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Muonium reactions with aromatics Wu, Zhennan 1992

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MUONIUM REACTIONS WITH AROMATICSByZhennan WuB. Sc., University of Science arid Technology of China, Beijing, China, 1964A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESCHEMISTRYWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAApril, 1992© Zhennan Wu, 1992In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives, It is understäod that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.Department of________________The University of British ColumbiaVancouver, CanadaDateDE-6 (2/88)AbstractPositive muons are produced at TRIUMF as pion decay products and form muonium atoms in media such as water during their two microsecond lifetime. Muoniuin is a hydrogen—like atom with virtually the same Bohr radius and ionizationenergy as ‘H, 2H and 3H, but with a mass one—ninth that of ‘H. Its reactionstoward solutes are studied by SR (the muon spin rotation) and LCR (muonlevel crossing resonance spectroscopy).In this thesis, the reactions of mnuonium with some substituted aromnatics andN-heterocyclic compounds were studied. Reaction rate constants were measuredin many cases, and products were identified as mnuonated free radicals formedby muonium addition to a ring-C. Muon hyperfine coupling constants of somemuonated cyclohexadienyl-type radicals and all muonated mono- and diazineradicals studied here were determined. The LCR spectra of muonated radicalswere recorded and the resonance signals were assigned to particular nuclei ofthese radicals. Radical isomer distributions and partial rate constants for monosubstituted benzenes and N-heterocyclic compounds were estimated. 7r-electrondensities and radical localization energies of neutral aromnatics were calculatedby the Hiickel MO method. For N-containing compounds LUMO levels as wellas these parameters were also calculated by the same method. It was found thatthere exists a good correlation between partial rate constants and radical localization energies, which implies that muonium addition rates in these systems aremainly governed by an activation barrier l)roPortiollal to the radical localizationenergies of the reactants.HTable of ContentsAbstract iiTable of Contents iiiList of Tables viiList of Figures xiAcknowledgement xiv1 Introduction 11.1 Muon and IVluonium 11.2 Hückel Molecular Orbital Theory 61.3 Description of Thesis 92 Background and Experimental 112.1 Muon production and clecay 112.2 Transverse field JLSR techniques 142.2.1 Muon Spin Rotation(1iSR) 152.2.2 Muonium Spin Rotation(MSR) 182.2.3 Muonium-R.adical Spin Rotation(MRSR) 242.3 Muon Level Crossing Resonance Spectroscopy (LCR) 272.4 Experimental set-up 322.4.1 Set-up for TF-1LSR experiments with backward muons . . 32in2.4.2 Set-ui) for LCR experiments with surface muons 372.4.3 Data analysi.s 422.5 Chemicals and sample solutions 423 Muonium Reaction with Some Substituted Benzenes 453.1 Introduction 453.2 Results 463.2.1 Reaction rate constants 463.2.2 Muon hyperfine coupling constants 473.2.3 LCR experiments 503.2.3.1 Benzoic acid and benzoate 503.2.3.2 Terephthalic acid 533.2.3.3 Other substituted benzenes and benzoic acids 553.3 Discussion 583.3.1 Benzoic acid and benzoate 583.3.1.1 Resonance peak assignment 583.3.1.2 Hyperfine coupling isotol)e effect 603.3.1.3 Partial rate constants 623.3.2 Terephthalic acid 663.3.3 Other mono-substituted benzenes and p-substituted benzoic acids 683.3.4 Correlation between the partial rate constant and HMOparameters 703.3.4.1 HMO results 703.3.4.2 Partial rate constants 72iv3.3.4.3 Correlation between rate constants and HMO parameters 733.4 Conclusion 754 Muonium Reaction with N-Heterocyclic Compounds 764.1 Introduction 764.2 Results 784.2.1 Reaction rate constants 784.2.2 Diamagnetic yield measurement 804.2.3 Muon hyperfine coupling constants 814.2.4 LCR. experiments 854.2.5 HMO results 884.3 Discussion 904.3.1 LCR. peak assignment and yields of individual radicals . 904.3.1.1 Pyrazine 904.3.1.2 Pyridine 944.3.1.3 Pyrimidine 954.3.1.4 Pyridazine 974.3.2 Reaction rate constant 984.3.2.1 Partial rate constant 994.3.2.2 Correlation between rate constants and HMO parameters 994.3.2.3 Comparison of Mu with H 1064.4 Conclusion . 106Bibliography 108VA ppendix 112A Collaborative work already published 112B LCR peak assignment 115B.1 Terephthalic acid 115B.2 Beuzonitrile and p-cyanobenzoic acid 117B.3 p-Hydroxybenzoic aci(1 118B.4 Aniline and p-aminobenzoic acid 121viList of Tables1.1 Some physical parameters of positive muons 11.2 Some physical parameters of the muonium atom 23.1 Parameters obtained from the FFT analysis of high field TF-iSRspectra of benzoic acid, p-hydroxy and p-amino benzoic acids (asbenzoates) 493.2 The resonance 1)oSitiOnS, linewidths and amplitudes of the LCRspectra. of 10mM benzoic acid at pH--’2 and 15mM henzoate atpH 9.5 in aqueous solutions 513.3 The resonance positions, linewiciths and amplitudes of the LCRspectrum of 20mM terephthalic acid in aqueous solution at pH 12* 533.4 The resonance positions (BR), linewiciths (B08) and amplitudes(Ampi) of the LCR spectra of the substituted benzenes and benzoic acids in aqueous solutions studied here 563.5 Hyperfine data and calculated radical yields of 10mM benzoic acidin water at pH 2; method of the LCR peak assignment 593.6 The hyperfine (lata and radical yields of 15mM benzoate in aqueous solution at pH 9.5 643.7 The substituent effect of —C00 group on nmon hyperfine coup1mg constant of muonated henzoa.te radicals 653.8 The hyperfine coupling constants and LCR peak assignment ofMuTPA2and MuC6H radicals 67vii3.9 The hyperfine data and isomeric radical yields for 13.9 and 15mMhenzonitrile in water 683.10 The hyperfine data and radical yields of 15mM phenol in water 693.11 The ir electron density distribution and radical localization energyas calculated by HMO for henzene, inonosubstituted benzenes andp-hydroxy-benzoic acid 713.12 The overall and partial rate constants of Mu reactions with themonosubstituted aromatics