with ~500 MeV protons from the cyclotron. The pion then decays with a mean lifetime of 26 ns to give a muon and a muon neutrino. 7T + —• (i+ + Up (2.1) Subsequently, the muon itself decays (r ~ 2.2 /is) giving an easily detectable positron, an electron neutrino and a muon anti-neutrino. H+ —• e + + ve + i/M (2.2) The pion is a spin-zero particle, but the neutrino has spin | with negative helicity so that the particle spin is represented in a left-handed sense to the di-rection of the particle momentum, and this forces the muon also to have negative 11 Chapter 2. Background and Experimental 12 helicity according to the conservation of angular momentum. This ensures that the muons coming from pions which are at rest will be 100% longitudinally po-larized with spin opposite to their direction of motion. They are also essentially monoenergetic. Since these muons originate from pions which come to rest near the surface of the production target, they are called surface muons. They have an energy of 4.1 MeV, a momentum of 29.8 MeV/c and a range of only about 1.4 mm in water. When the pion is allowed to decay 'in flight' within a beamline, the muons are emitted in a forward or backward direction relative to the pion's motion and such muons are called forward or backward muons, respectively. A series of dipole magnets is used to select the desired charge and momentum of the muons. A backward muon beam is very clean, has positive helicity and is 60 -90% polarized. These muons are sufficiently energetic to penetrate thick walled glass cells. Backward and surface muons are both used in different experiments of this study. The parity-violating asymmetry in the formation and decay of a muon leads to an anisotropic angular distribution of the positrons emitted. In this three body decay the positron is emitted in a direction, making an angle 6 to the in-stantaneous muon spin direction, with a probability proportional to (1 + a'cos#), i.e., preferentially along the muon spin direction. The asymmetry parameter a is a function of the emitted positron energy with an average value of 0.33; but, due to a number of experimental imperfections, it is usually only ~ 0.2. Several experimental techniques have been developed [3] based on this asym-metric muon decay. They involve the stopping of muons from a spin polarized beam in the sample placed in an external magnetic field which can be perpendic-ular (transverse) or parallel (longitudinal) to the muon polarization. Then the Chapter 2. Background and Experimental 13 evolution of muon spin polarization in the sample is monitored by the detection of the decay positrons using either a single particle counting technique (time differential measurement) or by simply comparing the counts in the forward and backward directions (i.e., time integrated measurements). The experiments for the work presented in this thesis were all carried out at T R I U M F on three different channels (M20 A and B, M15 and M13). The transverse field (TF) time differential (TD) measurements were done using both backward muons (at M20A) and surface muons (at M20B, M15 and M13), whereas for the longitudinal field (LF) time integrated and time differential measurements only surface muons were used (at M15 and M20B). 2.2 Transverse field //SR. Measurements //SR is the acronym used for muon(/z) spin(S) rotation, relaxation or resonance(R). Most of the chemical studies have been performed using the time differential transverse field muon spin rotation method, and here //SR is used for these mea-surements at various magnetic fields. When muons enter and equilibrate in a chemical sample, they exist as different forms of associated species as described in Section 1.1. Different ranges of magnetic fields have to be selected for studying the free muonium atoms (usually 0.3 - 1.0 mT) , diamagnetic muon states (5 -100 mT) and muonium containing free radicals (0.1 - 3 T) . The transverse field is supplied by means of magnetic coils to produce a homogeneous field centered at the sample position. When this magnetic field is greater than ~ 0.4 T, the beam is bent significantly before it enters the sample if the field is transverse to the momentum. Consequently, high magnetic fields such as are provided by the superconducting longitudinal coils S L C (used for Chapter 2. Background and Experimental 14 time integrated longitudinal field measurements, fiLCK - see Section 2.3.1) must be applied longitudinal relative to the beam direction, in order to avoid beam bending. For high transverse field studies, the muon spin must be rotated 90° by means of DC separators prior to its entry in the sample, so that the magnetic field which is longitudinal to the beam is perpendicular, or transverse, with respect to the muon spin polarization. 2.2.1 Experimental set-up The experimental set-up for a backward muon beam is depicted by Figure 2.1. The apparatus used (at M20A) was 'SFUMu'. Not all the counters are shown in the picture. There are usually two coincidence counters in each set of positron telescopes giving forward, backward, up and down (perpendicular) histograms. In Figure 2.1, A is lead shielding, DEG is a remotely adjustable water block to degrade the muon energy, B is a set of lead collimators, C & D are the muon 'start' counters, S is the sample, H are the magnetic coils (up to 0.4 T) giving a field out of the paper so that the longitudinally polarized muon precesses in the plane of the paper. E &z F are the positron 'stop' counters in the 'forward' direction. Due to their higher energy, backward muons they can pass through the sample. Therefore, in order to distinguish decay positrons from muons, electronic logic vetos are used to separate the two particles. For a good event in the histogram, the muon 'start' signal is registered by CDE (E is 'not E') and the decay positron 'stop' signal by E F Z ) . The difference between a backward muon set-up (as in Fig 2.1) and a surface muon set-up (not shown) is largely due to the low energy of surface muons. In this set-up, the snout is an extension of beam pipe used to bring the low energy Chapter 2. Background and Experimental 15 / \ B / \ - / C D E F \ II \ A : Lead shield B : Lead collimator DEG : Degrader C,D : start counters E,F : stop counters S : Sample H : Helmholz coil \ Start 1! / LOGIC Stop Clock //SR Histogram « ml Figure 2.1: Schematic representation of time differential TF-/xSR apparatus us-ing backward muons Chapter 2. Background and Experimental 16 surface muons under vacuum as close to the target as possible. The incident muons, collimated to a 2 cm beam, trigger the thin counter (TM) sending a '// - stop' (p stopped in target) signal to the 'start' input of a time digitizing converter (TDC) clock. Then decay positrons detected by either the left or right coincidence telescopes trigger a signal to the 'stop' input of the TDC clock. The resultant time interval is then routed to the appropriate time bin in the left or right histograms. 2.2.2 Electronic logic The basic methods (TF-//SR at various fields), whether employing surface or backward muons, involve nuclear physics counting logistics. Scintillation coun-ters detect incoming muons and corresponding decay positrons, and an ultrafast digitizing clock measures the time interval between these two events - i.e., the lifetime of individual muons in the sample - with a resolution of about one nanosecond. A fast electronic logic system discriminates between good and bad events. A pile-up gate is used to avoid counting two events at a time. Typical electronic logic and the timing for a TDC start are shown in Figure 2.2. The number of decay positrons, N, as a function of decay time interval is stored in a CAMAC histogramming memory which is periodically read out by a PDP -11/40 or /60 minicomputer. The process is repeated until sufficient statistics are obtained in a time spectrum. A more detailed explanation of the electronics and computer logic can be found elsewhere. [19] 2.2.3 Data analysis The transverse field (TF) //SR technique at various fields provides different infor-mation about the system under study. The raw histograms obtained at selected Chapter 2. Background and Experimental Figure 2.2: Logic diagram for TF-^xSR Chapter 2. Background and Experimental 18 fields are fitted to appropriate equations. The technique and the appropriate data analysis are discussed in terms of the field at which the measurement is made. 2.2.3.1 T F - / i S R : 5 to 100 m T When a / i + stops in a target perpendicular to a magnetic field (B) its spin (|) precesses at its Larmor frequency, uv = 7,B (2.3) where 7^ (= 0.1355 MHz/mT) is the muon gyromagnetic ratio and = 8.516 x 108 rad .s _ 1 T - 1 . Figure 2.3 indicates the time-dependence of the fi+ spin as seen by the detector D at an angle <f>0 to the initial muon spin in diamagnetic states (p+) and in Mu. They precess in opposite directions with different Lar-mor frequencies, (same as U£>) and UJM w -103u;M. It should be noted that the triplet frequency that one observes in this method is degenerate at low fields. To observe this transverse field precession phenomenon, one can simply place a positron counter in the plane of the fi+ precession at angle </>0 with respect to the initial muon spin direction; so at time t the angle between the / i + spin and e + detector when the p+ decays will be 4>Q + u^t. As a result, the e + detection probability N(t) will be proportional to 1 + A(M)COs(<^o + wMi), where A(^ ) is the experimental muon asymmetry (proportional to the muon polarization) and its magnitude depends on detector dimensions, target geometry and beam polar-ization. This method, the muon spin rotation technique, allows one to monitor the magnitude and time dependence of the muon polarization for all muons in diamagnetic states, such as free fi+ or MuH or MuCl, etc. The diamagnetic muon precession in (i) dimethylformamide and (ii) dimethylthioformamide are given in Chapter 2. Background and Experimental Figure 2.3: Time-evolution of fi+ spin in diamanetic states and in Mu. Chapter 2. Background and Experimental 20 Figure 2.4. The original raw histogram has the form N(t) = N0.e-t/T»[l + ADe-XDtcos(ujDt + cj>D)} + Bg (2.4) where is a normalization factor, Bg is the time -independent background, rM is the muon lifetime (2.2 /is), Ar> is the experimental diamagnetic asymmetry or amplitude, XD is the exponential decay constant (usually zero), U>D is the preces-sion frequency, and <f>D is the initial phase of the diamagnetic muon precession. Raw histograms were fitted to Equation 2.4 by the x 2 - minimization program MINUIT until the best fit was obtained. The fitted AD was used to calculate a fractional PJJ value assuming that AD in C C 1 4 liquid corresponded to 100% PD[20]. Figure 2.4 shows that P ^ (proportional to the amplitude of the asym-metry, AD) of DMF is about twice that of DMTFA. 2.2.3.2 T F - M S R : 0.3 to 1.0 mT It was found in 1976[21] that Mu can be observed directly by the muonium spin rotation (also known as MSR) technique, provided the liquid is relatively pure and oxygen free. In muonium, the muon spin is coupled not only to the external field but also to the electron spin through the hyperfine interaction. So, this method is a result of hyperfine interaction between the magnetic moment of the muon and that of the electron (hyperfine field = Bo = 0.1585 T) giving rise to two net spin states of F = 0 (singlet) or F = 1 (triplet). The observable spin state is that of the triplet which precesses in weak fields at 13.94 MHz/mT, about 103 times faster than the free muon in the same magnetic field. Experimentally, the positron detection probability in this muonium spin rotation technique now acquires another term of the form 6 = 4>Q + OJMt with a new empirical amplitude AM- Therefore, one has the Mu precession signal added to (multiplied by) the Chapter 2. Background and Experimental 21 BLMW MiMbtr 3192 w i l n i rtUOHTCH »n .fllSUnkMi J>W H i a v 166G «JP lfc>31tl9 1-6UG-69 l i n i f r m 1 U 1196 V l i o t u i 17S.ee C»v»r*s»d Ov»r 3 b i n s ) C h l - t o -760.11 1 . 637 c O o Time / LIS l u n Mwnbvr i 21(9 u s i n g VtUOHrCD en _r*13vAX ! i «£A1 6*1Tf6, 66C. UP 1&:34I62 1-6UC-69 • in« f r o * 1 TO 1199 V l i f . l t f > SB.79 384.67 C*v*r«*«d »v»r 3 b i n t ) Chl-Sa - 6.991 c o o Time / LIS Figure 2.4: Time histogram showing the diamagnetic signal for target solution of (i) DMF at 10 mT and (ii) DMTFA at 8 mT. The line is the computer fit to the muon components in equation(2.4). Chapter 2. Background and Experimental 22 p+ precession signal, while both are superimposed upon the exponential decay of the muon. In addition, there might be exponential damping on the oscillatory term due to possible phenomenological depolarization and/or chemical reaction of Mu. Here, the positron time distribution takes the form N(t) = N0.e-t/T»[l + ADcos(uDt + fo) + AM.e-XMtcos(-uMt + <f>M)] + Bg (2.5) where AM is the Mu - decay constant (and where Arj has been taken = 0). Mu is a highly reactive chemical species, but it is stable in several saturated inert liquids like water and alkanes. Solutes can be added to these solvents at con-centrations where Mu reactions occur mainly in the 1 0 - 7 to 10 - 5 s observation-window. Typical raw and asymmetry //SR histograms (after the // lifetime term and Bg are removed by the computer) are displayed in Figure 2.5. (The histograms of Figure 2.5 cover the //SR observation time-window from 10 - 7 s to several microseconds.) The Mu relaxation coefficient, AM, is just the rate of decay of the spin polarization; but in chemistry it is generally representative of a chemical reaction of Mu. In the presence of solute, S, at concentration [S] the equation 2.6 generally holds good: AA = A M - A0 = kM[S] (2.6) where k f^ is the bimolecular rate constant for reaction of Mu with S, and A0 is the 'background' value of AM as found in the solvent at [S] = 0. Figure 2.6 gives the plot of observed (fitted) AM from two different histograms for aqueous solutions of /?-D-ribose at room temperature. The magnitude of individual errors in each of these values was taken from the standard deviation of the fitting, which was ~10%. However, deviations due to values from different histograms increased the overall error. Generally, the error involved in the k M values calculated from AA is ~20%. Chapter 2. Background and Experimental 23 Figure 2.5: (a) Raw and (b) asymmetry /iSR histograms at 0.8 mT for a target solution of 3 x 10 - 2 M thiourea in water. The line in (a) is the computer's best fit to equation(2.5). Chapter 2. Background and Experimental 24 Ribose in water 1.4 i i i i i i i i i T 1.2 CO o \ 1 -< i .8 d u a -6 o • r-t -K .2 0 i i i i i i i i i 0 .05 .1 .15 .2 .25 .3 .35 .4 .45 5 [Ribose]/M Figure 2.6: Plot of observed Mu - decay constants (XM) against solute concen-tration [ribose] at room temperature. Slope equals k/y/. o and A are data from two different positron counters. Chapter 2. Background and Experimental 25 2.2.3.3 T F - / / S R : 0.1 - 3 T When a Mu atom adds to a double bonded system, a free radical will be formed. At low magnetic fields, there are many transitions with the muon polarizations distributed among them. This complexity delayed the direct observation of Mu-radicals until 1978[22]. By applying high magnetic fields (B > 0.1 T), the con-siderable number of radical frequencies collapsed to give just two transitions (Figure 2.7). The numerical problem was solved by Roduner and Fischer[23]. It was shown that in the high field limit the radical frequencies and the muon hyperfine coupling constant, A M , axe related by 2i;+Ttf (2'7) As the third term is very small, the diamagnetic muon frequency changes with field, while A M remains independent of field. This decoupling method of applying high magnetic fields to observe Mu-radicals is called the muonium-radical spin rotation (MRSR) technique. Here, the general form of the histogram is given by N(t) = AVe- t / T " [ l + ADcos(uDt + <f>D) + Si?,(i)] + Bg (2.8) and Ri(t) = AK.e-Xitcos(uit + <f>i) (2.9) where R (^t) represents various contributions of the ith radical amplitude [Aft,- at the i t A frequency (w,-) with relaxation rate A,]. The magnetic fields selected for this type of measurement are usually of the order 0.1 to 1 T so that the muon frequency (7^B) and at least one of the radical frequencies (VR) will be observed within the frequency range 0 - 250 MHz, a region accessible with good timing resolution. The fast Fourier transform of the MRSR spectrum of thioacetamide is shown in Fig 2.8. Chapter 2. Background and Experimental 26 Breit—Rabi diagram for 2 spin 1/2 system + e ji Figure 2.7: Breit - Rabi diagram for a two-spin-^ system. This shows the effect of transverse fields on the energy levels from the splitting of the triplet. In very low field (Section 2.2.3.2), v\2 and u23 are observable and they are degenerate; but at high field two radical frequencies v\2 and i / 3 4 are observable (Section 2.2.3.3). Chapter 2. Background and Experimental 27 0.75 M TA at 0.3 T 4 .E-4 -o o-"C n o 0> O 3 o 50 100 150 200 250 300 350 400 Frequency (MHz) .75 M TA in -water at 0.4 T. 50 100 150 200 250 300 350 400 Frequency (MHz) Figure 2.8: The power spectrum of the fast Fourier transform (FFT) in frequency space for 0.75 M thioacetamide in water at 2 different fields. Chapter 2. Background and Experimental 28 The T F - //SR method is also used for calibrating the high longitudinal fields used for muon level crossing resonance studies (LCR). The observed muon fre-quncy, up, is given by 7^B, from which B can be easily calculated. Chapter 2. Background and Experimental 29 2.3 Longitudinal field pSK measurements 2.3.1 Time integrated L F measurements and L C R A block diagram of the experimental set-up used for muon level crossing reso-nance studies employing surface muons is shown in Figure 2.9. In longitudinal field measurements, muons are spin polarized in the direction of the field and hence there is no rotation. They enter the sample between the cylindrical back-ward counters (BL and BR), stop in the sample, associate chemically, then start to decay. Their asymmetric decay gives a higher rate in the backward counters than in the forward counters (FL and FR) when using surface muons (negative helicity). In the absence of any relaxation of the spin polarization, the forward and backward histograms merely show the asymmetry in the muon decay and their ratio remains constant. When only diamagnetic muon states are present, the asymmetry (A) and any spin-lattice relaxation or spin exchange interaction (collectively characterized by a relaxation time Tj) may be evaluated by fitting to an equation of the form, N(t) = Ar0.e-'/T"[l ± A.e-W] + N0Bg (2.10) When Mu is formed there are additional contributions to depolarization[24]. In zero field, the polarization of r M u is stationary but that of 5 M u oscillates between + 1 and -1 averaging to 0. This results in the muon polarization being reduced by ^h\f, (see Figure 2.9, LF-quenching curve) where h ^ is the fraction of the muons initially forming Mu. In fields larger than the hyperfine field, this depolarization in 5 M u is quenched by the decoupling of the hyperfine interaction, and one observes the full polarization. At intermediate fields, the polarization of 5 M u oscillates between +1 and (a;2 — l)(x2 +1) where x = 73/0.1585 T. Chapter 2. Background and Experimental 30 B R &c B L F R <Sc F L SC : Supe rconduc t i n g so lenoid MC : Field modulat ion coi l S : Sample M : Thin coun te r BR.BL : Backward c o u n t e r s LOGIC MEMORY FR .FL F o r w a r d c o u n t e r s L F "quenching ' c u r v e f V Longitudinal magnetic field B Figure 2.9: Schematic representation of time integrated LF-/zSR (LCR) appara-tus using surface muons Chapter 2. Background and Experimental 31 There is a reduction in muon polarization (Fig. 2.9) at low fields due to muon - electron hyperfine interactions. A similar effect was predicted by Abragam at high fields with a level crossing resonance, which occurs due to mixing of degenerate states and polarization transfer from muon to other nuclei (with a non-zero spin) in the molecule. Indeed, sharp dips at characteristic resonant fields BR were observed. The position, amplitude and width of these signals yield information about the muonated free radicals present. In LCR the integrated count rates in the forward (F) and backward (B) direc-tions were recorded as a function of longitudinal magnetic field. The integrated muon asymmetry, A, is given by A = (F-B)/(F + B) (2.11) Figure 2.10 gives the hardware configuration used for the LCR experiments. In order to reduce systematic errors data were accumulated only while the beam rate was within a given tolerance (±20%). Also, the magnetic field is alternately shifted by ~5 mT above and below the nominal field (i.e., square-wave modu-lated) at a rate on the order of 1 Hz, dependent on the preset count required (106) before field shift. Baseline shifts were avoided by displaying and analyzing the spectrum as A + - A - , where the + and - refer to the sign of the modulation field. If the resonance line width is greater than the modulation amplitude, the result-ing lineshape is approximately field differential (as seen in all the LCR spectra presented here). Data were acquired over 20 modulation cycles (toggles) before the main field was stepped. The resonant states involved in the LCR and the LCR condition are shown in Figure 2.11. An example of LCR as observed under these experimental conditions is shown in Figure 2.12. This type of LCR signal obeys the selection rule A(m^ — mp) = 0, where m denotes the z component of Chapter 2. Background and Experimental 32 Driver slot 19 bit 0  bit 1  bit 2 i i L i . C212 (lorn) slot 22 ,-Strobe In 1 jnT (up Scaler to 6) slot 9 -Inhibit enable DAC slot 20 Start 222 Gate Generator Del ~ 1 psec Start 222 Gate Generator Latch gStop Start Clear Input j . Preset Scaler Prn Carry Start. Stop 222 Gate Generator Latch Li Disc To modulaton coil To magnet supply Figure 2.10: Time integrated LF-//SR (LCR) Hardware configuration the spin. Figure 2.11(b) shows the schematic diagram of the three types of LCR's predicted[25]. They are characterized by the quantity A, which is the difference in (rn.fi + mk) between the two hyperfine levels involved. Here, only one type of LCR is discussed, namely that for A=0. v} = (1 - A)u£ (2.12) The states related by A(m^ + m*) = 0 cross energy at a resonant field, i \ i r - i v 7.(4. - 4 ) / Chapter 2. Background and Experimental 33 Energy levels for the system p.+—e —p+. at low magnetic fields. e P t t t t t I t 4, t t 4 LCR state LCR state e M P T T t T T 4, t I t t 4, 4. at high magnetic fields. 4=2 Figure 2.11: (a) Breit-Rabi diagram for 3 spin \ system and (b) LCR condition Chapter 2. Background and Experimental 34 LCR of Benzene (neat) .03 .02 -.01 i + -.01 --.02 --.03 1 1 1 r J I I I I I I L 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.1 2.11 2.12 Longitudinal Magnetic Field (Tesla) Hyperfine parameters deduced A„ = 514.0 MHz; AH = +126.6 MHz. Figure 2.12: LCR signal observed for CHMu proton in muonated cyclohexadienyl radical Chapter 2. Background and Experimental 35 where M = me + mM + ^kmk-For > Ak only the states with me — | cross, and for A^ < Ak only those with m e = —\. The energy gap (or the LCR frequency) becomes, where c = [J*(J* + 1) - M(M - 1)]1/2, and I* is the spin of the nucleus. The resonances due to inequivalent nuclei will not usually overlap and can be treated separately. For equivalent spins, introduction of the total nuclear spin operator K = T,Ik reduces the problem to that of a number of three spin systems with degeneracies g(K). When several muonated species axe formed, the total signal is a sum of the LCR transitions due to the 2Ik lines weighted according to their degeneracies. When Ik > |, as in the case of nitrogen for which Ik = 1, the M values are different from those calculated for two equivalent protons with T,Ik = 1 and the two lines observed for nitrogen overlap with each other to give a single line. On each of these LC resonances a fraction of the muon polarization is expected to oscillate at frequency uT (actually, u^). The average value of Pz may be calculated using the following expression for Pz as a function of magnetic field[26]: — 2 v2 P z { B ) = 1 " N E " [[(B - £ £ ) ( 7 „ - (1 - A) 7 n )] 2 + + (Xo/2ny) ( 2 J 5 ) and the depolarization amplitude at the LCR position by which is a sum of Lorentzian lines with full width at half maximum. A B | i = 2[,;+(V2,)r ( 2 1 7 ) 7M In Chapter 2. Background and Experimental 36 The N in the above equations is given by TV = 4rijt(2/fc + 1) i.e., the total number of spin states for the e-//-n system. (For methyl protons, £ J f c = | and N = 32, corresponding to the 3 equivalent protons of the CH3- group, i.e., JJ term in equation 2.16 must be replaced by 2x^ i.e., ^.) The depolarization amplitude is a function of the LCR frequency vr and a decay constant A (which can be included to eliminate the effect due to any relaxation process removing the muon from the LC resonant state). The //LCR signal was fitted for position, linewidth and amplitude as a difference of Lorentzian lines (arising from the modulation field). 2.3.2 Time differential L F measurements Time differential longitudinal measurements were carried out with aqueous M n 2 + solution (0.85 M) and with a MnF 2 crystal. These were undertaken in order to determine the experimental asymmetry Af,/ (i.e., the backward to forward ratio) as a function of magnetic field. The fitted values for asymmetry were plotted against longitudinal magnetic field. The value of Abj varies from 0.117 to 0.121 for the region 0 - 0.4 T [using Mn(N0 3) 2 solution] and 0.151 to 0.251 for the region 0 - 2 T (using a MnF 2 crystal). Figure 2.13 shows the variation of A^j with field. There is a deviation between the two measurements because of their different densities. An extrapolation of the lower line to the higher field range was done to get the values for the entire field range. Chapter 2. Background and Experimental Asymmetry vs Field T I I 1 I I I I T I I I I I I I I I 0 .2 .4 .6 .8 1 1.2 1.4 1.6 1.8 2 Longitudinal Magnetic Field / T .CIO .25 .225 u -p 6 to ~ .175 .2 CD U 9) ft X .15 .125 Figure 2.13: Plot of experimental asymmetry against magnetic field Chapter 2. Background and Experimental 38 2.4 Positronium Annihilation Lifetime measurements Positrons emitted as a result of a radioactive decay lose their kinetic energy, and when they reach thermal energies, can combine with electrons to form the Ps atom. For this study, the positron emitter was 2 2 Na. It decays under emission of a positron to the excited state of 2 2Ne, which in turn undergoes de-excitation under emission of a 1.28 MeV 7-photon. This decay scheme is given in Figure 2.14[13]. ,Na 22 1.28 MeV 10 Ne 22 f 90%, EC 10% 0.05% Figure 2.14: Decay scheme for 2 2 Na A positron source consisting of ~ 4 /xCi of 2 2 Na sandwiched between two thin mylar sheets was used for positron lifetime measurements. About 2 mL of the appropriate solution under study was placed in a tube with the positron source centered in the liquid sample. The solution was deoxygenated by bubbling with N 2 gas using a hypodermic needle through a septum. All measurements were made at ~ 20°C. Positron lifetimes were measured by observing the time elapsed Chapter 2. Background and Experimental 39 Constant Fraction Differential Discriminator V0.511 MeV Delay Stop Detector Positron source + sample Time to Pulse Height Converter (TPHC) T to computer for data anlysis Multichannel Analyser (MCA) Constant Fraction Differential Discriminator 1.28 MeV/ Start Figure 2.15: Experimental set-up for PAL measurement between the emission of a positron into the sample and its subsequent annihila-tion. The high energy (1.28 MeV) 7-photon is emitted simultaneously with the positron and this is used as the trigger. The positron lifetime was determined as the time difference between the detection of the 1.28 MeV photon and detection of one of the 0.51 MeV annihilation photons, using a fairly conventional delayed coincidence method[13]. A schematic of the experimental set-up is shown in Figure 2.15. The resolution of this system was determined to be less than 350 ps by measuring the coincident photons from a 6 0 Co source. It consisted of a fast circuit which measured the time between detection of two photons (1.28 MeV and 0.51 MeV). The detection of a photon on the start side triggers the time-to-pulse height converter (TPHC) to begin building a pulse until a stop signal Chapter 2. Background and Experimental 40 is received. The amplitude of the TPHC output is proportional to the time dif-ference between the two signals. The time signal was routed to the multichannel analyser (MCA) and was stored in a channel corresponding to its amplitude; MCA is coupled to a PC where the data acquisition can be monitored. A typical lifetime spectrum is composed of about 106 events. Positrons emitted from the nuclear decay are thermalized in condensed matter (water in this case) within picoseconds, when some of them pick up electrons from the track to form Ps atoms. Annihilation occurs from all positron states. Some annihilate directly with electrons of the medium or after the formation of weak positron or positronium associations, others form p-Ps (too short-lived to study) and others form the relatively long-lived ortho-positronium atoms. Each of the annihilation processes contributes an exponential decay with a mean lifetime, r,, to the spectrum. The lifetime spectrum is analysed as a sum of exponentials, as in equation, Nt = Z^Aiexpi-t/n) (2.18) where n corresponds to the number of components, 1/r, is the annihilation rate constant of each component, and A, is its amplitude. The spectra obtained (as in Figure 2.16) were resolved into a multiexponential function by a x2-minimization computer program POSITRONFIT EXTENDED[27]. The results reported (in Chapter 4) are from three component fitting, x2 values ~1. The resolved three different lifetimes were typically TX ~ 0.125 ns, r2 ~ 0.50 ns, and r 3 ~ 1.50 ns, corresponding to different positron and positronium states. The longest lived component r 3 is due to the annihilation of free o-Ps atoms, which gives information about the chemical reactivity between Ps and molecules in the system. An intrinsic r 3 decay in pure water of 1.8 ns restricts the time Chapter 2. Background and Experimental 6 5 cn o 3 2 0 i 1 1 1 1 _ .'"\ v.. . "V "\w. , 1 1 I I 0 50 100 150 200 250 channel # (53ps/chonnel) Figure 2.16: Positronium annihilation lifetime spectrum (counts vs Chapter 2. Background and Experimental 42 range that can be used to study Ps to about IO - 9 and therefore to concentrations of solutes > 10~2 M for kp < 1010 M _ 1 s - 1 . The relationship between the concen-tration of solute molecule [S], the measured o-Ps lifetime 7*3, and the chemical reaction rate kp is written as K = (7 " (2.19) where T3 and 7-3 are, respectively, the measured o-Ps lifetimes in aqueous (or aqueous micelle) solution with and without the solute present. 2.5 Chemicals and sample solutions Solutes were purchased as reagent grade chemicals or better. Aqueous solu-tions were prepared using triply distilled water. The surfactants used include CTAB (cetyltrimethylammonium bromide), SDDS (sodium dodecylsulphate), SOS (sodium octylsulphate) and SHS (sodium hexylsulphate). All the micel-lar solutions contained concentrations of the surfactant which are well above the CMC. Equation 2.20 was used to determine the concentration of micelles. . . . [surf] - CMC [mic] = L# (2-20) (Agg# is the mean number of surfactant molecules in a micelle.) The sample cells used for //SR studies were essentially of two types. One was a thick walled round bottom glass cell with a septum on its mouth for bubbling an inert gas to eliminate 0 2 . These could be used with backward muons because of their high penetration. The other cells had thin mylar windows for use with low-energy surface muons. In all the experiments, samples were deoxygenated. For LCR studies, a new cell was designed in such a way that temperature could be maintained, and the size of it was optimized within the cylindrically arranged Chapter 2. Background and Experimental 43 counters for maximum exposure to the collimated beam. A closed cycle pumping arrangement (shown in Fig 2.17) allowed fresh samples to be inserted without moving the cell. TC : Temperature control P : Pump F : Flowmeter SC : Sample compartment S : Sample GC : Gas compartment 0 : Overflow AB : After bubbler Figure 2.17: Schematic arrangement of the closed cycle pumping used to deoxy-genate samples for LCR studies. Chapter 3 Rate constants for Muonium reactions 3.1 Introduction Simple organic compounds which are constituents of biological systems were se-lected for this study of reactivity toward muonium. The functional groups studied were mainly amides, carbonyls, thiocarbonyls, carboxylic and amino acids. Some representative DNA and RNA bases were also examined, as well as a sugar, a nucleoside and a nucleotide to compare with the corresponding base. Some other compounds are also included in the list for comparison purposes. Motivation to study reactions of Mu with these compounds in aqueous solu-tions with and without micelles was due to the following reasons. Firstly, these simple constituents of macro molecules (i.e., proteins, DNA, RNA etc.) play a vital role in many biological interactions and it is important to understand the individual reactions of each of them separately. Secondly, Mu, being a light iso-tope of H with a short lifetime, is a sensitive atomic probe that can be used to study these reactions without introducing extra constraints on the experimental system (as is necessary for 1H). Thirdly, micelles were introduced into the so-lution to create a membrane-like structure (a micelle is the simplest of all the membrane-mimicking systems), and the same reactions studied again to see the kinetic effect of a membrane structure on these types of reactions. Of course, this might not give a complete picture because of the over simplifications involved, 44 Chapter 3. Rate constants for Muonium reactions 45 but it does provide some useful information for understanding some biological reactions. 