studied here (plus benzene) 724.1 The concentrations of pyrimidine and miaonium decay constantsin aqueous solutions at room temperature and neutral pH for upand clown counters 784.2 The bimolecular rate constants of inuonium reaction with the Nheterocyclic compounds and benzene in aqueous solutions 804.3 Diamagnetic yiel(ls of neat pyridine, pyridazme, water and benzene 814.4 Experimental values of frequencies obtained by FFT analysis ofhigh field 1tSR spectra of N-heterocycles in water and adopted A,,values 824.5 LCR. positions(BR), linewiciths (B0bS), amplitudes (Ampi) andcalculated radical yields (PR) for the N-heterocyclic compoundsin water 874.6 The LUMO, ir-electron density distribution and radical localization energy of benzene and N-heterocyclic compounds calculatedby HMO method 894.7 The proton hyperflne coupling constants of MuBz and MuPz radicals and LCR 1)eak assignment for the latter radical 93viii4.8 The hyperfine coupling constants (An), LCR resonance positions(BR), radical yields (PR), the hyperfine coupling isotope effect ofthe second kind (f2) and the LCR peak assignment for 20 mMpyridine in water 954.9 The hyperfine coupling constants (An), LCR resonance positions(BR), radical yields (PR) for 0.3M pyrimidine in water 964.10 The BR, PR and the LCR peak assignment for 20mM pyridazine in water 984.11 The partial rate constants of Mu reactions with mono- and diazines 994.12 The rate constants of e;9 with the N-heterocyclic compounds andbenzene and the LUMO levels of the reactants 101B.1 The observed values of BR for 20mM p-CN-BA in aqueous solutionat pH 9, the assumed values of fj. and the deduced values of A1,A IH, R an RB.2 The observed values of BR for 20mM p-CN-BA in aqueous solutionat pH 9, the assumed values of A and the deduced values of AH,PR and P 118B.3 The O1)SerVe(l values of A and BR for 20mM p-hydroxybenzoicacid in aqueous solution at pH 8, the assumed values of andthe deduced values of AH, ff2, PR and P 119B.4 The observed values of BR for 20mM p-hydroxybenzoic acid inaqueous solution at pH 1.7, the assumed values of A and thededuced values of AH, f2, PR and P 120ixB.5 The observed values of BR for 20mM p-hydroxybenzoic acid inaqueous solution at. pH 1.7, the assumed values of f12, and thededuced values of A,1, PR and P 120B.6 The observed value of BR, deduced values of AH, f2 and PR for15mM aniline in aqueous solution at pH 8 121B.7 The observed BR, assumed f2 and deduced A,1, AH and PR for15mM aniline in aqueous solution at pH 2 122B.8 The observed values of A,, and BR and deduced values of AH, ff2,PR and P for 20mM p-aminobenzoic acid in aqueous solution at1)H 10 123B.9 The observed BR, assumed f2 and deduced A,,, AH and PR for2OmIVI p—ammobenzoic aci(l in Aqueous Solution at 1)11 2 123xList of Figures2.1 The 1LSR time histogram of neat pyridme at 125 G. The solid lineis the computer fit 172.2 A representative Breit-Rabi diagram of Mu, which is a two spin-isystem 192.3 (a) Raw and (1)) asymmetry, of a MSR histogram of 0.34 mMpyrimicline in water at 8 G 212.4 Representative plot of mnuonium relaxation rate AM vs. pyridazmeconcentration in water. Data points are from both up and downcounters. The soli(l line is a computer fit 232.5 The PET spectra of muonated styrene radicals. (a) at magneticfield 1.5 kG, (b) at magnetic field 2.5 kG 262.6 The schematic diagram of energy levels involved in the LCR transition for e_ft+_p+ three spin—k system 292.7 The experimental set-ui) for a backwar(l muon 1)eam on SFUMu.A—lead beam shielding, DEG—water degrader, C—beam collimator,TM, M2, Ml, Fl, F2, Ui, U2, Dl and D2—plastic scintillatorcounters, S—sample cell, H—Helmholz coil 342.8 A layout of the electronic detection scheme for the TF-SR method 362.9 The block diagram of the experimental set-up for LCR studiesusing surface muons 382.10 A block diagram of the electronics for LCR studies 39xi2.11 Typical LCR spectra: (a) from neat benzene, (b) and (c) from13.9mM benzonitrile in water 412.12 The schematic arrangement of the pumping system for LCR studies 443.1 The FFT of the 1iSR spectra of of the aqueous solutions of (a) 1Mp-aminobenzoic acid at pH 10 and (b) 1M p-hydroxybenzoic acidat pH 8. Both at about 3.9 kG 483.2 The LCR spectrum of 10mM benzoic acid in water at pH2:shown as the normalized forward-to-backward asymmetry difference (A+, with a small modulation field applied with the mainfield, A—, with it opposed) as a function of longitudinal magneticfield (in Tesla, 104G). The solid line is the computer fit 523.3 The LCR. spectrum of 20mM terephthalic acid in a.dlueous solutionat pH 12 543.4 The LCR. spectra of 20mM p-hydroxybenzoic acid in aqueous solutions. (a) at pH 1.7 and (b) at pH 8 573.5 An example showing the meaning of hyperfine coupling isotope effects of the first kind (fi) and the second kind (f2). fj=A7/A,613.6 The plot of log k vs. L for Phenol, benzoic acid and benzonitrile.k in units of L. in units of LB. The solid line is thecoml)uter fit 744.1 The structures and numbering of the N-heterocyclic compounds 774.2 The plot of Mu decay constant ..\ v. pyrimidine concentration atroom temperature. Slope equals kM. Data are from the up (x)and down ( ) counters. The solid line is the computer fit 79xii4.3 The FFT of the 1SR spectra of 1M pyrazine in water, presented asFourier power against frequency: (a) at about 2 kG; (h) at about4.8 kG 844.4 The LCR spectra of 20 mM pyrazine in water 864.5 The structures and numbering of MuBz and MuPz radicals . . 