3.2 Results Table 3.1 lists the //SR. data (A, same as \M of Eq 2.5) for the reaction of Mu with some amides, diamides and substituted amides. The calculated values of kjvf and ^M(mic) me also given. This class of compound was usually unreactive or slow reacting as seen from the k\j values. The k.M(mic) values were calculated mainly from data using the CTAB micelle (see sec 3.2.3), which is a large micelle with very small critical micelle concentration. Due to the limitations involved in the fj.SH study (see Section 2.2.3.2), sub-millimolar concentrations of solutes and/or micelles will give only a upper limit (viz. < 109 M _ 1 s _ 1 ) for the kM(mic) value. In this case, if the A value is close to A0 then there is a large error involved on the deduction of the k ^ ( m t c ) value from the measured A A. In order to get a better limit on these numbers, some smaller micelles, such as SOS and SDDS, were used to bring the upper limit down to ~ 107 M _ 1 s - 1 . Those solutes which were minimally soluble in micelles (e.g. urea, guanidine and thiourea) yielded no useful information about membrane structure effects, but were used only for k\{ purposes or to determine the muonium residence time at micelles[28]. The general structure of these compounds are given in Fig 3.1. Table 3.2 gives the data for the thioamides studied. The rate constants for some of these solutes were also studied at pH = 1 in order to help sort out the type of reaction involved in different thiocarbonyl compounds. Wherever the k M value corresponded to a diffusion-limited rate the k ^ ( m t c ) values were not determined (e.g. DMTFA). Chapter 3. Rate constants for Muonium reactions 46 Table 3.1: The summary of observed A and calculated k f^ in aqueous solutions for the reaction of Mu with some amides and diamides in the presence and absence of micelles. [solute] /10" 3M [ C T A B U /10" 3M A / 1 0 V 1 AA / l O V 1 / M - V 1 Formamide 1000 0 0.27(.02)* 0.01 < 105 2000 0 0.35(.03) 0.08 0.150 0.050 0.62(.l) 0.20 l x l O 9 12 4 (SOS) 0.86(.l) 0.08 7xl0 6 Acetamide 1750 0 0.34(.06) 0.07 < 105 0.120 0.040 0.50(.06) 0.13 l x l O 9 0.180 0.060 0.72(.06) 0.29 N-methyl- 1500 0 0.29(.03) 0.03 < 105 - acetamide 0.075 0.025 0.38(.03) 0.06 ~109 0.135 0.045 0.48(.05) 0.11 N,N-dimethyl- 1000 0 0.32(.03) 0.05 < 105 -acetamide 0.135 0.045 0.45(.05) 0.08 0.180 0.060 0.51(.05) 0.09 ~109 12 4 (SOS) 1.10(.l) 0.31 2xl0 7 Urea 1000 0 0.23(.02) 0 < 10s 0.135 0.045 0.44(.04) 0.07 <109 0.180 0.060 0.51(.04) 0.09 Urea pH=l 1000 0 0.59(.02) 0.34 < 106 Guanidine 1000 0 0.56(.05) 0.29 1500 0 0.71(.07) 0.44 3xl0 5 2000 0 0.91(.09) 0.65 0.150 0.050 0.44(.04) 0.02 <109 Tetramethyl- 500 0 0.41(.05) 0.18 4xl0 5 -urea 1000 0 0.61(.05) 0.35 0.075 0.025 0.46(.04) 0.14 0.135 0.045 0.78(.05) 0.40 2xl0 9 0.180 0.060 0.85(.06) 0.43 *: The numbers in parantheses represent the magnitude of error in A (e.g., 0.27±0.02). Chapter 3. Rate constants for Muonium reactions o II R-C-NH, H, formamide = NH,, urea CH 2 =CH-C-NH 2 ocrylamide benzoquinone 0 II R-C-OH benzophenone 0 II N = C - C H 2 - C - 0 - C H 3 methylcyanoacetate R = CH 3, acetic acid 9 = CH j -C - , pyruvic acid = HO-C-, oxalic acid 0 2—thiouracil (CH-j)2CH- , valine methionine H 0 I II R-C -C -OH l NH, = H S - C H 2 - , cysteine CH, l 3 = HS—C- , penicillamine CH, R = C=C -CH 2 - , histidine N N Figure 3.1: The general structure of compounds listed in Tables 3.1 to 3.5 Chapter 3. Rate constants for Muonium reactions 48 Table 3.2: The summary of observed A and calculated in aqueous solutions for the reaction of Mu with some thioamides in the presence and absence of micelles. [solute] /10" 3M [CTAB]mt-c /10" 3M A / l O V 1 AA / l O ^ " 1 / M ^ s - 1 /M~ls~l Thioacetamide 0.050 0 1.90(.2) 1.60 0.075 0 2.31(.25) 2.05 3xl0 1 0 0.100 0 3.35(.6) 3.05 0.075 0.025 2.90(.5) 2.58 0.135 0.045 3.32(.5) 2.95 3xl0 1 0 0.180 0.06 4.62(.8) 4.22 N,N-dimethyl- 0.030 0 2.41(.2) 2.20 thioformamide 0.015 0 1.20(.12) 0.99 7xl0 1 0 -(DMTFA) 0.010 0 0.90(.07) 0.69 Thiourea 30 0 1.75(.2) 1.53 5 xlO 7 50 0 2.79(.3) 2.52 0.075 0.025 0.36(.04) 0.04 0.135 0.045 0.51(.05) 0.14 <109 0.180 0.060 0.63(.08) 0.21 30 30 9 (SOS) 4 (SOS) 4.20(.35) 2.55(.2) 2.90 1.77 7xl0 7 Thiourea 1.0 0 2.05(.12) 1.80 at pH=l 0.8 0 1.63(.l) 1.38 2xl0 9 N,N,N'N'-tetra- 0.030 0 1.43(.l) 1.16 -methylthiourea 0.050 0 2.21(.2) 1.99 4xl0 1 0 (TMTU) 0.075 0.075 0 0.025 2.61(.2) 1.85(.2) 2.34 1.62 0.135 0.045 3.28(.3) 3.06 2xl0 1 0 0.180 0.060 4.91(.5) 4.69 T M T U at 0.1 0 0.56(.04) 0.31 pH=l 0.5 1.0 0 0 1.64(.15) 2.98(.25) 1.39 2.73 3xl0 9 Chapter 3. Rate constants for Muonium reactions 49 The simplest thiocarbonyl compound, thioacetone,is not listed because it was unavailable as a stable compound. Table 3.3 records the data obtained for some of the compounds selected for comparison purposes. Acrylamide, with a C = C unsaturation centre, may be compared with the amides and substituted amides, acetone with amides hav-ing carbonyl and thiocarbonyl groups, and methylcyanoacetate ( -C=N) with compounds having the > C = N - group (adenine etc). Benzoquinone and ben-zophenone were included to indicate the reactivity of a carbonyl group in a ring structure or involved in delocalization of electrons. Table 3.4 contains the data for some simple carboxylic acids, whereas Table 3.5 lists the data for some amino acids of interest. The carboxylic acid group is evidently not reactive but additional functional groups present in them enhance the reactivity. Also, the rate constants of this class of compound in micelles were of less importance than those at a low p H . The amino acids selected for this study contain an additional functional group which essentially controls the reaction. The large variation in rate constants was due to different types of reac-tions, but none of them seemed to be affected to a large extent by the presence of micelles. Table 3.6 lists the data for some constituents of D N A and R N A . This includes the purine and pyrimidine bases, sugar units (ribose and deoxyribose), a nucleoside (base and sugar) and a nucleotide (nucleoside and phosphate). Dis-odium hydrogenphosphate and ribose-5-phosphate are also listed for comparison. The structure of some of these are given Fig 3.2. Chapter 3. Rate constants for Muonium reactions 50 Table 3.3: The summary of observed A and calculated kjvf in aqueous solutions for the reaction of Mu with some related compounds (for comparison) in the presence and absence of micelles. [solute] [CTAB]m,-c A AA / /10" 3M /10" 3M / l O V 1 l O V 1 / M - 1 s _ 1 Acrylamide - - - ^1.9xl0 1 0 0.075 0.025 1.52(.l) 1.17 0.135 0.045 3.03(.2) 2.68 1.8xl010 0.180 0.06 3.95(.35) 3.53 Acetone - - - - ^1.1x10s 0.09 0.03 3.54(.3) 3.20 0.135 0.045 3.77(.3) 3.42 2.5xl010 0.180 0.06 4.01(.35) 3.59 Ethyl formate 30 0 1.17(.l) 0.92 50 0 1.32(.l) 1.07 2.2xl07 100 0 2.75(.2) 2.50 Ethyl acetate 100 0 1.75(.2) 1.50 1.5xl07 0.075 0.025 1.77(.2) 1.37 1.8xl010 Methylcyano- 10 0 1.13(.l) 0.93 1x10s -acetate 0.075 0.025 0.38(.03) 0.07 0.135 0.045 0.40(.03) 0.05 < 109 0.180 0.06 0.43(.03) 0.01 Benzoquinone 0.03 0 1.10(.l) 0.89 0.05 0 1.36(.l) 1.15 2.5xl010 0.075 0 1.87(.15) 1.66 0.06 0.02 1.87(.l) 1.52 2.5xl010 Benzophenone 0.03 0 0.775(.05) 0.565 0.06 0 1.504(.l) 1.294 2xl0 1 0 -0.09 0 1.72(.15) 1.51 Thiouracil 0.05 0 1.29(.l) 1.04 0.1 0 2.33(.2) 2.08 2xl0 1 0 -(a) reported earlier in ref [29]. (b) reported to be 8.7 x 107 M ^ s ^ a t pH 1) in ref [30]. Chapter 3. Rate constants for Muonium reactions 51 Table 3.4: The summary of observed A and calculated in aqueous solutions for the reaction of Mu with some carboxylic acids, at various pHs. PH [solute] /10" 3M A / l O V 1 AA / l O V 1 / M - V 1 Acetic acid 1000 0.25 0 < 105 Pyruvic acid 2.0 1.2 3.50(.3) 1.64(.l) 3.235 1.43 l x l O 9 1.0 0.6 1.0 0.62(.04) 1.45(.08) 0.41 1.20 l x l O 9 Oxalic acid 50 5.016(.6) 4.751 10.4 1.0 30 10 10 10 2.453(.23) 1.136(.l) 0.225(.03) 2.823(.3) 2.188 0.871 ~o 2.558 9xl0 7 < 105 2.5xl08 Chapter 3. Rate constants for Muonium reactions 52 Table 3.5: The summary of observed A and calculated in aqueous solutions for the reaction of Mu with some amino acids in the presence and absence of micelles. [solute] [ C T A B U A AA / ^•M(mic) /1G- 3 M /10~ 3M / l O V 1 l O V 1 / M _ 1 s _ 1 / M _ 1 S - 1 Valine 107 0 0.77(.l) 0.56 150 0 1.12(.13) 0.86 5 xlO 6 0.18 0.06 0.58 0.02 < 108 12 4 (SOS) 1.42 0.64 5xl0 7 Histidine 0.2 0 0.70(.05) 0.44 0.35 0 1.21(.l) 0.94 2.5xl09 0.5 0 1.68(.16) 1.42 0.075 0.025 0.49(.07) 0.15 3 xlO 9 0.18 0.06 1.37 0.76 Methionine 10 0 0.37(.02) 0.16 50 0 0.81(.07) 0.60 1.4xl07 100 0 1.45(.13) 1.24 0.9 0.3 (SDDS) 0.72(.07) 0.01 1.5 0.5 (SDDS) 0.75(.07) 0.01 l x l O 7 Penicillamine 0.10 0 0.55(.04) 0.34 0.20 0 1.08(.l) 0.87 4x109 0.4 0 1.93(.16) 1.72 0.06 0.02 0.67(.05) 0.32 0.18 0.06 2.04(.15) 1.43 7xl0 9 Cysteine 0.25 0 1.49 1.24 0.50 0 3.42 3.17 6 xlO 9 -Chapter 3. Rate constants for Muonium reactions 53 Table 3.6: The summary of observed A and calculated ICA/ for the reaction of Mu with some constituents of DNA and RNA in the presence and absence of micelles. [solute] /10" 3M [ C T A B U /10" 3M A / l O V 1 AA / 1 0 V 1 / M - 1 s _ 1 /M-h-1 Uracil 0.15 0 1.45(.12) 1.19 0.2 0 1.58(.l) 1.32 6xl0 9 0.4 0 2.48(.2) 2.22 0.06 0.02 0.68(.05) 0.33 5xl0 9 0.18 0.06 1.53(.05) 0.92 Cytosine 0.1 0 0.62(.06) 0.35 0.2 0 0.92(.08) 0.65 3.5xl09 0.3 0 1.52(.l) 1.23 -1.0 0 2.82(.27) 2.56 Thymine 0.2 0 0.99(.09) 0.72 0.6 0 2.03(.2) 1.76 3xl0 9 0.18 0.06 1.15(.05) 0.54 3xl0 9 Adenine 0.3 0 0.95(.07) 0.68 0.5 0 1.29(.08) 1.02 2xl0 9 1.0 0 2.24(.2) 1.98 0.075 0.025 0.51(.07) 0.17 0.18 0.06 0.98(.05) 0.37 2xl0 9 Ribose 100 0 0.42(.04) 0.16 200 0 0.61(.04) 0.35 2xl0 6 280 0 0.83(.06) 0.57 500 0 1.19(.08) 0.93 0.9 0.3 (SDDS) 0.97(.07) 0.16 1.5 0.5 (SDDS) 0.99(.07) 0.19 1x10s 2-Deoxyribose 250 0 0.64(.04) 0.39 310 0 0.77(.06) 0.52 2xl0 6 500 0 1.67(.08) 1.42 12 4 (SOS) 1.10(.07) 0.32 3xl0 7 Ribose phosphate 73 0 0.95 0.70 l x l O 7 -Adenosine 0.24 0 0.83(.06) 0.56 0.48 0 1.37(.l) 1.10 2xl0 9 1.0 0 2.65(.26) 2.39 0.075 0.025 0.61(.06) 0.27 0.18 0.06 1.01(.05) 0.40 2xl0 9 Na 2HP0 4 500 0 0.37 0.12 < 105 -AMP 0.5 0 1.22(.l) 0.97 0.75 0 1.88(.l) 1.63 2xl0 9 0.18 0.06 1.11(.05) 0.50 3xl0 9 Chapter 3. Rate constants for Muonium reactions Structure of part of DNA (or RNA) chain. - I 0-P=0 I o J H2C H Base H r 0 H H (or OH) 0-P=0 H2C» Base H H H 0 H 1 (or OH) Some bases and a nucleotide. NH, Adenine 0 0 Uracil Thymine NH, 0^1<r Cytosine NH, rS|\ Adenosina-5'-phosphate (AMP) Figure 3.2: The structure of some constituent molecules of RNA and DNA Chapter 3. Rate constants for Muonium reactions 55 Table 3.7 lists the values obtained in aqueous solutions, and at pH = 1, for some solutes which undergo different types of reactions with Mu. These kjvf values at pH = 1 were determined in order to compare our Mu data with published H data, which were obtainable only at pH = 1[32]. Though there are a number of biological molecules and several reactions possible, the number of different kinds of mechanism is limited. For this reason the different types of reactions are compared with each other, rather than the molecules themselves. Table 3.7: Rate constants for the reaction of Mu with selected compounds at natural pH and at pH = 1. Solute Reaction kM/M-ls~l kM/M-ls~l Qualitative pH = 7 pH = 1 pH effect NaN03 ? 1.5xl09 1.9xl09 none K3Fe(CN)6 reduction 2xl0 1 0 3.2xl01 0 (small)acid| KMn04 combination 2.5xl01 0 1.7xl010 none HCOONa abstraction 8 xlO 6 9.2x10s acid]. (CH3)2CHOH abstraction 1.3xl06 5.9x10s acidj (CH3)2CO addition l . l x l O 8 8.7xl07 none Urea abstraction <105 <106 -Thiourea ? 5xl0 7 2xl0 9 acid 7 T M T U addition 4xl0 1 0 3xl0 9 acidj. Uracil addition 6xl0 9 4.3xl09 none ? : reaction type not known. Chapter 3. Rate constants for Muonium reactions 56 3.3 Discussion Muonium has been shown previously to react with different solutes in a variety of ways, by addition across double or triple bonds, by abstraction of H, by reductive electron transfer, and by electron spin exchange. Rate constants ranging from 105 M - 1 s _ 1 to 7 x 1010 M _ 1 s - 1 have been observed where the latter seems to be at the diffusion-controlled limit. Furthermore, kinetic isotopic effects, relative to protium, have been found to vary considerably - from at least 102 to IO - 2 . 3.3.1 Sensitivity of to functional groups The reactivity of Mu with different organic compounds depends on the func-tional groups present in them and hence on the possible types of reaction. The amides listed in Table 3.1 are all unreactive (or slow reacting by the standards of interactions of free atoms). The most likely reaction is probably abstraction of a H from the C-H (in formamide) or from C H 3 (in other amides) since addition across these carbonyls is at least two orders of magnitude slower than reaction with acetone (Table 3.7). But the reaction type can change due to different adjacent groups to the C=0. Consider, for example, comparison of acetamide, acetone and thioacetamide. 0 0 s II II II C H 3 — C — NH 2 C H 3 — C — C H 3 C H 3 — C — NH 2 (i) < 105 M ^ s " 1 (ii) 8.7 x 107 M ^ s " 1 (iii) 3 x IO10 M ^ s " 1 Their rate constants differ by more than 5 orders of magnitude. Changing the -N H 2 group to - C H 3 (i and ii) increases the rate by at least 2 orders of magnitude, whereas the change of carbonyl group to thiocarbonyl group (i and iii) increases the rate by >5 orders of magnitude. This trend can be explained by the fact that Chapter 3. Rate constants for Muonium reactions 57 the amide linkage, - C O N H 2 , is rigid and there exists a maximum conjugation of 7re~s in the C=0 bond and the non-bonding pair of the - N H 2 group, giving it a coplanar structure, which makes it less reactive towards Mu addition, so Mu can merely abstract H (from - C H 3 or -NH 2 ) . In the case of acetone, the lone-pairs of electrons on the carbonyl oxygen are more available for Mu addition. So Mu, being a weak nucleophile, adds to the 0 of the carbonyl (because addition to the C is not favourable with two electron-releasing methyl groups). The > C-OMu formed is stabilized by the hyperconjugation effect. In thioacetamide, however, the reaction is different and occurs at C. This can be explained by the nature of the >C=S group which can exist in the following resonance structures: s s*- s ^ v. s+ \ © C — NH 2 <—• C ' — NH 2 <—• C = NH 2 / . . / / C H 3 CH3 C H 3 • (a) (b) (c) The dipole moments of the thioamides are larger than those of corresponding amides and because of the marked e - derealization (c) is favourable. The C=S group is inherently more polarizable than the C=0 group on account of the larger kernal of e_s in the S atom, which tends to weaken the double bonds. This leads to the addition of Mu to C of C=S rather than S. The observed reactions of Mu with these three solutes can be written as follows: o o II . II C H 3 — C — NH 2 + Mu —• MuH + C H 2 — C — N H 2 (3.1) Chapter 3. Rate constants for Muonium reactions 58 0 OMu II I C H 3 — C C H 3 + Mu —> C H 3 — C — C H 3 S S-II I C H 3 — C — NH 2 + Mu —> C H 3 — C — N H 2 I Mu (3.2) (3.3) Reaction 3.1 is an abstraction and the other two are addition. These radicals formed by addition are characterized by both T F - / J S R and LCR techniques (see Section 2.2.3.3 and 2.3.1). Another comparison of interest is that involving the reaction rates of Mu with urea, thiourea and guanidine (Table 3.1 and 3.2). Here the three different groups are, >C=0, >C=S and >C=NH but only the thio compound reacts rapidly. The preferred conformation for these compounds are given as: e e e O S s N H 2 \ © \ © \ © \ = NH 2 — NH 2 <—^C — N H 3 = NH 2 NH 2 NH NH 2 which should allow both abstraction (of a H from - N H 2 or =NH group, or from the -SH group in the case of thiourea) and addition to a C=NH group. Since the rates are different, the reaction mechanism is unlikely to involve C=NH. For thiourea the reaction type is not clear. It falls midway between thiocarbonyls and amides. Also, there is a contradiction to that predicted in H-atom data (discussed in Section 3.3.2) where there is no difference in the rates of H with thioacetamide and thiourea. It may be a relatively slow addition, as in the case of acetone, to S rather than to C. If it were addition to C of C=S, the radical formed would have been characterized as in the case of thioacetamide. However, Chapter 3. Rate constants for Muonium reactions 59 we observed no LCR in the expected ranges for an S radical. The other thio-compounds studied (i.e., tetramethylthiourea and dimethylthioformamide) have kjv/ values closer to that of thioacetamide implying that the reaction is similar to 3.3. Though the amido group is unreactive, Mu readily adds across the C=C group in the case of acrylamide, so the reaction rate is controlled by the addition across the carbon chain double bond [33]. 0 0 II II C H 2 = CH — C — NH 2 + M u - 4 MuCH 2 — CH — C — NH 2 (3.4) The carbonyl group in conjugation with the C=C may increase the rate of ad-dition of Mu to C=C. Some of the other compounds in Table 3.3 also show the same trend with faster rates seen for benzoquinone and benzophenone as com-pared with benzene. In the case of methylcyanoacetate addition to -C=N greatly exceeds that of >C=NH in guanidine. The reaction of Mu with carboxylic acids (Table 3.4) showed a variation of the rate constant with pH. This could be due to the different structural forms of the solute, or due to the effect of pH on the intrinsic rate of Mu reactions. In other systems, the latter is shown to be negligible (see Table 3.4). Therefore, the results obtained for oxalic acid, for example, are attributed to the acid existing in different forms at pH 1 and at pH 10 (where the rate constants are very different). The acid form H 2 C 2 0 4 has two - O H H's for abstraction whereas the base form C 2 04 - has no H for abstraction and also the addition of a weak nucleophile Mu to this ion is unlikely to be favourable. It is worth noting, however, that the Chapter 3. Rate constants for Muonium reactions 60 H atom reaction with oxalic acid (pH=l) is reported to proceed 100% through addition [34]. The amino acid {-CH(NH2)(COOH)} functional group is evidently not very reactive in itself; but the rates are enhanced for some of the amino acids due to the presence of another reactive site. Some examples are given in Table 3.5. Valine is slow reacting like 2-propanol, because of the same type of sec-H ab-straction; histidine reacts like any other addition reaction in C=C system; while in methionine the abstraction is faster due to the presence of S at the /? position to abstraction site (the product being stabilized by overlapping of the unpaired electron with the lower lying 7r electrons of sulfur). The reaction of Mu with penicillamine is of some interest because we appear to have an abstraction re-action being faster than that with the H atom. Usually abstractions are much slower for Mu than H. In penicillamine the - S - H bond may be weakened and the H made more labile for abstraction because of the solvation shell around S. For this reason Mu reacts faster than H in this particular abstraction. Mu reacts much slower than H with strongly bonded H atoms [35]. Lack of micelle enhancement in the reaction of Mu with the RNA and DNA bases suggests that they all undergo an addition across a C=C double bond with rate constants all >109 M _ 1 s - 1 . The reactivity of Mu toward the ribose and 2-deoxyribose sugar units of RNA and DNA is not very fast, on the order 106 M - 1 s _ 1 , typical of an abstraction reaction from a secondary carbon. The phosphate backbone structure of the nucleic acid helix also is not very reactive, as indicated by the rate constant of disodium hydrogenphosphate itself (< 105 M _ 1 s - 1 ) . The corresponding sugar phosphate, namely ribose-5-phosphate, seems to be somewhat faster reacting than either of the separate constituents but still relatively slow (~107 M - 1 s - 1 ) . Comparison of the rate constants of adenine, Chapter 3. Rate constants for Muonium reactions 61 adenosine and adenosine-5'-phosphate (AMP) (see Table 3.6) indicates that the presence of the sugar or the phosphate group does not significantly affect the rate of reaction of Mu toward these solutes. It is the base groups which control the reactivity of nuleic acids. Table 3.7 lists a selection of solutes which undergo different types of reactions with Mu. They were studied in neutral solution and at pH 1 to check for any rate dependence on the pH of the solution. The solutes which had a different rate at pH 1 and 7 were thiourea, T M T U , formate and 2-propanol. The first shows an increase with [H+] and the other three decreases. For thiourea, the reaction at pH = 7 seems to be mainly abstraction, so the implication is that when the urea's acid form predominates, the addition of Mu becomes the dominant reaction. For T M T U , the normal addition reaction seems to be inhibited somewhat by high [H+]. For the cases of formate and 2-propanol, which are solutes showing kinetic isotope effects favouring H over Mu by ~102-fold, protonation evidently reduces the abstraction of H even further. Several reactions, on the other hand, are seen to be unaffected by the solution's pH, which suggests that Mu and M u H + react similarly (or that M u H + barely forms at pH = 1). 3.3.2 Comparison of with k# Table 3.8 lists the published values of k# for the solutes for which k^ is deter-mined here. The values in the fourth column of the table gives the kinetic isotopic effect (KIE) of Mu compared with H, and the last column states the probable type of reaction. Values of KIE which are lower than 1 are generally for abstrac-tion reactions and those greater than 1 are for addition reactions. There are some exceptions, however, like thiourea (pH = 1), oxalic acid, and penicillamine. If the addition reaction is already diffusion-controlled then the KIE is necessarily Chapter 3. Rate constants for Muonium reactions 62 Table 3.8: Rate constants for the reaction of Mu compared with that of H. Solute fc^/M-'s-1 kn/M-h-1 Reaction Formamide < 105 - - abstraction Acetamide < 105 1.5xl05 <1 abstraction N-methylacetamide < 105 - - abstraction N,N-dimethylacetamide < 105 - - abstraction Urea < 105 3xl0 4 <3 abstraction Tetramethylurea 4xl0 5 - - abstraction Guanidine 3xl0 5 1.2xl06 0.25 abstraction Thiourea 4xl0 7 6xl0 9 0.007 ? Tetramethylthiourea 4xl0 1 0 - - addition Thioacetamide 3xl0 1 0 6xl0 9 5 addition Dimethylthioformamide 7xl0 1 0 - - addition Acetone 8.7xl07 2.6xl06 33 addition Acrylamide 2xl0 1 0 3.1xl01 0 0.6 addition Methylcyanoacetate l x l O 8 - - addition Benzophenone 2xl0 1 0 6xl0 9 3 addition Benzoquinone 2.5xl01 0 8.3xl09 3 addition Thiouracil 2xl0 1 0 - - addition Acetic acid <105 9.8xl04 <1 ? Pyruvic acid l x l O 9 2.3xl09 0.4 addition Oxalic acid 9xl0 7 3.3xl05 270 ? Oxalic acid(pH=l) 2.5xl08 3.3 xlO 5 750 ? Valine 5xl0 6 1.2xl07 0.4 abstraction Histidine 2.5xl09 2.3xl08 11 addition Methionine 1.4xl07 3.5 xlO 8 0.04 abstraction Penicillamine 4xl0 9 2.3xl09 1.7 abstraction Cysteine 6xl0 9 1.2xl09 5 addition Uracil 6xl0 9 3.8xl08 16 addition Cytosine 3xl0 9 9.2xl07 33 addition Thymine 3xl0 9 5.7xl08 5 addition Adenine 2xl0 9 1.0x10s 20 addition Ribose 2xl0 6 5.1xl07 0.03 abstraction 2-Deoxyribose 2xl0 6 2.9xl07 0.015 abstraction Adenosine 2xl0 9 1.6xl08 12.5 addition Ribose- 5-phosphate l x l O 7 - - abstraction Na 2 HP0 4 <105 <5xl04 ? ? AMP 2xl0 9 1.9xl08 10 addition Chapter 3. Rate constants for Muonium reactions 63 approximately unity since Mu and H have similar diffusion coefficients [14]. Mu reacts much more slowly than H in abstraction reactions; and this is attributed to the higher zero-point vibrational energy of the transition state involving a lighter isotope. H atom reactions should be affected by quantum mechanical tunneling[36]; and such effects should be much more imporatant for Mu than for H[37]. Model calculations support this view since they show a strong dependence on barrier height and width. For relatively slow reactions (such as abstractions) the bar-riers are high, and the zero-point vibrational term dominates the KIE. For fast reactions the barriers are lower and narrower, and the tunneling term dominates. This is found to be the case with Mu addition to unsaturated compounds. 3.3.3 Rate constants in micellar solution, \s.M(mic) The rate constants for Mu reactions with the solutes of interest were also studied in dilute micelle solutions. Values calculated for the enhancement factors are listed in Table 3.9. Micelles are one of the simplest types of chemical system used to mimic features of real biological membranes (see Section 1.3) and have concentrations given by Equation 1.6. The CMC and aggregation number differ for various micelles. Figure 1.1 shows the different regions where the solutes could be located when present in solution. Micelles were used for solubilizing organic solutes which were not very solu-ble in water. This allowed /JSR experiments to be carried out in a hydrocarbon medium (i.e., micellar interior, where the solutes were located) with the forma-tion of Mu atoms in the bulk aqueous phase. The study of reactions in hydrocar-bon medium is otherwise very difficult due to the high A0 for hydrocarbons. The micelles themselves were not very reactive towards Mu in contrast to H . H reacts Chapter 3. Rate constants for Muonium reactions 64 Table 3.9: The enhancement factor i.e., k\f(mic)/^M for the compounds studied. Solute Micelle used Formamide CTAB <10000 Formamide SOS <70 Acetamide CTAB <10000 N-methylacetamide CTAB <10000 N, N- dimethy lacet amide CTAB <10000 N, N-dimethylacet amide SOS <200 Urea CTAB <10000 Tetrarnethylurea CTAB 5000 Guanidine CTAB <3000 Thioacetamide CTAB 1 Thiourea CTAB <20 Thiourea SOS 1.4 Tetramethylthiourea CTAB 0.5 2-Propanol CTAB 20000 Ethyl acetate CTAB 1200 Acetone CTAB 290 Acrylamide CTAB ~1 Methylcyanoacetate CTAB <10 Benzoquinone CTAB ~1 Valine CTAB <20 Valine SOS 10 Histidine CTAB ~1 Methionine SDDS 0.8 Penicillamine CTAB 1.3 Uracil CTAB 1 Thymine CTAB 1 Adenine CTAB 1 Adenosine CTAB 1 Ribose SDDS 50 2-Deoxyribose SOS 10 Adenosine monophosphate CTAB 1 Chapter 3. Rate constants for Muonium reactions 65 with the surfactant molecules at a rate of ~107 M - 1s - 1[16], so this is another advantage of studying Mu reactions. The rate of reaction of Mu with a solute in a micelle depends on 3 factors: firstly, on the location of the solute in the micelle, secondly, on the type of reaction with that solute inside the micelle; and thirdly, on the number of solutes per micelle in solution. We have shown that Mu penetrates the micelle and also that it does not 'permanently' localize in the micelle, but that it just traverses through the micelle, spending only ~ 2 ns or so there[28]. The number of solutes per micelle, Ns, is expected to be based on the Poisson - distribution functional]. By always using Ns = 3 there is less than a 10% chance of Mu encountering an empty micelle; but the 3 is only an average and some micelles contain many solutes. The location of the solute depends on the polarity or bond dipole of the solute. The interface of a micelle is thought to have a dielectric constant of about that corresponding to ethanol, showing that it is fairly polar. Also, the water penetration near the interface would preferably localize polar solutes near the Stern layer. Ionic solutes should stay in the Gouy-Chapman layer. During its lifetime Mu evidently visits many micelles at the concentrations used here. In order to determine the residence time of Mu at micelles it was necessary to observe the effect of added micelles on the rate with which Mu reacted with a solute in the water. Kinetic analysis reveals a mean residence time for Mu at SDDS micelle of only 2 ns[28]. For reactions occurring inside and outside the micelles the mechanism can be written as: Muaq + 5, aq Product (3.5) Chapter 3. Rate constants for Muonium reactions 66 Muaq Product (3.6) Muaq + mice ^ J f - Muem (3.7) M u e m ^ • Product (3.8) Muaq + mic0 ^^MUom (3.9) Muom + Smic Product (3.10) Muom -^ 22, • Product (3.11) where is the rate at which Mu diffuses to reach a micelle, k/, the rate at which it leaves or comes out of the micelle when there is no solute, k;/ is the same as k/ but for an occupied micelle in which the solute alters the rate of leaving, k^ is the rate constant of Mu with solute S in water, k m is the rate constant of Mu within a micelle reacting with a solute within the same micelle (the observed k\{(mic) is related to k m through N s , size and concentration of the micelle). Reactions 3.5 and 3.6 occur in aqueous solution when there are no micelles present. Reactions 3.7 and 3.8 proceed when micelles are added but the solutes remain preferably in aqueous bulk (empty micelle experiments), reactions 3.5 through 3.11 occur when the solutes are present in both aqueous and micellar phase. Kinetic treatment of this mechanism gives the following equation: A A = kM[S]aq + km[S]om + yhMrnicV + kMrnrcU Kiki> where k' is the rate constant for the reaction of Mu with the blank micelle solutions (which have the relaxation coefficients A 0i and A02 respectively). The values listed in Table 3.9 show that it is not the particular type of reaction which is enhanced, it is essentially the reaction site and the particular functional group which goes through the reaction. Not all the abstraction reactions are enhanced Chapter 3. Rate constants for Muonium reactions 67 20000x as in the case of 2-propanol [17]. The reactions of Mu with simple amides are not enhanced, substituted ones are slightly enhanced. (The upper limits reported as enhancement factors with CTAB micelles[38] for some of the solutes are modified somewhat using- SOS and SDDS, as in Tables 3.1, 3.5 and 3.6, because of the bigger concentration range possible.) It is reasonable to assume that urea, thiourea and guanidine may not enter the micelle for the reaction to be enhanced because they are so soluble in water. Addition reactions, being fast already, are not enhanced much in micelles. The difference between k\f and k;v/(mic) may arise due to various factors: 1. If the solutes are localized within the micelle or bunched around the micelle in the Gouy-Chapmann layer, the local concentration of the solute is dif-ferent from that in the aqueous bulk. This can result in an increase in the encounter probability. In this effect, the rate constant can be increased by a factor from 10 to 50 (the ratio of the size of the micelle and the solute). This appears to be the case with some amides and sugars. 2. When the solutes react at a diffusion limited rate in water, and are soluble in micelle to a reasonable extent, then the addition of micelles results in a net decrease in the effective number of species for encounter. This will reduce the observed rate constant. This is seen in the case of tetramethylthiourea. 3. When the solutes are present at the interface of the micelle and not much altered structurally by the presence of the polar head groups, then the rate constant is almost the same as that in water. This is applicable for the case of amino acids, uracil, thymine, cytosine, etc. 4. A very large enhancement (enhancement factor > 1000) is observed for Chapter 3. Rate constants for Muonium reactions 68 some compounds like 2-propanol[37] and ethyl acetate. When a solute is present within the micelle and close to the interface, it can be associated with the polar head group to have a specific location. If this association favours the particular reaction, in this case abstraction of H by M u , then the electromeric effect of the functional group present in the solute and its particular site can create a 'potential energy well' which can localize M u for a longer time and thus react faster with the solute. 3.4 Conclusion Rate constants for the reaction of M u with some organic compound of biological importance in aqueous and in dilute micelle solutions are reported, k ^ values are sensitive to different functional groups and also to the type of reactions, k^/ values are compared with k# values (from the literature) to calculate the kinetic isotope effect. kM(m.c) values are determined using various micelles and the enhancement factor (kM(mic)/k-M) is calculated for each solute. Tables 3.8 and 3.9 show that it is not a particular reaction type which gives a large enhancement, but it is a particular functional group attached to the reaction site which is responsible for the enhancement. Large enhancements are seen for alcohols and esters, while a small enhancement was observed for amides and sugars. But unsaturated compounds (with >C=C<) show no appreciable enhancement. kjv/ values at pH 1 show that some solutes go through a different reaction pathway at different p H . This information indicates that any reaction mechanism predicted by the H atom kinetics may not be correct if the system refered to is not at p H 1, since all the k# measurements in the literature were done at pH 1. Chapter 3. Rate constants for Muonium reactions 69 So, extrapolations from H atom studies cannot be directly made to physiological reactions which occur at a pH of ~7, whenever the Mu rate constants are different at pH 1 and 7. Chapter 4 Rate constants for Positronium reactions 4.1 Introduction As indicated in Chapter 1, positronium (Ps) is not expected to behave as a true isotope of H; but it is an elementary atomic species that might be expected to undergo several types of chemical reactions. Its comparison with Mu is partic-ularly interesting, though it might be anticipated to show quantum mechanical effects more akin to solvated electrons than to Mu or H. Several studies of Ps as a chemical species have been attempted previously[13], but here the focus relates directly to muonium. Specifically, Ps is compared to Mu in the following respects: How is its lifetime influenced by added micelles, and what is its reten-tion time in the hydrophobic phase? Are its abstraction reactions enhanced by orders of magnitude in rate as muonium's are by addition of micelles? Does it react exceptionally rapidly with thio-compounds, and could it add to the C of a C=S bond to produce a RS radical (as Mu does - Chapter 5)? Does Ps add to the benzene ring of benzoic acid as Mu does, and if so, to what extent does the Hammett a function of a second substituent influence that rate? Finally, does the different formation mechanism of Ps compared to Mu show-up in the primary yields of Ps in aqueous solutions of electron scavengers. 70 Chapter 4. Rate constants for Positronium reactions 71 Table 4.1: Lifetime values obtained for o-Ps with SHS micelles [SHS] ( m t c )/M [ S H S ] ( W ) / M r 3 /10"9s water 0 1.815(.02) 0.010 0.70 2.164(.02) 0.015 0.84 2.295(.02) 0.019 0.98 2.445(.03) 0.024 1.12 2.557(.03) 0.029 1.26 2.608(.03) 0.033 1.40 2.818(.04) 0.050 1.90 2.991(.04) 0.057 2.10 3.024(.04) n-heptane 0 3.537(.05) 4.2 Results Representative data are listed in Tables 4.1 through 4.6, r 3 being the o-Ps lifetime, and I3 its yield. Table 4.1 gives the variation of o-Ps lifetime with respect to SHS micelle concentration. Figure 4.1 is a plot of the inverse of these lifetimes against concentration of SHS micelle. Tables 4.2 and 4.3 record the lifetime, and the difference in the lifetime from the solvent (Ar 3), due to the presence of some amides and diamides as solutes in aqueous and dilute micelle solutions. Thio-compounds are included there. Table 4.4 gives the fitted lifetime and intensity of o-Ps formed in dilute solutions of benzoquinone in water, in n-heptane, in 0.015 M micellar SHS solution, and in aqueous solution containing 0.015 M a-cyclodextrin. Figures 4.2 and 4.3 give the plot of r3~* against concentration of benzoquinone for these solutions. The lifetime and the calculated rate constants for the reaction of o-Ps with some benzoic acid derivatives (in ethanol for reasons of solubility) are listed in Table 4.5. Table 4.6 summarizes the fitted parameters for the reaction of o-Ps with sodium nitrate in water and in SHS micelles. Chapter 4. Rate constants for Positronium reactions 72 SHS micelle in water .0 .55 i i water i i i .5 - \ -.45 -1 .4 w °b i \ .35 -.3 .25 .2 i i n-hep_tane 1 i i 0 .01 .02 .03 .04 .05 .06 [SHS]mlc/M Figure 4.1: Plot of l / r 3 against micelle concentration for SHS micelles with [S] = 0. Chapter 4. Rate constants for Positronium reactions Table 4.2: The summary of observed o-Ps lifetime in aqueous solutions of amides in the presence and absence of micelles. Solute [solute]/M [SHS]m t c/M T 3 /10 - 9 S Ar 3/10- 9s Formamide 1.0 0 1.949(.014) -0.13 2.0 0 2.009(.015) -0.19 Neat 0 2.113(.030) -0.30 0.06 0.020 2.398(.023) 0.05 0.1 0.033 2.767(.030) 0.05 Acetamide 2.0 0 1.974(.016) -0.16 3.0 0 1.964(.024) -0.15 0.06 0.020 2.626(.030) -0.18 0.1 0.033 2.777(.030) -0.04 N-Methyl- 1.0 0 2.025(.020) -0.21 -acetamide 2.0 0 2.080(.025) -0.27 0.06 0.020 2.456(.024) -0.01 0.1 0.033 2.792(.030) -0.03 N,N-Dimethyl- 1.0 0 2.014(.025) -0.20 -acetamide 2.0 0 2.023(.016) -0.21 Neat 0 2.364(.022) -0.55 0.06 0.020 2.515(.032) -0.07 0.1 0.033 2.748(.030) 0.07 Thioacetamide 0.8 0 1.926(.030) -0.11 1.0 0 1.864(.026) -0.05 0.06 0.020 2.609(.030) -0.16 0.1 0.033 2.916(.030) -0.10 Chapter 4. Rate constants for Positronium reactions 74 Table 4.3: The summary of observed o-Ps lifetime in aqueous solutions of some diamides in the presence and absence of micelles. Solute [solute]/M [ S H S U / M T 3/10- 9S Ar3/10-95 Urea 2.0 0 1.913(.019) -0.10 4.0 0 1.811(.024) 0.01 0.06 0.020 2.481(.020) 0.03 0.1 0.033 2.724(.030) 0.09 Thiourea 1.0 0 1.871(.028) -0.06 2.0 0 1.894(.020) -0.08 0.06 0.020 2.598(.030) -0.15 0.1 0.033 2.658(.025) -0.16 Tetramethyl- 0.5 0 1.899(.018) -0.08 -urea 1.0 0 2.041(.024) -0.23 0.06 0.020 2.581(.033) -0.13 0.1 0.033 3.313(.030) -0.50 Tetramethyl- 0.1 0 1.901(.019) -0.09 -thiourea 0.25 0 1.994(.020) -0.18 0.06 0.020 2.643(.032) -0.20 0.1 0.033 2.846(.030) 0.03 Guanidine 1.0 0 1.861(.023) -0.05 2.0 0 1.864(.016) -0.05 0.06 0.020 2.437(.031) -0.01 0.1 0.033 2.761(.030) -0.06 Chapter 4. Rate constants for Positronium reactions 75 Table 4.4: The summary of observed r 3 and I3 and kp (from Figs. 4.2 and 4.3) for the reaction of Ps with benzoquinone in different media. solvent [BQ] TS Is hin TS1 kp / M /10"9s 1% / l O ^ " 1 /M^s-1 0 1.815(20) 25.5(.3) 1.00 0.551 W 0.0125 1.386(.018) 20.4(.5) 0.80 0.722 1.25 x 1010 A 0.015 1.372(.082) 16.0(2.0) 0.63 0.729 T 0.025 1.211(.024) 18.6(.8) 0.73 0.826 E 0.045 0.867(.075) 23.0(5.0) 0.90 1.153 R 0.050 0.846(.013) 20.0(1.0) 0.78 1.182 0.075 0.706(.015) 16.0(10.0) 0.63 1.416 n-H 0 3.537(.026) 29.4(.14) 1.00 0.283 E 0.0015 2.818(.023) 57.0(.6) 1.94 0.355 P 0.003 2.396(.026) 43.0(2.0) 1.46 0.417 T 0.005 1.695(.022) 52.3(1.3) 1.78 0.590 4.2 x 1010 A 0.0075 1.608(.023) 44.8(1.2) 1.52 0.622 N 0.010 1.445(.040) 36.9(2.7) 1.26 0.692 E 0.015 1.378(.020) 27.4(1.0) 0.93 0.726 0 2.077(.089) 17.0(.4) 1.00 0.481 0.015M 0.015 1.669(.107) 14.8(1.2) 0.86 0.599 SHS 0.045 1.401(.110) 8.5(1.0) 0.50 0.714 0.62 x 1010 mic. 0.075 1.087(.105) 7.6(1.6) 0.45 0.920 (aqu.) 0.105 0.877(.152) 8.2(4.0) 0.48 1.140 0.135 0.787(.202) 9.9(8.3) 0.58 1.271 0 1.805(.020) 21.4(.2) 1.00 0.554 * 0.015M 0.015 1.341(.024) 27.1(1.0) 1.27 0.746 1.3 x 1010 a- . 0.03 1.08(.016) 17.9(.7) 0.84 0.926 1.2 x IO10 CD 0.045 1.239(.067) 14.7(2.0) 0.69 0.807 0.56 x 1010 (aqu.) 0.070 1.632(.123) 4.6(.6) 0.22 0.613 0.08 x 1010 * : kp values (in 0.015 M a-cyclodextrin) are based on [BQ] in solution. Chapter 4. Rate constants for Positronium reactions 76 Figure 4.2: Plot of l / r 3 against concentration of benzoquinone in (a) water and (b) n-heptane. Chapter 4. Rate constants for Positronium reactions 77 B e n z o q u i n o n e i n m i c e l l e ( N a H S ) (a) 1.4 | , 1 , , , .4 I i i i i i i 0 .02 .04 .06 .08 .1 .12 .14 [ b e n z o q u i n o n e ] / M B e n z o q u i n o n e i n a l p h a — C D .01 .02 .03 .04 .05 .06 .07 .08 .09 .1 .11 [ b e n z o q u i n o n e ] / M Figure 4.3: Plot of I/T3 against concentration of benzoquinone in (a) 0.015 M SHS micelle and (b) 0.015 M a-cyclodextrin. Chapter 4. Rate constants for Positronium reactions 78 Table 4.5: The summary of observed r 3 and I3 and calculated kp for the reaction of Ps with some benzoic acid derivatives in ethanol. sample T 3 /10"9s I3 1% / 1 0 V 1 kp Ethanol (absolute) Benzoic acid 1.0 M p-Chlorobenzoic acid 0.1 M m-Chlorobenzoic acid 1.0 M m-Nitrobenzoic acid 0.1 M p-Cyanobenzoic acid 0.1 M p-Hydroxybenzoic acid 0.1 M 3.219(.070) 3.043(.070) 2.965(.060) 2.879(.050) 0.861(.010) 3,147(.060) 3.326(.060) 15.0(.3) 11.9(.4) 13.5(.4) 10.9(.4) 11.9(2.4) 13.1(.4) 14.0(.4) 0.311 0.328 0.337 0.347 1.161 0.318 0.301 1.8(1.5) x 107 2.6(1.5) x 108 3.6(1.3) x 107 8.5(0.2) x 109 7.0(1.3) x 107 <107 Table 4.6: The summary of observed r 3 and I3 for the reaction of Ps with nitrate in the presence and absence of SHS micelle. [NaN03] [mic]S//s T 3 I3 / M / M /10"9s /% 0 0 1.815(.02) 25.5(.2) 0.5 0 1.776(.02) 8.5(.2) 1.0 0 1.702(.03) 4.8(.2) 1.5 0 1.953(.ll) 2.9(.2) 2.0 0 1.837(.09) 2.9(.2) 0 0.05 3.024(.03) 12.0(.2) 0.15 0.05 2.919(.05) 8.9(.l) 0.30 0.05 2.798(.05) 8.0(.l) 0.50 0.05 2.932(.06) 6.0(.l) 1.00 0.05 2.618(.09) 4.3(.l) 1.50 0.05 2.756(.13) 2.9(.l) . Chapter 4. Rate constants for Positronium reactions 79 4.3 Discussion 4.3.1 kp compared with kp(mtc) For all the amides, diamides and thio—compounds studied as solutes, reaction with o-Ps was not detected and only upper limits to the rate constants could be evaluated. These are summarized in Table 4.7. The short lifetime of Ps requires very high solute concentrations, especially when the rate constant is <109 M _ 1 5 _ 1 . Furthermore, there are no significant changes when micelles were added. This contrasts sharply with muonium. Table 4.7: Upper limits to the positronium rate constants^. Solute Cone, range/M kP /M^s-1 Cone used*6* with mic./M kp(mic) /M^s-1 Formamide 2 < 108 0.1 < 109 Acetamide 3 < 108 0.1 < 109 (N)-Methylacetamide 2 < 108 0.1 < 109 (N,N)-Dimethylacetamide 2 < 108 0.1 <5xl08 Guanidine 2 < 108 0.1 < 109 Urea 4 <108 0.1 <3xl08 Tetramethylurea 1 < 108 0.1 < 109 Thiourea 2 < 108 0.1 < 109 Tetramethylthiourea 0.25 < 109 0.1 < 109 Thioacetamide 1 < 108 0.1 < 109 Thymine 0.01 < 109 0.05 lxlO 9 Uracil 0.02 < 109 0.05 lxlO 9 Cytosine 0.01 < 109 0.05 lxlO 9 Benzoquinone 0.075 1.3xl010 0.045 0.6xl010 W (a) The absence of a detectable decrease in o-Ps lifetime gives a measure of the upper limit to kp and fcp(mtc). (b) Always three solutes per micelle, on average. (c) If the concentration of occupied mic. were used then fcF(mtc)=1.8xl010M_1.s_1. A mean residence time for o-Ps at SHS micelles can be deduced from the data Chapter 4. Rate constants for Positronium reactions 80 of Fig 4.1 in the following way. In micelle solutions, a mechanism of localization and equilibrium-dominated return to the aqueous phase, each with separate inherent annihilation rates, A„ and A m , is assumed, o-Ps(aq) + mic ^l*- o-Ps(mic) A„ \ / A m (4.1) para — Ps A single exponential with summed exponents evidently applies to the o-Ps com-ponent, so we will write Eq.(4.2), Kb3 = Kfa + Xmfm (4.2) where /„ and fm are the fractions of time Ps spends in the aqueous and micellar phases respectively. This ratio effractions can be expected to be given on average by Eq.(4.3) fa/fm = (Va/Vm)(k,/kd[mic}) (4.3) where Va and Vm are the volumes of water and micelle, which depend on micelle concentration [mic]. On combining Eq.(4.2) and (4.3) yields Eq.(4.4), Aq - Xobs _ [mic)2Vm kd 4^ A0&* - A m 1 - [mic]Vm' kj where Vm is just the molar volume of the micelle. The left-hand side of Eq.(4.4) was plotted against the first term on the right. A m was used as an adjustable parameter to get a linear fit and corresponds to 0.31, which is a reasonable extrapolation of Fig 4.1. It is somewhat larger than the intrinsic decay rate in n-heptane, a pure hydrocarbon of comparable size to the surfactant. The slope of the plot gives kd/ki = 500 M - 1 . Taking Chapter 4. Rate constants for Positronium reactions 81 kd ~8 x 1 0 1 0 M - 1 s - 1 from Mu studies[28] gives fc/ = 1.6 x 108-s-1 and a mean residence time of ~6ns. Since the mean lifetime of o-Ps is much less than 6 ns, o-Ps is pretty well confined to the first micelle it localizes at. When that contains at least one solute molecule even the resulting 'confined-diffusion' kinetics[39] still does not produce reaction to the extent of observing micelle-induced enhancement. o-Ps (at 6 ns in SHS) is confined more strongly than Mu (at 2 ns in SDDS[28]). 4.3.2 Reactivity of o-Ps Positronium evidently does not react rapidly with amides or diamides, nor with their thio counterparts. In this latter respect it also differs sharply from Mu which reacts at >1010 M - 1 s _ 1 with TA and T M T U , adding to the C to give a RS radical (Chapter 5). o-Ps also does not add to the benzene ring as rapidly as Mu does, as seen by the benzoic acid data of Table 4.5. Electron-withdrawing second substituents do not enhance the rate markedly so the sign of the Hammett a function could not be deduced. It was only in the case of nitrobenzoic acid that kp was much greater than 108 M - 1 5 _ 1 . Ps has already been established to react exceptionally with most nitro compounds[41]. Benzoquinone has previously been shown to react rapidly with o-Ps in water, kp = 1.37 x IO10 M - 1 ^ - 1 [40,41]. However, Table 4.4 and Figs 4.2 and 4.3 show that the rate constant changes with medium - being much faster in a hydrocarbon environment. Addition of micelles reduces the rate compared to that in pure water and this suggests the solute is present in the micelle boundary. A fall-off in kp (Table 4.4) is found when the benzoquinone concentration exceeds the cyclodextrin concentration. This suggests that caging decreases the Chapter 4. Rate constants for Positronium reactions 82 Nitrate in water and in micelle 30 25 20 15 \ 10 W 5 0 0 .2 .4 .6 .B 1 1.2 1.4 1.6 1.8 2 [NaNOj/M Figure 4.4: Plot of I3 against concentration of NaN03 in (a) water and (b) SHS micelle. effective concentration of the solute in a 'bunching' effect. 4.3.3 Yield of Ps Benzoquinone has a strong effect on I3 (the yield of o-Ps) as seen in Table 4.4; increasing it in n-heptane and decreasing it in water with SHS or cyclodextrin added. Nitrate as a solute also affects the yield in water, without reacting with Ps itself (see Table 4.6). Fig 4.4 shows the dependence of I 3 on [NOJ]. Such data are consistent with Ps being formed by intraspur processes (e+ + ej?)[42] since NO3 is a good electron scavenger. Chapter 4. Rate constants for Positronium reactions 83 4.3.4 kp compared with k# and k -o-Ps reactions are evidently much more limited than those of Mu, since it does not show abstraction or addition reactions. Its reactions proceed by 'pick-off' or 'spin-exchange' and are written as 2 7 4 ^ - o - Ps "S1 [pa _ S) 2 7 (4.5) where A, and Ac are the annihilation rates with solvent and in complex. Table 4.8 lists the published values of rate constants of H and e~q for some of the solutes studied here, when available, to compare with our values of kp and kjtf. Reactions with amides tends to proceed through an abstraction of H, and fast additions take place with C=C and C=S, in most cases. However, Ps, being a particle with no nucleus, does not appear to abstract nor to add. Also, it is not affected by a thio-substituted unsaturation center. 4.4 Conclusion Rate constants for the reaction of o-Ps with some amides, diamides, thiocarbonyls and some biologically important compounds are reported. The comparison of kp with kfj and k\f shows that Ps is not an isotope of H. Whenever the solute acts as an electron scavenger, the intensity of the o-Ps formed is reduced (e.g., ben-zoquinone in water and in micelle, NOj in water) showing that the positronium formation proceeds through a 'spur' model. The effect of added micelles on kp values showed that unlike Mu, reaction rates are not enhanced, despite its mean residence-time at a micelle being greater than Mu. The goal of this experiment was to cover most of the solutes studied with Mu to compare and contrast their Chapter 4. Rate constants for Positronium reactions 84 Table 4.8: Rate constants for the reaction of Ps compared with that of Mu, H, and e" . Solute kM/M-ls~l ke- /M^s-1 (°) kp/M-'s'1 Formamide < 105 NA 1.8xl07 < 108 Acetamide < 105 1.5xl05 4.5xl07 < 10s N-methylacetamide < 105 NA 2.3xl06 < 108 N,N-dimethylacetamide < 105 NA 9.0xl06 < 10s Guanidine 3xl05 1.2xl06 1.6xl08 < 10s Urea < 105 3xl04 3xl05 < 10s Tetramethylurea 4xl05 NA NA < 108 Thiourea 4xl07 6xl09 2.9xl09 < io 8 • Tetramethylthiourea 4xl01 0 NA NA < 109 Thioacetamide 3xl010 6xl09 NA < 108 Acetone 8.7xl07 2.6xl06 6.5xl09 < 108 Benzoquinone 2.5xl010 8.3xl09 3.5xl010 1.3xl010 K3Fe(CN)6] 2.0xl010 3.1xl09 1.9xl010 Cytosine 3xl09 9.2xl07 1.3x1010 < 109 Uracil 6xl09 3.8xl08 1.5xl010 < 109 Thymine 3xl09 5.7xl08 1.8xl010 < 109 (a) From ref [18] Chapter 4. Rate constants for Positronium reactions 85 reactions and formation. Some of the solutes could not be studied because of the limitation involved in the experiment which requires a high concentration of the solute in solution for o-Ps because of its very short lifetime. Chapter 5 Muonated Thiyl Radicals Studied by TF-/zSR and / i L C R 5.1 Introduction The biological significance and chemistry of sulfur-centered free radicals are dif-ferent in many aspects from those of carbon, oxygen or nitrogen-centered radicals and have been well documented elsewhere[43]. Attempts to observe and char-acterize radicals of the type RS in solution were not successful because of their rapid decay through combination reactions. A thiyl radical, RS, is not directly detectable by (normal) ESR because of its broad signal. However, it is now possible to detect these radicals by the spin trapping ESR technique[44]. The muon spin rotation technique has been shown to be a useful method to study muonium substituted free radicals in general, and recently, the muon-electron hyperfine coupling constants were reported for some pure compounds that form radicals of the type >CSMu or >C(Mu)S[45]. The limitation of the TF-/iSR technique is that it is restricted to the study of radicals formed in <10-9s. Also, it only gives information about the muon-electron hyperfine in-teraction and does not provide data on the other nuclear hyperfine parameters. But, the level crossing resonance (LCR) technique provides for the determination of these parameters. This technique allows one to observe the radicals formed up to 10_6s after implantation of a muon. The aim of the present study was to try to observe and characterize a thiyl 86 Chapter 5. Muonated Thiyl Radicals Studied by TF-fiSR and pLCR 87 radical in aqueous solution by determining its rate of formation, hyperfine param-eters, and radical yield. This was accomplished by using low and high transverse field //SR, and the /tLCR technique for aqueous solutions containing thioac-etamide and dimethylthioformamide (hereafter refered to as TA and DMTFA respectively). 5.2 Results The transverse-field //SR experiments were carried out on aqueous solutions con-taining 0.75 M TA and 0.4 M DMTFA. Figure 5.1 (and 2.8) shows the fast Fourier transform (FFT) spectra obtained at different magnetic fields (B) with the TF-//SR method. The fitted frequencies correspond to VD (the signal corresponding to diamagnetic muon compounds) and v\i & ^34 of the muonated radical. These latter signals are distributed on either side of up. The calculated A^ values (using the equation 2.8) are listed in Table 5.1. Table 5.1: A^ values derived from the fitted frequencies of TF-//SR measurements on TA and DMTFA Solution B / T vD /MHz u12 /MHz 1/34 /MHz A M /MHz 0.75 M TA 0.2998 40.62 149.2 239.4 388.6 0.3979 53.91 136.7 251.8 388.5 0.5996 81.25 111.1 277.3 388.6 0.4 M DMTFA 0.2998 40.62 169.3 264.3 433.6 0.3979 53.91 156.5 277.3 433.8 0.5016 67.97 143.1 290.8 433.9 Chapter 5. Muonated Thiyl Radicals Studied by TF-LISR and fiLCR 88 ( a ) O . E — 4 —* (-1 CD OW 3.r—» Cu t— B.HS—« <u> (-1 l . E — 4 o ( b ) d> 4 . E -o P-i 3 . K -t - i CD O (<=) O K — * * . » : — 4 cu o_ 3.r—« _cu e.i— « ° E o o B O l O O I S O eoo eoo 3 0 0 3 B O « O D Frequency (MHz) O BO lOO 1BO aoo aso SOO 3BO t o o Frequency (MHz) eo 1 0 0 iso BOO aso soo aso 4 0 0 Frequency (MHz) Figure 5.1: The F F T of TF-/iSR spectra of 0.4 M DMTFA in water at (a) 0.3 T, (b) 0.4 T and (c) 0.5 T. Chapter 5. Muonated Thiyl Radicals Studied by TF-fiSR and pLCR 89 Figures 5.2 and 5.3 give a selection of the LCR spectra obtained for aqueous solutions containing TA and DMTFA. Table 5.2 contains the LCR field, B^, and the calculated A p values using BR and gyromagnetic ratios in Eq(2.14). Table 5.3 records the fitted parameters of the LCR spectra obtained for these Table 5.2: The Hyperfine parameters Radical formed hfcc/MHz BR/T Thioacetamide A„=388.5(aq) Ap=52.1 1.8025 Dimethylthioformamide AM=433.8 A,v=28.6 1.5300 compounds at various concentrations in water. Table 5.4 lists the same for TA in water in the presence of micelles, and with benzene or styrene as competing solutes. The fourth column in these two tables gives Ampl/Aj,/ instead of just Ampl, in order to eliminate the effect of experimental asymmetry, A^f (which differs a bit for different beam periods and for different channels), on the am-plitude. The plots of Figures 5.4 & 5.5 give the variation of Ampl/A0y and linewidth, respectively, with concentration of the solute. Table 5.5 lists some compounds containing carbonyl or thiocarbonyl groups and their rate constants, 1CM , for reaction with Mu. Chapter 5. Muonated Thiyl Radicals Studied by TF-ftSR and pLCR 90 - . 0 0 2 5 -1 . 7 4 1 . 7 6 1 . 7 8 l . S 1 . B 2 1 . B 4 C O .ooe . 0 0 2 0 — . 0 0 2 5 — .ooo * J 1 1 L _ 1 1 . 7 4 1 . 7 8 1 . 7 8 l . B 1 . 8 3 1 . B 4 L o n g i t u d i n a l M a g n e t i c F i e l d / T Figure 5.2: The LCR spectra of (a) 0.4 mM, (b) 12.5 mM and (c) 50 mM TA in water. Chapter 5. Muonated Thiyl Radicals Studied by TF-ySR and fiLCR 91 (a) .002 -I .001 -.001 -.002 -.0025 (b) .002 .001 I < I + -.001 -.002 h -.0 25 -i 1 r-V - \\W 1 1 1 1 W • 1 1 1 1 I 1 1 . 1 1.48 1.5 1.52 1.54 1.56 1.58 _i i_ 1.48 1.5 1.52 1.54 1.56 1.58 Longitudinal Magnetic Field /T Figure 5.3: The LCR spectra of (a) 0.1 mM and (b) 1 mM DMTFA in water. Chapter 5. Muonated Thiyl Radicals Studied by TF-pSR and pLCR 92 Table 5.3: LCR positions, linewidths, and amplitudes for the radicals formed with TA and DMTFA in solutions. Sample I V T A B / mT Ampl/A 6 / 0.06mM TA/water 1.8031 10.0(2) 0.0196 0.1 mM TA/water 1.7994 10.0(2) 0.0151 0.4mM TA/water 1.8033 10.0(2) 0.0294 l.OmM TA/water 1.8019 9.9(2) 0.0238 4.0mM TA/water 1.7994 10.0(2) 0.0305 7.5mM TA/water 1.8015 9.8(1) 0.0264 12.5mM TA/water 1.8030 12.3(2) 0.0328 30mM TA/water 1.8028 16.2(4) 0.0270 50mM TA/water 1.8038 17.8(4) 0.0280 0.1M TA/water 1.8025 21.4(4) 0.0165 0.25M TA/water 1.8086 43.0(6) 0.0189 0.25M TA*/water 1.8021 44.0(6) 0.0174 0.75M TA/water 1.8000 >60 <0.0005 ~0.5mM TA/n-hex 1.8000 >50 <0.0005 O.lmM DMTFA/water 1.5340 8.4(3) 0.0060 l.OmM DMTFA/water 1.5280 6.0(2) 0.0084 •k : repeated with a recrystallized sample of TA. Chapter 5. Muonated Thiyl Radicals Studied by TF-pSR and fiLCR 93 Table 5.4: LCR positions, linewidths, and amplitudes for the radicals formed with thioacetamide in solutions containing micelles. Sample B( r e s)/ T A B / mT A m p / A t / 0.2mM TA/0.06mM CTAB 7.5mM TA/2.5mM DTAB 30mM TA/lOmM SOS 1.8039 1.8000 1.8000 7.6 >15.0 >15.0 0.0204 <0.0005 <0.0005 7.5mM TA/7.5mM Bz/DTAB 7.5mM TA/7.5mM Bz/DTAB 7.5mM Bz/2.5mM DTAB 1.8000 2.0852 2.0854 >15.0 5.91 6.53 <0.0005 0.0059 0.0370 7.5mM TA/7.5mM Sty/DTAB 7.5mM TA/7.5mM Sty/DTAB 7.5mM Sty/2.5mM DTAB 1.8000 0.9105 0.9107 >15.0 3.67 3.57 <0.0005 0.0080 0.0095 Table 5.5: The rate constants for the reaction of Mu with some carbonyl or thiocarbonyl compounds. Compounds kM/M-'s-1 Acetone 8.7xl07 Acetamide < 105 Thioacetamide 3xl01 0 Dimethylthioformamide 7xl01 0 Urea < 105 Thiourea 5xl07 Thiourea (pH=l) lxlO 9 Tetr amethylt hiourea 4xl01 0 Chapter 5. Muonated Thiyl Radicals Studied by TF-p,SR and fiLCR 94 Thioacetamide in water .035 .03 .025 < .02 \ .01 .005 0 6.E-5 2.E-4 7.E-4 .002 .005 .02 .05 .1 .2 [TA]/M Figure 5.4: The Ampl./Af,/ plotted against [TA] (log scale). Ampl./Af,/ is used instead of Ampl. in order to eliminate the effect of variation in experimental asymmetry, Abf on amplitude. Chapter 5. Muonated Thiyl Radicals Studied by TF-LISR and fj,LCR 95 Figure 5.5: The linewidth plotted against [TA] (log scale). The linewidth is the half-width-at-half-maximum (HWHM) of the fitted (Lorentzian) curve. • : aqueous solutions and X : micelle solution. Chapter 5. Muonated Thiyl Radicals Studied by TF-pSR and pLCR 96 5.3 Discussion 5.3.1 Hyperfine coupling constants The A M values obtained here for TA and DMTFA in aqueous solution are 388.5(5) and 433.8(5) MHz respectively. These radicals, formed by the addition of Mu to a thiocarbonyl group, have a much higher A M value than those corresponding to an addition to a carbonyl group. The high A M value is explained by Mu adding to the carbon rather than to the sulfur of thiocarbonyl in TA and DMTFA. S S • II I C H 3 — C — NH 2 + Mu —» C H 3 — C — NH 2 Mu (5.1) s s • II I H — C — N(CH 3) 2 + M u ^ H — C — N(CH 3) 2 I Mu (5.2) When addition of Mu to the sulfur of TA leads to a >C-SMu radical, the hy-perfine coupling constant is expected to be about 25 to 30 MHz, a value derived from the radicals of the type C-SH[46], which would agree with the Au value for acetone (where, addition of Mu occurs at the oxygen of the carbonyl group), where A^ = 22.6 MHz. The values of A^ obtained here in aqueous solutions are very much different from those reported recently[45] for pure liquid (DMTFA) or non-aqueous solution (TA in an aprotic solvent), indicating that there is a considerable solvent shift. Some solutes (e.g., acetone[17]) are affected by the Chapter 5. Muonated Thiyl Radicals Studied by TF-LISR and yLCR 97 polarity of the solvent and their A M values shift by up to 15%, while other so-lutes (e.g., benzene) shows little, if any, solvent affect on A^. In the case of Mu adding to the carbon of TA's thiocarbonyl group, the Mu would not un-dergo any hydrogen-bonding and the polarizability of the sufur could lead to a 3e~ bonding dipolar interaction of the sulfur-centered radical with water[43]. The latter would reduce the availability of the electron density for the coupling, which would lead to a reduction in the observed aqueous A M value. The ESR spectra of RS radicals in solution are not detectable because of the extensive line broadening arising from the near degeneracy of the singly-occupied-molecular-orbital (SOMO) and the other TT orbitals around sulfur. The same reason could explain the non-detection of /zSR lines[45]. But in aqueous solution the hydrogen bonding could lift the degeneracy and make the observation of the lines possible. The derealization of the unpaired electron would also raise the energy of the SOMO with respect to the other sulfur 7r-level. Sulfur has been proven to be more effective at delocalizing unpaired spin than oxygen[47]. The A p value of 52.1 MHz for the methyl protons of TA was determined from the LCR position, A^ value and the magnetogyric ratios using eq (5.4). This value is close to that obtained for the methyl protons of acetone where the location for Mu addition is the oxygen of the carbonyl group. Because the position of these protons with respect to the unpaired electron is /3 in the case of acetone and 7 in TA, one might at first think the latter A M should be much smaller. However, the high value for these 7- protons can be rationalized on the basis of the structure of this sulfur-centered radical in which the sulfur is /? to the methyl carbon[48]. The LCR spectra obtained for DMTFA (Fig. 5.3) could be due to either H or N. Assuming it is due to H, the A p value for the C-H proton of DMTFA was calculated from the level crossing resonance position to Chapter 5. Muonated Thiyl Radicals Studied by TF-fiSR and pLCR 98 be 147.6 MHz; and it is ruled out for the following reason: the LCR frequency and hence the theoretical linewidth calculated using these hyperfine parameters give a higher value (16.0 mT) than the experimental value (6.5 mT). But the other possible assignment for this resonance i.e., due to the N of-N(CH 3) 2 , gives a value for (28.6 MHz) that agrees with reported values[49] for /?-N, and also the observed linewidth (6.5 mT) is greater than the theoretical linewidth (3.0 mT). Some experiments to detect the muonated DMTFA radical by spin-trapping with dimethylbutadiene (DMBD) were reported[50], but none were observed. The authors attribute this to one of the following possible reasons: (i) a of <109 M _ 1 5 _ 1 , (ii) the radical reacting with substrate at < 10 - 7 M - 1 s - 1 , and (iii) that Mu is not formed at all. The rate constant of DMTFA with Mu in water is measured to be a diffusion-limited rate, 7 x 1010 M - 1 $ - 1 . So the non-observance of the DMBD-DMTFA radical might be due to the fact that the fast reacting DMTFA could form the radicals and relax immediately, because the low concentration of DMBD could not trap the radicals fast enough. Even in aqueous solution, the relaxation effects are large enough that the LCR spectrum is not observed when the solute concentration is greater than 10 mM. 5.3.2 L C R Parameters Section 2.3.1. gives the level crossing resonance condition and the different pa-rameters involved in the data analysis. The level crossing resonance condition is seen from Fig. 2.11b to be !/* = (!- AK± (5.3) Chapter 5. Muonated Thiyl Radicals Studied by TF-fiSR and yLCR 99 and the states related by A(m^+mjt) = 0 cross energy at a resonant field, 1 (A„ - A, Al-2MA\\ where M = m e + mM + Etm^. The energy gap (or the LCR frequency) becomes, where c = [I*(I*+1) - M(M-1)] 1 / 2, (I* is the nuclear spin). On each of these level crossing resonances a fraction of the muon polarization is expected to oscillate at frequency vr (actually, vf). The depolarization amplitude at the LCR position is given by, which is a sum of Lorentzian lines with full width at half maximum. A B | t = 2[,; + ( A 0 / 2 , ) T / ' { 5 7 ) The N in equation 5.6 is given by N = 4ITi(2Ifc-fl) i.e., the total number of spin states for the e-^-n system. (For methyl protons, EIfc = | and N = 32, corresponding to the 3 equivalent protons of the C H 3 - group, i.e.,, the ^ term in equation 5.6 must be replaced by 2x^ i.e.,, ^ .) The depolarization amplitude is a function of LCR frequency, vT, and a decay constant A (which can be included to eliminate the effect due to any relaxation process removing the muon out of the LC resonant state). The /zLCR signal was fitted for the position, linewidth and amplitude as a difference of Lorentzian lines (arising from the modulation field). These parameters are discussed separately. Chapter 5. Muonated Thiyl Radicals Studied by TF-pSR and pLCR 100 5.3.2.1 L C R Amplitude Aqueous solutions of TA in the concentration range 6 x 10 - 5 to 7.5 x 10_1 M were used for this LCR study. LCR amplitudes increased with increase in solute concentration up to ~10 - 3 M as in systems studied before[33,51] (where ampli-tude increases up to a certain concentration and then levelled off), suggesting that there is some process that reduces the radical yield at the lower end of the concentration range (longer Mu lifetimes). In the particular case of TA, the am-plitude starts to decrease at concentrations >10 -2 M showing that there is some process that removes the muonated radical from the LCR state within the earlier lifetime of Mu. The concentration effect up to 0.05 M in the amplitude plot in Fig. 5.4 can be explained (as in the case of acrylamide) by TA scavenging Mu to form the radical (see section 5.3.3). At concentrations >0.05 M however, there is a decrease in the yield. We attribute this either to a chemical reaction involving the decay of the muonated radical, thereby removing a part of the muon polarization in the resonant state, or due to an electron spin exchange process (with Mu) to produce various effects on both the amplitude and the linewidth (depending on the magnitude of vr). It could be a combination of both processes to give the observed overall effect. The effect of a chemical reaction rate (\chem) and a (longitudinal) residual relaxation rate (A°o n s) on the amplitude and the linewidth can be incorporated into the expressions for these parameters (Eqs. 5.6 and 5.7) by replacing the term (A0/2rr)2 by (Ai/27r)2, in which Ax is a function of A0, Khem and A°o n 5. The effect of electron spin exchange (also known as Heisenberg spin exchange, HSE) should be treated differently for various reasons. The observed trend on the amplitude can be explained by assuming (i) a constant contribution Chapter 5. Muonated Thiyl Radicals Studied by TF-pSR and fiLCR 101 of A°onfl and (ii) a chemical reaction which does not affect the amplitude and width until ~ 10 - 2 M, and thereafter affects it to a larger extent. Based on this assumption Ai is calculated as reported in Table 5.6. The aqueous solutions containing 10 - 3 and 10 - 4 M DMTFA give LCR signals with different amplitudes i.e., lower for the lower concentration. 5.3.2.2 L C R Linewidth The linewidth of the LCR signals observed for various concentrations of TA in water is constant up to 10 - 2 M, then it increases as shown in Fig 5.5. This figure gives the concentration dependence of half-width-at-half-maximum (HWHM) of the LCR signal. At concentrations >10-2 M, when the amplitude starts to de-crease, linewidth increases rapidly. The theoretical linewidth, however, is smaller than this constant linewidth showing that there is a small amount of constant contribution to the A term from the non-resonant spin-states to the LCR state (ie- A?onfl). The A value for the relaxation processes is calculated (A2 in Table 5.6) from the experimental linewidth (which has the A term) and the theoretical linewidth using equation 5.6 in which Ao is replaced by A2 (see footnotes of Table 5.6). The uncertainty involved in this calculation arises from the LCR frequency used. Since there are three equivalent protons in TA, the total nuclear spin operator K(=5Z/fcIfc) has two values, | and |, with the degeneracy ratio 1:2. So, the LCR signal obtained will be due to the four lines arising from these two K values (total number of degenerate lines is 2Ifc). Theoretical values corresponding to these four lines are given in Table 5.7. The LCR frequencies of these lines are different because of the different values of c which appears in eq 5.4. Chapter 5. Muonated Thiyl Radicals Studied by TF-pSR and pLCR 102 Table 5.6: LCR linewidths, amplitudes and calculated relaxation parameters for the radicals formed with TA in water. [TA]/mM A B / mT Ampl/A 6 / A 2 f 0.06 10.0(2) 0.0196 2.23 2.23 0.151 0.1 10.0(2) 0.0151 2.22 2.23 0.120 0.4 10.0(2) 0.0294 2.23 2.23 0.227 1.0 9.9(2) 0.0238 2.23 2.23 0.192 4.0 10.0(2) 0.0305 2.23 2.23 0.235 7.5 9.8(1) 0.0264 2.23 2.23 0.251 12.5 12.3(2) 0.0328 3.04 3.06 0.383 [TA]/mM A B / mT Ampl/Ai,/ V A 2 + A3* 12.5 12.3(2) 0.0328 3.04 3.06 0.0 30 16.2(4) 0.0270 3.46 4.33 0.44 50 17.8(4) 0.0280 3.38 4.84 0.80 100 21.4(4) 0.0165 4.24 5.96 0.82 250 43.0(6) 0.0189 4.32 12.1 6.0 250(p) 44.0(6) 0.0174 4.53 12.7 5.8 750 >60.0 <0.006 - - -• : Ai is calculated using APZ = £™plR and AP* = and which gives (V27T) 2 - ! K 2 t : A2 is calculated using equation 5.7 in which A0 is replaced by A2, and then rearranging to give (A2/2TT)2 = (Mii^zlnii _ „2 ) % : when Aj = A2, A3 should arise from a term that is given in { } minus 1 in the following equation (from ref [52]). AP 2.(A7i t^) 2 = \ . "* » { 1 + T - ^ ' — } • Substituting for APZ and A B 2 and rearranging, A3 = [ - ^ • A B ' ' ^ ' ]. Chapter 5. Muonated Thiyl Radicals Studied by TF-fiSR and p.LCR 103 Table 5.7: The calculated LCR frequencies and HWHM for the three equivalent protons in TA for the transition K,m* to K,m*-1. K,m* c i/ r/MHz HWHM/ mT 3 3 2' 2 V3" 0.3471 3.8 3 1 2' 2 2 0.4008 4.4 3 1 2' 2 v/S 0.3471 3.8 1 1 2' 2 1 0.2004 2.3 The sum of these Lorentzians will, to a reasonable accuracy, give a single Lorentzian[26]. Though the fitting does not suffer any deviation due to the combination of these four lines, the relaxation effects alter the linewidth very much due to the different magnitudes of these frequencies. For LCR spectra of aqueous solutions of DMTFA, the experimental linewidth (6.0 mT) is also greater than the theoretical value as in the case of TA. The theoretical value was calculated assuming the resonance is due to the nitrogen of H-(Mu)C(N(CH3)2)-S. The other possibility for this resonance being due to H of H-C(Mu)-S could be ruled out for the reasons given above (sec 5.2.1). 5.3.2.3 L C R Position The resonance fields (BR in Table 5.3) are not affected significantly over a large range of concentration for TA. Fig 5.2 shows that the LCR's of TA at differ-ent concentrations correspond to the same resonance position though they have changing amplitude and linewidths. The resonance position for the DMTFA Chapter 5. Muonated Thiyl Radicals Studied by TF-^SR and uLCR 104 solutions seems to have shifted slightly, but this is based on only two concentra-tions. 5.3.3 Radical Yield The muon depolarization amplitude depends on the amount of muonated radical formed, i. e.,, on the radical yield, P,R. The depolarization amplitude, APZ, should be equal to the amplitude of the LCR signal only if P ^ and the experimental asymmetry are both unity. But the experimental asymmetry, Abj, given by Afc/=(N/—N0)/(N/-|-ND), where the N/ and Nj, are the number of muon counts in the forward and backward counters respectively, is far from unity under all experimental conditions. In fact, it is determined to be ~0.20(3) for different longitudinal fields in different apparati and on different beamlines. Also, the radical yield cannot be unity for any medium for which there is a non-zero diamagnetic yield (P.o). However, we can compute PR as follows. The fitted value of LCR amplitude can be related to the depolarization amplitude and experimental asymmetry: Assuming the signal remains Lorentzian even if there are some relaxation effects (chemical reactions), the radical yield can be calculated from Different lines (from various K values) would be affected to a different extent by the relaxation processes. Assuming that there is only chemical reaction (such as free radical decay), PR can be calculated using the above equation. It will not be correct, however, Ampl = APzAbfPR (5.8) Ampl.(AB)2(lti - 7p)2 (5.9) Chapter 5. Muonated Thiyl Radicals Studied by TF-pSR and pLCR 105 if there is any contribution from the HSE relaxation to the broadened linewidth. Theoretical work by Heming et a/[52], predicts a constant value for the product (APZ)(AB)2 when there is only chemical reaction and only the contribution from HSE relaxation could increase this value. Our PR values obtained for acrylamide in water and benzene in n-hexane show that the product (APZ)(AB)2 increases (because of the increasing PR) even when there is no HSE relaxation contribution. The constant linewidth obtained for a wide range of concentrations suggests there is no relaxation effect on the linewidth. Based on this fact, the PR value can be calculated for the concentration range where there is no change in the linewidth (and a steady increase in amplitude) with a reasonable accuracy. When the linewidth increases, the PR value calculated will have a larger error. Even though the amplitude decreases at high concentrations of TA, the increase in linewidth could counter-balance this effect leading to a correct value of P H , if the line shape is maintained as a Lorentzian. The plot of P H VS concentration of TA is shown in Fig 5.6. The PR values calculated for the concentration range 10 - 5 to 10 - 2 M can be compared with that for acrylamide in water[33]. In aqueous solutions (for which P ^ = 0.62) the only possible precursor for the formation of radicals is thermalized muonium. The value of PR for 0.0075 M TA in water (i.e.,, 0.25) is the maximum value prior to the steep increase. The processes by which muonium is lost in the 10 -9s timescale include any chemical reaction of Mu with track species like e~g and OH radical in competition with TA. The PR values for TA at higher concentrations are very high due to the large increase in the linewidth, and hence they are not included in Table 5.6. Any PR value in excess of 0.38 (1 - PD in water) is evidently coupled to the line broadening relaxation effects and we can use this excess value to calculate a Chapter 5. Muonated Thiyl Radicals Studied by TF-fiSR and fiLCR 106 Thioacetamide in water .45 I 1 1 1 1 .4 -.35 -T3 * - 3 • l - H (0 .15 r i I 1 l l : l 0 .0025 .005 .0075 .01 .0125 [TA]/M Figure 5.6: Radical yield, PR plotted against [TA]. Chapter 5. Muonated Thiyl Radicals Studied by TF-fiSR and fiLCR 107 relaxation parameter which would include A c / t e m , X°ONG and A e x (based on ref[52]). This parameter can be derived from A3 of Table 5.6. 5.3.4 Relaxation effects The theoretically calculated values of linewidth and amplitude are different from the experimental values. This difference could be used to determine the effect of the processes taking place in the systems under study. If we assume A0 is the only contribution to A the rate of any process which could take muon amplitude out of the LCR) then the theoretical linewidth and the experimental linewidth will be the same. The additional terms in A could be due to a combination of spin relaxation processes and chemical reactions. The increase in linewidth for the different solutions of TA indicates that there is some effect due to A in this system. Recent work by Heming et a/[52] gives an empirically derived linear relation applicable for the LCR signals affected by chemical and HSE relaxation. APz.{ABthf = V l (l + A e ; I. (5.10) The treatment given is applicable to our system because the LCR frequency is very much higher than Ao (in frquency units). The two processes (exchange relaxation and chemical reaction) have different effects on the LCR signal in contrast to the TF-//SR, where they are indistinguishable. The depolarization amplitude is usually decreased by chemical reaction, but increased by a small exchange rate (depending on the magnitude of the exchange rate compared with the LCR frequency). The linewidth increases monotonically with increasing A as given by equation 5.7 with A in place of Ao. Two different calculations (see footnotes of Table 5.6) are done here. First Chapter 5. Muonated Thiyl Radicals Studied by TF-pSR and pLCR 108 assuming that there is no HSE relaxation, Ax and A2 are calculated from the APZ, Ampl, Abf (for Ai), vT and AB (for A2). Another assumption involved here is taken from the fact that the acrylamide PR value levelled off with a P H of 0.38, i.e.,, the P H at the maximum amplitude is taken as 0.38. Second, one assumes that the contribution from both relaxation processes (Eq. 5.9) is used to get the ratio of [. A"—1. The former calculation indicates that there is a constant contribution to A in the lower concentration range, which can be appropriately attributed to A°onfl rather than \chem (because it does not vary with various concentrations). Table 5.6 lists the experimental values of linewidth and amplitude along with the calculated P H and A values. The P H values are calculated using equation 5.9. In the calculation of Ax and A 2, A0 is replaced by these in equations 5.5 and 5.6 to include the relaxation processes. A3 is the term \Q+\xchcm in equation 5.10. These observations could be explained by a process involving a spin exchange interaction in the range where the linewidth increases ( A 3 ^ 0). In that case the concentration dependence of the relaxation process can be explained. It may arise because the sulfur-centered radical, which is different from a carbon-centered radical, has the ability to form a three electron bond with another molecule containing sulfur, oxygen, or nitrogen[43]. 5.3.5 Effect of micelles The addition of micelles to an aqueous solution containing solutes will result in localization of the solutes either inside the micelle, or at the interface of the micelle, depending on the aqueous solubility of the solute. TA, being more soluble in water than in hydrocarbon, is likely to be concentrated at the interface of the micelle. In this case its bulk aqueous concentration is different (lower) than its local (micellar) concentration. Chapter 5. Muonated Thiyl Radicals Studied by TF-pSR and pLCR 109 The LCR of TA was not seen with DTAB and SOS micelles, yet when TA was added to a solution containing micelle and another radical-forming solute (like benzene or styrene), the amplitude of that solute was considerably decreased due to the presence of TA (compare lines 5 and 6 of Table 5.3). The absence of LCR spectra of TA in DTAB or SOS micelles might be due to high local concentrations which could have broadened the line and merged it with the background. When a large micelle like CTAB was used (where the CMC is small, ~ 10~5 M), and with Ns=3 (as always), the local and the bulk concentrations were reduced and the LCR was seen. The amplitude fits well with the data for aqueous solutions without micelle (compare line 1 of Table 5.3 with line 1 of Table 5.4). But the linewidth is higher than expected, showing that the local concentration is more than the bulk and that the relaxation effects are larger than in water. 