934.7 The plot of log k vs. ir electron density for mono- and diazines.k1 in units of M1s 1044.8 The plot of log k vs. L for mono and diazines. k in units ofM1s, L in units of 105xiiiAcknowledgementThe author wishes to take this opportunity to express his sincere thanks tohis research supervisor Dr.David C. Walker for his continual encouragement,guidance and enlightening discussion during the course of study. It is -such agreat privilege having him as a teacher and an advisor.The author also wishes to give his sincere thanks to Dr.D.P.Chong for hisgreat help in HMO calculations.Special thanks are extended to Dr.R.F.Snider and other members of his advisory committee for their help aid attention during this work, especially toDr. Snider for his reading through the draft of this thesis and many good suggestions.The author is very grateful to his collaborators, Drs. J. M. Stadlbauer,K.Venkateswaran, M. Barnabas, R.F.Kiefi, B.W.Ng and G.B.Porter for theirassistance dunng this work.The author would like to thank members of the ILSR, group at TRIUMF,particularly to Drs.J.Brewer, S.Kreitzman and R.F.Kiefi for writing the fittingsoftware, and to Curtis Ballard and Keith Hoyle for their continued assistancewith the equipment. Without their help, this thesis could not have been completed.The generous financial support from the University of British Columbia isgratefully acknowledged.xivChapter 1Introduction1.1 Muon and MuoniumMuons (i) are elementary particles of the lepton family which occur in two chargestates: positive muon (p+) and negative muon (). The muon was first observedas a component of cosmic rays by Anderson and Neddermeyer in 1937[1}. Sinceonly positive muons will he dealt with throughout this thesis, they will he simplyreferred to as the muon hereafter.The muon’s mass is about one nint.h the mass of a proton, or about 207 timesthe mass of an electron. It undergoes radioactive decay with mean life of 2.2 is.In many events, the muon behaves as if it were a very light proton. Some of itsproperties are given in Table 1.1.Table 1.1: Some pliysical parameters of positive muonsCharge +eSpinlifetime 2.1971x10”6sMass 0.1134amu=206.77mf=0.1126mMagnetic moment 4.49048x10°JG’’3. l8334p=O.OO4836ig-factor 2.0023318= 1 .000006geGyromagnetic ratio 13.5544 kHz G1Chapter 1. Introduction 2Muonium (chemical symbol, Mu) is the atom consisting of a positive muonas its nucleus and an electron orbiting the muon. This bound state of the muonwas first proposed by Friedman and Telegdi in 1957[2). In 1960, Hughes et al.[3]discovered free Mu atoms in argon gas. In 1976, the first direct observation ofMu in water was achieved by Percival et al.[4]. Now, it is well known that inmost gases, liquids and solids, some of the positive muons capture an electronfrom the medium during the final stages of their thermalization process to formmuonium[5J. The muonium atom is viewed as the simplest atom since boththe muon and the electron are leptons[6J. Some of the physical parameters ofmuoniurn are summarized in Table 1.2.Table 1.2: Some physical parameters of the muoniurn atomMass 0.1 l4Oamu=207.Srnf =0. ll31mReduced mass 0.9956 times tha.t of HBohr radius 1.0044 times that of HIonization energy 0.9956 times that of HMean velocity at 300 K 7.5x103ms=2.97 times that of HHyperfine frequency 4463 MHz (2.8044x10’°rad s’)Although muonium has only one ninth the mass of the H atom, its reducedmass is almost the same as tha.t of H, and consequently the Bohr radii and theionization potentials of Mu and H are essentially the same. Therefore, in manyevents, chemically. muonium is analogous to hydrogen, and it can be regarded asthe ultralight, radioactive isotope of the hydrogen atom. Its radioactive characterenables one to observe its chemical reactions under conditions where H wouldbe obscured, and with greatly improved sensitivity. Because of the mass ratiosMu:H:D:T 1:9:18:27, mass-dependent phenomena such as kinetic isotope effectsand quantum mechanical tunnelling should be most evident when comparingChapter 1. Introduction 3reactions of Mu with those of the other H isotopes.Being an isotope of H, Mu is expected to undergo the same types of reactions that H atoms do and more [7]. For example, as a reducing agent, it canundergo redox reactions. It can also carry out abstraction reactions (mainly Habstraction). Being one of the simplest free radicals, it can combine with another free radical. In 1963, Brodskii[8j pointed out that Mu should be able toadd to unsaturated molecules forming muonated free radicals. Indeed, in 1978,Roduner et al.[9] first observed muonated radicals in the liquid phase. Sincethen, many types of muonated free radicals have been observed and their muonhyperfine coupling constants have been measured. The Mu atom has two spinstates, called here SMu and TM11, with the muon and electron spins paired orunpaired, respectively. Only the TMu state is presently observable experimentally. This leads to observation of eectron spin flip reaction, which the H atommay also undergo but cannot be detected experimentally. These main types ofchemical reactions are exemplified below:Chapter 1. Introduction 4Redox reactionMu + Fe3 —* Mu(orii) + Fe2 (1.1)AbstractionMu+HCO —* MuH+CO (1.2)AdditionMu +C6H5H = CH2 —bC6H5H - CH2Mu (1.3)CombinationMu+OH—÷MuOH (1.4)Electron Spin flipMu(t) + Ni2{.) —* Mu(Jj + Ni2(t) (1.5)Muons appear in nature extremely rarely, only when cosmic particles interactwith the atmosphere. However, they are artificially produced with high energyparticle accelerators available at several places in the world. The principal facilities active in North America are at TRIUMF (the ‘Tn-Universities MesonFacility’, Vancouver) and at LAMPF (meson facility of the Los Alamos NationalLaboratory, New Mexico); those in Europe are at CERN (European Laboratory for Particle Physics, Geneva), PSI (Paul Scherrer Institute, Villigen, nearZurich), RAL (Rutherford Appleton Laboratory, Oxfordshire, UK); and in Japanat KEK (National Laboratory for High Energy Physics: University of Tokyo Meson Science Laboratory, Tsukuba, near Tokyo). Those at TRIUMF and PSI arechapter 1. Introduction S‘continuous’ sources and now especially noteworthy for their high intensity andrange of experimental facilities. These facilities produce energetic spin polarized beams and provide the opportunity of studying 1i and Mu as chemicalspecies.In 1957 Garwin el al.[1O} and Friedman et al.[1l] made the first experimentalobservations of the breakdown of the principle of parity invariance[12] in thedecay of positive muons. Their methods are forerunners of the present day iSR(muon spin rotation) technique.The pSR technique monitors the time evolution of muon spin polarization ina uniform magnetic field perpendicular to the muon spin polarization direction.One of the identifiable chemical states accessible t.o the pSR technique is a muonin a diamagnetic environment. Others include that of the free Mu atom andvarious muonated free radicals. The yields and reaction rates from these statesare determined on the iO to 105s timescale—the period over which manyfundamental physico-chemical interactions occur.Muons in diamagnetic states include bare free muons. solvated and trappedmuons and all diamagnetic molecules incorporating the muon, such as MuH andMuOH. These different states cannot he distinguished from each other by the1iSR technique since their chemical shifts’ are currently beyond the frequencyresolution. However, Mu and muonated free radicals have distinct muon spinrotation frequencies, therefore they are separately identifiable.The possibility of using level crossing resonance (LCR.) spectroscopy in pSRwas first pointed out by Abragam in 1984 [13]. The first demonstration soonfollowed, at TRIUMF, when Kreitzman et al. utilized the LCR phenomenon todetermine the nuclear quadrupolar interaction of the nearest neighbour nucleito muons in copper [14]. Extension of LCR to muons in paramagnetic systemsChapter 1. Introduction 6was proposed by Kiefi and Kreitzman et al., and strong LCR signals were detected from muonium-substituted free radicals [15]. This paved the way for theinnovation of muon Level Crossing Resonance Spectroscopy (LCR). This is wellestablished as a technique now and particularly suitable for muonated free radicalstudies. The principle of the LCR method is based on the transfer of spin polarization from a muon to some other nucleus in the coupled spin system throughmutual spin flips, by matching the muon transition frequency to that of the othernucleus at specific magnetic fields. At such a field, a pair of nearly degenerateenergy levels having different. Spin orientations for the muon and another nucleusare mixed by the hyperfine interaction. This results in a reduction of muon spinpolarization and a resonant-like change in the forward to backward count ratioof the LCR spectrum as the magnetic field is swept (details in Chapter 2).1.2 Hückel Molecular Orbital TheoryMolecular-Orbital (MO) theory. especially Hückel Molecular Orbital (HMO), iswidely appreciated by chemists in most a.reas of research and teaching. Althoughthe quantitative aspects of molecular orbital theory are now well beyond theHückel method, due to powerful modern computer techniques, Hückel theory isstill useful and gives qualitative and in some cases quantitative results.The original, simplest Hückel Molecular Orbital Theory is for ir-conjugated,especially aromatic, hydrocarbons. It assumes molecular orbitals are linear combinations of atomic orbitals (LCAO-MO theory)= Cjrr (1.6)where ‘T! is the jh molecular orbital.,.is the atomic orbital of atom r and c.?,. isthe coefficient. of the atomic orbital of atom r in the jth molecular orbital. TheseChapter 1. Introduction 7coefficients and the energies f molecular orbitals can be obtained by solving theSchrödinger Equation H’I=E’1 with the variation method.Hückel made the following assumptions [16,17]:1. The Coulomb integrals, c, are set equal to the common value, a, for allcarbon atoms, irrespective of their environment in the conjugated system. Thus,Hrr = = JcbrHrdr = a, r = 1,2,...n. (1.7)where the integration is taken over all space.2. All resonance integrals (also called bond integrals), /3rS, are taken to be zeroif atoms r and s are not bonded neighbours. If r and s are bonded neighbours,then /3,.. is given the same value. 3. for all carbon-carbon bonds, irrespective oftheir environment in the conjugated system.r 1 ü r,s not adjacent3rs= J .rHQsdT = (1.8)r,s are adjacent atomswhere r,s=1.2....n and the integration of the space element dr is taken over allspace. The individual MO’s have energies of the form= a + j/3 (1.9)where j is a coefficient. for the Ith MO. The total ir electron energy of a systemis the sum of the energy of all ir electrons in the system.This method can be extented to substituted aromatics and heteroconjugatedsystems [16,17]. The Coulomb integral for some hetero-a.tom at position r in theconjugated system. can be given asQr0c+h9 (1.10)Chapter 1. Introduction 8where c is the Coulomb integral for carbon atom as a standard, /3 is the standardresonance integral of a carbon-carbon bond in benzene and h is a parameter forthe hetero-atom.The resonance integral /3 is also affected by the presence of hetero-atom(s).In practice, the following empirical equation is used= k,.3I3cc (1.11)where j3,. is the resonance integral for atoms r and s, one of them is the heteroatom. /3CC is the resonance integral for carbon-carbon atoms in benzene as astandard and k,., is an empirical parameter for the bond r-s involving a heteroatom [16].When an aromatic system is under attack by species Y, which could beneutral(Y°) or charged (Y or Yj, there will be a stage in the reaction when Yis attached to the rth carbon atom, and the H originally bonded to this carbonatom is still there. This arrangement is called the Wheland intermediate state.In this state, the total ir-electron energy is different from that of the originalmolecule. The difference between these two energies is called the Localisationenergy L [16,17]. This localisation energy can also be obtained by the HMOmethod. In this thesis the values of radical localisation energy Lr for radicalattack are calculated.The relative reactivity at a particular position in an aromatic system hasbeen related to both the ir electron density and the localisation energy at theparticular position in the ring.Chapter 1. Introduction 91.3 Description of ThesisThis study deals with muonium reactions with substituted benzenes and nitrogenheterocyclic aromatic compounds in aqueous solutions.Chapter 2 introduces all SR techniques involved and the experimental details.Chapter 3 deals with muonium reactions with aromatic compounds, mainlymonosubstituted benzenes and benzoic