5.3.6 Rate constants The reaction rates of Mu with many organic compounds can be compared with those of H atom in order to determine kinetic isotope effects. But some of the muonated radicals observed apparently do not have H atom analogues, showing that the reactions may be of a different type. These two compounds, TA and DMTFA, containing the C=S group, are observed to show Mu adding to the C to give an S radical. H apparently does not do this. The rate constants also give some idea about the type of reaction. As seen in Table 5.5, addition reactions are faster than abstractions, and the addition of Mu to a carbonyl group is much slower than the addition to a thiocarbonyl group. The latter is clear from the comparison of acetone with TA. Comparison of thiourea with TA suggests that the site of addition also changes the rate considerably. In thiourea, the smaller rate could indicate one of two Chapter 5. Muonated Thiyl Radicals Studied by TF-fiSR and pLCR 110 things: thiourea may go through a slow addition reaction as in the case of acetone, or there may be a combination of H abstraction from -SH and addition to C=N (due to the different resonant structures possible for thiourea - section 3.3.1). The muonated radical formed with thiourea, if any, could be observed by LCR only by using 1 3 C enriched thiourea because of the otherwise weak coupling of NH2 protons. It should be possible to observe the N of NH 2 if R-S is formed (as in the case of DMTFA) but this is questionable because of its slow reaction. The solubility of thiourea is not enough to get the nanosecond timescale required for carrying out a TF-//SR measurement, so no radicals could be seen by TF-//SR and therefore could not be located for /xLCR. The high rate constant reported for the H atom reaction with thiourea could possibly be due to abstraction from -SH (which is ~ 109 M - 1 5 _ 1 ) because, in the solution at pH 1, thiourea predominantly exists as a thiol form (C-SH, which is known to undergo abstraction reaction) rather than in thiocarbonyl form (C=S, which can undergo only addition). The rate constants for TA, tetramethylthiourea (TMTU) and DMTFA are of the same order, showing that the reaction is an addition of Mu to C of the C=S giving rise to S. Again, the LCR of the radical formed with tetramethylthiourea was not looked for since there is no magnetic nucleus nearby to transfer muon polarization. On the other hand, its A M was seen by the TF-/xSR method to give a pair of radical frequencies with A M = 322 MHz, a value which can be compared with that of TA and DMTFA (Table 5.1). 5.4 Conclusion Addition of muonium across the thiocarbonyl group evidently leads to the for-mation of R-S free radicals. The first observation of thiyl radicals in the liquid Chapter 5. Muonated Thiyl Radicals Studied by TF-pSR and pLCR 111 phase seems to have been the very recent TF-//SR observation of thiyl radicals in pure DMTFA and TA (reported to be in aprotic solvent)[45]. In that study the formation mechanism of the observed muonated radical could have been a direct hot atom reaction or an ionic insertion of the charged muon. No ESR studies seem to have found such radicals when using normal free-radical initiators in solution. In the present studies, analogous R-S free radicals have been observed fol-lowing the addition of thermalized muonium atoms to thiocarbonyls in dilute aqueous solution. These radicals were observed using the LCR technique - a method which also provides the proton and/or nitrogen hyperfine coupling con-stants in the various radicals. The fitted parameters (line width and amplitude) of the LCR spectra for these sulfur-centered radicals, at various concentrations in water, show a trend which is similar to that observed for carbon-centered radicals (e.g., acrylamide in water[33] and benzene in n-hexane[51]) in the lower concentration range. At higher concentrations relaxation effects contribute to the linewidth and amplitude to change them drastically. The LCR position was also used to calculate the hyperfine coupling constants of the equivalent pro-tons/nitrogens in resonance, which otherwise are not available from ESR. Chapter 6 Muonated Radicals of Uracil and its Derivatives 6.1 Introduction DNA and RNA bases have been studied extensively in the past to arrive at the role of these bases in biological reactions. The site of attack of H atoms or OH radicals is of interest in order to find out the properties of the radicals formed with these bases. It is shown in Chapter 3 that the reactions of muonium with the components of DNA and RNA, i.e.,. the bases, the sugar units and the phosphate group, have different rate constants. Also, the reaction toward a base (mainly, addition across C=C) seemed to be much more favourable than the abstraction of a hydrogen atom from the sugar unit. This implies, essentially, that the backbone sugar-phosphate unit is of less importance in governing the biological reactions and that the interior bases are responsible for most of the reactions. This motivates one to study, in detail, the reaction of Mu with these bases in order to understand the mechanism of strand breaks and base release, since these are reported to be mainly induced by hydrogen atoms [53]. ESR studies give some information about the structure and properties of the free radicals through the coupling constants. But emphasis is given, in most of the cases, to those systems having well defined spectra. For example, though thymine and uracil are of equal significance, thymine was given preference because of its well defined signals[54]. One difference between DNA and RNA is the sugar 112 Chapter 6. Muonated Radicals of Uracil and its Derivatives 113 unit, 2-deoxyribose in DNA and ribose in RNA; but, in addition to this, there is a change in the base sequence which arises from the replacement of thymine by uracil in RNA, while the other three bases, adenine, guanine and cytosine are the same. 6.2 Results The muon(-electron) hyperfine coupling constants, A M , for muonated uracil rad-icals were obtained from transverse field x^SR measurements on aqueous solution containing 1.0 M uracil (at pH~10, in order to increase the solubility). As be-fore, the A M values were calculated by summing the frequencies of the observed peaks centered on vry. Although the FFT spectra are not as clear as one would like (not enough statistics due to experimental time constraints), A M values for both uracil and thiouracil in water can be estimated. Uracil produced two sets of radical frequencies arising from Mu addition to the C(5) and C(6) carbons of the ring. The A„ values were determined to be 379.1 MHz and 424.0 MHz, respectively, obtained from data at two different magnetic fields, 0.15 T and 0.45 T. For thymine, a similar measurement at 1.0 M was not possible because of its low solubility (and hence the slow formation of the radical) and because of the limitation placed by the transverse field /xSR technique which only allows the study of radicals formed in <10~9 s. An aqueous solution containing thiouracil (1.5 M) was also used for this measurement to compare with that of uracil; and it gave an A M value of 351.0 MHz. The muon level crossing resonance technique, described in Section 2.3.1, has a wide observational time-window that allows the resonance to be observed even in Chapter 6. Muonated Radicals of Uracil and its Derivatives 114 dilute solutions where the radicals are formed only slowly (<10-6s). These pLCR experiments were carried out on aqueous solutions containing 7.5 mM uracil(Fig 6.1), thymine(Fig 6.2) and thiouracil. Uracil was also used to study the effect of pH and the effect of added micelles. The fitted parameters of the observed LCR spectra are listed in Table 6.1. When benzene was a co-solute present in the micelle, the level crossing resonance of the benzene adduct was not seen (i.e.,. its amplitude was too small for the computer to fit). The amplitude of uracil was not altered in the presence of benzene, but the width was reduced. These results are recorded in Table 6.2. Table 6.1: LCR parameters and calculated P # values for the radicals formed in uracil and thymine in solutions. Sample B f l / T A B / mT A m p / A t / P H 7.5 mM Uracil/water 7.5 mM Uracil/water 1.6799 1.8247 7.20(2) 10.7(2) 0.0184 0.0122 0.113 0.097 7.5 mM Uracil/water 7.5 mM Uracil/2.5 mM DTAB 7.5 mM Uracil/2.5 mM DTAB 2.3678 1.6820 2.3683 4.80(1) 8.2(2) 5.3(1) 0.0184 0.0146 0.0164 0.120 0.116 0.131 7.5 mM Uracil at pH=l 7.5 mM Uracil at pH=l 1.6798 2.3684 6.9(2) 4.4(1) 0.0184 0.0218 0.105 0.122 7.5 mM Uracil at pH=10 7.5 mM Uracil at pH=10 1.6807 2.3681 8.3(2) 6.7(1) 0.0166 0.0162 0.136 0.207 7.5 mM Thymine/water 1.6928 30.0(10) 0.0151 -Chapter 6. Muonated Radicals of Uracil and its Derivatives 115 (cOb, to* . 0 0 3 - e C — - O O B h — . 0 0 3 -— . 0 0 1 - " ' _ l I 1 L l . O Z 1 . 0 3 1 . 9 4 l . a S l . O O 1 . B 7 l O O l . O B 1 . 7 1 . 7 1 1 . T 2 ( b ) Longitudinal Magnetic Field, T . 0 0 3 . O O S B -. 0 0 2 . O O I B I « a ; .001 t-I B.E-4 — 6 . E - 4 -— . 0 0 1 — . 0 0 1 0 1 . T 6 1 . 7 7 1 . 7 8 1 . 7 0 1 . 8 l . O l 1 . 8 2 1 . 8 3 1 . 8 4 1 . 8 6 1 . 8 8 1 . 8 7 ( c ) Longitudinal Magnetic Field, T Figure 6.1: The LCR spectra of 7.5 mM uracil in water centered at (a) 1.68 T, (b) 1.82 T, and (c) 2.37 T. Chapter 6. Muonated Radicals of Uracil and its Derivatives 116 (a) .003 -.001 -- . 0 0 1 5 I 1 1 1 1 L _ 1 1.62 1.64 1.66 1.68 1.7 1.72 1.74 1.76 Long i tud ina l Magne t i c F ie ld , T (b) .002 I 1 1 1 1 1 1 1 1 1 1 .0015 -.001 -5 .E -4 - " II " 1 1 , , , , U ' ' ' 1 1 -i n " + - 5 . E - 4 - " < - .001 -- . 0 0 1 5 -_ .002 I 1 ' 1 1 1 1 1 1 1 1 2.3 2.31 2.33 2.35 2.37 2.39 2.4 2.41 Figure 6.2: The LCR spectra of 7.5 mM thymine in water (a) centered at 1.68 T, and (b) the region 2.3 to 2.4 T where the resonance is expected if thymine forms a radical similar to uracil. Chapter 6. Muonated Radicals of Uracil and its Derivatives 117 Table 6.2: LCR parameters for the radicals formed with uracil (7.5 mM) in DTAB micelle (2.5 mM) in the presence and absence of benzene (7.5 mM). Sample B H / T A B / mT Amp/A o / Uracil/DTAB Uracil + Benzene/DTAB Uracil + Benzene/DTAB Benzene/DTAB 1.6820 1.6818 2.0821 2.0914 8.2(2) 6.6(2) <2.0(10) 12.3(1) 0.0146 0.0150 <0.0003 0.0357 For thymine, the level crossing resonances were searched for over the ranges 1.5 to 2.0 T and 2.2 to 2.5 T, but no strong resonances were found. For the regions where the two resonances were observed for uracil 1 (namely 1.68 and 2.37 T), thymine showed the results given in Fig 6.2. For thiouracil, these two regions were scanned but both resonances were absent. 6.3 Discussion Different techniques, including photolysis and pulse radiolysis, have been used to generate free radicals by addition of H and OH to DNA and RNA bases, which were analysed using electron paramagnetic resonance and UV absorption spectra[56,55]. In most cases the calculation of the yield was indirect as the predictions had to be made based on the nature of the product of the reaction which the radical underwent. Our study, however, allows a direct calculation of the yield of different free radical adducts. Deviations may also be due to the replacement of H by Mu. 1The third resonance at 1.82 T was observed towards the end of this study. Therefore, that region was not looked at for the studies with micelles, pH dependence, or for the search with thymine and thiouracil. Chapter 6. Muonated Radicals of Uracil and its Derivatives 118 6.3.1 Hyperfine Parameters The hyperfine coupling constants were derived in two steps. Firstly, the radi-cal frequencies obtained from the fast Fourier transform of the transverse field //SR spectra give the magnitude of the muon-electron coupling constant, A M , by the sum of the precession frequencies. Secondly, the magnetic field position (BR) at which the longitudinal muon polarization is transferred to the other nu-cleus/nuclei in the system, which gives the value of |A M -A n |, by use of equation 6.1 Ifi ~ In 7e(-A/i — A n ) which is used to arrive at the nuclear-electron coupling of those nuclei. The radicals involved are likely to be: (6.1) 0 II HN CH Mu HN 0 o N I H 0 II N I H C < H Mu H HN + 0-0 II N I H C < Mu H because Mu is expected to add to >C=C< much faster than other reactions. The LCR spectra which were observed for the muonated uracil radical could arise from muon polarization transfer to the following nuclei: (the two pairs of radical frequencies arise from the radicals formed by the addition of Mu to C(5) and C(6) positions in uracil.) Chapter 6. Muonated Radicals of Uracil and its Derivatives 119 C(5) adduct C(6) adduct 1 a proton 1 a proton 2 0 protons (the CH and NH) 1 0 proton 1 a nitrogen 2 (3 nitrogens The lower value of 379.1 MHz is assigned to the C(5) adduct and the other (424.0 MHz) to the C(6) adduct. This assignment is based on the comparison of the magnitude of the reduced muon hyperfine coupling constant, A'^, with the proton coupling constant, AH, when Mu is added in each position. [A^ is related to AM by the magnetic moments of muon and proton, namely, A M = (PHIPH) where Pn/v-H = 3.18.] The A' values are found to be substantially greater than the AH values, in this case A'^/AH is 1.33 for the C(5) adduct and 1.10 for the C(6) adduct. The computer fitted values of the LCR field, BR, are used to calculate the proton/nitrogen coupling constants using the equation 6.1. The three resonances observed for uracil could arise from both the C(5) and C(6) radicals, each having the possibility of resulting from the polarization transfer to either an a or a (3 proton or to a nitrogen. All the possible values are calculated and the resonances are assigned (see Section 6.5) by taking into account the following facts: (i) the AH0 is always negative and the AHP is positive, and (ii) the theoretical linewidth of the LCR, when calculated using these hyperfine coupling constants (i.e.,. from VR in eq. 5.3), should always be < to the observed linewidth. The proton coupling constants derived for Ana are closer to the value reported for H atom data, but those for AH$ are lower than the values for the corresponding H atom adducts, showing that Mu addition affects the structure of the radical in such a way that the coupling between the unpaired e~ and the f3-rl is reduced. Chapter 6. Muonated Radicals of Uracil and its Derivatives 120 Table 6.3: Hyperfine coupling constants for uracil. Sample A„ /MHz AH / M H Z BR/T vr /MHz ABth/ mT A B o 6 , / m T C(5) (aH) 379.1 -60.9 2.3680 0.174 4.05 4.5(1) C(5) (/5H) 379.1 +66.9 1.6798 0.269 6.01 7.2(2) C(6) (0E) 424.0 +84.9 1.8247 0.352 7.74 10.7(1) This is reasonable because the replacement of H by Mu will reduce the overlap of the /?-H with TT orbitals due to the larger effective size of Mu and longer bond length for C-Mu compared with C-H. For thymine (same as uracil except for a C(5) - C H 3 group in the place of H), the resonance observed is attributed to the methyl protons of the C(6) adduct. The addition to C(5) will be restricted for steric reasons. Also, in the C(5) adduct there is only one a proton, which typically gives a narrow resonance, no /? proton (other than the NH proton), and the NH /3-proton is not expected to give a broad resonance. Methyl protons, usually give a broad resonance because of the overlap of four lines arising from three equivalent protons. Assuming the proton coupling constant to be 56 MHz (as in acetone, for example[17]), a value for A^ was calculated to be 371 MHz. (It was reported in an earlier indirect study on dilute solution of thymine by a low field transverse field /JSR technique that the radical frequencies and the hyperfine parameters were consistent with A M ~ 350 MHz[57].) When these parameters are used to calculate the theoretical linewidth it is determined to be 8.3 mT (using c=\/Z). This can be compared with the observed width of 15 mT. Line broadening by a factor of ~2 is found. We attribute it to relaxation effects due to either chemical reaction or Ti electron relaxation processes [58]. Chapter 6. Muonated Radicals of Uracil and its Derivatives 121 6.3.2 L C R parameters and Radical Yield The fitted parameters for the observed LCR spectra are listed in Table 6.1. The concentration dependence of the LCR amplitude and linewidth are not given importance here, in contrast to the case of thiocarbonyl compounds (Chapter 5), for the aim is to calculate only relative yields of the two radicals (C(5) and C(6) adducts of uracil) formed, and to study their variation due to different effects like pH change and addition of micelles. The treatment explained in section 5.3.3 for the radical yield calculation is used to get the PR values for these two radicals. The P R values calculated are about the same for the C(5) (0.115) and C(6) (0.095) adducts, as seen in Table 6.1, implying that muonium does not have preference (significantly) to one of the sites. This is opposed to H atom addition where addition is favoured at C(5) over C(6) in the case of uracil by a factor of 2.3, and attributed to the high electron density at C(5)[43]. The sum of the P R values for the two radicals formed with uracil equals ~0.22. This suggests that P R has not reached its maximum value at this concentration of 7.5 mM because in aqueous solutions the total muonium yield was found to be 0.38[33]. The lower value obtained for uracil shows that some Mu atoms are lost by other processes over a period ~25 ns, i.e.,. during the time taken for the formation of radicals in 7.5 mM uracil, for which = 6 x 109 M _ 1 5 _ 1 (Chapter 3). 6.3.3 Effect of p H The level crossing resonances for muonated uracil radicals were obtained at two different pH values. The resonances observed in the low pH (~1.5) solution have a narrow linewidth with not much variation in the amplitude (see Table 6.1), which implies the P R values (calculated using equation 5.8) are lower than those Chapter 6. Muonated Radicals of Uracil and its Derivatives 122 in neutral solution. On the other hand, the high pH (~10) solution resulted in resonances with broad linewidths, showing that there exists some type of relax-ation which broadens the linewidth. This could be due to the formation of a dimer at high pH (as reported for uracil at pH 10[59]). Also, it is theoretically predicted that any irreversible chemical reaction which takes the muonated rad-ical out of the LCR spin state will broaden the linewidth with a reduction in the depolarization amplitude[52], as is the case here. A comparison of the linewidths of these LCR spectra is shown in Fig 6.3. 6.3.4 Effect of micelles The addition of 2.5 mM DTAB micelles to the solution containing 7.5 mM uracil altered the LCR as shown in Fig 6.4. In the presence of micelles, solubilized solutes are located either inside or outside the micellar core depending upon the low or high polarity of the solute. Therefore, the bulk concentration is different from the local concentration; and, since the solute to micelle ratio is kept at 3 always, there will be at least one solute per micelle in ~ 90% of the micelles. Even though the encounter probability is increased due to the larger size of the micelle (radius = 20 A), the number of species available for encounter is actually decreased for diffusion limited rates, because of the clustering of the solutes around or in micelles. A combination of these two effects has to be considered to account for the observed values. The fitted LCR parameters (see Tables 6.1 and 6.2) show that the linewidths are increased and amplitudes decreased slightly in the presence of micelles. Line broadening could be due to the interaction of a muonated radical with another uracil molecule in the near vicinity. Chapter 6. Muonated Radicals of Uracil and its Derivatives 123 (a) . (b) IM IM ISt Vfl IB IM 11 L71 in Longitudinal Magnetic Field, T J006 I i i 1 1 i IM IM IM iKI L68 L89 11 L71 L72 Longitudinal Magnetic Field, T • i i i i i i Figure 6.3: LCR's of 7.5 mM uracil in water at (a) pH = 1 and (b) pH = 10. Chapter 6. Muonated Radicals of Uracil and its Derivatives 124 Figure 6.4: LCR spectra of 7.5 mM uracil in 2.5 mM DTAB micelles with and without benzene, (a) uracil/DTAB, (b) uracil+benzene/DTAB, Uracil reso-nance, (c) benzene/DTAB and (d) uracil+benzene/DTAB, benzene resonance. Chapter 6. Muonated Radicals of Uracil and its Derivatives 125 6.4 Conclusion The results obtained in this study indicate that Mu adds to uracil at both C(5) and C(6) positions with almost equal probability. The values calculated for these two adducts are 0.12 and 0.10, which add to give a total PR of 0.22. This is only ~60% of the free muonium yield[14]. In the presence of micelles, the PR values are slightly higher. Addition of Mu to thymine at the C(6) position was deduced from the observation of an LCR spectrum due to polarization transfer to C(5)-CH3 protons. The non-observation of LCR spectra for thiouracil, at those regions where uracil spectra were observed, indicates that the addition to C=C does not predominate in thiouracil as it does in uracil (because the AM values of uracil and thiouracil are close to each other). Addition at other sites, particularly C=S, will give LCR spectra at different field positions and subsume LCR spectra due to C=C addition. 6.5 'Appendix to chapter 6': Assignment of L C R spectra of uracil The addition of H to uracil formed C(5) and C(6) adducts, which are character-ized by ESR studies [55] as shown in Figure 6.5. These parameters are used to calculate the possible A ,^ values for muonated radicals. The values derived here are incorporated with the transverse field //SR measurements to arrive at the re-ported muon-electron hyperfine coupling constants listed in Table 6.3. Equations used for these calculations are: Chapter 6. Muonated Radicals of Uracil and its Derivatives 126 ABth — 2\v1 + (AQ /27T) 2 ] 1 / 2 (6.4) 7/i ~7n where c=l for one equivalent nucleus. The LCR field, BR is used to calculate lAp — An\; the A n (or AH, for a proton) values reported by ESR are used to calculate the possible A^ values assuming that every resonance could arise from either C(5) adduct (HQ or H^) or C(6) adduct (HQ or H^). The twelve different possible values derived for A^ arising from three resonances are used along with the appropriate A// value to calculate the theoretical linewidth for the LCR. Observed linewidths are always larger than the theoretical values and hence a number of combinations of A M and AH which give a larger theoretical value than the observed one are ruled out. Also, the comparison of the magnitude of the reduced muon hyperfine coupling constant, A^, with the proton coupling constant, AH, when Mu is added in respective position, rules out some A^ values because the A^ values are always found to be substantially greater than the AH values. This comparison is useful also for assigningthe lower A M value for the C(5) adduct. Table 6.4 gives the possible A M values and the corresponding vr and ABJ/J values. Chapter 6. Muonated Radicals of Uracil and its Derivatives 127 Q, 89.9 MHz 1 H7 H H«—54.9 MHz Hi * 0 H -52.6 MHz H 5 MHz Figure 6.5: C(5) and C(6) adducts formed by H atom addition to uracil and the kH values (from ESR data, ref [55]) Table 6.4: A M values for muonated uracil radical calculated using BR and A# (from ESR) BR / T Nucleus A M /MHz vT A B t / l /mT 1.680 C(5) a-H 259.5* 0.145 3.5 (AB o 6 s = C(5) /?-H 402.0| 0.384 8.4 7.0 mT) C(6) a-H 257.2* • 0.150 3.6 C(6) /?-H 433.6| 0.550 12.1 1.825 C(5) a-H 286.5 0.147 3.5 (AB o b s= C(5) 0-H 429.0 0.377 8.3 10.7 mT) C(6) a-H 284.2* 0.152 3.6 C(6) /3-H 460.6J 0.547 11.9 2.368 C(5) a-H 387.4 0.154 3.6 (AB o t s = C(5) p-E 529.9J 0.359 7.9 4.5 mT) C(6) a-H 385.1* 0.159 3.8 C(6) /9-H 561.5J 0.514 11.2 * : these values are ruled out because they were lower than the reduced muon-electron coupling constant. % : these values are eliminated because they give a theoretical linewidth which is higher than the observed values. Note : the A^ values derived (form /?-H) for the resonance at 1.680 T are slightly higher because the reduced coupling for /3-H with Mu adduct. But the assigned A^ values give linewidths lower than the experimental linewidths. 128 Summary Some of the interesting findings from the work presented in this thesis include the following. 1. The observation and characterization of thiyl radicals (RS) by fj.SK and piLCR which are otherwise not seen directly. 2. The prediction of preferable addition site for Mu (as compared with H) in the biologically important bases uracil and thymine. The presence of the C H 3 has a much bigger effect on Mu than H. 3. The determination of rate constants for Mu reactions with various solutes in the presence and absence of micelles, and calculation of enhancement factor which has a wide range of 0.5 - 20000. 4. Kinetic isotope effect calculated for various solutes ranging from 0.01 to 750, and the possibility of different reaction pathway for some solutes at various pH's. 5. The limited number of reactions for Ps compared to Mu. Ps is not an isotope of H. Bibliography [1] S. H. Neddermeyer and C. D. Anderson, Phys. Rev., 54, 88 (1938). [2] V. W. Hughes, D. W. McColm, K. Ziock and R. Prepost, Phys. Rev., A l , 595 (1970). [3] (a). J. H. Brewer, K. M. Crowe, F. N. Gygax and A. Schenck, in Muon Physics, eds. V. W. Hughes and C. S. Wu, Academic Press, New York (1975). (b). J. H. Brewer and K. M. Crowe, Ann. Rev. Nucl. Part. Sci., 28, 239 (1978). [4] D. C. Walker, J. Phys. Chem., 85, 3960 (1981). [5] R. L. Garwin, L. M. Lederman and M. Weinrich, Phys. Rev., 105, 1415 (1957). [6] J. L. Friedman and V. L. Telegdi, Phys. Rev., 105,1681 (1957). [7] C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes and R. P. Hudson, Phys. Rev., 105, 1413 (1957). [8] V. W. Hughes, D. W. McColm, K. Ziock and R. Prepost, Phys. Rev. Lett, 5, 63 (1960). [9] (a) P. W. Percival, E. Roduner, H. Fischer, M. Camani, F. N. Gygax and A. Schenck, Chem. Phys. Lett, 47, 11 (1977). (b) E. Roduner, Progress in Reaction Kinetics, 14, 1 (1986). 129 Bibliography 130 [10] R. W. Fessenden and R. H. Schuler, J. Phys. Chem., 43 2704 (1964). [11] A. Abragam, C. R. Acad. Sc. Paris, 299, series II, 3, 559 (1984). [12] T. G. Eck, L. L. Foldy, and H. Wieder, Phys. Rev. Lett, 10, 239 (1963). [13] H. J. Ache, Positronium and muonium chemistry, Advances in Chemistry Series, 175, 1 (1979). [14] D. C. Walker, Muon and muonium chemistry, Cambridge University Press, 1983. [15] J. H. Fendler, Membrane mimetic chemistry Wiley-Interscience, New York, 1982. [16] M. Gratzel, J. K. Thomas and L. K. Patterson, Chem. Phys. Lett, 29, 393, (1974). [17] K. Venkateswaran, M. V. Barnabas, Z. Wu, J. M. Stadlbauer, B. W. Ng and D. C. Walker, Chem. Phys. Lett, 143, 313 (1988). [18] G. V. Buxton, C. L. Greenstock, W. P. Helma and A. B. Ross. In Critical review of rate constants for reactions of hydrated electrons, hydrogen atoms, and hydroxyl radicals in aqueous solutions. NSRDS-NBS, 1988. [19] D. M. Garner, Ph. D. Thesis, University of British Columbia, 1979. [20] D. G. Fleming, D. M. Garner, L. C. Vaz, D. C. Walker, J. H. Brewer and K. M. Crowe, (Muonium chemistry - a review) in Positronium and muonium chemistry, Advances in Chemistry Series 175, 279 (1979). [21] P. W. Percival, H. Fischer, M. Camani, F. N. Gygax, W. Ruegg, A. Schenck, H. Schilling, H. Graf, Chem. Phys. Lett, 39, 33 (1976). Bibliography 131 [22] E. Roduner, P. W. Percival, D. G. Fleming, J. Hochmann and H. Fischer, Chem. Phys. Lett, 57, 37 (1978). [23] E. Roduner and H. Fischer, Chem. Phys., 54, 261 (1981). [24] J. H. Brewer, K. M. Crowe, F. N. Gygax and A. Schenck, in Muon Physics, vol 3 ed. V. W. Hughes and C. S. Wu, New York, Academic Press, pp 3-139. [25] R. F. Kiefl, Hyperfine Interactions, 32, 707 (1986). [26] M. Heming, E. Roduner, B. D. Patterson, W. Odermatt, J. Schneider, Hp. Baumeler, H. Keller and I. M. Savic, Chem. Phys. Lett, 128, 100, (1986). [27] P. Kirkegaard and M. Eldrup, Compt Phys. Comm., 7, 401 (1974) [28] K. Venkateswaran, M. V. Barnabas, B. W. Ng and D. C. Walker, Can. J. Chem., 66, 1979 (1988). [29] J. M. Stadlbauer, B. W. Ng, D. C. Walker, Y. C. Jean and Y. Ito, Can. J. Chem., 59, 3261 (1981). [30] P. W. Percival, E. Roduner and H. Fischer, (Radiation chemistry and reac-tion kinetics of muonium in liquids) in Advances in Chemistry Series 175, 335 (1979). [31] K. Kalyanasundaram, Chem. Soc. Rev., 7, 453 (1978). [32] P. Neta, Chem. Rev., 73, 533 (1972). [33] K. Venkateswaran, M. V. Barnabas, R. F. Kiefl, J. M. Stadlbauer and D. C. Walker, J. Phys. Chem., 93, 388 (1989). [34] R. A. Witter and P. Neta, J. Org. Chem., 38, 484 (1973). Bibliography 132 [35] P. Neta and R. H. Schuler, Radiat. Res., 47, 612 (1971). [36] L. Melander and W. H. Saunders, Reaction rates of isotonic molecules, (Wi-ley Interscience, New York) 1980 [37] E. Roduner and H. Fischer, Hyperfine Interactions, 6, 413 (1979) [38] M. V. Barnabas, K. Venkateswaran and D. C. Walker, Can. J. Chem., 67, 120 (1989). [39] M. Tachiya in Kinetics of Non-homogeneous Processes, Editor G. R. Free-man, Chapter 11, p575, Wiley-Interscience, 1987. [40] Y. C. Jean and H. J. Ache, J. Amer. Chem. Soc, 99, 7504 (1977). [41] Y. C. Jean and H. J. Ache, J. Phys. Chem., 81, 2093 (1977). o [42] O. E. Mogensen, J. Chem. Phys., 60, 998 (1974). [43] see for example: C. von Sonntag, The Chemical Basis of Radiation Biology, Ch 11, Taylor and Francis, London, 1987. [44] H. Taniguchi, J. Phys. Chem., 88, 6245 (1984). [45] C. J. Rhodes, M. C. R. Symons and E. Roduner, J. C. S. Chem. Comm., 3 (1988). [46] M. C. R. Symons, J. C. S. Perkins II, 1618 (1974). [47] I. Biddies, A. Hudson and J. T. Wiffen, Tetrahedran, 28, 867 (1972). [48] P. J. Krusic and J. K. Kochi, J. Amer. Chem. Soc, 93, 846 (1971). [49] C. A. McDowell and W. C. Lin, D201-1 .... Bibliography 133 [50] E. Roduner, Hyperfine Interactions, 32, 741 (1986). [51] D. C. Walker, M. V. Barnabas and K. Venkateswaran, Radiat. Phys. Chem., in press. [52] M. Heming, E. Roduner, I. D. Reid, P. W. F. Louwrier, J. W. Schneider, H. Keller, W. Odermatt, B. D. Patterson, H. Simmler, B. Pumpin and I. M. Savic, Chem. Phys., 129, 335 (1989). [53] S. Das, D. J. Deeble and C. von Sonntag, Z. Natureforsch, 40C, 292 (1985). [54] M. C. R. Symons, Chemical and Biological aspects of ESR Spectroscopy, Van Nostrand Reinhold, Workingham, 1978. [55] H. M. Novais and S. Steenken, J. Amer. Chem. Soc, 108, 1 (1986). [56] D. J. Deeble and C. von Sonntag, Z. Natureforsch, 40C, 925, (1985). [57] C. Bucci, G. Guidi, G. M. De'munari, M. Manfredi, P. Podini, R. Tedeschi, P. R. Crippa and A. Vecli, Chem. Phys. Lett, 57 41, (1978). [58] K. Venkateswaran, M. V. Barnabas and D. C. Walker, J. Phys. Chem. in press. [59] P. C. Shragge, A. J. Varghese and J. W. Hunt, J. C. S. Chem. Comm., 736, (1974). Appendix Collaborative work already published All the work presented through chapter 6 are experiments of my own undertak-ing. In this appendix, however, various other projects are presented which were of a collaborative nature. The major investigator was Dr. K. Venkateswaran and the other collaborators included Dr. J. M. Stadlbauer, Dr. B. W. Ng and Mr. Z. Wu. Most of this work has now been published in various journals as listed below and copies of reprints/preprints are attached. These projects are included as a part of my thesis in this appendix because of my full involvement in the experiments and in the data analysis. Due to the nature of the TRIUMF beam-time system - one in which each group of experimenters is given on average one week of experimental time every 4 months - all projects must be done in close collaboration, with 4 to 6 people involved. 1. Muonium Atoms Compared to Hydrogen Atoms and Hydrated Electrons Through Reactions with Nitrous Oxide and 2-propanol. K.Venkateswaran, M. V. Barnabas, Z. Wu, and D. C. Walker, Radiat. Phys. Chem., 32, 65-9 (1988). 2. Micelle-induced Enhancement of the Reactivity of Muonium Atoms in Di-lute Aqueous Solution. K. Venkateswaran, M. V. Barnabas, Z. Wu, J. M. Stadlbauer, B. W. Ng and D. C. Walker, Chem. Phys. Lett, US(3), 313-6 134 Appendix . Collaborative work already published 135 (1988). 3. A Level-Crossing-Resonance Study of Muonated Free-Radical Formation in Solutions of Acetone in Hexane, Water and Dilute Micelles. K. Venkateswaran, R. F. Kiefl, M. V. Barnabas, Z. Wu, J. M. Stadlbauer, B. W. Ng and D. C. Walker, Chem. Phys. Lett., 145(4), 289-93 (1988). 4. Effect of Added Micelles on the Reaction between Muonium and Ionic Solutes in Water. K. Venkateswaran, M. V. Barnabas, B. W. Ng, and D. C. Walker, Can. J. Chem., 66, 1979 (1988). 5. Muonium and Free Radical Yields as Determined by the Muon-Level-Crossing Resonance Technique in Aqueous and Micelle Solutions of Acry-lamide. K. Venkateswaran, M. V. Barnabas, R.F.Kiefl, J. M. Stadlbauer, and D. C. Walker, J. Phys. Chem. 93, 388 (1989). 6. Muon level crossing resonance study of radical formation in allylbenzene, styrene and toluene. K. Venkateswaran, M. V. Barnabas and D. C. Walker, Chem. Phys. - in press. 7. Line broadening of level crossing resonance spectra of muonated free radi-cals. K. Venkateswaran, M. V. Barnabas and D. C. Walker, J. Phys. Chem. - in press. 8. Muonated Cyclohexadienyl Radicals Observed by Level Crossing Reso-nance in Dilute Solutions of Benzene in Hexane Subjected to Muon-Irradiation. D. C. Walker, M. V. Barnabas and K. Venkateswaran, Radiat. Phys. Chem. - in press. Appendix . Collaborative work already published 136 Radio: Phys. Chem Vol. 32. No. 1. pp. 65-69. 1988 0146-5724:88 $3.00 + 0.00 In: J. Radio: Appl. Inurum Par: C Copyright T 1988 Pergamon Journals Ltd Printed in Great Britain. All rights reserved MUONIUM ATOMS COMPARED TO HYDROGEN ATOMS AND HYDRATED ELECTRONS THROUGH REACTIONS WITH NITROUS OXIDE AND 2-PROPANOL KRISHNAN VENKATESWARAN, M A R Y BARNABAS. ZHENNAN W U and DAVID C. WALKER Chemistry Department and TRIUMF, University of British Columbia. Vancouver. British Columbia, Canada V6T IY6 {Received 30 April 1987) Abstract—N,0 and 2-propanol constitute a pair of solutes with completely opposite relative reactivities towards H and <•,",. It is observed in the present study that muonium atoms (Mu) fall directly between H and efor both of these reactions. Aspects of mass-dependent processes and kinetic isotope effects are discussed with regard to these findings INTRODUCTION Mixtures of N 2 0 and 2-propanol can be used to make a chemical distinction between the conjugate acid-base pair H and because of the following rate constants."1 f- + N;0 —N:+0-. *, = 8.7 x l O ' M - ' s - ' H + N . O - ^ N j + OH. k2 - 10 ! M-'s- ' e.-, + (CH3) :CHOH-^P], Aj« l O ' M - ' s - 1 H + (CH,) :CHOH ~ H : + (CH,) :COH, kt = l x 10' M - ' s - ' . Thus, a measurement of the N , / H : product ratio from a range of N20,'2-propanol mixtures proves definitively whether H or is the reactive agent involved. Such competition played a pivotal role in the 1960's in showing that ?M was the principal reducing precursor in the radiation chemistry of water,'11 and in other processes.'31 The purpose of the present study is lo see where muonium lies in this respect. Muonium (chemical symbol Mu) is the neutral atom having a short-lived muon as nucleus and an electron in a Is orbital almost identical lo that in H. For this reason Mu is expected to emulate a super-light hydrogen isotope, with just one ninth the mass of 'H. But kinetic isotope effects can occasionally make it look more like than H 4 . EXPERIMENTAL Muonium atoms form at the end of some muon tracks when energetic positive muons (from pion decays) are injected into water. They are observed in transverse magnetic fields by the muon spin rotation technique (JJSR).'*' Chemical reaction rate constants of Mu are evaluated from the spin precession signals as the relaxation constant (/.) of the "triplet" muonium signal oscillating at the Larmor frequency of 1.39 MHz G " 1 . A MINUIT r-minimization fit of the muon lifetime histogram to equation (1). A', = A !0exp(-r/T) x [1 +AM exp(-/./)cos(coMl + <pM) + ADcos(ujDt + (pD)] + B (1) gives /. as one of the fitted parameters. (In equation (1). A', is the number of counts in the histogram corresponding to time /; N0 a normalization factor; T the mean muon lifetime; AM and AD, o>„ and coD, and d>M and <pD are the asymmetries, frequencies and initial phases of the "muonium atoms" and "dia-magnetic muon components", respectively; and B is the time-independent background signal.) /. is the parameter of interest in this study. A representative raw fiSR spectrum is shown as Fig. 1(a) for a 2-propanol solution. The "asymmetry" plot after computer fitting to equation (1) is shown as Fig. 1(b) once the exp( —//r) and B terms have been removed. In the example shown /. =0.5 x 10* s"1. These experiments were performed on the M20A beam channel at the TRIUMF cyclotron in Vancouver using ~ 30 MeV "backward" muons. Solutions were contained in SO ml glass cells sealed with septa and deoxygenated by bubbling with pure helium through fine hypodermic needles. Three muon lifetime histograms of ~I07 events each were col-lected for every solution, fitted to equation (I) sep-arately, and the values of x averaged. Since only one muon exists in solution at a time (/JSR is a single-event nuclear counting technique), these are ideal pseudo-first kinetic conditions. A chemical reaction, such as Mu + R H -* R, transforms the magnetic state 65 Appendix . Collaborative work already published 66 KMSHSAN VENKATESWARAN ei al. I ! I ! 