acids. Muon hyperfine coupling constantsare measured for the free radicals formed when muonium reacts with benzoicacid and para-substituted benzoic acids in aqueous solutions at high pH. TheLCR spectra of the muonated radicals formed by muonium atoms adding toaromatic compounds in acidic and/or basic aqueous solutions are recorded, andthe resonance signals are assigned to the particular nuclei of the related radicalisomers. Radical isomer yields are estimated. The relative reactivities towardmuonium attack at the different sites of these aromatic compounds are relatedto radical localisation energies obtained by HMO calculations.In a fairly similar way as in Chapter 3, Chapter 4 deals with muonium reactions with nitrogen heterocyclic aromatic compounds in aqueous solutions.Pyridine and the three diazines, pyrazine, pyrimidine and pyridazine, are chosen as reactants. Reaction rate constants obtained by uSR are reported. Muonhyperfine coupling constants of the muonated radicals formed when muoniumatoms react with these solutes are measured and the corresponding LCR spectraare recorded. The resonance peaks of these spectra are assigned to particularisomeric radicals and their yields are estimated. These results are related to their-electron density distribution and radical localization energy obtained by theHMO method. Some comparison of reaction rate constants of muonium atomsChapter .1. Introduction 10with hydrogen atoms and/or hydrated electrons towards the N-heterocyclics aremade. The isotope effects on rate constants and hyperfine coupling constants arereported. Based on the results of chapters 3 and 4, some general conclusions onthe reaction of muonium with aromatic and N-heterocyclic aromatic compoundsare drawn.In addition to the work mentioned above, the author was involved in severalother projects, most of which have now been published. This work is presentedin the Appendix as ‘collaborative work’.Chapter 2Background and Experimental2.1 Muon production and decayAt TRIUMF, the positive pion is produced by bombarding a target such as berylhum with high energy protons (typically about 500 Mev) via the nuclear reaction:9Be + p —‘10Be + (2.1)The positive pion then decays with a mean life of 26ns to give a muon and amuon-neutrino [18]:+ + v (2.2)This decay process is parity-violated, exoergic by about 34 MeV, and producesa 4.1 MeV muon. The pion is a spin-zero particle but the muon neutrino is a.spin-i particle with zero rest mass and 100% negative helicity, ie., its spin isantiparallel to its momentum. As a. consequence of the conservation of linearand angular momentum. the muons emitted from the decay process (2.2) alsohave 100% negative helicity in the pion’s rest frame.At TRIUMF. there are many beamline channels, experimental beam portsand facilities, and ,u+s can be manufactured in different modes of beam operation. In ‘conventional’ mode, pions decay in flight, in the beam line to give twotypes of muons, forward and backward muons (in the pion rest. frame, forward11Chapter 2. Background and Experimental 12muons are emitted in the pion’s momentum direction while backward muons areemitted in the opposite direction). They have very different energies. A seriesof quadrupoles and bending magnets is used to select and focus the muon beaniwith the desired energy. A backward muon beam is relatively clean. It haspositive helicity and is typically about 80% polarized. These muons are sufficiently energetic and can penetrate 2 to 3 g cm2, therefore, they are suitablefor experiments in thick-walled glass cells.Alternatively, the beamline may be tuned to the particular energy, 4.1 MeV,which selects muons coming only from the decay of pions that come to rest nearthe surface of the production target. Such a ‘surface muon’ beam (also known,in recognition of its developers, as an ‘Arizona’ beam) has a polarization close to100%. The stopping range of the surface muon is correspondingly low and welldefined. This is 0.15 ± 0.01 g cm2,which corresponds to a penetration depth ofabout 0.2 mm in metallic copper, 1.5 mm in liquid water or 1 m in He gas at STP.Surface muons are therefore suitable for samples that are only available in smallquantities (such as rare metallic foils, and for gas-phase studies). Thin windowsin the beamline and sample holders are required to allow the muon to reach thesample. Both surface and backward muons are used in different experiments ofthis study.The muon itself decays (r=2.2 ps), emitting a positron (ej, an electronneutrino (ne) and a muon anti-neutrino (i) [19]:e+ + v + i, (2.3)Both positron and muon are detectable with scintillation counters.Chapter 2. Background and Experimental 13This muon decay process also violates parity conservation. The electron-neutrino has negative helicity while the positron and the muon antineutrinohave positive helicity. Because of the conservation of energy, linear and angularmomentum, this three body decay of the muon is spatially anisotropic withrespect to positron emission. As a result, the positron is preferentially emittedalong the instantaneous spin direction when the muon decays. In general, theanisotropic angular distribution of the emitted positron is given by (1 + a cos8)[20]. Here, 8 is the angle between the positron momentum and the muon spindirection, ‘a’ is the so-called asymmetry parameter. It is a function of the emittedpositron energy with an average value of 1/3 [21]). In practice, it is usually only‘—p0.2 because of a number of experimental imperfections.Based on this asymmetric muon decay, several experimental techniques havebeen developed [21,22,23]. All these techniques involve the injection and stopping of muons from a spin polarized muon beam into the sample mounted in anexternal magnetic field. Depending on whether the magnetic field is perpendicular or parallel to the muon beam polarization, the techniques are classified astransverse field (TF) or longitudinal field (LF) methods. In transverse field methods, the evolution of muon spin polarization in the sample is monitored by thedetection of the decay-positron using a single particle counting technique (timedifferential measurement). In longitudinal field methods, the decay-positrons inthe forward and backward directions are separately counted and information isdrawn by comparing these count rates ( ie., time integrated measurements).The experiments for the work presented in this thesis were all conducted atTRIUMF on the M2OA muon channel with backward muon beams, or on theM2OB channel with surface muon beams. Some of the collaborative work in theChapter 2. Background and Experimental 14Appendix was also done on M13 or M15. With backward muons, only the transverse field time-differential measurements were performed, whereas with surfacemuons, both longitudinal field time-integrated measurements and transverse field(with muon beam spin rotated by 900) time-differential measurements were performed. These techniques will be discussed in more detail below.2.2 Transverse field 1iSR techniquesThe initials‘1iSR’ stand for muon spin rotation, relaxation or resonance, depending on the variant of the technique used—or for muon spin research, to cover allpossibilities. So far, most of the chemical studies have been carried out using thetime-differential transverse field muon spin rotation technique, and here iSR isused for measurements at various magnetic fields. When muons are implantedinto a chemical sample, they can quickly lose their kinetic energy by collisionwith the molecules of a medium and thereby come to rest, and react chemicallyduring their 2.2 ts lifetime. As mentioned in Chapter 1, the + may exist in oneof three magnetic states: in a diamagnetic state, as a free muonium atom (Mu)or in a muonated free radical. These three types of magnetic states of the muonare readily distinguishable by muon spin rotation, even when present togetherin a medium. However, different ranges of external magnetic fields have to beemployed for studying muons in the diamagnetic states (typically 50 to 200 G),the free muonium atom (<lOG) and muonium containing free radicals (usually1 to 10 kG).The external magnetic field is supplied by means of Helmholtz electric coils.The field should be homogeneous at the sample position. If the magnetic fieldperpendicular to the muon beam direction is too high, the beam will be bentChapter 2. Background and Experimental 1.5significantly before it enters the sample. In order to avoid beam bending, highmagnetic fields such as are provided by superconducting coils (e.g., Helios) mustbe applied longitudinally relative to the muon momentum. For high transversefield studies, the muon’s spin must be rotated by 900 with a ‘spin rotator’(whichexerts crossed magnetic and electrostatic fields on the muon) prior to its entry inthe sample, so that the magnetic field which is longitudinal to the beam becomestransverse to the muon spin polarization.2.2.1 Muon Spin Rotation(tSR)The Muon Spin Rotation(1iSR) technique is used to monitor the magnitude andtime dependence of the muon polarization for all muons in diamagnetic states,such as the bare ,u or MuOH. This technique utilizes an external magnetic fieldof 50-200 0. When a muon stops in a target placed in a transverse magneticfield, its spin precesses at its Larmor frequencyWD = (2.4)where (=13.55kHz/G) is the muon gyromagnetic ratio, and B is the transversemagnetic field experienced by the muon.To observe this transverse precession, one needs to place a positron counterin the plane of the muon precession at an angle co with respect to the initialmuon spin direction. Since muon decay is spatially asymmetric, the probabilityof detecting the decay positron rises and falls as the precessing muon spin swingspast the fixed positron detector. The resultant SR histogram (known as a rawhistogram) thus has the form [7]N(t) = No.e_uh’n1[1 + ADe_’’-’tcos(wDt + )] + Bg (2.5)Chapter 2. Background and Experimental 16where N(t) is the number of the counts in a histogram time-bin correspondingto time t, No is a normalization factor, Bg is the time independent background,is the muon lifetime (2.2 is), AD is the experimental diamagnetic asymmetryor amplitude, ‘D is the exponential decay constant (usually negligible), WD isthe precession frequency, and is the initial phase of the diamagnetic muonprecession.Raw histograms are fitted to equation (2.5) by aX2-minlmization programMINUIT until the best fit is obtained. The fitted AD was used to calculatethe fractional yield of the diamagnetic states (PD )—the fraction of muons whichenters the media and exist in diamagnetic states. Since liquid CC14 shows allincident muons as diamagnetic states the diamagnetic asymmetry in liquid CC14is. under the same experimental conditions, always the highest (Amax). Thefractional yield for a diamagnetic species is then defined as PDAD/Amar [24].A typical pSR raw histogram needs 106 counts. Fig.2.1. shows the computerfitted 1tSR. time histogram of neat pyridine. The most dominant features arethe exponential muon lifetime upon which is superposed the oscillating muonasymmetry.Chapter 2. Background and Experimental 17Figure 2.1: The 1iSR time histogram of neat pyridine at 125 G. The solid line is0.5 .L.0 1.5 2.0 2.5 .0 3.5 4.0 4.5Ti.ie (,itcro—s.conds)the computer fit.Chapter 2. Background and Experimental 182.2.2 Muonium Spin Rotation(MSR)It was found in 1976 [4] that Mu can be observed directly by the Muonium SpinRotation (also known as MSR) technique, provided the liquid is relatively pureand oxygen free. In MSR, the muon spin is not only coupled to an externalmagnetic field but also to the electron spin via the hyperfine interaction. Sincethe muons are polarized while the captured electrons are unpolarized, the initialspin states are assumed to be 50% cae > and 50% °i/3e >, where the muonpolarization direction is the quantization axis. The spin Hamiltonian is given byEq.2.6 in frequency unitsH(M) l1eSz — l/,iIz + ASi (2.6)where tie and v are the Zeeman frequencies for electron and muon, respectively, Sand I are their spins, S and I are the components of these spins along the fielddirection, A is the electron-muon Fermi contact