1 | ! | | L. 0 05 i 0 i5 2 0 25 10 ' 0 a 5 Time 'n fj& (1.25 ns/Din) 1 lb) 1 1 l l i ! ! '"A ' 1 1 •if' i i i i i 0 05 iC '5 ?0 25 IG !5 « G <: ; 5C Time m JIS I K 25 ns/Din) Fig I. (a) The raw histogram for 0.2! M 2-propano! in pure water, given as counts against muon lifetime with a packing factor of 10 bins per datum point, each bin being 1.25 ns There was a transverse magnetic field of 8 G . The muonium precession signal at 10.8 M H z is observed as the superposed wiggle. It has a relaxation constant of ~0.5 p s " 1 . The solid line is a computer fit to equation (1). (b) The histogram of (a) is presented as a normalized "asymmetry" plot, after removal of the intrinsic muon decay term expf - r / r ) and the background B. of the muon from a free paramagnetic Mu species to a diamagnetic state (MuH) with a resulting relaxation in the Mu signal, A is measured as a function of solute concentration [S], then the bimolecular muonium rate constant (ku) is evaluated from equation (2), kmm&-X,)HS) (2) where Xc is the "background" value of X of the medium for [5] = 0. As the pSR technique utilizes the spontaneous decay of the muon to observe the pre-cession frequencies and amplitudes, it follows that >.must be of the order of the muon lifetime (2.2 ps on average). This restricts /.measurements to the narrow pSR time window of ~0.2 to ~4 ps. There-fore, the solute concentration is the experimental factor that is varied until A " 1 falls in this range. As a result, concentrations range from I to 10"'M, depending on kM. All solutions were made from triply distilled water, for which ;.„ •= (2.5 ± 0.5) x 10ss"'. The 2-propanol was BDH Aristar grade, and three sources of N : 0 were used in separate runs (from Matheson, Linde and from Aldrich) without further purification. Polyethylene(23)oxide iauryl ether (pEO), or cetyl-Appendix . Collaborative work already published C o m p a r i s o n o f M u l o H a t o m s a n d < • „ trimethylammonium bromide (CTAB). or sodium dodecylsulphaie (SDDS) surfactants were used for the micelle solutions after recrystaliization. pEO has a critical micelle concentration (CMC) of 6 x 10"' M and an aggregation number (A) of 50. For CTAB. CMC = 9.2 x 10"4M and A = 80: for SDDS, CMC = 8.1 x 10"'M and A =62. RESULTS AND DISCISSION (a) Muonium rate constants Table 1 contains the observed rate constant results. The most accurate range for /. is (I to 2) x I0 ls"'. so that once the appropriate solute concentration has been found in this regime, kM can be determined from a single concentration measurement. It transpired that saturating water with N : 0 by bubbling the gas through a hypodermic needle at 1 atm pressure gave /. in this best range. The value of <rM for N.O was then calculated from the published solubility of N.O (3.4 x 10"5M per torr at 22;C)."' For 2-propanol, concentrations up to 0.7 M were needed. Because of the very high concentrations of 2-propanol used to bring /. into the observable range, it is possible that traces of impurities in the alcohol could be involved. Carbonyl groups are reactive toward Mu. For instance, propanone (acetone) reacts with Mu at k„ = 8.7 x 107 M " 1 s~ " " so that if present at 0.0105 M in the 0.70 M of 2-propanol (1.5%) it could account entirely for the observed /.. Any such reactive impurity would render the (1.3 +0.2) x 10'M _ 's~' value of kM for 2-propanol as an upper limit. To test this possibility, surfactants were added above their CMC to diluted solutions of the same 2-propanol stock. The results are given in Table 2. It can be seen that with three solutes per micelle on average. /. becomes (1 to 2) x 10' s~' at 2-propanol concentrations of only 10- 4-10 _ 5M. Therefore the effective kM has increased to ~ 3 x 10 l oM-'s"'. (This is not due to reaction of Mu with the sur-factants, since their solutions were used as /.„ in equation (2).) Such lO'-fold enhancements for 2-propanol are Tabic 1. Muonium atom rate measurement results Solute Cone (M) A (I0S- 1) k'u (M" ' s - ' l 0 0.25 ± 0.05 — 2-propanol 0.21 0 52 ± 0 07 1.3 x 10* 2-propanol 0.70 1.16 ± 0 10 1.3 « 10* N,0 2.6 x 10' : 1.95 ± 0.20 6.5 x 10' 'Calculated from equation (2). 67 being analyzed in terms of confined-diffusion kinetics and reduced activation barriers in the lipid phase."" But the result is important here because ku (effective) ~3x 10"'M"'s _ l is about the maximum possible value, corresponding closely to the diffusion-limited k for Mu encountering micelles'" Therefore it could not have arisen from an impurity of the 2-propanol present at a few per cent. If it were acetone at 1.5% then the effective kM would have had to be 5x IO' : M"'s" ' , which is impossibly high. An equally persuasive point is the fact that the vast majority of CTAB micelles would not have contained an impurity molecule. Consequently, on localizing at such micelles. Mu would have been inhibited in its decay. In effect, these few results with added micelles show that the kM data in Table 1 for 2-propanol do not stem from its impurities. (b) Comparison of Mu ttith H and For both of these particular solutes, muonium's reactivity is seen to fall squarely between H and e;„. With N ; 0 , the order of increasing rate is H. Mu and ; while for 2-propanol it is e^, Mu and H. The ratio of rale constants and the expected H ; / N . prod-uct ratios are recorded in Table 3. The 2-propanol reaction is almost certainly a H-atom abstraction reaction, whereas in the case of N,0 it could be a dissociative attachment or a simple association reaction. There are many factors to consider when com-paring H. Mu and f , " q . First is the quantum-mechanical tunneling efficiency, then the zero-point energy factor, followed by the charge and electron-donating effects, then the relative diffusion co-efficients, the mean velocity ratio of the panicles, and finally their relative solvation energies, reduction potentials, and hydrogen bonding.'1' Ordinary kinetic isotope effect should be particu-larly pronounced in the comparison of Mu with H (because of their nine-fold mass difference for atoms of almost exactly the same size and binding energy) Table 3. Ratio of rate constants (*t»^,,/*,;^,il. and ™<'° of expected Nj/H. product yields from an cquimolar mixture of NjO/2-propano). for H. Mu and f^' H Mu '« *lS;0|/*,l.^oPi 1.4 x 10"> 50 >8 x 10' Expected H ./NJ 7 x i o - 0020 <1.2 x 10 * Relative masses 1836 207 1 'Ratios of k'% and expected product yields are based on the published"' values of k„ and and on A M determined here 'For Mu, H : will be MuH. Table 2. Effect* of added mice!lei on A M for 2-propanol Solute (cone., M) Micelle (cone.. M) /. <!0*|-') «•„ ( M ' s - ' l 0 CTAB (2.5 x 10' ) 0.35 2-propanol (7.5 x IO'1) CTAB (2.5 K 10') 2.20 2.5 x 10" 0 pEO (1.2 x 10"*) 0.25 2-propanol (3 84 x 10 ') pEO (1.2 x 10') 1.70 3 7 x IO'0 * « M calculated from equation (2). « M - (I - «.)/12-propanoll. where *. is taken u the A in the above table with micelle present but with |5] - 0. Appendix . Collaborative work already published KRISHNAN VENKATESWARAN et al 68 For the abstraclion reaclion involving 2-propanol there is undoubtedly a substantial activation barrier: indeed, Mu studies have revealed an Arrhenius ac-tivation energy of ~33kJmol"' for the analogous reaction with formate."' Quantum mechanical tun-neling through this barrier would strongly favour Mu over H, because of its much lower mass. In contrast, zero-point energy considerations favour H. Normally one thinks of zero-point motion favouring the lighter isotope, bul this is not so when reactions of free atoms are involved, for then the isolopic difference in vibrational rotational energy appears only with the activated complex and products. So the activation barrier to reaction is larger for Mu than for H. In the case of 2-propanol. this zero-point energy factor evidently wins easily over tunneling since kHlkM - 10:, at least for room temperature. [In the gas phase. Mu wins due to tunneling for the reaction towards F : and CI,. but zero-point energy wins at high temperatures for reaction with H ; .] '" The comparison of Mu with H is particularly interesting for the N : 0 reaction because only two other reactions have shown kM!kHi> 1 in solution, and both are "curiosities'". One is reaction of NO,". where triplet Mu is seen to decay at t M = 1.5 x 10* M"' s"', some 150 limes faster than H. Its mech-anism remains obscure, and it is possible that Mu undergoes an electron spin exchange converting to the "singlet" state by forming a relatively long-lived paramagnetic intermediate (MuNO; ). This would make the observation peculiar to pSR and not com-parable to H-atom data, where such depolarizations do not register as "reaction" decay channels. The second example with * M S> kH is acetone. Mu is known to "add" across this carbonyl n-bond. be-cause the resulting muonated free radical has been observed by pSR in acetone-water mixtures using both transverse-fields and level-crossing-resonance methods."0' It is not at all clear why H does not undergo that particular addition reaction (kM!kH = 40 for acetone) because in general H-atom additions to double bonds occur with no kinetic isotope effect. The possibility exists that Mu adds across the n system of NjO (and with much greater propensity than H) to give a free radical rather than giving N ; by following the dissociative attachment ofc^, (which derives enormous exothermicity from the solvation energy of 0 „ ) . Regardless of the mechanism, how-ever, this will be a useful muonium reaction in practice for comparison purposes because of the case of bubbling a solution with N 2 0 in situ, then flushing it out with an inert gas. Neither of these reactants are involved at the diffusion-controlled limit where H, Mu and all approach the same value of - 2 K I0 '°M-' This common limit shows that diffusion is governed by solvent properties—such as the displacement mobility of solvent cavities or vacancies—rather than mean thermal velocity, even for atoms as small as M u and H. Most addition reactions occur at this limit. Hammett p parameters have been determined for addition reactions just below k,e.n] and. again, place Mu directly between H and P.",. In the case of addition to the benzene ring for substituted benzoic acids, the electron-donating effects of the second substituents have yielded the following p parameters: for H - 0.18;"" for Mu + 0.23,";' and-for e + 4.8."" H differs from Mu and in being electrophilic rather than nucleophilic. but Muis numerically much closer to H than to e~q. Mu does not show partial charged character nor undergo long-range electron or muon transfer, because primary kinetic salt effcel studies based on the Bronsted-Bjerrum treatment showed it to be neutral at its point of reaction with charged solutes."41 What about the relative reducing powers of H. Mu and f ,"Q? The standard reduction potentials of H and f,"„ are known to be —2.1 V and ^ -2.67 V."5' but that of Mu has not yet been deduced. Based on Pf«,i + <,("p.,-'5Mu:.!i it is probably more negative than H because the bond energy of Mu. should be smaller than that of H;. and the free energy of solvation of u " is less negative than that of H * . There are two factors in this latter point: first the zero-point motion of, p" is higher, and secondly, unlike H * , p' is distinguishable from the hydrons hydronium species around it that constitute the hydrogen-bonded structure of water. It would not be surprising then to find the reduction potential of Mu to fall between H and e,~ . Acknowledgements—We g r e a t l y a p p r e c i a t e t h e a s s i s t a n c e o f o t h e r m e m b e r s o f t h e T R I U M F /JSR g r o u p , p a r t i c u l a r l y J . M. S t a d l b a u e r a n d B . W . N g . a n d f i n a n c i a l s u p p o r t b y N S E R C o f C a n a d a . REFERENCES 1. NSRDS—SBS Compilations 43 and 51. 2. (a) J. K Thomas, in Advances in Radiation Chemistry (Edited by M. Burton and J L Magee) Vol. I. p 103 Wiley. New York. 1969; (b) E. J. Han and M. Anbar. The Hydrated Electron. Wiley; New York. 1970 3. D. C. Walker. Can. J. Chem 1966. 44, 2226. 4 Y. C. Jean. J. H. Brewer. D. G Fleming. D. M. Garner. R.J Mikula. L C. Vaz and D: C. Walker. Chem. Phvs. Lett. 1978. 57. 293. 5 (a) J. N. Brewer and K. M Crowe. Ann. Ret. Sue!. Part Sci. 1978. 28, 239; (b) A. Schenck. Muon Spin Rotation Spectroscopy. Adam Hilger. 1985. 6. Handbook of Chemistry and Physics. 59th edn. BI43. CRC, Boca Raton. Fla., 1978. 7. D. C. Walker, Muon and Muonium Chemistry. Cam-bridge University Press. 1983. 8. (a) K. Venkateswaran and DC. Walker. Hyper. Inter. 1986. 32. 559, (b) K. Venkateswaran et al. To be published. 9. (a) D. M. Gamer, D. G. Fleming and J. H. Brewer. Chem Phys. Lett. 1978, 55, 163; (b) I. D. Reid. D. M. Garner. Y. L. Lee. M Senba. D. J. Arseneau and D. G. Fleming. J Chem. Phys. 1987. 86, 5578. 10. (a) A. Hill. M. C. R. Symons. S. F. J. Cox. R. de Renzi. Appendix . Collaborative work already published Comparison of Mu to H atoms and C A. Scott. C Bucci and A. Vecli. J. Chem. Soc. Faraday Trans. I 1985. 81, 433; (b) E. Roduner. Radial. Phys. Chem. 1986. 28, 75; (c) M. Heming. E. Roduner. B D. Patterson. W. Odermatt, J Schneider. H Baumelar. H Keller and 1. M. Savic. Chem. Phys. Leu. 1986, 128, 100. IIP. Neta, Chem. Rei 1972, 73, 533. 12. J. M. Stadlbauer. Y Miyake, B W. Ng. E. C Phillips and D. C Walker. Radial. Phys. Chem. 1986. 28, 95. 13. M. Anbar and E J Hart. J Am. Chem. Soc. 1964. 86, 5633. 14. Y. C Jean. i. H Brewer. D G. Fleming. D. M. Garner and D. C Walker. Hyper. Inter. 1979. 6, 409. 15. J H. Baxendale. Radial Res 1964. Suppl. 4. 139. Appendix . Collaborative work already published Volume 143. number 3 CHEMICAL PHYSICS LETTERS 141 15 January- 1988 M I C E L L E - I N D U C E D E N H A N C E M E N T O F T H E REACTIVITY O F M U O N I U M A T O M S IN D I L U T E A Q U E O U S S O L U T I O N * Krishnan V E N K A T E S W A R A N , Mary V. BARNABAS, Zhennan W U , John M . S T A D L B A U E R ', Bill W. N G 2 and David C. W A L K E R Chemistry Department and TRIUMF, University of British Columbia. 203b Main Mall, Vancouver. British Columbia. Canada 1 '67" / Y6 Received 26 Ociober 1987 Enhancements in rate constants from 10" M " ' s~ 1 lo more than 10"' M ~ 1 s 1 have been found for the reaction of muonium atoms with 2-propanol in water when micelles are added. 1. Introduction It was shown [ 1 ] previously that the critical mi-celle concentration ( C M C ) of a surfactant could be identified by th: onset of an increase in the rate at which naphthalene reacted with the muonium atom (Mu, the light hydrogen isotope having a short-lived positive muon as nucleus [2]). No explanation was available as to why micellization of the solute caused an increase in rate rather than a decrease, but it would not have been caused by Coulomb forces or vast changes in solvation energy, as is the case for several micelle-induced processes [3], because muonium is strictly neutral [4] and reacts with a Hammett p fac-tor close to zero [5]. Furthermore, as in the present study, the same effect occurs in anionic, cationic or neutral micelles. On investigating this effect further we have found iis magnitude to depend on the type of muonium re-action involved. Muonium atoms are formed in the bulk aqueous medium and react chemically with sol-utes to form muonated molecules or free radicals in a variety of reactions analogous to that of H [ 6 ]. Ad-ditions of micelles are found here to increase some reactions (including those of styrene, acetamide and 1 Permanent address: Department of Chemistry', Hood College, Frederick, MD 21701, USA. 2 Permanent address: Chemistry' Department. Winona State University. Winona, MN 55987, USA. aliphatic alcohols [7]), to not affect others (such as with methylcyanoacetate, N,N-dimethylacetamide and a-cyclodextrin [ 7]) and to decrease slightly those taking place in the aqueous phase (as with N O ^ or S203~ with anionic micelles [7,8]). The largest en-hancement actually measured to date is that for 2-propanol. This solute has been shown by paramag-netic-ion-induced Tt N M R relaxation studies to be strongly localized at dilute micelles in water [9]. The reaction is presumed to be (by analogy with H) M u + ( C H 3 ) ; C H O H ^ M u H + ( C H 3 ) : C O H . (1) 2. Experimental Muon spin rotation (uSR) studies [2] in low (8 G) transverse magnetic fields were used to deter-mine the time dependence of free muonium atoms as a function of concentration of added soluie. In the analysis of a uSR lifetime histogram one of the fitted parameters is the time constant (/) of the exponen-tial relaxation of the imposed muonium precession signal at 1.39 MHz G ~ ' . Bimolecular rate constants (kM) fora reaction (Mu + S —product) are then given by A.-M = AA/[S], where A / equals/, with solute at con-centration [S] minus A 0 in the same system (includ-ing micelle) but with [S] = 0. Only the narrow time window a; 0.3 to * 4 LIS is accessible to uSR as it uti-lizes the muon decay (T = 2.2 us), so [S] has to be 0 009-2614/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) 313 Appendix . Collaborative work already published 142 Volume 143. number 3 CHEMICAL PHYSICS LETTERS 15 January 1988 varied until )~' falls in this range. For very slow re-actions (such as (I)) significant changes in k occur with [S] 5:0.1 to 1 M , but for very fast reactions (such as styrene, or (1) in the presence of micelle) [S] need be only IO"5 to IO"4 M . The 2-propanol was BDH Aristar grade (and Fluka samples were also employed). It was up to 0.7 M , hopefully without interference from its impurities. (If impurities account for kM = 1.3X 106, as below, then the real enhancements are actually larger than calculated. Also, if only a fraction of the 2-propanol is in fact localized at the micelle then the real en-hancement is again larger than calculated here.) n-hexane was used as supplied by Fluka. All solutions were thoroughly deoxygenaled by bubbling with pure N : . Three micelle-forming surfactants were used: cationic CTAB (cetyltrimethylammonium bromide, C M C = 9.2x 10"4 M and aggregation number (A) = 80). anionic SDDS (sodium dodecylsulphate, C M C = 8.1x10"-3 M and A = 62) and neutral pEO (polyox\ethylene) 23 )dodecanol, C M C = 6xlO - 5 M and .4 = 50) [10]. At concentrations of surfactant well above the C M C the micelle concentration was eval-uated from [mic] = ( [surfactant]-CMC)/A . (2) 3. Results Fig. 1 shows that enhancement of reaction (1) oc-curs in the concentration range of the C M C for a rel-atively small and for a large micelle. (The onset is not expected to be particularly sharp because eq. (2) does not hold there and a range of micelle sizes ex-ists.) Both charged and neutral micelles show similar effects. C T A B had the most suitable C M C for the maximum enhancement with 2-propanol. To avoid the possibility of Mu accociating with "empty" mi-celles, a [2-prop]/[mic] ration of 2 to 4 was main-tained in the present study. Although this means that there were 2 to 4 solutes in each micelle, on average, there should always be < 15% unoccupied micelles, based on Poisson distributions [11]. The enormous effect of adding micelles to reaction (1) in water can be seen in fig. 2 by the different ab-scissa scales of (a) compared to (b). An enhance-ment factor of 20000 is calculated for kM based 3.0 » 2.0 o o l.u 0 0 (a) c / / y C M C 5 10 15 20 ' [ s u r f ] / 10" 3 M 2.0 i lb) " 1.5 1.0 0.5 oo * ^ cue 00 .05 [surf] .15 / 10 M Fig. 1. (a) Variation of A/, with SDDS as surfactant for aqueous solutions of 2-propanol (all at 3.0 x 10"' M as SDDS surfactant was added), (b) A/, for 2-propanol solutions at 3.85X 10" - M as pEO surfactant was added. Note. J/. = / . - /^ where /. is the u.SR relaxation constant with [2-propanol] as given above and the same surfactant solution but with no 2-propanol (i.e. A/, takes account of the small background reaction of Mu with surfac-tant). CMC marks the surfactant's critical micelle concentrations. simply on the overall [2-prop] in the solution. In n-hexane the reaction is about five times faster than in water. Table 1 contains representative data, plus re-sults using styrene and N O j as solutes for compar-ison purposes. Styrene reacts with a high rate constant in water, so the observable enhancement is corre-spondingly small. 4. Discussion With reactants present at < IO""1 M , muonium spends much of its chemical lifetime (0.3-4 us) dif-fusing through water before reaching a micelle for the first time. For instance, with kldMMton)^ 10" M ~ ' s _ 1 (based on an encounter probability with a mi-314 Appendix . Collaborative work already published 143 Volume 143. number 3 CHEMICAL PHYSICS LETTERS 15 January 1988 5 0 O 10 10 10 " M c " 1 5 i o r 0.5 0 0 .00 Oi -prop] .06 ICf3 M OB Fig. 2. (a) /. versus [2-propanol] in water (•) and in n-hexane ' •). There was a large background XQ in n-hexane. probably due to impurities, (b) A/, versus [2-propanol] with CTAB micelles present at l - i those concentrations (i.e. 2-4 solutes per micelle, on average). celle being about five times that of a normal solute [6]) and with [mic] =2x 10"5 M , one has a mean diffusion time of 0.5 us. So reaction with 2-propanol occurs nearly every time Mu encounters an occupied micelle (and, indeed, the rate eventually becomes es-sentially independent of the [2-prop]/[mic] ratio [ 7 ]). The observed reactivity is seen to approach the diffusion-controlled limit. Under such conditions it is appropriate simply to calculate a rate constant for reaction with an occupied micelle: designate it kimicl-A/J[occ. mic.]. When this is done for these data with 2-propanol one gets fc(mjc) = 7.5x 10'° M ~ ' s _ l and therefore an effective enhancement factor '^(m.cAvtcwauri equal lo 60000. (It is impossible to decide at this stage whether 60000 is the upper limit to this type of enhancement: one cannot use con-centrations lower than « 10"5 M , because diffusion already uses up the Mu lifetime; nor can one use in-trinsic reaction rates slower than & M s: 106 M - ' s~'. because they cannot be measured reliably due to im-purities when [S] > 1 M.) What causes this enormous enhancement? Three possibilities have been considered. First, it is the changed microenvironment from water to hydrocar-bon that alters the intrinsic reactivity by four orders of magnitude. (If this resides with the activation en-ergy then it would need to be reduced from *33 kJ/mol (its presumed value in water by analogy with formate [6]) to ^9 kJ/mol in the lipid phase of the micelle.) However, this explanation seems unlikely because reaction (1) is seen to be enhanced only five-fold when pure n-hexane is used as solvent and such an enhancement can be largely accounted for by the three times faster diffusion in n-hexane than in water due to the threefold lower viscosity (Mu obeys the Stokes-Einstein law [6]). The second possibility is that Mu, as well as 2-pro-Table I Summary of reactivity of muonium atoms, expressed as changes in the pseudo first-order coefficient (AX) and the calculated second-order rate constant (A\,) with and without added micelle at (Sj/[mic] = 3. The last column gives the enhancement factor (kM with micelle/without). All solutions were in pure deoxygenated water except for the last, in which n-hexane was used as a representative hydrocarbon solvent Solute Concentration (M) Micelle Concentration ( M ) A;. < 10" S" ' ) Enhancement 2-propanol 0.70 0 0.91(8) l.3x I0 6" 1 20000 2-propanol 7.5X10" 5 CTAB 2.5x IO"5 1.85(8) 2.5x10'"*' styrene 2.I4X I0"J 0 2.03(20) 9.3x10" 1 9 styrene 4.5x10-' CTAB l.5x IO- ! 3.5(4) 8x 10'° J NOf l.Ox 10-' 0 1.58(8) l.6x 10" } « NOj" 1.0xl0- J SDSS 5xl0- J 0.80(5) 0.80x10' 2-propanol 0.115 0.81(20) 7x 10*" From slopes of fig. 2. 315 Appendix . Collaborative work already published 144 Volume 143, number 3 panol, is specifically localized by the micelle phase, and that this occurs long enough to ensure reaction by multiple encounters under confined-diffusion conditions. However, this too seems unlikely for the following reasons: The mutual concentrating effect (water-to-micelle volume ratio of the solutions) is in the range 1300-6700 for the data of fig. 2b, so this still leaves an intrinsic enhancement factor of 10 or more. Furthermore, the experiments with N0 3~ so-lutions to which unoccupied micelles were added for Mu to be localized, showed only a trivial extension to the muonium lifetime. For the results reported in table 1, for instance, five times as many micelles as N0 3~ ions were required to halve the muonium re-action rate, from which the mean residence time of Mu is calculated to be only s=1.5 ns [8]. This is comparable to the extra time required for Mu to dif-fuse through the highly viscous (rj^30 cP [12]) mi-celle phase compared to an equal volume of water, which implies that Mu is not localized. The third possibility lies in some unusual property of Mu or the micelle. Our present thinking is that either (i) Mu traps preferentially at a dislocation created by a solute within the micelle, or (ii) that the extended residence time (even to only 1.5 ns) and structured medium allow Mu to react by a quantum-mechanical tunnelling mechanism. Whatever the ul-timate explanation, these enhancements are now being exploited to study Mu reactions with hitherto unreactive solutes. They can also be used to repre-sent muonium's heavy isotope hydrogen, which can-not be studied directly under these conditions because H reacts a hundred times faster with the surfactants themselves [13]. Acknowledgement Technical support by the uSR group at T R I U M F , 15 January' 1988 particularly J. Worden, K. Hoyle and I. Reid, was very much appreciated. Financial support by NSERC of Canada is gratefully acknowledged. References [ 1 | Y.C. Jean, B.W. Ng. J.M. Sladlbauer and D.C. Walker. J. Chem. Phys. 75 (1981 ) 2879. [2] V.W. Hughes, Ann. Rev. Nucl. Sci. 16 (1966) 445: J.H. Brewer and K_M. Crowe. Ann. Rev. Pat. Sci. 28 (1978) 239. [3] M. Gratzel, J.K. Thomas and L.K. Patterson, Chem. Phys. Letters 29 (1974) 393; J.K. Thomas. Accouns Chem. Res. 10 (1977) 133: T. Proske and A. Henglein, J. Am. Chem. Soc. 100 (1978) 3706; A. Levaskov, V.L Pantin and K. Martinek, Kolloid Zh. 41 (1979) 453. [4] Y.C. Jean, J.H. Brewer, D.G. Fleming, D M . Garner and D.C. Walker. Hyperfine Interactions 6 (1979) 409. [ 5 ] J.M. Stadlbauer, B.W. Ng, R. Ganti and D.C. Walker. J. Am. Chem. Soc. 106 (1984) 857. [6] D.C. Walker. Muon and muonium chemistry (Cambridge Univ. Press, Cambridge, 1983) pp. 8, 115, 117. [7] K. Venkateswaran. M. Barnabas and DC. Walker, to be published. [8]K. Venkateswaran and D.C. Walker. Hyperfine Interac-tions 32 (1986) 559. [9] NR. Jagannathan. K. Venkateswaran. F.G. Herring. G.N. Pateyand D.C. Walker, J. Phys. Chem. 91 (1987) 4553. [10] J.H. Fendler, Membrane mimetic chemistry (Wiley-lnterscience, New York, 1982). [ 11 ] K. Kalyanasundaram, Chem. Soc. Rev. 7 (1978) 4531 N.J. Turro, M. Gratzel and A.M. Braun, Angew. Chem. In-tern. Ed. Engl. 19 (1980) 675. (t2] M. Shinitzky. AC. Dianoux, C. Gitler and G. Weber. Bio-chemistry 10 (1971) 2106; M. Gratzel and J.K. Thomas, J. Am. Chem. Soc. 95 (1973) 6885. [13] K.M. Bansal, L.K. Patterson. E.J. Fendler and J.H Fendler. Intern. J. Radial. Phys. Chem. 3 (1971) 321. CHEMICAL PHYSICS LETTERS 316 Appendix . Collaborative work already published 145 Volume 145, number 4 CHEMICAL PHYSICS LETTERS 8 April 1988 A L E V E L - C R O S S I N G - R E S O N A N C E S T U D Y O F M U O N A T E D F R E E - R A D I C A L F O R M A T I O N IN S O L U T I O N S O F A C E T O N E IN H E X A N E , WATER A N D D I L U T E M I C E L L E S Krishnan V E N K A T E S W A R A N , Robert F. KIEFL, Mary V. BARNABAS, John M . S T A D L B A U E R ', Bill W. N G 2 , Zhennan W U and David C. W A L K E R Departments of Chemistry. Physics and TRIUMF. University of British Columbia. Vancouver. British Columbia. Canada V6T IY6 Received 29 December 1987; in final form 27 February 1988 The (CH3) ;COMu radical forms when positive muons are stopped in pure acetone and dilute mixtures of acetone in n-hexane or water. Muonium is the precursor of the radical in dilute solution and evidently differs from hydrogen in adding readily to the carbonyl group. In micelles this addition reaction appears to be superceded by enhancement of the abstraction reaction because the radical is not observed. 1. Introduction Until recently, muonium-containing free radicals could only be observed by the high transverse-field muon-spin-rotation technique ( T F uSR) [ 1 ], where the radical had to be formed very rapidly ( « 10~9 s) so that initial coherence of the muon spin was pre-served. This excluded the possibility of observing radicals formed by secondary thermal chemical re-actions in dilute solution. It meant that the only de-tectable radicals were those produced at the end of the muon track in pure unsaturated compounds or concentrated mixtures. However, the recent devel-opment of the muon level-crossing-resonance (LCR) technique [2,3], when applied to organic free radi-cals [4,5], allows Mu-containing radicals of the di-lute solute to be seen even when they form a microsecond or so after implantation of the positive muon in the solvent [6,7]. An rf resonance tech-nique also now does this [8]. Acetone has been shown by T F uSR to produce the ( C H 3 ) j C O M u radical in pure liquid acetone [9-12] and in mixtures with water down to 20% 1 Department of Chemistry, Hood College, Frederick, MD 21701, USA. 2 Chemistry Department, Winona State University, Winona, MN 55987. USA. [13,14]. Also, the LCR spectrum in pure acetone has already been reported [6], where the six equivalent protons lead to a single unresolved multiplet. Ace-tone is particularly suitable for the present study, be-cause its reactivity towards the muonium atom ( u + e - , chemical symbol Mu) is known in water and in micelles [15], and the results can be compared with hydrogen atoms [16]. Though the muonium atom normally emulates a light hydrogen isotope in its reaction kinetics, when reacting with aqueous acetone Mu reacts much more quickly than does H [17]. 2. Experimental Details of the L C R method applied to muonated free radicals of liquids have been given previously [4,5,18]. In brief: a beam of spin-polarized 4.1 MeV positive muons from the M15 beamline at T R I U M F are stopped in deoxygenated solutions in a thin-walled teflon cell. A superconducting magnet was used to apply magnetic fields up to 30 kG along the initial polarization direction which is parallel to the beam direction. A square-wave modulation field of 55 G was applied to minimize systematic errors. This permitted the L C R signal to be recorded as the dif-ference in opposite modulation fields (A + —A~), 0 009-2614/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) 289 Appendix . Collaborative work already published 146 Volume 145. number 4 CHEMICAL PHYSICS LETTERS 8 April 1988 where A is the integrated muon-decay asymmetry (normalized backward-to-forward count rates). Best fits were obtained by fitting the data to a difference of two Lorentzian lines using a ^ -minimization rou-tine. The conventional uSR measurements were per-formed with a 240 G transverse field using backward muons on the M20A beamline. ' The acetone was Analar grade from B D H , the n-hexane was Puriss grade from Fluka Chemicals, and the water was triply distilled. Solutions were deox-ygenated by bubbling with pure N 2 prior to being pumped through a closed system into the irradiation cell. Micelle solutions were prepared as described in ref. [19]. 3. Results Fig. 1 shows the L C R spectra of (a) pure acetone, (b) 30% (v/v) acetone in water, and (c) 30% (v/v) acetone in Ai-hexane. Spectrum (a) is consistent with that already published by Heming et al. [6]. Spec-trum (b) shows that dilution by water shifts the res-onance position by + 280 G and reduces the intensity. Spectrum (c) shows that dilution by n-hexane shifts the resonance to lower fields than pure acetone by — 115 G and is comparable in intensity to that in (b). Table 1 lists the fitted values for resonance fields (z? r „), and amplitudes (Amp) as percent reduction in muon decay asymmetry on resonance. The data for 0.1 and 0.01 M acetone in water are also given in table 1. A very dilute micelle solution of acetone was stud-ied by LCR and compared with other unsaturated organic compounds. Bm was determined for the four solutes (acetone, acrylamide, styrene, and benzene) as shown in table 2, column 3. In each case the solute was at 9x I O - 5 M and the micelle C T A B (cetyltri-methylammonium bromide) was at 3x 10~5 M , so, on average, there were three solutes localized in each micelle. Acetone differs from acrylamide, styrene, and benzene in that the yield of the Mu radical is zero under the same conditions in which the others gave substantial yields of their radicals [20]. Conventional uSR experiments were performed on various solutions in order to provide information about radical yields and their formation mechanism. Table 3, column 2, contains diamagnetic yields (PD) < 1 600 600 10OO 1200 1400 16O0 1600 COOO £200 2400 •OO 600 1000 1200 1400 1600 1600 2OO0 3200 2400 LoeJItttdlB*] HMlitut n«l6 (Ctow) Fig. 1. LCR speclra of: (a) pure acetone, (b) 30% (v/v) acetone in water and (c) 30% (v/v) acetone in n-hexane. {A* — A' is proportional to the LCR amplitude.) Table 1 LCR positions (Bm) and amplitudes (Amp) for solutions of acetone Acetone solution Amp (%) / V " pure 1540(3) 0.526(10) (0.41) 30% in hexane 1425(2) 0.376(10) 0.29 30% in water 1820(2) 0.348(9) 0.27 0.1 M in water 1820(2)" 0.208(13) 0.16 0.01 M in water 1820(2) 0.140(10) 0.11 Derived radical yields based on a PR of 0.41 (3) in neat ace-tone by Roduner [11]. 290 Appendix . Collaborative work already published 147 Volume 145, number 4 CHEMICAL PHYSICS LETTERS 8 April 1988 Table 2 Data on Mu-radical formation in aqueous solutions containing 9X 10~5 M solute + 3x 10"5 M CTAB micelles Solute Radical's/)„•' (MHz) (G) k cl (M-'s" ' ) Enhancement factorcl acetone 26.1 2.5x10'° 290 acrylamide 317.0 13620(3) 2.5x10'° 3 styrene 213.5 9066(3) 8 X10'° 9 benzene 514.6 20848(3) 8 xlO 1 0 25 " Published data (see ref. [17]). 6 1 The vinyl (HB) for acrylamide and styrene were used, and H(6) in the case of benzene. c l * . 'Mnr, ic i> s 'he rate constant as determined from Mu-decay measurements in water with micelles by the uSR technique, and kM the value in the absence of micelle [15]. Amp = 0, i.e. no LCR signal seen at 1820G in this micelle solution. obtained at transverse fields of 240 G . These yields represent the fraction of the incident muons which are observed to have been incorporated in diamag-netic molecular states in times shorter than w 1 0 - 9 s. 4, Discussion 4.1. Resonance shifts The L C R field at which the muon spin polariza-tion in the ( C H 3 ) 2 C O M u radical is transferred to the six protons via hyperfine coupling is given to a very good approximation by [4,5], B m = \ Q . S [ ( A v - A H i ) K y v - y p ) - (Av +AHe)/yc] | , (1) where the y's are the magnetogyric ratios of the muon, proton and electron, and Au and AHf are the muon and proton hyperfine coupling constants respec-tively. For pure acetone our value of Z?rcs=1540 G equals that reported by Heming et al. [6]. The shift of +280 G in B m on dilution of acetone (to 30% (v/v) in water) gives a value ^ H „ = 55.5(5) M H z (using /1M = 22.0(4) MHz, as measured by T F uSR by Hill et al. [ 13]). This value of AHi equals within the error bars that obtained for pure acetone [6] showing that there is no solvent effect on AHt. Our observed negative shift of - 115 G on dilution with /i-hexane (fig. lc) gives a value of/l M = 29.4 M H z in the hydrocarbon medium. These B m shifts provide strong support for the hy-drogen-bonding (Mu-bonding) concept [13,14], because the order of increasing polarity is hexane, acetone, water. This can be seen in the following way. Table 3 Tally of yields. Experimental diamagnetic yields (PD). radical yields (PR) and inferred sources of radicals Solution R D D b> ' R V ' pure acetone 0.55(1) 0.41(3) 0.04(3) 30% (8 M ) acetone in n-hexane 0.63(1) 0.29 0.08 30% (8 M ) acetone in water 0.63(1) 0.27 0.10 0.1 M acetone in water 0.63(1) 0.16 0.21 0.01 M acetone in water 0.62(1) 0.11 0.27 *' As determined here at 240 G by uSR. For pure hexane PD=0.61 and water 0.62. PR as in table 1 (see text). " f L= l-P0-P„-PM (/>„ = 0 with acetone present). 291 Appendix Collaborative work already published 148 Volume 145, number 4 The exceptionally large isotope effect on substituting Mu for H (Atl/Ap = 9) [9] arises from the change in moment of inertia, due to the C - O - M u bond angle not being 180° . But the muon's coupling to the un-paired electron density is reduced by Mu bonding to the O of water much more than Mu bonding to O of acetone in pure acetone [13]. Hence, Av is reduced by dilution with water (shift to higher Bm)An con-trast, when acetone is diluted by n-hexane, which provides no hydrogen-bonding, the residual Mu bonds to other acetone molecules are weakened, and the shift is now observed in the opposite direction. 4.2. Yields In muon chemistry there are three distinguishable chemical states in which the muon appears: diamag-netic molecules (fractional yield, PD), free-radicals ( P R ) , and free muonium atoms (PM). In each case there is the proviso that the state exists at a 10~6 s, can be seen during the muon's decay, and that the muon is not depolarized (or dephased by precession in precursor states in rotation studies). Depolari-zation and dephasing lead to a missing fraction PL = 1 — PD — PR — PM. Our fractional radical yields ( P R ) , as given in the last column of table 1, were es-timated from the observed L C R amplitudes (Amp) and by equating the amplitude of 0.526% in pure acetone with Roduner's absolute determination of P R = 0.41 as obtained by T F uSR [11]. The major assumption involved in this procedure is that any re-laxation affects the amplitudes to the same degree (because in each solution the linewidths are about twice the theoretically determined widths). This as-sumption comes from the expectation that the broadening is not caused by a solvent-induced re-laxation. This normalization procedure also seems appropriate because pure acetone has been shown to have a negligible missing fraction (PL»0.04) [11]. The difference in experimental asymmetry at 1425 and 1820 G has been shown to be negligible [20]. Table 3 records the yields obtained in these dif-ferent acetone solutions. For pure acetone and the 30% solutions there can be direct radical formation from hot-atom interactions or u + adducts [ 11-14,17]; but for the 0.1 and 0.01 M aqueous so-lutions, the only possible precursor to the radical is Mu, the free thermalized muonium atom. For these 8 April 1988 dilute solutions hot-atom insertions would be neg-ligible, and u + would be solvated and converted to M u O H before it could encounter acetone, so the maximum radical yield will equal the non-depolar-ized muonium yield at the time of the reaction Mu + ( C H 3 ) 2 C O - ( C H 3 ) 2 C O M u , ArM = 8 . 7 x l 0 7 M - ' s - 1 . (2) At 0.1 M the radical will be formed on average about 0.1 us after Mu formation. This means that most of the Mu atoms constituting the missing fraction in water (/>I_ = 0.18) will be lost and only />M = 0.20 is available as the source of PR via reaction (2). Fur-thermore, not all of the muon polarization in muon-ium is observable because the longitudinal field (Bm = 1820 G ) is not large enough to decouple com-pletely the hyperfine oscillation (for which / / 0 = 1585 G ) . Instead, the number of polarized Mu atoms available is the yield with unpaired spins (0.10) plus the fraction x 2 / ( 1 +x2) of the paired yield (also 0.10), where x=BrJH0. This total equals 0.157 for Bm= 1820 G . Our observed radical yield for the 0.1 M solution is 0.16. For 0.01 M aqueous acetone solution there is an-other factor to consider. Here, the mean formation time of the radical (expected to be about 1.1 us) is comparable to the observation time so that the L C R amplitude is reduced from its value at 0.1 M . In fact, when the theory [7] is applied, it results in a re-duction in PR from 0.13 to 0.11. This confirms that the rate of decay of M u in the presence of acetone, as observed by |iSR, is due largely to the addition reaction (eq. (2)). In other words, we have actually observed the rate of formation of the radical to be equal to the observed rate of decay of Mu. 4.3. Micelle solutions Acetone shows micelle-induced enhancement in reaction with Mu, like many organic solutes [19] (table 2, columns 4 and 5, records some relevant data). But Mu radicals are evidently not the prod-ucts of the enhanced reaction, because they were not observed by L C R under conditions where acrylam-ide, styrene and benzene showed them (table 2). Furthermore, we have searched for the acetone rad-ical in more concentrated micelle solutions (up to CHEMICAL PHYSICS LETTERS 292 Appendix . Collaborative work already published 149 Volume 145, number 4 0.002 M micelle and 0.012 M acetone) and found none. The implication is that reaction (2), which dominates the reaction in water, must have been superseded by a competitive reaction which is en-hanced much more by localization in micelles. Ab-straction reactions have been found to give enhancement factors of 104-fold or more [49], so it looks as if the reaction M u + ( C H 3 ) 2 C O - . M u H + C H 3 C O C H 2 , (3) takes over in the micellar phase. This means that mi-celles can be used to change the distribution of prod-ucts when more than one reaction channel is available, as they have different micelle-induced en-hancement factors. Finally, it is interesting to note in this connection that, for H atoms, the abstraction reaction H + ( C H 3 ) 2 C O - . H 2 + C H 3 C O C H 2 , / t H = 2 . 4 x l 0 6 M - ' s - 1 , (4) dominates over the addition H + ( C H 3 ) 2 C O - ( C H 3 ) 2 C O H , A.-H = l . l x l 0 6 M - ' s - ' , (5) in water [16], and that, in general, abstractions show an isotope effect (kH/kM) of about 102 [17]. If this also occurs for acetone then kM for reaction (3) would only be = 1 X 10" M ~ 1 s"': in which case mi-celles would have given rise to a 106-fold enhance-ment of the abstraction reaction. Acknowledgement The assistance of the staff of the uSR group at T R I U M F (J. Worden and K. Hoyle) is, as always, very much appreciated. Financial assistance for these experiments came from the N S E R C of Canada. 8 April 1988 References [ 1 ] R. Roduner and H. Fischer, Chem. Phys. 54 (1981) 261. [21 A. Abragam, Compt. Rend. Acad. Sci. (Paris) Ser. 11 299 (1984) 95. [3] SR. Kreitzman. J.H. Brewer, D.R. Harshman, R. Keitel, D.L. Williams, K.M. Crowe and E.J. Ansaldo. Phys. Rev. Letters 56 (1986) 181. [4) R.F. Kjefl, Hyperfine Interactions 32 ( 1986) 707. (5 ] R.F. Kiefl, S.R. Kreitzman. M. Celio, R. Keitel. J.H. Brewer, C M : Luke, D.R. Noakes. P.W. Percival, T. Matsuzaki and K. Nishiyama, Phys. Rev. A 34 (1986) 681; R.F. Kiefl, p.W. Percival, J.C. Brodovitch, S.K. Leung, D. Yu. K. Venkateswaran and S.F.J. Cox, Chem. Phys. Letters 143 (1988) 613. [6] M. Heming, E. Roduner, B.D. Patterson. W. Odermatt, J. Schneider, Hp. Baumeler. H. Keller and IM. Savic. Chem. Phys. Letters 128 (1986) 100. [7 ] M. Heming, E. Roduner and B.D. Patterson. Hyperfine In-teractions 32 ( 1986) 727. [8]T. Azuma, K. Nishiyama, K. Nagamine, Y. Ito and Y. Tabata, Hyperfine Interactions 32 ( 1986) 837. [9]E. Roduner, in: Exotic atoms '79, eds. K.M. Crowe. J. Duclos, G. Fiorentini and G. Torelli (Plenum Press, New York, 1980) p. 379. [10] A. Hill. G. Allen, G. Stirling and M.C.R. Symons. J. Chem. Soc. Faraday Trans. I 78 (1982) 2959. [ 11 ] E. Roduner, Radiat. Phys. Chem. 28 ( 1986) 75. [12] S.F.J. Cox, D.A. Geeson, C.J. Rhodes, E. Roduner, C.A. Scotland M.C.R. Symons, Hyperfine Interactions 32 (1986) 763. [ 13 ] A. Hill, M.C.R. Symons, S.F.J. Cox, R. de Renzi. C.A. Scott, C. Bucci and A. Vecli, J. Chem. Soc. Faraday Trans. I 81 ( 1985) 433. [14] S.F.J. Cox and M.C.R. Symons. Radiat. Phys. Chem. 27 ( 1985) 53. [15] K. Venkateswaran, M.V. Barnabas. J.M. Stadlbauer and D. C. Walker, to be published. (16) R.A. Witter and P. Neta, J. Org. Chem. 38 (1973) 484. (17] D.C. Walker, Muon and muonium chemistry (Cambridge Univ. Press, Cambridge, 1983). [18] P.W. Percival. R.F. Kiefl. S.R. Kreitzman, D.M. Gamer, S.F.J. Cox, G.M. Luke. J.H. Brewer. K. Nishiyama and K. Venkateswaran, Chem. Phys. Letters 133 (1987) 465. [ 19] K. Venkateswaran, M.V. Bamabas, Z. Wu, J.M. Stadlbauer. B. W. Ng and D.C. Walker, Chem. Phys. Letters 143 ( 1988) 313. [20] K. Venkateswaran, M.V. Bamabas, R.F. Kiefl, J.M. Stadlbauer and D.C. Walker, to be published. CHEMICAL PHYSICS LETTERS 293 Appendix . Collaborative work already published 150 1979 Residence-time of muonium at micelles: Effect of added micelles on the reactivity of muonium towards ionic solutes in water KRISHNAN VENKATESWARAN. M A R Y V . BARNABAS, B I LL W . N G , 1 AND DAV ID C . W A L K E R Chemistry Department andTRIUMF. University of British Columbia, Vancouver, B.C.. Canada V6T JY6 Received November 15. 1987 This paper is dedicated to Professor Charles A. McDowell on the occasion of his 70th birthday KRISHNAN VENKATESWARAN. MARY V . BARNABAS. BILL W. NO , and DAVID C. WALKER . Can J . Chem. 66. 1 979 ( 1 9 8 8 ) The effective rale constant for the reaction of muonium with N 0 3 " , S i 0 3 3 - , and TI* ions in water is altered by the addition of micelles. There is a decrease when the charge on the micelle is the same as that of the solute and an increase when their charges are opposite. From the magnitude of the effect a mean residence-time for muonium of 2 ns has been deduced for dodecyl sulphate micelles This suggests there is barely any preferred localization, because 2 ns is smaller, even, than the expected diffusion time if the micelle core is as viscous as reported. This use of muonium atoms to probe the dynamics of micelles seems to support the view that there are regions of low microviscosity and considerable water penetration within the micellar structure. KRISHNAN VENKATESWARAN. MARY V . BARNABAS, BILL W . N G et DAVID C. WALKER . Can. J . Chem. 66, 1 9 7 9 ( 1988 ) . La consume de vitesse effective de la reaction du muonium avec les ions NO.-T. Sj0 3 2 ' et TI* dans l'eau est modified par l'addition de micelles. II se produit une diminution lorsque la charge de la micelle est la meme que celle du solutC et une augmeniation lorsque leurs charges sont opposies. En se basant sur l'amplitude de l'effet, on a pu d^ duire un temps moyen de residence du muonium de 2 ns pour les micelles de sulfate de dodecyle. Ceci suggere que la localisation preTe>entielle existe a peine puisque 2 ns est un temps qui est plus court que le temps attendu de diffusion si le coeur de la micelle est aussi visqueux qu'on l'a rapporte\ L'utilisation d'atomes de muonium pour £tudier la dynamique des micelles semble apporter un support a l'hypothese selencounters a micelle, then it will be isolated from the reactive species in ton laquelle il y a beaucoup de penetration par l'eau et beaucoup de regions comportant de faibles microviscosit£s a I'interieur de la structure des micelles. (Traduit par la revue] Introduction It was recently demonstrated that colossal enhancements can occur in the reactivity of muonium towards organic solutes when the solutes are incorporated in the lipid phase of dilute micelles in water (1). The simplest explanation for such en-hancements lies with the possibility that muonium atoms also localize preferentially at the micellar phase because, if mutual confinement of both reactants occurred, there would be a "con-centrating effect" that would naturally lead to an equivalent increase in the observed pseudo first-order rate constant. But muonium is a free thermalized neutral atom (2), and there are no obvious reasons why this light isotope of hydrogen (3,4) should prefer the organic phase when initially formed in the bulk aqueous phase. The experiments reported here were designed to look directly at the degree of localization of muonium at micelles, simply by observing the effect of added "empty" micelles on the rate of muonium reactions with ionic solutes taking place in water. Experimental Muonium atoms (u.*e~, chemical symbol Mu) form at the end of some muon tracks when energetic positive muons (from pion decays) are injected into water. They are observed in transverse magnetic fields by the muon spin rotation technique (u-SR) (4, 5). Chemical reaction rale contains of Mu are then evaluated from the spin precession signals (as in Fig. 1) as the relaxation constant (X) of the "triplet" muonium signal oscillating at the Larmor frequency of 1.39 MHz G" 1 . A M1NUIT x:-minimization fit of the muon lifetime histogram to eq. (1 ] gives X as one of the fined parameters. (In eq (1 ], /V, is the number of counts in the histogram corresponding to time 1; N0 a normalization factor; T the mean muon lifetime; A M and A D . XM and XD, and 4>M and <t>D are the asymmetries, frequencies, and initial phases of the "muonium atoms" and "diamagnetic muon components", respectively; 'Present address: Chemistry Department, Winona State University, Winona, MN 55987, USA. and B is the time-independent background signal.) X is related to a bimolecular chemical rate constant of Mu (iM) through eq [2]. where X is the observed value with solute present at concentration [S] and XQ is the background value in the same medium, including micelle, but with [S] = 0. A narrow observational time-window of 0.3-4 u.s is imposed by the u.SR technique, because it is a nuclear physics technique based on the intrinsic decay of the muon (T = 2.2 u.s). Therefore, all solutions to be studied must have their muonium chemical lifetimes carefully selected so that X falls in the limited range of 3 x 106-2.5x lO's"1. This precludes the possibility of studying broad concentration depen-dencies as one would normally like to undertake in a complete kinetic analysis. Furthermore, the micelle concentrations are restricted to M because, with 50-80 surfactant molecules per micelle, the rale of reaction of muonium with surfactant, or its inseparable impuri-ties, forces the "background" relaxation rate (Xo) loo close to X for reasonable accuracy. In fact, hydrogen atoms cannot be studied at all under these conditions because of their much greater reactivity towards the surfactants (6). 11] N, — No exp (—f / T ) ( 1 + AMexp(-Xr)cos(u>Mr+ <i>M) + AD COS (ury + d>D)] + B 12] AM = (X-X < ))/l5] = A\/[5] The presence of added micelles creates a second phase, a microen-vironment separated from the bulk aqueous phase (7, 8). If Mu pref-erentially localizes for its entire lifetime (—2 u.s) as soon as it encoun-ters a micelle, then it will be isolated from the reactive species in these systems (NO3", S2O3 3-, and TI* ions) because they are in the water. Under such conditions the "trapped" Mu would exhibit a decay con-stant characteristic of the micelle. To analyse for this the muonium fraction of eq. 11 ], the A M term, was replaced by eq. [3] (9), with two independent exponentials for the two fractions of the Mu ensemble. A test target for this two-component modification of eq. |I] was con-structed partly of aqueous N0 3" solution (10"3 M where X = 1.8 x 10° s"') and partly of crystalline quaru(X -0.3 x 10* s"1) (10). A portion of the beam struck the quartz crystal and the muonium atoms formed therein were long-lived, being unable to react with the nitrate. |3) M M i exp(- X,/) + A M j exp(- Xj/)) cos (u>„; + <J>M) Appendix . Collaborative work already published 151 1980 CAN 1 CHEM VOL 66. 1988 TABLE 1. Parameters used to establish the concentrations required for the experiments [solute] / 10" 3 M Solute *M/10,0Ar' s-' (togive AX= 1.5 x 10"s"') NOj" • 0.15 1.0 s,o,2 2.60 0.07 Ti* 0 08 2.0 Na\S042" . Br" <0.0001 Critical micelle Micelle Charge concentration / M A° Rc/nmh /Wnm'' [mic]m m/M r SDDS _ 8lxirr 3 62 1.7 2.1 1.3xKr" DDTAB •+ 1.5 x Ifj2 60 1.7 2.1 soxifr" pEO 0 6.0xl0r5 50 1.7 3.2 1.2X10-6 'A is the aggregation number. "Rc is the micelle's core radius and RM the total radius (ref. 7). Taken as the micelle concentration when half the surfactant molecules are in micelles as calculated from |mic] = ([surf] - CMC)/A. 1 1 1 1 1 1 1 1 ' . (b) hi D. 6 1 . 0 1 . 6 2 . 0 2 . 6 3 . 0 T i n ( a i. c r o —• « c o n a • ) 3 . 6 A. S FIG. 1. (a) Asymmetry plot (A vs. t) for the quanz/NGy solution artificial two-phase system. The solid line was obtained for the parameters in the text using the two-muonium function of eq. [3]. (b) Asymmetry plot for [NCVJ = 0.7 x I0~5M and [mic] = 10 x 10"3M. The line is the same as the usual one-component fit since J4M; = 0. Aqueous solutions were made from triply distilled water and reagent grade chemicals. They were thoroughly deoxygcnated by bubbling with pure N 2 . The u,SR equipment on beamline M20 at the TRIUMF cyclotron was used. NaN03, Na2S20j, and T1S04 were used as reac-tive solutes for Mu, and the micelles were sodium dodecylsulphate (SDDS). dodecyltrimethylammonium bromide (DDTAB), and polyoxy(23)ethylenedodecanol (pEO). These ionic solutes were selected for their known values of kM Mid matched appropriately with the charge on the micelle. Relevant kM values and micelle properties are provided in Table 1. The concentration of the solute in water was always taken so that X "= 1.5 x 106 s"1, its most sensitive region. Micelles were added and the change in X determined. Appendix . Collaborative work already published 5.0 152 VENKATESWARAN ET AL. 1981 i n o 2 4 . 0 -3.0 2 .0 1.0 0.0 T T 4.00 "a 3.oo -\ 2.00 • 1.00 f-0.00 i ' i i f = r i i i i i 0 0 0.2 0.4 0.6 0.8 1.0 [mic] / 10° M 0.0 1.0 2.0 3.0 4 .0 5.0 6.0 [m i c ] / 1 0 ~ 3 M FIG. 2. Plot of JcM versus concentration of added micelles for NCV solutions with [S] = I x Ifr3 M (•) for SDDS, (•) for DDTAB, tfx)) for pEO . micelles. Results The effect of adding micelles to 1.0 x 10"3 M N0 3~ solutions can be seen in Fig. 2. When the anionic micelle SDDS was added the observed muonium rate constant was reduced. With five times as many micelles as solutes the rate was essentially halved. On the other hand, a cationic micelle (DDTAB) in-creased the observed rate (doubling it approximately in a one-to-one mixture), while the neutral micelle (pEO) had no observable effect. These data are presented as kM values determined from eq. (2J. Unfortunately pEO and DDTAB cannot be taken to higher concentrations because of their background corrections (Xo). Similar effects, which depend primarily on the relative charge of solute and micelle, can be seen for other solutes. Table 2 shows data obtained for S 2 Oj 2 ~ (which reacts with Mu at the diffusion-limited rate (10)) and for TI* (which oxidizes Mu relatively inefficiently (10)). The two-component overall muonium relaxation (eq. [3]) was found to apply well to the artificial two-phase system consisting of one-third quartz and two-thirds aqueous NO3" at 10~3 M . The asymmetry plot (after T and B of eq. [1] were removed (4)) is shown in Fig. 1 (a). The best reduced \ 2 values are A M | = 0.019 with X, = 1.8 x 10* s'1 and A M j = 0.033 with X 2 = 3.5 x 10s s"'. This is about what was expected since the muonium yield in quartz is 3.5 times larger than in water (10) but only one-third of the muon beam stopped in the quartz. These data verify that if the Mu ensemble is rapidly subdivided into two isolated fractions then the double-exponential fit of eq. [3] identifies it. However, for all the micelle solutions this two-component fit gives A M , = 0, regardless of how one tries to drive it with different limits on X, and X2. An example is shown as Fig. 1 (b). It means that the regular fining equation (eq. [1]) applies to micelle solutions, and, therefore, that all muonium atoms have access to the same decay channels. We also report here that the data points of some of the occupied-micelle solutions studied previously (1) were sub-jected to eq. [3] incorporated in eq. [1]. In an aqueous solution containing styrene at 7.5 x 1 f r ' M and micelles at 1.5 x 10~5M the best fit always gave A M , = 0. In this system the solute (styrene) was strongly localized in the micelle core without a significant chance of relocating during the 2-y.s period corre-sponding to the muon lifetime. There are twice as many micelles as solutes in the solution, so about 61 % of the micelles, based on Poisson distributions (11,12), would be unoccupied, and about 8% would contain two styrene molecules. So, again, the failure of the analysis to see any fractionation of the Mu ensemble strongly implies that they localize at micelles for periods much shorter than their chemical lifetimes. Discussion These data show that muonium's effective rate of reaction towards a solute was decreased by adding a micelle of the same charge as the solute, increased by a micelle of the opposite charge, and barely affected when the micelle was neutral. Mil-limolar concentrations of micelles were needed to alter the chemical lifetime of muonium significantly. In these experiments most muonium atoms were created Appendix . Collaborative work already published 153 1982 C A N J C H E M V O L 66. 1988 TABLE 2. Effect of added micelles on tM: representative data from Fig. 2 for NOV. and data for S JOJ 3 " and T T with S D D S micelles Concentration Concentration AX" Solute / I f r ' M Micelle /10" 3M / 1 0 V /IO u M-'s- ' N0 3- 1.0 0 1.50(10) 1.5 N O 3 - 1.0 SDDS 5.0 0.80(10) 0.80 NOj- 1.0 DDTAB 1.0 3.70(30) 3.7 N O 3 - 1.0 pEO 0.1 1.50(10) 1.5 s 2 o 3 J - 0.05 — 0 1.32(10) 26.5 S 2 O 3 3 - 0.10 SDDS 0.2 2.40(20) 24.0 s 2 o 3 J - 0.10 SDDS 0.5 1.95(20) 19 5 s 2o 3 J- 0.10 SDDS 1.0 1.95(20) 19.5 TT 0.4 — 0 0.30(10) 0.75 TI4 0.8 SDDS 0.33 1.20(10) 1.5 TI* 0.4 SDDS 0.20 0.80(10) 2.0 IT* 0.4 SDDS 0.50 1.25(10) 3.2 "Observed 'Calculated from eq |2] for each solution. initially in the aqueous phase, because water was by far the major constituent, but on encountering a micelle during its random diffusion Mu could localize there. ("Localization" will be used here to mean that Mu spends a greater fraction of its time in the micelle than the volume fraction of that phase in the whole solution. It does not take account of the different diffusion coefficients in the two phases.) The distributions of the ionic solutes are also influenced by the micelles, being preferentially caught in the ion atmospheres when of opposite charge and specifically excluded when of the same charge. The enhanced rate when the solute is localized is consistent with Mu also being localized, especially if the "fjord-like" character of micelles is appropriate (7, 13, 14) where there is considerable water penetration. However, it is impossible to use these enhancement data quantitatively without knowing in detail about the mutual localization and local structure. Instead the discussion will focus on the decreased rates. Four possibilities present themselves regarding the localiza-tion of Mu: (a) it may be confined exclusively to the aqueous phase, (b) treat micellar and aqueous phases alike (no localiza-tion), (c) localize "permanently" (a microsecond or so here) in the micelle phase, or (d) localize to a limited extent at the micelle. Possibility (a) can be discarded, because enhancements in Mu rates have been observed for many organic solutes (I) that are themselves fully localized in micelles, (b) can be ruled out, because there would have been almost no effect, and what little there was would have been in the opposite sense to that seen, because the solutes of opposite charge to the micelles would have been "bunched" around them, thereby reducing the effec-tive concentration of solute as seen by a randomly diffusing Mu. (c) can also be discarded, because the rate did not drop to almost zero in the highest concentration N0 3"/SDDS case, for in-stance, whereas Mu would have had the chance to react with N0 3" only prior to its first localization with a micelle at 5 x 1 f r 3 M . Furthermore, any such permanent disbursement of Mu into the micelle phase would have led to a two-component muonium fit, as with the quam/N03-experiment. This leaves possibility (d) , a limited degree of localization. In quantitative terms there are three approaches: (/) estimate the localization time from the failure to observe two separate Mu components, (ii) calculate the residence time from the extended lifetime of Mu divided by the total number of encounters it makes with micelles, and (iii) propose a kinetic model. Approach (i) can only give an upper limit and is not very useful because of the difficulty in actually evaluating the point at which separation would be evident. One can assert only that less than hall the muonium atoms spent less than half their lifetimes localized. This puts an upper limit of =250 ns on the mean residence time (7"R). A lower limit of 7"R can be deduced from the time Mu would take to traverse an equal volume of water using 7"R > d2/2D, where D is its diffusion coefficient in water (= 7 x. 10~5 cm 2 s - 1 (15), taking it to be the same as H (10)) and \/dz is the mean diffusion distance (= micelle radius). For SDDS (r = 1.7 nm) this gives 7 R > 0.21 ns, so we have 0.21 < 7R < 250 ns. The second approach (ii) is to calculate 7"R from the changed Mu lifetime (AX(~„Sir) - AX^1,) for a reaction of given efficiency (JtM/Jt(oifT)) due to the relative number of encounters with micelle and solute for solute-to-micelle ratios in concentration (ISl/lmic]) and radii (rti)/r{mic)) according to eq. [4], Based on the most sensitive NO3-/SDDS data (lines 1 and 2 of Table 2, extremes of Fig. 2) we have the Mu lifetime increasing from 670 to 1250 ns, with a concentration ratio of 1:5, for species whose radii ratio is = 1:5, and for a reaction that occurs about once per 13 encounters ( i M = '-5 x 109 M " 1 s"' for N0 3 " whereas the diffusion controlled limit, *<difr,. for Mu with ions in aqueous solution averages to 2 x 10'° M"' s"1 (10)). These values yield T R = (1250 - 670)(l/13)(l/5)(l/5) = 1.8 ns. Let us take 7"R = 2 ± 1 ns in view of the uncertainty in the r ( 5 ) / r ( m i o factor (an effective encounter radius for N 0 3 _ of 0.3 nm has been assumed). |4] 7R = (AX7m' ic) - AX7,,'))(<:M/*difT)([S]/Imic])(r(4,/r(miC)) For approach (iii), the following mechanism is proposed: Mu,.,, + em ^ Mil,™,, A M Mu,,,, + S,.,, P, Mu l^/fern) —* P2 Appendix . Collaborative work already published 154 VENKATESWARAN ET AL 2.0 3.0 J.O 5.0 6.0 [em] / I O " 3 K' FIG 3. iM|S],^,/AX ploned against concentration of unoccupied SDDS micelles ((em)). (•) for NCV as solute. (•) S :0 3 2" as solute. where "em" represents an empty (unoccupied) micelle. In u.SR experiments no distinction is possible between Mu in different phases, and because of (/) above, eq. |5] applies. 15] -d[Mu]/d, = MlMu, e m l ] + |Mu l a q]) Since (ii) above has indicated that the Mu residence time (7"R) is very much shorter than the chemical lifetime (X - 1), an analysis ' that leads to eq |6). based on pre-equilibrium approximations, is appropriate. This can be rearranged to eq. [7], and the plot of the left-hand side against lem] is shown in Fig. 3 for the NOr/SDDS data. A good straight line is obtained with slope equal to 175 ± 39 M" 1 . The more limited S 2 0 3 J 7 S D D S data are also included, thereby giving an overall least-squares fit of 167 ± 37 M" 1 . Since this equals kjkt, an estimation of ka must be made. Based on eq. 18], (since the micelle is much larger and more sluggish than Mu (10)), one gets ka = 8.8 x 10'° M" 1 s"1 using data already given. (This agrees well with the factor of =5 taken for radii ratios since k(Mri for small molecules is 2 x 101 0 M - 1 s"1). Therefore, * c is deduced to be 5.3 x 108 s~' and 7"R. its inverse, equals 1.9 ns. Everything points to a mean residence time for Mu at an empty SDDS micelle of 2 ns. 16] AX = * M l S U & / ( W e m U , , + *l) 17] * M [ S ] u q l / A X = 1 +t d(em)/t, 18] *„ = r,micAMu.(4TT/VA10-3) This is much too short a localization time for "confined diffusion" to be responsible for the colossal enhancements that have been seen for some Mu reactions taking place inside micelles (1). The natural concentrating effect due to the water-to-micelle volume ratio evidently pertains only for 2 ns; there-fore, the total number of encounters falls far short of that required to explain the lO^-fold enhancements (1). In fact, this 2 ns is probably no longer than the extended time scale caused by Mu having to traverse the more viscous phase of 19S3 a micelle's interior. In this case localization has not occurred; the muonium atom has merely been slowed down by the changed microviscosity. Pursuing this point further: if we assume Mu follows the Stokes-Einstein relationship inside micelles, as it does in water (10) , then eq. [9] applies, where r\ is the local viscosity and / \ , M u ) is the effective radius of Mu. Even on taking the minimum value for the latter, namely the Bohr radius of 0 . 0 5 3 nm, one calculates 7"R = 10 ns for T| = 3 0 cP (which is reported to be the internal viscosity, from fluorescence studies based on the mobil-ity of pyrene (16)) . In other words, the expected diffusion time is at least fivefold larger than the observed residence time. Or, put the other way, using 7"R = 2 ns in eq. |9], one gets an effective viscosity of only 6 cP. Since we know Mu penetrates the central core of micelles, because it reacts readily with organic solutes such as styTene localized there, our T R value suggests that there is considerable water penetration into micel-les and a large viscosity gradient across them. Coupled with this is the possibility that the hydrocarbon tails are more randomly oriented than hitherto supposed. The value of T\ = 6 cP presum-ably represents the mean microviscosity sensed by the track of a muonium atom; 6 cP lies squarely between that of pure water ( 0 . 30 cP) or dodecane ( 0 . 43 cP) on the one hand, and the viscous intertwining ( 30 cP) of surfactants in micelles as seen by a large organic molecule such as pyrene (16) on the other. [9] rR = 3mP* ( M U )T , / * B r Acknowledgements The assistance of Dr. J . M. Stadlbauer, Zhennan Wu. and the staff of the u,SR group at TRIUMF is very much appreciated. Funds for these experiments came from NSERC of Canada. The continuous support of this research program by the Directors of TRIUMF and the Heads of the Department of Chemistry over the years is gratefully acknowledged. 1. K. VENKATESWARAN, M. V . BARNABAS, Z. W U . J. M. STADLBAUER. B. W. NG , and D. C. WALKER. Chem. Phys. Leu. 143,313(1988). 2. Y. C . JEAN. J. H. BREWER, D. G . FLEMING, D. M. GARNER, and D. C. WALKER. Hyperfine Interact. 6, 409 (1979). 3. V . W . HUGHES. Annu. Rev. Nucl. Sci. 16,445(1966). 4. J . H. BREW'ER and K. M. CROWE. Annu. Rev. Nucl. Pan. Sci., 28,239(1978). 5. A. SCHENCK. Muon spin rotation spectroscopy. Adam Hilger, Bristol and Boston. 1985. 6. K. M. BANSAL, L. K. PATTERSON. E. J. FENDLER, and J H. FENDLER. Int. J . Radiat. Phys. Chem. 3, 321 (1971). 7. J . H. FENDLER. Membrane mimetic chemistry. Wiley-Intersci-ence. New York. 1982. 8. J . K. THOMAS. Acc. Chem Res. 10. 133 (1977). 9. K. VENKATESWARAN and 1. D. REID. TRIUMF 'DIMUO' u.SR MINUrr fitting program. 10. D. C. WALKER. Muon and muonium chemistry. Cambridge Uni-versity Press, Cambridge. 1983. 11. K. KALYANASUNDARAM. Chem. Soc. Rev. 7 . 4 5 3 (1978). 12. N. J. TURRO, M. GRATZEL, and A. M. BRAUN. Angew. Chem. Int. Ed. Engl. 19,675(1980). 13. F. M. MENGER, J . M. JERKUNICA, and J . C. JOHNSTON. J . Am Chem. Soc 100,4676(1978). 14. F. M. MENGER and B. J . BOYER. J . Am. Chem. Soc 102, 5936 (1980). 15. V . A. BENDERSKII and A. G . KRIVENKO. High Energy Chem. (Engl. Transl.) 14, 303 (1980). 16. M. GRATZEL and J. K THOMAS. J . Am. Chem Soc. 95. 6885 (1973). Appendix . Collaborative work already published 155 Reprinted from The Journal of Physical Chemistry. 1989, 93, 388. Copyright © 1989 by the American Chemical Society and reprinted by permission of the copyright owner. Muonium and Free-Radical Yields As Determined by the Muon-Level-Crossing-Resonance Technique In Aqueous and Micelle Solutions of Acrylamide Krishnan Venkateswaran, Mary V. Barnabas, Robert F. Kiefl, John M. Stadlbauer,* and David C. Walker* Departments of Chemistry, Physics and TRIUMF. University of British Columbia. Vancouver, B.C.. V6T IY6. Canada (Received: May 4. I988j Muonated free radicals that form in pure unsaturated organic compounds are also found to occur in dilute aqueous micelle solutions of these compounds, where thermalized muonium atoms are the only possible precursors For 2 X IO"4 M acrylamide solutions in pure water, the fractional yield of the CHj(Mu)CHCONH) radicals is observed by LCR to be 0 2 (consistent with the muonium yield by uSR). The Mu radical yield increases with acrylamide concentration until at —0 2 M it equals 0.38. which, along with the fraction of muons in a diamagnetic environment, account for the entire muon polarization. Hyperfine coupling constants of the protons in the CH,(Mu)CHCONH, radical have also been determined. Introduction The development of the muon-level-crossing-resonancc (LCR) technique1 and its application to free radicals in unsaturated organic compounds1 allows the products of muonium reactions occurring on the microsecond time scale to be observed.'"* A radio frequency (if) resonance method has also been demonstrated 'Department of Chemistry. Hood College. Frederick. MD 21701. to do this,1 although the LCR method has the advantage of not requiring an rf field. Prior to these developments, muonated (I) Kreitzman. S. R.. Brewer. J H . Harchman. D. R.; Keitel. R Wit-liami. D LI.; Cro»e. K M.; Ansaklo. E. J Pliyi. Kn. Lett St. 181 (21 (al Kiefl. R F. Hyptrflnt Inttrocl \HU>. 32. 707. (b) Kiefl. R. F.; Kreuzman. S. R.; Cclio. M.; Keitel. R.; Bre»er. J H.: Luke. O. M.: Noakes. D R.: Percival. P W ; Mauuzab. T.; Siihiyama. K fhyi. RK. A I9U. 34. 681. O022-3654/89/2O93-O388SO1.50/O £ 1989 American Chemical Society Appendix . Collaborative work already published 156 Muonium and Free-Radical Yields .003 -.0:3 I ' ' /I—' 1 ' 1 1.314 I.3SE4 I.4E4 1.8514 2X4 2 . 0 S E 4 L o n g i l u d l D A t M a c t k t ' . l c r i e l d ( G ) Figure 1. LCR spectrum of I M acrylamide in water, given as asym-metry against longitudinal Held. Resonances were found only at 13.6 and 19.9'kG. radicals were observable only in pure materials or concentrated mixtures by the transverse-field muon spin rotation method (TF (iSR).' In this method the radicals had to be formed in less than 10"* s to ensure initial phase coherence. In the concentrated media needed for the T F method, the radicals could be formed from the incident muons by ionic processes or by direct epidermal muonium atom additions. In the present paper, using LCR, the organic compounds were at low concentration in water or localized in micelles at only 2 X I0" ] M (1 M = 1000 mol m"J). Experimental Section These studies utilized 4-MeV positive muons that were spin polarized parallel to their momentum on the M20 channel at the T R I U M F cyclotron. For L C R studies the magnetic field was applied parallel to this direction, and for the T F uSR measure-ments it was applied perpendicularly by rotation of the muon spins. Details of the experimental method have been described previ-ously.2" An integral technique was used to detect the level crossings. Resonant transfer of polarization from the muon to a particular nucleus (H in this case) occurs at particular magnetic fields where the muon transition frequency is matched to that of the proton. This results in a decrease in the muon polarization averaged over the muon lifetime (T, •= 2.2 us) and is detected experimentally as a reduction in the muon decay asymmetry along the applied field direction. A small square-wave field modulation of 55 G (5.5 mT; IO4 G « 1 T = 1 V s m"3) was used to average systematic errors, which results in the differential appearance of the resonance (see Figure 1). Each group of equivalent protons gives rise to a single unresolved multiple! whose central position (fiR) is given to a very good approximation by 1 Bt-O.SUA,-At)/{y.-yr)-lAm + Ar)/i,] (1) where the Vs are the magnetogyric ratios of muon, proton, and electron, and A's are hyperfine coupling constants. The solutions were deoxygenated by bubbling with pure N 2 prior to being pumped through a closed system into a Teflon irradiation cell. The position of this cell remained unchanged throughout (3) Heming. M.; Roduner. E.; Pattenon. 8 D.; Odermatt. W.; Schneider. J . Baumeler. Hp.; Keller. H.; Savic. I M Chtm. Phys. Ult. I9M. 128. 100. (4) Percival. P. w.; Kiefl, R. F.; Kreitzman. S. R.; Garner. DM.: Cox. S. F Luke, G. M.; Brew. J. H ; Nahiyama. »U Voikauswarmn. K. Chem Phys. Un. 1*87. 133. 465. (5) Kiefl, R. F.; Percival, P. W.; Brodovilch. J. C ; Leung. S. K.; Yu. D.; Venkaleswaran. K.; Co». S F. 1. Chem. Phys. Lilt. I»M. 143. 613. (6) Venkateawaran. K ; Kiefl, R. F^ Barnabai. M V.; Stadlbauer. J. M.; Ng. B W.; Wu. Z.; Walker. D. C. Chem Phys. Un. 1**8 14}. 289. (7) Azuma, T.; Nishiyama. K.; Nagamine. K.: ho. Y.; Tabata. Y. Hy-ptrflnt I m tract I*M. 32. 837. (8) (a) Roduner. E.; Percival. P. W.; Fleming. D. G.: Hochmann. J.; Fischer. H. Ctitm. Phys. Un. 19T». 57. 37. (b) Roduner. E.; Fischer. H. Chtm. Phys 1*81. 54. 261. The Journal of Physical Chemistry. Vol. 93. A'o /. 1989 389 TABLE I: LCD Positions. Line Widths. Amplitudes, and Calculated Yields for tbe Two Resonances of Acrylamide in Aqueous and Dilute Micelle Solutions AM1/M |SOS]/M' B,/kG AJ/G ampl/'S. P*' 0.0002 0 13.644 (5) 164 (7) 0.132 (11) 0.18 0.0006 0 13.637 (4) 162 (4) 0.194 (14) 0.26 0.002 0 13.626 (4) 159 (6) 0.234 (14) 0.30 0.006 0 13.641 (4) 155 (6) 0.270 (15) 0.33 0.02 0 13.638 (3) 153 (5) 0.287 (11) 0.34 0.06 0 13.643 (3) 155 (6) 0.304 (15) 0.37 0.2 0 13.639 (3) 155 (6) 0 319 (15) 0.39 0.6 0 13.635 (3) 161 (5) 0.291 (15) 0.38 1.0 0 13.642 (3) 159 (5) 0.275 (14) 0.35 0.0006 0 19.963 (6) 85 (4) 0.127 (15) 0.23 0.006 0 19.967 (3) 77 (3) 0.213 (14) 0.31 0.06 0 19.958 (5) 83 (4) 0.200 (15) 0.35 0006 0.002 13.642 (3) 152 (4) 0.291 (14) 0 34 0.012 0.002 13.642 (3) 156 (6) 0.266 (14) 0.33 0.02 0.002 13.643 (3) 155 (6) 0.299 (14) 0.36 0.03 0.002 13.638 (3) 153 (6) 0.303 (14) 0.36 0.04 0.002 13.640 (4) 159 (7) 0.264 (14) 0.34 0.006 0.002 19.961 (4) 82 (6) 0.176 (14) 0.29 0.012 0.002 19.977 (6) 84 (8) 0.142 (15) 0.24 0.02 0.002 19.976 (4) 81 (4) 0.191 (14) 0.31 0.03 0.002 19.970 (3) 82 (6) 0.223 (15) 0.37 0.04 0.002 19.973 (5) 88 (5) 0.175 (15) 0.33 •Sodium octy! sulfate micelles where AM is known to localize. * Calculated by using eq 8. TABLE II: LCR Positions, Line Widths, Amplitudes, and Calculated Yields for tbe C<o)(Mu>-H Resonance of C*H« and "C(6><Mu)-H Resonance of , JC#H« in Cy clone xane sample B^fVC AB/G ampl/S? />R' ChHt (neat) 20.776 (1) 148 (2) 1.974 (14) 0.82 uCtH6/cyclohexane 21.803 (4)* 39 (2)* 0.52 (2)* 0.30 'Calculated by using cq 8. *Data taken from ref 5; these experi-menis were carried out at TRIUMF on the M1 5 beam line where the Ax value is 0.2. TABLE III: Fitted Parameters of the FTT for tbe TF *iSR Spectra of ] M Acrylamide in Water field/kG » 0 / M H z •*/MHZ AJMHz 28.87 391.3 157.7 316.0 26.65 361.1 204.1 314.7 23.30 315.7 158.4 315.4 19.34 262.0 104.3 316.4 15.49 209.9 52.5 315.8 8.00 108.4 48.4 315.9 4.06 55.0 100.5 315.3 these experiments. All solutions were made from triply distilled water in which the chemical lifetime of the muonium atom (u*e~. symbol Mu) is known to exceed 4 (is.