hyperfine coupling constant.At zero magnetic field Mu has a singlet and a triplet spin state. If a magneticfield is applied to muonium, the degeneracy of the triplet state is lifted. Fig.2.2.describes the variations of the energy levels of the four spin states as a function ofthe strength of the applied field (Breit-Rabi diagram). In general, in a transversemagnetic field, the time evolution of the muon spin polarization in Mu is quitecomplicated, but it is much simpler in the weak field limit (10 G). In thelatter case, half of the spins (triplet) precess at the muonium Larmor frequency,WM=1O3D, in the sense opposite to the free muon precession; the remainder(singlet) of the muon polarization oscillates at the hyperfine (hf) frequency, wo= 2.8x101°rad s1. Since the experimental resolution of tSR is about 2 ns for aconventional apparatus, the latter hyperfine oscillation is not observable and thisportion of muonium ensemble (singlet) appears to be totally depolarized [29].Chapter 2. Background and Experimental 19Figure 2.2: A representative Breit-Rahi diagram of Mu, which is a two spin-isystem.— +et fV01 tChapter 2. Background and Experimental 20Monitoring the time evolution of the p spin in Mu in weak transverse magnetic fields via the asymmetric muon decay of Mu forms the basis for studyingmuonium. The method is identical with that of diamagnetic muons except thatthe muon precession frequency in Mu is 103 times faster than the free muon inthe same magnetic field, and that the muon asymmetry in Mu is reduced by half.Experimentally, the positron detection probability in this MSR technique nowacquires another term at the frequency WM with a new empirical amplitude AM.Both the muonium precession and the diamagnetic precession are superimposed upon the exponential decay of the muon. In addition, there might beexponential damping on the oscillatory term caused by possible phenomenological depolarization and/or chemical reaction. Hence, the positron distributiontakes the formN(t) No.e_T[1 + ADCOS(WDt + qSD) + AM.eMtCOS(WMt— cM)j + Bg (2.7)where ‘M is the Mu decay constant (and \D has been taken as zero here).Mu is a highly reactive chemical species, but it is stable in several saturatedinert liquids such as water and alkanes. Solutes can be added to these solvents atconcentrations where Mu reactions occur mainly in the iO to iO s observationtime window, so that the value of AM falls within the working range of ‘5x106to —‘2x105s1.Typical ‘raw’ and ‘asymmetry’ tSR histograms (the latter after the muonlifetime term and the background Bg are removed by the computing program)are displayed in Fig.2.3.Chapter 2. Background and Experimental(0)C,)C00z(b)= A,exp(—)t)cos(c,t—Ø) + ADcos(Dt+ØD)21Figure 2.3: (a) Raw and (b) asymmetry, of a MSR histogram of 0.34 mM pyrimidine in water at S G.N.=Nexp(—t/r)[1+Aexp(—Xt)cot—+ ADcos(crJ+ØD)] + N09gTime / s2 3 4>sC)EE>‘U)Chapter 2. Background and Experimental 22The muonium relaxation coefficient, AM, is just the relaxation of the spin polarization, but in chemistry it is generally representative of a chemical reactionof Mu. It varies with the addition of a reactive solute S at concentration [S] inaccordance with equationAM=Ao+kM[Sj (2.8)where A0 is the ‘background’ muonium relaxation constant found in the solvent at[S]=O. The linear relationship of AM and [S] is illustrated in Fig.2.4. It is worthemphasizing that never more than one muon at a time is in the solution, so (AM- A0) represents a pseudo first-order rate constant as in Eq.2.8 and a plot of AMvs. [5] gives the slope as kM, which then represents the bimolecular rate constantfor the reaction of Mu with substrate S. Furthermore, the time scale over whichthe relaxation was observed is much later than the slowing down process of themuon, so kM is indeed a thermal rate constant.A typical raw MSR histogram takes iO counts. The magnitude of statisticalerrors in A from each histogram is about 10-15%. Deviations due to values fromdifferent experimental factors results in an overall error in kM of about 25%.Chapter 2. Background and Experimental 23U)C21. (iFI)Figure 2.4: Representative plot of muonium relaxation rate ç vs. pyridazineconcentration in water. Data points are from both up and down counters. Thesolid line is a computer fit.C .02S .05 .075 .1 .125 .15 .175 .2 .225 .25 .275Chapter 2. Background and Experimental 242.2.3 Muoniurn-Radical Spin Rotation(MRSR)Radicals are molecular species which are paramagnetic by virtue of a single unpaired electron. The majority of radicals are reactive species. Measurementsof nuclear hyperfine couplings not only serve to identify the species, but alsoprovide information on molecular structure.When a Mu atom adds to an unsaturated molecule, a muonated free radicalis formed. In muonated radicals containing magnetic nuclei besides the muon,the unpaired electron spin is coupled to these nuclei, as well as to the muon. Thespin Hamiltonian used for such a multispin system in gas and liquid phases isH = yeS: — — + AMSI + AkSJk (2.9)k kwhere S, I and 1k are the spins of electron. muon and nucleus k (k standsfor nuclei such as protons). respectively, S, I: and Jkz are the components ofthese spins along the field direction. v’s are the Zeeman frequencies and A’sare the Fermi contact hyperflne coupling constants. For N nuclei with spinsJk, this Harnilt.onian leads to 4fl(2Jk + 1) eigenstates. The selection rule forthe transitions between these states is M = ±1 with M = m + m + k mk(where m’s are spin quantum numbers of electron, muon and nuclei) [25], andthe system generally oscillates between many of these eigenstates. Consequently,the muon polarization is distributed over many frequencies. In low fields, thisrenders the detection of muonated radicals difficult or even impossible. However,in higher fields satisfying the condition v much greater than A and Ak for allk, the spin system is decoupled, therefore the frequency spectrum is considerablysimplified. Under such conditions, the simple product spin states are usually goodapproximations to the eigenstates of the spin Hamiltonian, and