* Acrylamide and benzene were of Analar reagent-grade quality. Micelles of sodium octy! sulfate (SOS) were used at 2 X 10"J M where they react at a negligible rate with Mu. Results The LCR spectrum of I M acrylamide in water is shown in Figure 1. It consists of resonances centered at 13.64 and 19.97 kG. Their real amplitudes and full widths at half-maximum were obtained by a MINUIT reduced-*' Glting program to the difference of two Lorcntzians separated by the modulation field of ~55 G ! Table 1 records the resonance position (BR). amplitudes (ampl) and line widths (AB) obtained from the LCR spectra of 10 so-lutions of acrylamide in water from I M to IO"4 M. Data obtained for solutions to which 2 X 10"1 M of SOS micelles had been added are also given there. Table II contains LCR fitted values obtained in pure benzene for comparison purposes. Table II also includes (9) Walker. D. C. Muon and Muonium Chtmisiry, Cambridge University Press: Cambridge. 1983. Appendix . Collaborative work already published 157 390 The Journal of Physical Chemistry. Vol. 93. So I. I9S9 published data' on the Mu"C t H t radical in cyclohexane. The hyperfine coupling constant of the Mu radical involved (AJ was determined b> TF t&R from trie muon precession frequencies of I M acrylamide in water in fields of 4-26 kG. The results for the lower frequency («•*) and for diamagnetic muons (*0) are reported in Table III following fast Fourier transform. Con-ventional »iSR experiments were also performed on acrylamide solutions in water with the following results relevant to this study: the diamagnetic yield P0 (fraction of muons found in diamagnetic Hates) of 1 M acrylamide was 0.62 (indistinguishable, therefore, from pure water') and AM • 2 x 10'° M"1 s"' in acrylamide solutions at — 10"4 M (similar to that obtained for other acrylic solutes'). Discussion Hyperfine Coupling Constants. Muonium atoms in water evidently react with acrylamide (kH = 2 x 10'° M*' s'1) according to Venkateswaran et al. Mu + CH.=CHCONH, MuCH ;CHCONH; (2) io give the radical shown (with one o-H and two fi-Hs). The value of AR was determined from the TF »iSR data in Table 111 by the use of * A./2 + A.'/4yrB (3) which applies to a good approximation' (± refers lo the z com-ponent of the electron spin). The values calculated for each transverse Held (if) are given in Table 111. and the mean value of 315.6 (5) MHz is taken as thai corresponding to the Mu radical shown in eq 2. Applying this to the LCR fields of 13.64 and 19.97 kG through eq I results in the two values for Ap of -56.0 and +61.0 MHz The former undoubtedly belongs to the o-H since ESR data on analogous radicals with various initiators have given At •= ±56 MHz 1 0 Our result shows that the proper sign is in fact negative relative to the muon (proton) hyperfine constant. Our value of +61.0 MHz may be taken as the hyperfine coupling constant for the H atoms 8 to the centre of unpaired electron density in MuCH:CHCONHj Radical Yields. The amplitude of an LCR line should be given by the product of the mean reduction in muon polarization (AP,) and the absolute backward-to-forward asymmetry (Au). multiplied by the fraction of muons yielding muonated radicals (>*»): amp! m APrAtfPt (4) (Ati was determined experimentally under the actual operating conditions to be 0.135 at 13.64 kG, 0.142 at 19.97 kG. and 0.145 at 20.8 kG.) In the absence of spin relaxation, and for spin-'/j nuclei, the theoretical line width Az?iu„. is approximately given by' and A/>, by 21^ + (Xo/2')sl"V(->.-7p) ' " * W + (W2x)')] (5) (6) In these equations. X, is the intrinsic muon decay constant and », is the frequency splitting between the two nearly degenerate levels it Bf. and is given by (7) where r - 1 for the one o>H and c • 2 1" for the two 0-H's. AB observed is typically about twice the theoretical width, A£ ( l l,. The presence of spin relaxation can strongly influence the line shape." However, we will assume that the line shape remains (10) Takakura. K.; Ranby. B. A*. Cmtm Srr. 1***. No 91, 125. Mu ci.yj -. . l i t ! f \ ! • i M l 1 C 1C 0 oc 0C001 0 001 0 l 1 [ GC,:cr-..aej/t.'. Figure 2. Plot of radical yield (r\) against concentration of acrylamide (log scale). O and • points are for solutions in pure water for the resonances at 13.6 and 19.9 kG. respectively. X points are for those acrylamide concentrations lo which 2 x |0"J M SOS micelles were added. O represents the Z points but given as 2 x |0'J M (i.e.. the concentration of occupied micelle*, regardless of the number of acryl-amide* enclosed). V is the value at 2 x 1CT4 M corrected according to eq9. Lorentzian and that ampl(AD)! remains constant. This appears to be valid under our circumstances as shown below. Also, lime-differential measurements on and off resonance indicated no significant relaxation for this radical in water. Combining eq 5-7 with (4) now gives ampl(Ar?)3(-v. - -v,)3 (8) The applicability of this empirical relationship is justified in three ways. First, when calculated for both resonances (13.64 and 19.97 kG), where ampl and AJ3 are quite different, similar values are obtained for / y These values are recorded in the last column of Table 1 for the full range of acrylamide concentrations. Second, when applied to the benzene data of Table II. eq 8 gives P„ «= 0.82 (4). This yield corresponds closely to the recent value of P* •= 0.80 (2) obtained by TF MSR . " and it equals 1 - PD for benzene' Third, for the published "QH^ in cyclohexane solution,' eq 8 gives PK « 0.30. Again this is consistent with expectations, because the muonium yield in cyclohexane is of that order.15 In addition to the above three points, it is reassuring to find the values of Pr for acrylamide solutions to fit perfectly into the explanation offered below. Our Mu radical yields obtained through application of eq 8 to the data of Table I are plotted in Figure 2 against the logarithm of the acrylamide concentration. P* is seen to increase from ~0.18 at 2 x 10"* M to ~0.38 at 0.2 M. With reaction 2 as the source of the radicals, the amplitude is expected to be low at the 10""* M level, because the formation time (~0.5 «is) is comparable with the average muon lifetime (T, « 2.2 «is). A known collection for this effect can be applied by using' />» « &y[AM]/(X{. + iM[AMJ) (9) and the corrected value gives P„ " 0.20 at 2 X 10 - 1 M acrylamide (AM). At the high concentration end the radical yield (0.38) is very close to 1 - PD for water. This indicates that all muons that arc not directly incorporated into diamagnetic states can be picked (11) Hcming. M.; Roduner, rU Patterson. B. D. Hyptrfut Imrraa. 19M. S3. 727. (12) Roduner. E.. private communication. (13) ho. Y . Ng. B. W.: Jean. Y. C ; Walker. D. C. Can J. Ckem IM0. 51. 2395 Appendix . Collaborative work already published 158 Muonium and Free-Radical Yields up to give radicals under these conditions when acrylamide was localized in dilute micelles in the waier. the same radical is formed and with about the same yield as in the absence of micelle (see Table I) In Figure 2 these micelle data are plotted both as bulk concentrations (moles of acrylamide per liter of solution) and as concentration of occupied micelles In the former method they fall within the experimental error of solutions containing no micelle. On the basis of the latter method, the radical yield is higher for occupied micelles at 2 x 10"] M than for 2 x 10"' M acrylamide in water. This shows that the micelle's large encounter radius enhances the efficiency of reaction 2 somewhat. Furthermore, there is no detectable change in yield when the number of solutes per micelle is increased from 3 to 20. consistent with the diffusion-limited character of reaction 2 (An average ratio less than 3 was not used here to avoid a significant fraction of the micelles being unoccupied, since they can alter the chemical lifetime of muonium u ) The only possible precursor to the Mu radicals in these ex-periments is the muonium atom. These solutions were much loo dilute for significant "direct* effects from "hot" Mu atoms or "excited" states, and the results with charged micelles remove any possibility that muonated ions are the immediate precursors These radical yields therefore give a direct measure of the Mu atoms present in water at times given by I/AM[acrylamide]. This time scale is shown on the upper abscissa of Figure 2. Muonium Yields. For measurements in which the applied magnetic field is transverse to the muon polarization, it is well established that in pure water 625 of the incident muons become incorporated in diamagnetic states (PD = 0.62). 20% are observable as Mu. Pu = 0.20. and the remainder are lost—called the missing fraction. / ° L = 0.18." This lost fraction is though, to be due to lime-dependent interactions of Mu (including spin depolarization), since it can be "recovered" as an increase in PD by solutes that rapidly react with Mu to form diamagnetic states.' The LCR ' s in the present experiments are observed with large magnetic fields applied along the initial muon polarization direction. In this situation the muon and the electron spins are decoupled, so there is no "loss" here due to spin depolarization of the muon in muonium. Figure 2 is now readily interpreted in the following way. A l the low concentration end. P^ = 0.20 (2) corresponds to the full muonium yield surviving into the microsecond time scale of MSR (namely. PM = 0.20 (1)). In the high concentration limit, PH = 0.38 (2) corresponds to the initial muonium yield (namely, PM + PL) This shows that acrylamide. even at 0.2 M. picks up the whole missing fraction as well as PM. The ordinate of Figure 2 represents the fraction of Mu atoms surviving for the limes in-dicated by the upper abscissa scale. Evidently, the loss processes responsible for the missing fraction in these acrylamide solutions set in at about 3 ns and continue until 2S0 ns or so. Loss of Mu must occur because of a chemical reaction of Mu with species X Mu + X — M u X (10) in competition with acrylamide (reaction 2). If this were a simple competition, based on random distributions, then the kinetics would give ! I * * x [ X ] / t M ( A M ] and a plot of *V' against (AM]'1 should be linear. This plot is shown as Figure 3, but it is markedly curved (concave down) over the full range lvf-O^ M. Furthermore, if reaction 10 were occurring homogeneously, then a residual fraction of Mu atoms (Ml Vcnkauawaran. K.; Barnabas. M. V.; Ng. B W.; Walker, D. C. Can. J Chtm.. in p r c u . (151 Percival. P W.; FiKher. H.; Camani. M.; Cygaa. F. N.; Roegg. W.; Schenl. A.; Schilling. H : Graf. H. Chtm Phys Lett. 1*7.. )9. 333 The Journal of Physical Chemistry. Vol. 93. So. I. 1989 391 i. ± • ' 1 1 ' c i i c j 200C 2 L - C : ; e c : : ! . /[ C C ' y i = ~ : 5 f ] Figure 3. Plol of )/P, against 1/[AM] to lesl whether eo, I 1 applies (symbols are the same as in Figure 2). would not be observed much later by uSR. whereas, in fact, aboui half the initial muonium atoms are seen to be stable over the microsecond time scale, giving Pu - 0.2. These two effects can be explained by the local "concentration" of X in the vicinity of Mu decreasing with increasing time, so that nonhomogeneous kinetics pertain. This is lo be expected if species X consists of the reactive radlolysis products of the muon's track, because in an L C R experiment each track exists ir. solution in almost complete isolation. At the highest fluxes used there is only aboui one muon striking the cell per square centimeter per mi-crosecond, and it produces a track of some 10 ! hydrated electrons and O H radicals peaking in L E T toward the end (plus minor amounts of H-O; and H 3). Mu starts its chemical existence ai the end of this track of species. Diffusion leads to expansion of the track and overlap with Mu until, at ~10"* s. the local con-centrations have dropped to —10"* M when further reactions between species become improbable (see Figure 6.16 of ref 9). Figure 2 is not inconsistent with this picture, with half the Mu aioms lost between 3 X 1 0 " * and 5 x 10"1 s. It is further com-plicated, however, by the presence of acrylamide as a homoge-neously distributed solute at the various concentrations given Acrylamide converts e„ " and O H to free radicals, as in e „ " - t - A M — A M " (12) O H + A M — A M ( O H ) (13) at progressively shorter times for higher [AM] In effect X will consist of changing mixtures of e„." and O H . or A M " and A M -(OH), all of which should react with Mu at least as fast as reaction 2. i.e.. >2 x 10'° M" ' s"1. But A M " and AM(OH) diffuse much more slowly than e.," and O H . so there can be an inversion or extension of overlap lime with increasing [AM]. This may even account for the slight maximum seen at ~-0.2 M in Figure 2. Regardless of the details in the competition between reactions 2 and 10 there arc two general conclusions to be drawn from Figure 2 regarding the missing fraction PL. First, it occurs well after dissipation of individual spurs in these acrylamide solutions. Second, the loss process is not a "simple depolarizing encounter such as electron spin-exchange interaction, because it is seen here in the presence of large decoupling fields These results therefore suggest that the "loss" processes are combination reactions to give diamagnetic species, as in Mu + e^" — Mu" — MuH + O H " (14) Mu + O H — M u O H (15) where these products cannot contribute to the coherent PD yield Appendix . Collaborative work already published 159 392 in uSR. even in Ion transverse fields, because thev form too slou.K (>IO-'s). Summary A Mu radical has been observed by the LCR method to be the product of a muonium atom adding to acrylamide as a solute at concentrations down to IO"4 M. Its yield at the lowest concen-tration corresponds closely to the yield of Mu*observed by uSR between -3 x Ifr' and ~3 x IO"6 s {PM •= 0.20). At high |AM) the radical yield (0.38) corresponds very nicely to PM + >\ (and to I - PD) All the muons in water are thus accounted for: 62" of them are converted "directly" into diamagnetic slates, and all the rest appear as muonium atoms—about half of which escape from the muon track Acknovlrdgmtni Collaborations with Bill Ng and Zhennan Wu and the assistance of John Worden and Keith Hoyle are much appreciated. Financial support was provided by NSERC of Canada Registry No M U C H J - K T H C O N H J . 1 16887-3 ] -1. Appendix . Collaborative work already published 160 1 P r e p r i n t - i n p r e s s Chem. Phys. Muon Level Crossing Resonance Study of Radical Formation in Allylbenzene, Styrene and Toluene K r i s h n a n V e n k a t e s w a r a n , M a r y V . B a r n a b a s , Z h e n n a n W u , J o h n M . S t a d l b a u e r 1 , B i l l W . N g 7 a n d D a v i d C . W a l k e r D e p a r t m e n t o f C h e m i s t r y a n d T R I U M F , U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r , B . C . , V 6 T 1 Y 6 , C a n a d a . Abstract A l l c h e m i c a l s t a t e s o f t h e m u o n s i n a /*SR e x p e r i m e n t h a v e n o w b e e n d e t e r m i n e d i n t o l u e n e , a l l y l b e n z e n e a n d s t y r e n e . T h e r e a r e n o ' m i s s i n g f r a c t i o n s ' b e c a u s e t h e s u m o f t h e v a r i o u s m u o n - c o n t a i n i n g f r e e - r a d i c a l s e q u a l s \-PD, w h e r e PD i s t h e d i r e c t l y f o r m e d d i a m a g n e t i c f r a c t i o n . U s e o f t h e n e w t e c h n i q u e o f l e v e l c r o s s i n g r e s o n a n c e s p e c t r o s c o p y h a s e n a b l e d y i e l d s t o b e d e t e r m i n e d a n d i d e n t i f i c a t i o n o f i n d i v i d u a l i s o m e r i c r a d i c a l s . F o r t o l u e n e , t h e r e i s a t o t a l r a d i c a l f r a c t i o n o f 0 .77 a n d a d i s t r i b u t i o n o f 2.5:2:1 f o r o : m : p a d d i t i o n w i t h i n t h e r i n g . F o r a l l y l b e n z e n e , ~ 7 0 % o f t h e m u o n a t e d r a d i c a l s a r e s i d e c h a i n a d d i t i o n p r o d u c t s a n d o f t h e s e n e a r l y 4 0 % h a v e M u o n t h e s e c o n d C ; a n d , f o r t h e 3 0 % a d d i n g t o t h e r i n g , t h e r e i s v i r t u a l l y n o s e l e c t i v i t y o f s i t e a s t h e o : m : p r a t i o i s t h e s t a t i s t i c a l r a t i o 2 :2 :1 . T o l u e n e a n d a l l y l b e n z e n e , h o w e v e r , d i f f e r d r a m a t i c a l l y f r o m s t y r e n e . I n s t y r e n e , 8 0 % o f t h e m u o n s f o r m r a d i c a l s a n d 8 5 % o f t h e s e a r i s e f r o m f o r m a l a d d i t i o n o f m u o n i u m t o t h e e n d C o f t h e s i d e c h a i n t o g i v e t h e m u o n a t e d p h e n y l e t h y l r a d i c a l . T h e r e m a i n i n g 1 5 % a r e s e e n t o b e d i s t r i b u t e d ( 2 : 1 ) b e t w e e n t h e o r t h o a n d p a r a p o s i t i o n s o f t h e r i n g , w i t h n o a d d i t i o n a t t h e m e t a p o s i t i o n . T h e h i g h d e g r e e o f p r e f e r e n c e s h o w n b y s t y r e n e i n d i c a t e s s t r o n g s e l e c t i v i t y i n a c h i e v i n g t h e m o s t s t a b l e r a d i c a l . P r o t o n h y p e r f i n e c o u p l i n g s f o r a l l o f t h e s e r a d i c a l s h a v e aJ so b e e n d e t e r m i n e d . I n t r o d u c t i o n F r e e r a d i c a l s s u b s t i t u t e d w i t h m u o n i u m ( c h e m i c a l s y m b o l M u , t h e l i g h t h y d r o -g e n i s o t o p e ) h a v e b e e n o b s e r v e d b y t h e t r a n s v e r s e field m u o n s p i n r o t a t i o n ( T F - j i S R ) t e c h n i q u e [ l ] , a n d r e c e n t l y b y u s i n g m u o n l e v e l c r o s s i n g r e s o n a n c e ( L C R ) [ 2 - 4 ] o r r a d i o -f r e q u e n c y r e s o n a n c e t e c h n i q u e s [ 5 ] . W h e r e a s T F - / i S R r e q u i r e s t h e r a d i c a l s t o b e f o r m e d p r i o r t o a n y s i g n i f i c a n t s p i n p r e c e s s i o n i n t r a n s v e r s e m a g n e t i c fields ( < < I n s ) , t h e l a t -t e r t w o d o n o t i m p o s e a n y s u c h s h o r t t i m e s c a l e r e s t r i c t i o n s , w i t h t h e m u o n l i f e t i m e ( 2 .2/ i s ) b e i n g t h e f u n d a m e n t a l l i m i t a t i o n . I n f a c t , t h e L C R t e c h n i q u e a l l o w s o n e t o f o l l o w f r e e - r a d i c a l f o r m a t i o n [ 6 ] a n d d e c a y p r o c e s s e s [ 7 ] o c c u r r i n g o v e r m i c r o s e c o n d s , a s w e l l a s i n b e i n g a b l e t o d e t e r m i n e i n d i v i d u a l f r e e - r a d i c a l y i e l d s [ 8 ] . L C R i s a l s o a v a l u -a b l e c o m p l e m e n t t o E S R i n g i v i n g n u c l e a r h y p e r f i n e p a r a m e t e r s [ 9 , 1 0 ] a n d a l l o w i n g t h e s t u d y o f d y n a m i c a l e f f e c t s s u c h a s i n t r a m o l e c u l a r m o t i o n i n o r g a n i c f r e e r a d i c a l s [ l 1]. W h e n e n e r g e t i c p o s i t i v e m u o n s e n c o u n t e r a n u n s a t u r a t e d o r g a n i c c o m p o u n d , t h e y e n d u p i n o n e o f t h e f o l l o w i n g f r a c t i o n s : i ) i n a d i a m a g n e t i c s t a t e {PD) o r ( i i ) i n a m u o n a t e d r a d i c a l (PR), o r ( i i i ) t h e y u n d e r g o a l o s s o r d e p o l a r i z a t i o n p r o c e s s a n d a r e c o u n t e d i n t h e s o c a l l e d " m i s s i n g f r a c t i o n " (PL)- NO f r e e m u o n i u m a t o m s h a v e b e e n o b s e r v e d i n x - b o n d e d o r g a n i c m o l e c u l e s - . p r e s u m a b l y b e c a u s e t h e y r a p i d l y a d d a c r o s s t h e m u l t i p l e b o n d . I n n e a t u n s a t u r a t e d c o m p o u n d s t h e d e d u c t i o n o f m e c h a n i s m f o r ' D e p a r t m e n t o f C h e m i s t r y , H o o d C o l l e g e , F r e d e r i c k , M D 2 1 7 0 1 , U S A . 2 C h e m i s t r y D e p t . , W i n o n a S t a t e U n i v e r s i t y , W i n o n a , M N 55987 , U S A . Appendix . Collaborative work already published 2 radicaj formation (origin of PR) is complicated by tlie fact that, in addition to muonium atoms, species such as epithermal or "hot" Mu (Mu*) as well as ions[l2] ( transient cationic or anionic radical intermediates that are subsequently neutralized by track species) are thought to contribute. These possible mechanisms may be represented by the reactions: Mu + RCH : CHR\ —• RCHCHR\ (Aiu) (1) Mu* + RCH : CHRi —> RCHCHRi (Mu)' (2) -f RCH : CHRi —• RC+ HCHR1(Aiv),+e~ —> RCHCH Ri(Mu) (3) e~ -t- RCH : CHR\ —> RCHC~HRi —. RCHCHR^Mu) (4) For pure organic compounds containing jr-bonds, all four reactions are possible; but for dilute solutions, and in particular for dilute aqueous or micelle solutions, reac-tion (1), involving thermalized muonium atoms, is the only possible precursor to the radicals [6,8]. For pure benzene[]3], acetone[6,14], aqueous and micellar solutions of acryiamide[8], and for benzene solutions in hexane[l5], it has now been shown that all the muons are incorporated either in a diamagnetic state or as muonated radicals and that there is no "missing fraction". The origin of PL has been a matter of interest for more than a decade, with depolarization of Mu through spin-exchange encounters, or combination reactions to give diamagnetic states, as possible sources. In this paper, experimental results are reported for a comparative study of radical formation in substituted benzenes (methyl, vinyl and allyl) using the attributes of level crossing resonance. These systems have each been studied by TF-//SR and the relevant muon hyperfine coupling constants (hfcc) are available[16-19]. Here, proton hfcc's are also obtained and the results are used to calculate absolute yields for the different isomeric radicals. Experimental These studies utilized 4MeV positive muons spin polarized parallel to their mo-mentum on the M15 channel at the TRIUMF cyclotron. For LCR studies the magnetic field was applied parallel to this direction, and for the TF-j/SR measurements it was applied perpendicularly by rotation of the muon spins. Details of the experimental method have been described previously^',3,4]. An integral technique was used to de-tect the level crossings. Resonant, transfer of polarization from the muon to a given nucleus (H in this case) occurs at particular magnetic fields where the muon transition frequency is matched to that of the proton. This results in a decrease in the muon polarization averaged over the muon lifetime (rM = 2.2^s), and is detected experimen-tally as a reduction in the muon decay asymmetry along the applied field direction. A small square-wave field modulation of ± 5 m T was used to average systematic errors, which results in the differential appearance of the resonance (see Figs. 1-3). Each group of equivalent protons gives rise to a single unresolved multiplet whose central position (BR) is given to a very good approximation by Eq. (5)[6], BR = 0.5[(y,„ - Ap)/(y„ - Tp) - (AM + Ap)/yc] (5) where the 7s are the magnetogyric ratios of muon, proton and electron, and A s are hyperfine coupling constants of / i + and p + . Benzene and toluene were obtained from BDH and were of AnalaR grade purity while allylbenzene and styrene (Gold label) were from the Aldrich Chemical Co. These Appendix . Collaborative work already published 162 3 neat compounds were used in stainless steel cells (with thin windows to allow the low momentum muons to piss through) which were either vacuum sealed after freeze-pump-thaw cycles or were deoxygenated by bubbling with pure N2 through septa seais. A MINUIT reduced-xJ fitting program was used which allows the raw data to be analyzed using a difference ot two Lorentzians for BR (the LCR position), A S (width at half height of the LCR), and ampl (the amplitude of the LCR signal given as percentage). The muonated free radicals formed by stopping energetic muons in pure benzene, toluene, allylbenzene and styrene are represented in Scheme 1 and have structures I-XI. Figures 1-3 show the resonance spectra for the different protons (as marked) arising from the resonant transfer of spin polarization between the muon in the radical when its transition frequency is matched to that of another nucleus of non-zero spin (H here). Table 1 gives their experimental hyperfine parameters of A^iiom TF-/iSR), BR and AH values calculated using Eq. (5). The theoretical values of LCR frequencies (vp) and linewidths (A5(n)) were determined using the equations reported previously[8]. The experimental data fitted for BR, ampl and AS, along with the calculated PR fractions, are reported in Table 2. The PR values were determined from the observed parameters using Eq (6)[8], Using a PR value Of 0.82(3) for benzene, absolute asymmetries(y4(,/) were determined to be 0.133, 0.125 and 0.110 at 2.0,1.4, and 0.9T respectively. These Abl values were confirmed by two experimental methods. The first method used aqueous Mn 2 + solutions with the backward to forward asymmetry being measured as a function of field. Second, a single crystal of M n F 2 was used in time differential measurements as a function of field. The two approaches gave similar values. All PR values reported here carry an error of about 109c from this source. Conventional T F - / J S R experiments were also carried out to measure the PD values, typically at 0.08T. A tally of the observed radical and diamagnetic fractions is given in Table 3 (columns 2 and 8). Column 9 (1-Pxj) compares favourably with column 2. Discussion 1. Resonance Assignments and Proton Hyperfine Parameters: • (a) Toluene: The LCR spectrum of toluene is shown in Figure 1. Based on the reported muon-electron hyperfine coupling constants[l6] the three observed reso-nances can be assigned to those from the protons in substituted methylenes (-CHMu) in structures II(o,m,p). From the BR values and Eq. (5) we ob-tain the proton-coupling constants(A//) for ortho, meta and para additions in the range 120-130 MHz, as reported in Table 1 column 5. There is good agreement for the AH obtained in benzene also shown in Table 1 as well as to the values obtained from ESR measurements[23]. The neat benzene LCR's have been previously characterized[9]. At least eight more reso-nances have been observed due to other protons, once Mu adds to the R e s u l t s PR = (AB)7.ampl.(y. - 7p)2 Ab,.u} (6) Appendix . Collaborative work already published 163 4 or tho or para or meta sites. Their assignments and a detailed discussion is beyond the sqope of this paper and will appear as a separate publication. • (b) Allylbenzene: Eight resonances were observed in this compound (Fig. 2) and are assigned to those arising from the five different muonated radicals with structures shown in Scheme 1 (HI, IV, V (o,m,p)). By comparing Fig. 2 with Fig. 1 the resonances from 1.98 to 2.15T can be readily assigned to be those from radicals V(o,m,p) in Scheme 1. Assuming the A U values for ring radicals in allylbenzene to be similar to those in toluene (490 -510 MHz), the calculated AH values fall in the same range of 120-130MHz. The three strongest peaks observed (at 1.969, 1.274 and 1.312T) can be assigned to the predominant radical(III). This is the radical previously observed by transverse field ;;SR lechnique[l8,19] to have A„ ~ 306MHz. In this radical there are two 0 and one a positions. Assuming the two resonances of similar amplitude at 1.274T and 1.312T are due to the pro-tons on the 0 carbons, we calculate the corresponding hyperfine coupling constants AH?} and Ann to have values of +70.28 and +63.22 MHz re-spectively. Our specific assignment here to the protons attached to the 01 and 02 carbons (Scheme 1,111) is made by analogy with an ESR study of 0-hydroxyalkyl radicals by Kirino[24]. He reported hyperfine parameters of 70.62(methyl), 60.79(5-11) and 59.38(o-H) MHz for the CH3CHCH2OH radical produced by addition of Oil to propylene. We consequently assign the .emaining resonance al 1.9C9T to the 0. - proton and thus find a value of -58.81 MHz for A Ha in radical III. This is similar to A Ha in other vinyl compounds[29]. The radical IV has also been observed in TF-//SR and the muon hyperfine coupling constant was determined to be equal to 330.6 MHz[19]: so the remaining two LCR's observed here at 2.101 and 1.388T can be assigned to the o and 0 protons in this radical. Proton hyperfine parameters of -59.68 and +72.64 MHz are thus calculated for this radical for AHO and AHS respectively. They are seen to be typical of alkyl radicals[25,9]. For example, ESR measurements on the radical of n-propyl alcohol[25] gave coupling constants of 60.48 and 74.48 for the o and 0 protons respectively. The sign on the coupling constant is also determined relative to A^ in LCR measurements. • (c) Styrene: The phenylethyl radical (VI) has already been shown by TF-/iSR to be the most predominant muonated species in styrene[]8,19,2l]. This is thor-oughly endorsed by our present LCR results which show intense peaks at 0.907 and 1.393T. The former resonance corresponds to the 0 protons and gives AHS = +45.06 MHz, whereas the latter results in a value of—45.39 MHz for AHO- The signs on these parameters are consistent with those obtained for other vinyl monomers by LCR - with a H's negative and 0 H's positive [8,9,29]. Dobbs et al.,[26] obtained hyperfine couplings of 50.12 and 45.64 for the 0 and a protons in CtHsCHCHz, which are in reasonable accord with our values (bearing in mind the inability to obtain signs on the hyperfine constants by ESR). Our o>-H coupling constant is Appendix . Collaborative work already published 164 5 also similar to that reported for the benzyl radicaJ (C6 / / jC / /2 ) [27-29] . Two resonances of much smaller amplitude at 1.421 and 1.507T were also observed in pure styrene(Fig. 3). The assignment of these presents us with three possibilities, and we favour the first: (i) They are from Mu-*substituted methylene protons in cyclohexadienyl radicals (Vl l (o ,m,p) ) . Our transverse field /iSR measurement at 0.15T in neat styrene showed two minor radicals after 100-120 million events with muon hyperfine couplings of 424.8 M H z and 378.1 M H z (similar to that reported by Geeson et al.[l9] for the ortho and para substituted positions). We assign the resonance at 1.507T, which is of a larger amplitude, to the Mu-substituted methylene ortho to the substituent. AH values of 144.9 and 114.1 M H z are thus obtained for the ortho and para methylene protons respectively. The differences in these values compared to those in other cyclohexadienyl radicals (typically 120-130MHz) suggests a higher electron density at the ortho position due to significant delocalization on to the substituent. (ii) They could be due to the ring protons in the phenylethyl radical VI analogous to those observed for the benzyl radical[27]. If they were so, then one obtains AH values of-66.48 and -50.48MHz respectively for the ortho(1.507T) and para(] .42lT) resonances. These AH values are much larger than the E S R values for the the benzyl system (14.36 and 17.28 M H z for ortho and para respectively)[27]. Hence we rule out this possibility. (iii) One of these two resonances could also arise from muonium addition to the inner C of the vinyl group as shown in Equation 7, Mu + CtHiCH = CH7 — CtHiCH(Mu)CH2 (7) One can see that delocalization is broken by the Mu-substituted methylene in this radical. This possibility steins from the observation of C$HsC H2C Hi by Kochi and Krusic[30] at 240K. They reported an cr-H coupling of 61.6 M H z . The radical in Eq . 7 has not been observed in transverse field / iSR [18,19] and hence the muon hyperfine coupling is not known. A s -suming an AHO of -61 .6MHz we obtain AM values of 202.4(1.42lT) and 218.4MHz(1.507T) for BR values shown in parentheses. These A M values are very low considering the fact that there is little or no spin delocal-ization on to the ring with the unpaired electron on the terminal carbon of the substituent. A value around 280-330 M H z would have been more appropriate (based on other vinyl systems[8,3l] or ethyl[9] or closer to that cited here for the radical IV ). A l l of this strongly implicates the formation of one side-chain and two ring radicals (as in (i)) as seen in T F . 2. Radical Yields: • (a) Toluene: The L C R spectrum of toluene shows the occurance of three muonated free radicals. They are assigned to the radicals with Mu ortho, meta and para to the - C H j group, as in Table 2, by using the published values of A„ from TF-fiSR[16]. Applicat ion of E q . (6) gives the yields recorded in column 7 of Table 2, where it is seen that the relative abundances of o:m:p is 2.5:2:1. Appendix . Collaborative work already published 165 6 This is virtually the same ring selectivity found previously from the FFT's in TF-/iSR[lfj]. It favours ortho slightly over the statistical expectation of 2:2:1. On summing the yields of these isomeric radicals we find 'LPR = 0.77 (see Table 3). This corresponds closely to \-PD, because the diamagnetic yield is well established to be 0.25±0.02[l6,21]. It means that in pure toluene all muons are readily accounted for - they either become incorporated into dia-magnetic molecules such is MuH (probably during the pre-thermalization stage) or else they finish up as muonium atoms bonded in methylcyclo-hexadienyl radicals. The absence of a significant directional effect (2.5:2:1 compared lo 2:2:1) suggests that either (i) the radical precursor undergoes a non-selective, efficient interaction with the ring on first encounter, or (ii) there is only a very weak nucleopliilic or electrophilic interaction by the precursor (which implies attack by the neutral atom Mu rather than a cationic or anionic precursor). • (b) Allylbenzene: With a non-conjugated vinyl group in the side chain as in ally! benzene, a variety of muonated free radicals was found with the distribution reported in Table 2. About 70% of the radicals involved the side chain rather than the ring. As there are three times as many ring x-bonds as side chain x-bonds, this implies that side chain addition is some 7 times as efficient-per-encounter as is ring addition. Of the side chain additions, some 60% are with the end carbon. This is a much weaker preference, than would be expected from either a cationic or anionic intermediate. It therefore suggests a neutral precursor, such as the muonium atom. Furthermore, the 30% ring additions are distributed just in accordance with the statistical number of sites (2:2:1 for o:m:p) as if no electromeric effects are involved. This too seems to exclude ionic processes. For allylbenzene all the incident muons are also accounted for, since Y,PR = 0.65 and this equals \-PD- [The PD value determined independently by a /iSR experiment at 80G was equal to 0.33.] • Styrene: Again, all the muons appear as either diamagnetic molecules (PD = 0.18) or free radicals (?2PR = 0.82) as in Table 3. Neat styrene thus resembles toluene and allylbenzene (and other pure unsaturated compounds such as benzene[13] or acetone[14]) in having no 'missing' fraction. This implies that radicals are not lost by spin-exchange interaction in the radiation track. But, for styrene, there is very strong selectivity towards certain radicals. This selectivity appears in three forms. First, 85% of the radicals appear in the side chain, yet the number of side chain to ring carbons is 2 to 6 against. Second, for the side chain, the end C wins by at least 10 to 1 over the inner C. Third, for the 15% of the radicals arising from addition to the ring, none are observable at the meta position, while the o.p ratio is just about statistical(2:l). Appendix . Collaborative work already published 166 7 Such selectivity seems Io rule out epithermaJ insertion (reaction (2)) and suggests either: (i) thai the reaction cross-section of thermalized Mu (re-action (1)) towards the end C of the side chain exceeds all other addition points by at least an order of magnitude, or (ii) that a strongly favoured intermediate, 6uch as,a radical-ion (reactions (3) or (4)), dominates the overall reaction path. A carbocation also has merit in that it would favour ortho and para over mela, since neutralization would occur by a strongly nucleophilic species (electron or anion). However, it would be surprising to find a sudden shift from a neutral free radical precursor in the cases of toluene and allylbenzene to a cation (//"* or CcHiC4 HCHiMu) in the case of styrene, because all three compounds have similar dielectric properties and ionic affinities. Therefore we favour alternative (i) above. The radicals observed certainly represent those most stabilized by jr-delo-calization, as seen for other radicals [32]. This is clearly evident for the case of structure (VI) where the unpaired electron's p orbital mixes with the ring carbons' T-orbital, while the other side chain radical C^H\OH(M\i)CH2 would be non-conjugated and have no alternative resonant structures. Likewise within the ring. Addition of Mu at the ortho and para positions, allows resonant structures with derealization of the unpaired electron in-cluding the side-chain, whereas Mu at the meta position breaks up such conjugation. An additional reason which favours an enhanced kinetic attack by Mu at the end C of the side chain as the mechanism, is the fact thai Louwrier et al[33] have found Mu to react 16-times faster with styrene than with benzene, in n-hexane solution. Although the ratio seems to be less in wa-ter[33], the hydrocarbon medium more closely resembles the properties of these neat compounds. Furthermore, TF-/iSR studies on styrene/benzene mixtures showed styrene to win over benzene for the radical precursor by a factor of 6-8[l8,34]. Acknowledgements The continuous technical support from Keith Hoyle and Curtis Ballard as well as other staff at TRIUMF is appreciated. Financial support from NSERC of Canada is acknowledged. Figure Legends: • Scheme 1. Muonated free radical structures I—XII. • Figure 1. LCR spectra of the muonated methylene resonances in toluene, (as-signments as marked) • Figure 2. LCR spectra of proton resonances from muonated radicals in allyl-benzene. (assignments as shown in Scheme 1) • Figure 3. LCR spectra of proton resonances from muonated radicals in styrene. (assignments as marked). Appendix . Collaborative work already published 167 Table 1 Hyperfine Parameter^, Transition Frequencies and Theoretical Linewidths for Radicals Compound Radical / M H z /Tesla A w / M H z / M H z /mT Benzene I 514.0 2.0768(2) + 126.6 0.566 12.2 Toluene II(o) (2,6) = 489.6 1.9740(2) +122 .8 0.544 11.8 II(m) (3,5) = 509.3 2.0532(3) + 127.8 0.566 12.3 « ( P ) (4) = 496.4 2.0065(2) + 123.6 0.546 11.9 Allyl Benzene 111 307.0 1.9688(2) Q = -58.81 0.164 3.9 1.2740(2) 01 = +70.28 0.428 9.3 1.3120(2) 02 = +63.22 0.374 8.2 IV 330.6 2.1004(2) o' = -59.68 0.238 5.4 1.3882(2) 0' = +72.64 0.309 6.8 V(o) (2,6) = 489.6 1.9875(2) +120.3 0.529 11.5 V(m) (3.5) = 509.3 2.0523(3) + 128.0 0.567 12.3 V(p) (4) = 496.4 2.0151(2) + 122.0 0.537 11.7 Styrene VI 213.5 1.3934(2) o = -45.39 0.124 3.1 0.9066(2) 0 = +45.06 0.268 6.0 VII(o) 424.88 1.5069(2) + 144.9 0.729 15.7 Vll(p) 378.07 1.4208(2) + 114.1 0.542 11.8 Footnote: (a) Values of obtained from [16,17,19] T a b l e 2 L C R positions, amplitudes, linewidths, and calculated yields of radicals at 298K Appendix . Collaborative work already published Compound Radical Nuclei Bn / T am pi 1 % A S / mT P'n Benzene 1 < H(C) 2.0768(2) 2.38(1) 13.0(1) 0.82(3)" Toluene Il(o) H(2,6) 3.9740(2) 0.97(1) 12.8(1) 0.35 II(m) H(3.5) 2.0532(3) 0.67(1) 14.4(2) 0.28 H(P) H ( 4 ) 2.0065(2) 0.32(1) 14.0(1) 0.14 Allylbenzene HI Ho • 1.9688(2) 0.46(1) 4.8(1) 0.26 Hji 1.2740(2) 0.68(1) 9.6(1) 0.25 H/52 1.3120(2) 0.64(1) 8.8(1) 0.25 IV H . - 2.1004(2) 0.14(1) 10.6(1) 0.19 H f l . 1.3882(2) 0.16(1) 12.6(2) 0.19 V(o) H(2,6) 1.9675(2) 0.26(1) 11.6(1) 0.081 V(m) H(3,5) 2.0523(2) 0.23(1) 13.0(1) 0.078 V( P) H(4) 2.0151(2) 0.16(1) 11.7(1) 0.045 Styrene VI H . 1.393-1(2) 1.05(2) 4.0(1) 0.70 H* 0.9066(2) 1.23(2) 7.2(1) 0.71 VII(o) H(2,6) 1.5069(2) 0.21(1) 15.9(1) 0.07 VII(p) H(4) 3.420S(2) 0.14(1) 11-8(1) 0.05 Footnote?: (a) Calculated using Eq. 6. (b) For benzene, PR was taken to be 0.82(3). Tabic 3 Distr ibut ion of muon polarization and tally of yields Compou nd ^PR Distribut ion of ZP^%) PD i-PD o m V Benzene6 0.62(3) - - - - - 0.15c 0.85 Toluene 0.77 46 36 18 - - 0.25c 0.75 Allylbenzene 0.65 13 12 7 39 29 0.33 0.67 Styrene 0.82 9 - 6 85 - 0.37 0.83 Footnote: a. o, m, p, Si and s? denote ortho, meta, para and side chain radicals (like III, IV in Scheme 1). b. The benzene PR value from ref.[3 3]. c. From reference [21]. References [1] E. Roduner and H. Fischer, Chem. Phys. (1981), 54, 261. [2] R. F. Kiefl, Hyperfine Interactions (1986), 32, 707. [3] (a) R. F. Kiefl, S. R. Kreitzman, M . Celio, R.Keitel, J. H. Brewer, G. M . Luke, D. R. Noakes, P. W. Percival, T. Malsuzaki and K. Nishiyama, Phys. Rev. A (1986), 34, 681. [4] M . Heming, E. Roduner, B. D. Patterson, W. Odermatt, J . Schneider, Hp. Baumeler, H. Keller and I. M . Savic, Chem. Phys. Lett. (1986), 128, 100. Appendix . Collaborative work already published REFERENCES 10 [5] T . Azuma, K. Nishiyama, K. Nagamine, Y. Ito and Y. Tabata, Hyperfine Inter-actions 32 (1986 ) 837. [6] K. Venkateswaran, R. F. Kiefl, M. V. Barnabas, J. M. Stadlbauer, B. VV. Ng, Z. Wu and D. C. Walker, Chem. Phys. Lett. (198S), 145, 289. [7] 'M. Heming, E. Roduner, I. D. Reid, P. W. F. Louwrier, J. Schneider, H. Keller, W. Odermatt, B. D. Patterson, H. Simmler, B. Pumpin and I. M. Savic, Chem. Phys. (1989), 129, 335. [8] K. Venkateswaran, M.V. Barnabas, R.F. Kiefl, J .M. Stadlbauer and D.C. Walker, J. Phys. Chem. (1989), 93, 388. [9] P. W. Percival, R. F. Kiefl, S. R. Kreitzman, D. M. Garner, S. F. J. Cox, G. M. Luke, J. H. Brewer, K. Nishiyama and K. Venkateswaran, Chem. Phys. Lett. (19S7), 133, 465. [10] R. F. Kiefl, P. W. Percival, J. C. Brodovitch, S. K. Leung. D. Yu, K. Venkateswaran and S. F. J. Cox, Chem. Phys. Lett. (1988), 143, 613. [11] P. W. Percival, J. C. Brodovitch, S. K. Leung. D. Yu, R. F. Kiefl, G. M. Luke, K. Venkateswaran and S. F. J. Cox, Chem. Phys. (1988), 127, 137. [12] (a) A. Hill, M. C. R. Symons, S. F. J. Cox. R. De Renzi and C. A. Scott, J. C. S. Farad. Trans. I (1985), 81, 433. (b) S. F. J. Cox and M. C. R. Symons, Radiat. Phys. Chem. (1986), 27, 53. [13] E- Roduner, The Positive Muon as Probe in Free Radical Chemistry, Springer-Series No.49 (1988). [14] E. Roduner, Radiat. Phys. Chem. (19S6). 28, 75. [15] D. C. Walker, M. V. Barnabas and K. Venkateswaran, Radiat. Phys. Chem. (submitted). [16] E. Roduner, G. A. Brinkman and P. W. F. Louwrier, Chem. Phys. (1984), 88, 143. [17] E. Roduner, G. A. Brinkman and P. W. F. Louwrier, Chem. Phys. (1982), 73, 117. [18] (a) S. F. J. Cox, A. Hill and R. De Renzi, J. C. S. Farad. Trans. I (1982), 78, 2975. (b) J. M. Stadlbauer, B. W. Ng and D. C. Walker, Hyperfine Interactions (1986), 32, 721. [19] D. A. Geeson, C. J. Rhodes, M. C. R. Symons, S. F. J. Cox, C. A. Scott, E . Roduner, Hyperfine Interactions (1986), 32, 769. [20] J. M. Stadlbauer, B. \V. Ng, R. Ganti and D. C. Walker, J. Am. Chem. Soc. (1984), 10G, 3151. [21] D. C. Walker, Muon and Muonium Chemistry, Cambridge University Press, Cambridge, (1983). [22] M. Heming, E . Roduner and B. D. Patterson, Hyperfine Interactions (1986), 32, 727. [23] S. DiGregorio, M. B. Yim and D. E. Wood, J. Am. Chem. Soc. (1973), 95, 8455. [24] Y. Kirino, J. Phys. Chem. (1975), 79, 1296. Appendix . Collaborative work already published 170 [25] T. Shiga, J. Phys. Chem. (1965). C9, 3805. [26] A. J. Dobbs, B. C. Gilbert, R. O. C. Norman, J. C. S. Perkin II (1972), 1, 786. [27] P. Neta and R. H. Schuler J. Phys. Chem. (1973), 77, 1368. [28] VV. T. Dixon and R. O. C. Norman, J. Chem. Soc. (1964), 4857. [29] H . Fischer, 2. Natur/orsch A. (1965), 20, 488. [30] J. K. Kochi and P. J. Krusic, J. Am. Chem. Soc. (1969), 91, 3940. [31] K. Venkateswaran et al. (unpublished results). [32] J. M . Tedder and J. C. Walton, Tetrahedron (1980), 3G, 701. [33] P. VV. F. Louwrier, G. A. Brinkman and E. Roduner, Hyperfine Interactions, (1986), 32, 831. [34] B. W. Ng, J. M . Stadlbauer, V. Iio, V. Mivake and D. C. Walker, Hyperfine Interactions (1984), 17-19, 821. Appendix . Collaborative work already published VI V D (°) (») (P) SCHEME 1 Appendix . Collaborative work already published 172 .o 1 1.75 1.8 1.85 1.9 1.85 2 2.05 2.1 2.15 L o n g l t u d l n t l M a g n s l l c F i e l d ( T o U ) J R I N G R A D I C A L S .9 1 1.1 1.2 1.3 1.4 1.5 1.6 Lo n g i t u d i n a l Magnetic Field (Tesla) Appendix . Collaborative work already published 1 7 3 1 P r e p r i n t - i n p r e s s J. Phys. Chem Line Broadening of Level Crossing Resonance Spectra of Muonated Free Radicals Krishnan Venkateswaran, Mary V . Barnabas and David C . Walker Department of Chemistry and T R I U M F , University of British Columbia Vancouver. British Columbia , C A N A D A , V 6 T 1Y6 A b s t r a c t Ratio? of the observed-to-theoretical linewidths (squared) have been found to in-crease by as much as a factor of 5, for all available level crossing resonance data for muonated free radicals. However, in each case there is an equal decrease in the observed-to-theoretical amplitude, so that the observed product ( o r n j i l ) ( A B ) ! can be used to evaluate radical yields Intrinsic line broadening evidently arises from several sources. I n t r o d u c t i o n The union level crossing resonance technique ( L C R ) as applied to organic free rad-icals has opened new possibilities in the study of spectroscopy and reaction dynamics in solut ion[l ,2.3.4], One problem commonly encountered in the radical spectra is that of an intrinsic broadening of the linewidth. In all cases [2,5.6,7] so far, the observed linewidths have been greater than those calculated theoretically. Recent work on acrylamide/water [6] and benzene/n-hexane[7] systems have en-abled us to obtain radical yields from L C R data using the semi-empirical equation: Here. PR is the fraction of muons that form radicals, ampl^. and &B0bt are the observed resonance amplitudes and linewidths respectively, 7's are the magnetogyric ratios and VR is the transition frequency between two nearly degenerate levels on reso-nance. The latter is calculated from the resonance position and the muon and nuclear hyperfine coupling constants. At,; is the experimental forward-backward asymmetry. Eq. (1) is applicable to resonances involving a single spin 1/2 or two spin-1/2 nu-clei. In deriving it[6], we made the assumption that the lineshape remains Lorentzian and the product of observed amplitude and square of the linewidth equals the theo-retical value. To test this assumption we have evaluated the observed-to-theoretical linewidths(squared) and compared them with the observed-to-calculated amplitudes for all available data. R e s u l t s a n d D i s c u s s i o n Table 1 gives the relevant L C R parameters for the radicals observed in pure benzene (under three different experimental conditions), benzene in n-hexane solution (at two concentrations), 1 3 C benzene in cyclohexane (showing four , 3 C hyperfine couplings), acrylamide in water (showing both a and (3 proton couplings for the only radical formed - muonium(Mu) adding to the terminal C ) , pure acrylonitrile (both protons for the analogous" radical with Mu at the end) and pure toluene (the three radicals with M u ortho, mela or para to the methyl substituent). The acrylonitrile and toluene data are reported here for the first time, the others are taken from the literature. The observed linewidths (given as F W H M values, A£?ot») and amplitudes ( (amp/) o a j ) were obtained by computer fitting the resonance as before [5,6], and are tabulated in columns 4 and PR = (ornp/)ob,.(Az?<>6..)?(-r^ Ipf vRAtj ( 1 ) 5 of Table 2. Appendix . Collaborative work already published 174 2 Theoretical linewidths, A B n , were evaluated by use of Eq. (2) 7* - tF where A 0 , the muon decay constant, equals r " 1 (0.45/is - 1). In all cases (AI?ot«) is greater than (AB,N) and the square of this ratio changes from 1.1 to 5.0 as shown in the sixth column of Table 2. Predicted amplitudes, (om^l),), were calculated by use of Eq. (3) (ampl)th = AP.AtjPR (3) where A P ; is the mean reduction in muon polarization on resonance which in the absence of any relaxation effects is given by[2] Atj w a s determined experimentally by two alternative methods. The first method was using aqueous M n 2 + solutions where the backward to forward asymmetry was measured a s a function of field. Second, a single crystal of MnFj was used and time differential measurements as a function of field similar to those in aqueous M n 5 4 solutions were done. The two approaches gave similar values. A very weak field dependence was seen-a change by 20% from fields of O.lT to 2.2T. We estimate the errors in our individual Atj values to be at most 10%. The value for PB is taken here to equal \-PD, where Pr> is the fraction of muons found in diamagnetic states in these systems. Putting PB = \-PD seems to be well justified for all systems in which both yields have previously been independently determined, including pure unsaturated molecules like benzene[8], or acetone[9], and in water or hexane - where the radical fraction appears as muonium [6,7). The observed amplitudes are always less than those predicted by Eq. (3) and this inverse ratio is given in the seventh column of Table 2. They too vary from 1.1 to 5.1, and for each system they correspond very closely indeed to the square of ABotj/Ai?,^,. This confirms that it is the product (amp/)0fc,(AB0t,)7 that equals the theoretical value. Evidently, at least for these systems, whatever causes the line broadening also gives rise to a corresponding loss of amplitude. Heming et a)[4] have already discussed changes in lineshape in terms of isotropic T\ electron relaxation processes[4]. They have attributed it to residual longitudinal relaxation processes ( A ^ ^ ) . If we now equate either of the two ratios obtained (column 6 or 7 in Table 2) to the form ( l + A ^ j / A o ) then the values of A ^ j of the last column of Table 2 are obtained. It transpires that our value for benzene (0.20, except for the first row) agrees well with their value of 0.22. Reasonable agreement is also seen with the J3Ct//e-cyclohexane values that were obtained in [4] by simulated curves of A ^ j versus linewidths. Perhaps the variations of ^ l o n g shown in Table 2 will help delineate its origins. Its magnitude varies with the nature of the radical (benzene to AM), the transition frequency (VR) (Ha or Hp coupling), and on the spectrometer used, (comparing rows 1 and 2) suggesting that field inhomogenieties contribute to this residual broadening. Different solvent interactions may also be involved. Appendix . Collaborative work already published 175 3 In the presence of other paramagnetic species (such as DPPH in ref.[4]< perhaps O2 and track species) the*re can be extra relaxation processes. Heming et aJ have also discussed this at length, and present strong evidence for an equation of the form of Eq. (5) where A t I represents the rate constant for electron spin exchange interactions of the muonated radical, and \ c h t m represents any combination(irreversible) reactions. With these effects present the product (ampl)(AB)i can be greater than given in Eq. (1) by these additional processes. Table 1 L C R transition frequencies, calculated expected amplitudes and theoretical linewidths for muonated radicals produced in unsaturated organic compounds System Cone. / M Nucleus VR 1 MHz PR Abj amplth % 1 mT H ( 6 ) 0.566 0.246 0 .82° 0 .133 2.68 12.2 (pure) - - 1 > 0.24 0.145 4.84 2.92 " Cc He, 0.5 H ( 6 ) 0.560 0.246 0 . 3 5 6 0.24 2 .10 12.2 in n-hex 0.3 ., 11 ,, , , , , 11 0.03 C ( l , 5 ) 0.272 0.233 0 . 3 1 B 1.44 4.5 in c-hexc ) 1 C ( 2 . 4 ) 0 .209 0.223 1.38 3.6 > 1 C ( 3 ) - 0.270 0.233 1.44 4.5 C ( 6 ) 0.143 0.199 t 1 1.23 2.6 AM' 0.6 H 3 0.357 0.240 0 . 3 8 6 0.135 1.23 7.8 in water 0.06 , , , , Ho 0.159 0 .207 0.142 1.12 3.7 AN* H6 0 .332 0 .239 0 . 7 2 B 0.120 2.07 7.3 (pure) Ha 0.158 0.207 »» 0 .130 1.94 3.7 Ct.H.CHi H (2,6) 0.544 0 .245 0 . 3 6 S 0.133 1.18 11.8 (pure) H (4 ) 0.546 0.246 0 .13 0 .133 0.43 11.9 •1 H (3,5) 0.566 0.246 0.26 0.133 0 .85 12.3 Footnotes:(a) PR determined directly in this case[8]. This is quite close to 1 - P D [ 1 1 ] ' (b) Taken from ref.[ll] as \-PD. (c) Data from ref..[2] (d) An Ab/ value of 0.2 is assumed. (e) Acrylamide. (f) Acrylonitrile. (g) Distribution of PR between o,m, arid p taken from ref.[10]. IZPR = 1—/^[l 1]. Appendix . Collaborative work already published 176 Table 2 Observed linewidths and amplitudes and comparison with theoretical values System Solute Cone. / M f Nucleus 1 mT amplob, % ( • " " ' I n \0 a Along 1 us-1 Ce He. H(6) 13.0(2) 2.39(4)" 1.14 1.12 0.06 (pure) 14.6(2) 3.43(3)c 1.43 1.41 0.20 14.8(2) 1.98- 1.47 1.48 0.21 Cf, Ht 0.5 H(6) 14.5(3) 1.46(2) 1.43 1.44 0.20 in n-hex 0.3 14.5(3) 1.46(2) 1.43 1.44 0.20 1 3 C 6 / / C 0.03 C(1.5) 6.0(3) 0.92(3) 1.78 1.85^  1.57 0.35 in c-hex C(2,4) 4.9(2) 0.78(1) 1.77 0.39 C(3) 5.7(2) 0.93(2) 1.67 1.55 0.27 C(6) 3.9(2) 0.52(2) 2.25 2.37 0.57 A M 0.6 H 5 16.1(3) 0.29(1) 4.26 4.24 1.48 in water 0.0G 15.6(5) 0.30(1) 4.00 4.10 1.36 Ho 8.3(4) 0.22(2) 5.03 5.09 1.83 AN Hi 8.9(1) 1.36(2) 1.49 1.52 0.22 (pure) Ha 5.2(1) 0.99(2) 1.98 1.96 0.44 CtH-XHi H(2,6) 12.8(2) 0.97(1) 1.18 1.22 0.08 (pure) H(4) 14.0(2) 0.32(1) 1.38 1.34 0.17 H(3.5) 14.4(2) 0.67(1) 1.37 1.27 0.17 Footnotes: (a) Calculated from ratio of square of linewidths, as in text. (b) Measured using the new spectrometer in January 1989 on the M15 beamline at TRIUMF. These measurements on neat benzene were done thrice. (i)In a degassed target sealed in a stainless steel cell with a thin window, (ii)In a deoxygenated target septa sealed in a stainless steel cell by bubbling A'2 through hypodermic needles prior to the experiment and (iii) in a teflon cell, by pumping(closed cycle system set up) into it a deoxygenated target. (c) Measured using the old spectrometer with setup as in (b)(iii) on the M20B beamline in August 1988. (d) As in (c) but measurement done in January 1988. Abj values for these different benzene experiments are provided in Table 1. References [1] R. F. Kiefl, Hyperfine Interactions (1986), 32, 707. [2] R. F. Kiefl, P. W. Percival, J. C. Brodovitch, S. K. Leung, D. Yu, K. Venkateswaran and S. F. J. Cox, Chem. Phys. Lett. (1988), 143, 613. [3] P. \V. Percival, J. C. Brodovitch, S. K. Leung, D. Yu, R. F. Kiefl, G. M. Luke, K. Venkateswaran and S. F. J. Cox, Chem. Phys. (1988), 127, 137. Appendix . Collaborative work already published 177 REFERENCES 5 [4] M . Heming, E. Roduner, I. D . Reid, P. VV. F . Louwrier, J. Schneider. H . Keller, \ V . Odermatt, B. D . Patterson, H . Simmler, B. Pumpin and 1. M . Savic, Chem. Phys. (1989), 129. 335. [5] K . Venkateswaran. R. F. Kiefl, M . V . Barnabas, J . M . Stadlbauer. B. \ V . Ng, Z. Wu and D. C . Walker. Chem. Phys. Lett. (1988), 145, 289. [6] K . Venkateswaran. M . V . Barnabas, R . F . Kiefl, J . M . Stadlbauer and D . C . Walker, J. Phys. Chem. (1989). 93, 388. [7] D. C . Walker, M . V . Barnabas and K . Venkateswaran, Radiat. Phys. Chem. (submitted). [8] E. Roduner, The Positive Muon as a Probe in Free Radical Chemistry, Springer-Series No.49 (1988). [9] E. Roduner, Radiat. Phys. Chem. (1986), 28, 75. [10] E. Roduner, G . A . Brinkman and P. W . F. Louwrier, Chem. Phys. (1984). 88, 143. [11] D . C . Walker, Muon and Muonium Chemistry, Cambridge University Press, Cambridge, (1983). empty Appendix . Collaborative work already published 178 1 Preprint - in press Radiat. Phys. Chem. Muonated Cyclohexadienyl Radicals Observed by Level Crossing Resonance in Dilute Solutions of Benzene in Hexane Subjected to Muon-Irradiation David C. Walker, Mary V . Barnabas and Krishnan Venkateswaran Department of Chemistry and T R I U M F , University of British Columbia Vancouver, British Columbia, C A N A D A , V6T 1Y6 Abstract Benzene is used here as a scavenger of muonium to produce the muonated cy-clohexadienyl radical in dilute solutions in n-hexane. The radical was identified by level crossing resonance spectroscopy (LCR) by observing the proton resonance of the - C H M u group occurring at 2.059T. Its yield is found to equal the sum of the muonium atom yield and the "missing" muon yield in hexane (total 35% of the incident muons). Consequently; the complete dispersement of muons in different chemical associations is now accounted for in a saturated hydrocarbon liquid, and is seen to be similar to that in water. Introduction When energetic muons are injected into a liquid hydrocarbon, about 65% of them immediately become incorporated into diamagnetic molecules (such as MuH), 10 to 20% form long-lived muonium atoms (/i + e~, symbol Mu), and the remainder are lost (the so-called 'missing' fraction). Whether they form, as in radiation chemistry[l], by 'direct' or 'indirect' processes is a question which lies at the heart of many muon chemistry studies, including this one. Whereas the muon spin rotation (/*SR) technique requires the muon state ob-served over the muon lifetime (2.2/is) to have been formed prior to any spin precession in a transverse magnetic field (typically << lns)[2], the new technique of level cross-ing resonance (LCR)[3] imposes no formation-rate restrictions on the muon species which are actually observed as the / i + decays. This is because the muon LCR allows muonium-containing free radicals to be observed even when they are being formed over a microsecond timescale, as in dilute solutions of reactive solutes as small as 10~4M[4]. It also prevents spin-depolarization of the muon by internal hyperfine oscillations in the 'singlet' state of muonium (antiparallel (i* and e - spin state) so that the whole initial muonium yield can be delected, because the muon spin vector is held fixed in a strong, decoupling, longitudinal magnetic field. Benzene was selected as the solute for this study, because it is soluble in hydro-carbons and gives a Mu-radical which is already fully characterized in spectroscopic properties[5]. Also the radical yield is known[6] for the pure liquid, for normalization purposes. ri-Hexane was chosen as the solvent because it can be obtained fairly pure, and its muon yields have been determined by /iSR: they are, diamagnetic fraction (PD) = 0.65, muonium fraction {PM) = 0.13, and 'missing' fraction (PL) = 0.22[7]. The rate constant for Mu reacting with benzene in n-hexane has also been measured by uSR to be kM = (3.7 ± 0.8) x 10 'M~-s - , [8] . Experimental Appendix . Collaborative work already published 179 2 These experiments were performed on the M20B beamline at the TRIUMF cy-clotron using energetic spin-polarized muons (4.1 MeV). Magnetic fields from 0.01 to 3.0T (1 Tesla(T) = 104 Gauss) along the beam direction (and parallel to the muon spins) were provided by a superconducting magnet. The hexane was purchased from Fluka Chemicals, the benzene from BDH, and they were used without further purifi-cation. All solutions were thoroughly deoxygenated by bubbling with pure Nj before being pumped into the cell in a closed system. In the LCR technique, the muon polarization is measured as a function of magnetic field. Resonant transfer of polarization from the muon to a particular nucleus ( ]H(6) in this case, see Eq. (2) later ) occurs at a specific magnetic field where the muon transition frequency is matched to that of the proton. This results in a decrease in the muon polarization averaged over the muon lifetime and is detected experimentally as a reduction in muon decay asymmetry along the applied field direction. In order to reduce systematic errors, a small square wave field modulation ( ± 5 m T ) was used, which results in the differential appearance of the resonance. The resonance was recorded as A + - A ~ as the magnetic field is scanned (Fig. 1). ['A' is the integrated muon-decay asymmetry given by (B — F)/(B + F), where F and B are the total number of positron events in the forward and backward telescopes, respectively, and superscripts -f and - refer to the direction of the modulation field] A MINU1T reduced-x2 fitting program was used which allows the raw data to be analyzed using a difference of two Lorentzians for BR (the LCR position), A B (width at half height of the LCR), and Amp ( the amplitude of the LCR signal given as percentage). Results Figure 1 shows representative LCR spectra of benzene at three different concen-trations in n-hexane. The LCR amplitudes decrease as the benzene concentration falls. For the dilute hexane solutions, the muons invariably stopped in the solvent and reacted as thermalized species with the solute (benzene) to form the muonated cyclohexadienyl radical. The solid lines of Fig. 1 are the computer fits. The resonance position BR is given by Eq. (1) BR 0 . 5 [ ( ^ - AP)/(i„ - Tp) - MM + AP)h<) (1) where -j's are the magnelogyric ratios of the muon, proton and electron, and A„ and Ap are hyperfine coupling constants. The resonance in neat benzene centered at 2.072T has already[5] been assigned to the proton in the - C H M u group (H(6)) of the cyclohexadienyl radical arising from the addition of muonium to benzene, as in Eq- (2). A/« + C 6 / / e — • (2) For the n-hexane solutions BR was shifted by -12mT (or -0.6%) from the neat benzene value. VV'e attribute this change to a solvent effect on the muon hyperfine coupling constant, as in I 3C6H6 in cyclohexane[9]. There was no significant change in BR from the IM to the 3 x ] 0 - 4 M solutions. The linewidths (AB) changed negligibly from neat benzene to dilute solutions. The yield (PR) is defined as the fraction of incident muons which form the radical. Experimental values of PR were evaluated in this case simply by equating them to the amplitude (Amp) of the H(6) resonance, with normalization being based on the neat benzene Amp value equated lo PR of 0.82 ± 0.04. These values are recorded Appendix . Collaborative work already published ISO 3 in column 5 of Table 1. This is analogous to the procedure adopted for acetone solutions[lO]. Whether or not the vaJues of PR determined here are correct in an absolute sense depends on the validity of the normalization. Our procedure seems appropriate because all linewidths were similar, and the value of PR = 0.82 ± 0.04 covers the yield from three independent sources: (i) the measured backward-to-forward muon-asymmetry (At;) in experiments with neat benzene on beamlines M 1 5 and M 2 0 gave PR equal to 0.82 ± 0.04 using Eq. (3) as below[4]; (ii) Roduner determined PR = 0.80 ± 0.02 for pure benzene by transverse-field / i S R [ 6 ] ; and (iii) because it equals \-PD. An alternative method in calculating PR from A B and Amp data was used in the case of acrylamide solutions in water[4], because pure acrylamide - a solid - could not be used for normalization purposes. For that situation Eq. (3) was established AmrJABfhy - -)P)2 Ahj.l'r F b - 7—~i (3) where vr is the frequency splitting of two nearly degenerate levels at BR. In this equation vr is equal to cAhAP/2BR-)T, c being a constant equal to 1 when there is only one nucleus on resonance. Since A B changes negligibly for the present benzene solutions (column 3 Table 1), it is superfluous to use Eq. (3), except to check that the normalization was reasonable. With A B = 1 4 6 G , Amp = 3.43% for neat benzene and PR = 0 .82, Eq. (3) gives Atj = 0.24. This value is about what was expected: it is higher than that used for acrylamide solutions and previously for pure benzene[4] because in the present experiments the cell position was optimized for maximum experimental asymmetry. For the three lower benzene concentrations, the Mu-radical of Eq. (2) forms over the same timescale in which the muons decay, resulting in reduced L C R amplitudes. The extent of these reductions can be approximated by use of Eq. (4)[ll], where tjij is the rate constant for reaction (2) at a benzene concentration [S] and the muon decay constant Ao = 0.45 x 1 0 6 s - 1 . Values of PR corrected for this known effect on the L C R amplitude are given as positive values in column 6 of Table 1. Another correction given in column 6 (Table 1) is that expected for 'direct' effects on benzene during the thermalization process of the muon. It is presumed that direct effects are proportional to volume fraction (see below). Figure 2 shows P/^oo.trved) and P « < corrected) against benzene concentration, plot-ted (a) linearly, and (b) as log]o[C6Be] in order to display all data points. PR(CORT) is taken as the scavengable yield of thermalized radical precursors. Discussion Mu-radicals can form by any of the following mechanisms: (i) hot atom insertion at an epithermal stage: Mu + C 6B 6 Ct,Hc{Mu) (ii) addition of thermalized Mu atoms: Mu + C«B6 —• CcHc{Mu) Appendix . Collaborative work already published A (iii) / i + capture followed by neutralization with e~ from the track: / i 4 + C 6 W 6 —• Mu(CtHt)+ Mu(CtHt)+ + e" —- C6H6(Mu) or / i + + C 6 / / 6 - — CtHt(Afu) In pure benzene all three may contribute. For benzene solutions in hexane the direct process of (i) should be reduced in accordance with volume fraction, since PD falls linearly in benzene/cyclohexane mixtures[l2,13]. At IM this will be ~ 9% of the contribution to pure benzene, which we assume to be ~ (70 ± 30)% of total PR; at 0.3M only 3%; and negligible for lower concentrations. Mechanism (iii) was shown to be unimportant for the micelle solutions, by the charge, in the aqueous acrylamide system[4], but ionic precursors cannot be ruled out entirely for these hexane solutions. Any / i + ions which happen to survive the thermalization process unassocialed, could conceivably, be scavenged by dilute benzene with its large proton afftnity[l4] during their short lifetime prior to geminate neutralization, given sufficient mobility. However, for all the hexane solutions, mechanism (ii) is much more likely to be the dominant process. Mu has been observed in pure n-hexane by pSR with PM = 0.13 and these Mu atoms have a lifetime of 10 _ 6s or so[7]. Figure 2(a) shows the Mu-radicaJ yield (~ 0.35) to correspond very closely to \-PD for hexane, after making the correction for direct effects in the IM and 0.3M cases. Thus, all the muons are now accounted for in hexane: 63%[10] to 65%[7] form diamagnetic species directly (PD) and the rest can be scavenged by benzene at > 0.1M to give Mu-radicals. Free muonium atoms almost certainly account for a good fraction of these and probably them all. As in water, there is a significant missing fraction in pure hexane (Pi = 0.22), which may be muonium atoms lost during track expansion by depolarizing interactions or combination reactions. If the fall-off in PR at low benzene concentrations were due to the presence of an impurity (X) in hexane which competes for the radical precursor (presumed to be Mu here) by nomoc/eneotis kinetics: Mu + C6HC — CtHt(Mu) (5) Mu + A' — MuX (6) then PR = k„[CeHc] and , ( kx[X] \ where P / ^ m a i ) is the maximum radical yield obtainable at high benzene concentra-tions. If this were so, then a plot of P^1 against [CeHs]'1 would be linear. The data of Table 1 are plotted in this form in Fig. 3; but it is seen to be strongly non-linear. Evidently, Mu-radicaJ formation and CtHt(Mu) radical survival, are in compe-tition with non-homogeneoualy distributed reactive species such as those from the expanding radiation track of the high energy muon. Free radicals and unsaturates are Appendix . Collaborative work already published 1S2 produced by radiolysis in, the muon track and diffuse at rates comparable to those of Mu and Mu-radicals. Interactions with either will lead to a decreased PR. The fact that this falls significantly with [Ce/Ze] only at < J 0 - 1 M ( see Fig. 2(a)) suggests that reaction (6) competing non-homogeneously with reaction (5) is much more important than interactions of CtHe(Mu) once formed. The sharp fall-off in PD at low benzene concentrations may arise in part because Mu has a limited lifetime in hexane (~ 1/is), regardless of whether this arises from reaction (7) Mu + CcHlt MvH + C6Hi3 (7) or from the presence of advenlitous impurities. In conclusion, hexane is seen to give muon yields which are similar to those of water[4]. This indicates that free electrons and / i + ions play, at most, a minor role in muonium formation and loss: because, from radiolysis studies, geminate ion-recombinations dominate in non-polar liquids like hexane, whereas it is the free-ions which dominate the radiation chemistry of water[l3,l5]. The muonium chemistry de-scribed here is consistent with muonium being formed epithermally, with some 30 to 40% reaching thermal energy unassociated in saturated solvents. Acknowledge-ments Experimental assistance from Drs. J. M. Stadlbauer and B. VV. Ng and from Zhen-nan Wu is greatly appreciated. As always we wish to acknowledge technical support from the / iSR group and financial assistance from NSERC of Canada. References [l] J. H. O'Donnell and D. F. Sangster, Principles of Radiation Chemistry Edward Arnold (Publishers) Ltd., London, 1970. [2] S.F.J. Cox, J. Phys. C. Solid Slate Physics 1987, 20, 3187. [3] (a) S. R. Kreitzman, J . H . Brewer, D. R. Harshman, R. Keitel, D. LI. Williams, K. M. Crowe and E. J. Ansaldo, Phys. Rev. Lett. 1986, 50 181. (b) R. F. Kiefl, S. R. Kreitzman, M. Celio, R.Keitel, J. H. Brewer, G. M. Luke, D. R. Noakes, P. W. Percival, T . Matsuzaki and K. Nishiyama, Phys. Rev. A 1986, 34 681. (c) R. F. Kiefl, Hyperfine Interactions 1986, 32 707. [4] K. Venkateswaran, M. V. Barnabas, R. F. Kiefl, J. M. Stadlbauer and D. C. Walker, J. Phys. Chem (in press) [5] P. W. Percival, R. F. Kiefl, S. R. Kreitzman, D. M. Garner, S. F. J. Cox, G. M . Luke, J. H. Brewer, K. Nishiyama and K. Venkateswaran, Chem. Phys. Lett. 1987, 133 465. [6] E . Roduner, Private Communication, (1988). [7] Y. Ito, B. W. Ng, Y. C. Jean and D. C. Walker, Can. J. Chem. 1980, 58, 2395. [8] P. W. F. Louwrier, G . A. Brinkman and E. Roduner, Hyperfine Interactions 1986, 32, 831. [9] R. F. Kiefl, P. W. Percival, J. C. Brodovitch, S. K. Leung, D. Yu, K. Venkateswaran and S. F. J. Cox, Chem. Phys. Lett.143 (1988) 613. Appendix . Collaborative work already published 183 [10] K. Venkateswaran, R.,F. Kiefl, M . V. Barnabas, J. M . Stadlbauer, B. W. Ng, Z. Wu and D. C. Walker, Chem. Phys. Lett. 1988, 140 289. [11] M . Heming, E. Roduner and B. D. Patterson, Hyperfine Interactions 1986, 32 727. [12] Y. C. Jean, B. W. Ng. J. H. Brewer, D. G. Fleming and D.C. Walker, J. Phys. Chem. 1981, 85, 451. [13] D. C. Walker, Muon and Muonium Chemistry, Cambridge University Press, Cambridge, (1983). [14] J. L. Franklin, F. W. Lampe and H. E. Lumpkin, J. Am. Chem. Soc. 1959, 81, 3152. [15] A. O. Allen, NSRDS-NBS 1976, 57. Tabic 1 LCR positions, linewidths, amplitudes and calculated yields for the cyclohexadienyl radical from benzene in n-hexane solutions [CtHc] in hexane / mole dm~3 BR 1 T AB 1 mT Amp% PRiobs) Corrected P^b PRi C O T ) 11.24 (Neat) 2.0763(2) 14.6(3) 3.43(2) 0.82(4)c 0.62 1.0 2.0640(2) 14.5(3) 1.71(2) 0.41 -0.05(2) 0.36 0.75 2.0641(2) 14.4(3) 1.58(2) 0.38 -0.03(2) 0.35 0.5 2.0639(2) 14.4(3) 1.46(2) 0.35 -0.02(1) 0.33 0 3 2.0640(2) 14.3(3) 1.46(2) 0.35 -0.015(6) 0.34 0.25 2.0638(2) 14.6(3) 1.39(2) 0.34 -0.01(2) 0.33 0.15 2.0641(2) 14.3(3) 1.29(2) 0.31 0 0.31 0.1 2.0639(2) 14.8(3) 1.32(2) 0.32 0 0.32 0.05 2.0638(2) 14.6(3) 1.08(2) 0.26 0 0.26 0.01 2.0641(2) 14.4(3) 1.07(2) 0.26 0 0.26 0.007 2.0640(2) 14.5(3) 0.82(2) 0.19 0 0.19 0.003 2.0639(2) 14.3(3) 0.77(2) 0.18 +0.01 0.19 0.001 2.0639(2) 14.8(3) 0.60(2) 0.15 +0.02 0.17 0.0003 2.0641(2) 14.8(3) 0.33(2) 0.08 +0.03 0.11 Footnotes: (a) Negative corrections: estimated direct effects (based on volume fraction of solu-tions assuming that two-thirds of radicals in benzene arise through direct or ionic processes.) (b) Positive corrections: from Eq. (4). due to slow formation rate of the radical. (c) Normalization to absolute scale (Amp of 3.43% equated to PR of 0.82(4)). All other PR values carry this 5% error. Figure Legends • Fig. I. L C R spectra of muonated cyclohexadienyl radicals in hexane solutions at [CeHe] of (a) 1.0M; (b) 0.003M; and (c) 0.0003M , given as differential asym-metry against longitudinal field. • Fig. 2. Plot of radical yield (PR) against concentration of benzene: (a) linear scale (D) P/^,*,) and ( O ) denoting P « C or r ) ; »nd (b) log scale of [CtHt] • Fig. 3. Plot of 1/Pjxcor,) against 1/[C«/V 6] (3 x 10~ 4M not included because of significant decay of Mu) Appendix . Collaborative work already published . 0 1 3 .01 .00 3 0 -.003 -.01 }• -(a) - . 0 1 5 2 . 0 1 2 .03 2 . 0 5 2 . 0 7 2 . 0 9 . 0 1 5 -(b) - . 0 1 3 2 . 0 1 . 0 1 5 2 . 0 3 2 . 0 5 2 . 0 7 2 . 0 9 2 . 0 3 2 . 0 5 2 . 0 7 2 . 0 9 Longitudinal Magnetic Field / T Appendix . Collaborative work already published 185 CO.) .5 .45 .4 -.35 -.3 °-".25 .2 .15 t> .1 .05 i i — i — i i J 1 I L__l_ _1 I I 1_ 0 .1 .2 .3 .4 .5 .6 .7 .9 1 1.1 2.E-4 .001 .004 .02 .07 .2 .5 1 2 4 8 [C6H6] / M 0 100 300 500 700 900 1100 '/[CSH,] PUB. ICATIONS; 1. Muonium Atoms Compared to Hydrogen Atoms and Hydrated Electrons Through Reactions with Nitrous Oxide and 2-propanol. K. Venkateswaran, M. Barnabas, Z. Wu, and D. C. Walker, Radiat. Phys. Chem., 32, 65-9 (1988). 2. Micelle-induced Enhancement of the Reactivity of Muonium Atoms in Dilute Aque-ous Solution. K. Venkateswaran, M. V. Barnabas, Z. Wu, J. M. Stadlbauer, B. W. Ng and D. C. Walker, Chem. Phys. Lett., 143(3), 313-6 (1988). 3. A Level-Crossing-Resonance Study of Muonated Free-Radical Formation in Solutions of Acetone in Hexane, Water and Dilute Micelles. K. Venkateswaran, R. F. Kiefl, M. V. Barnabas, Z. Wu, J. M. Stadlbauer, B. W. Ng and D. C. Walker, Chem. Phys. Lett., 145(4), 289-93 (1988). 4. Effect of Added Micelles on the Reaction between Muonium and Ionic Solutes in Water. K. Venkateswaran, M. V. Barnabas, B. W. Ng, and D. C. Walker, Can. J. Chem., 66, 1979 (1988). 5. Comparison of Muonium and Positronium with Hydrogen atoms in their reactions towards Solutes Containing Amide and Peptide Linkages in Water and Micelle Solu-tions. M. V. Barnabas, K. Venkateswaran, and D. C. Walker, Can. J. Chem. 67, 120 (1989). 6. Muonium and Free Radical Yields as Determined by the Muon-Level-Crossing Reso-nance Technique in Aqueous and Micelle Solutions of Acrylamide. K. Venkateswaran, M. V. Barnabas, R.F.Kiefl, J. M . Stadlbauer, and D. C. Walker, J. Phys. Chem. 93, 388 (1989). 7. Positronium and Muonium Reactions in Micelles: A Kinetic Comparison. M. V. Barnabas, K. Venkateswaran and D. C. Walker, in Positronium Annihilation, Eds. L. Dorikens-Vanpraet, M. Dorikens and D. Segers, World Scientific, Singapore. p564, Sept 1988. 8. Muon level crossing resonance study of radical formation in allylbenzene, styrene and toluene. K. Venkateswaran, M. V. Barnabas, Z. Wu, J. M. Stadlbauer, B. W. Ng and D. C. Walker, (Chem. Phys. - in press) 9. Muonated Cyclohexadienyl Radicals Observed by Level Crossing Resonance in Dilute Solutions of Benzene in Hexane Subjected to Muon-Irradiation. D. C. Walker, M. V. Barnabas and K. Venkateswaran, (Radiat. Phys. Chem. - in press) 10. Line broadening of level crossing resonance spectra of muonated free radicals. K. Venkateswaran, M. V, Barnabas and D. C. Walker, (J. Phys. Chem. - in press) 

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