the selection rulebecomes = ±1, = 0 and mk = 0. Under this condition. there areChapter 2. Background and Experimental 25only two frequencies, v, in the radical spectra at [25]= hID AI (2.10)From Eq. 2.10, one gets the muon hyperfine coupling constant(2.11)orA —ii- v 212i’R Rdepending on the relative magnitudes. The diamagnetic muon frequency 1’Dchanges with field (-yB), while A, remains independent of field.For muonated radicals, the general formulation of the raw histogram is givenbyN(t) = No.efT[1 + ADCOS(LJJDt + D) + R(t)] + Bg (2.13)if all Mu atoms are converted to radicals, andR(t) AR1e_Aitcos(wjt + qj) (2.14)where R2(t) represents various contributions of the ith radical amplitude (AR1at frequency w1 with relaxation rate ). Fig.2.5 shows typical tSR Fouriertransform spectra for muonated styrene radicals at magnetic fields of 1.5 and 2.5kG.Chapter 2. Background and Experimental 266.E—45.E—44.E—43.E—402.E—41.E—404.E—43.5E—43.E—45 2.5E—42.E—4- 1.5E—41.E—45.E—501 1 1 I.(b)._.l__.L_b L I I A.L.t__o 25 50 75 100 125 150 175 200 225 250Frequency (MHz)Figure 2.5: The FFT spectra of muonated styrene radicals. (a) at magnetic field2.5 kG, (b) at magnetic field 1.5 kG.Chapter 2. Background and Experimental 27Using this jiSR technique, the information concerning nuclear hyperfine couplings is lost and the identification of the radicals has to rely on a comparisonof the muon hyperfine coupling constant with the proton hyperfine couplingconstant of the analogous hydrogen radicals. Moreover, in transverse magneticfields, muonated radicals can be observed only when the radical formation time r(=1/kM[Sj) is short. With muonium as precursor, r should be less than --1010s.As a consequence, samples to be studied by MRSR must have large radical formation rates and be in high concentration, i.e., even for concentrations in themolar range the rate constant should be larger than about 1010 M1s.2.3 Muon Level Crossing Resonance Spectroscopy (LCR)Muon Level Crossing Resonance Spectroscopy (LCR) is a longitudinal field time-integral technique for studying rnuonated free radicals. It utilizes a surfa.ce muonbeam (at. TRIUMF) and the external magnetic field is parallel to the muon beampolarization. In such an arrangement. there is no muon spin precession and nolimitation on the formation time.In t.he gas and liquid phases, the spin Ha.milt.onian for a muona.ted free radicalwith N magnetic nuclei besides the muon is given by Eq 2.9, in frequency units.In the high field limits, where the electronic Zeernan frequency is much largerthan the hyperfine frequencies, the multiple spin system is decoupled and itseigenstates ca.n be written in the basis of the product spin states. Under theseconditions the integrated muon decay asymmetry along the field direction, Az,is close to its maximum value. However, the muon polarization may developlarge amplitude oscillations at specific magnetic fields where two muon-nucleushyperfine levels. which are characterized by different values of spin quantumChapter 2. Background and Experimental 28number m, and mk, are energetically close. Consequently, a resonant-like effecton Az is expected as the magnetic field is scanned.Due to the dominance of the electron Zeeman term in the Hamiltonian (Eq.2.9),the energy levels form two well separated groups according to the sign of the electron spin quantum number me. In practice, the transitions to be observed arebetween states with the same m.There are basically three types of LCR’s predicted. These LCR’s may becharacterized by the quantity , which is the difference in (m,L+mk) betweenthe two hyperfine levels involved [26]. In the liquid phase, which is the case ofthis study, only the LCR signal for z=O is observable. Therefore, no furtherdiscussion on LCR for iO will be given. A schematic diagram of energy levelsinvolved in the LCR transition is shown in Fig.2.6 for a three spin-i system withan electron, a muon and a proton as a simplest example [26].Chapter 2. Background and Experimental 29Energy levels for the system —e—p.at low rriagnetic fields.— +eipt1iti,t44,4tMagnetic fieldat high magnetic fields.Figure 2.6: The schematic diagram of ener levels involved in the LCR transitionfor e .p+p+ three spin-i system.—epptt1t tt44CtLCR stateLCR state4,ft*—0Chapter 2. Background and Experimenta.1 30The LCR signal occurs at the specific magnetic field BR (the resonance field)given by [27)l(A—Ak A—2MABR= —______— (2.152 7k 7e(Asu — Ak)where M = me + m + Ekmk. At this field, the following equation holds(2.16)where v and Vk are the transition frequencies for muon and nucleus k, respec.tively, ± stands for electron Spin directions [27].The LCR transition frequency at resonance field BR is given byVr= C.A,.Ak (2.17)2BR-ywhere c = [Jk(Jk+1) — I\I(M1 )]1/2 and Jk is the spin of the nucleus involved.The resonances due to inequivaient nuclei usually do not overlap and can betreated separately.The muon polarization (Pz) in a multi-spin system in the high field limit isa function of the field. The generai expression for the average value, Pz(B) isgiven by [27]z(B) = 1- [[(B- BR)( - 7:)]2 + v + (/2)2] (2.18)where N is the dimension of the Hamiltonian matrix and \ is the damping rate,which describes all processes that take the muon out of resonance, usually thephysical muon decay a.nd chemical reactions. When no chemical reaction is involved, A is simply equal to the muon decay rate A0. This has a Lorentzian lineshape. The depolarization amplitude at the LCR position is given by9 2L, Vr 19Z— N ii + (A/27r)2Chapter 2. Background and Experimental 31and the line width at half maximum for Pz(B) is given byIBth= 2[v + (A/2ir)2}” (2.20)—7kOne of the most remarkable features of the LCR’s in high field is that the positionand magnitude of each resonance is insensitive to the number of nuclei off resonance. This characteristic makes the LCR technique suitable to measure nuclearhyperfine parameters in complicated spin systems involving a muon. Besides,the LCR signal is sensitive to the relative signs of the muon hyperfine frequencyand that of the coupled nucleus.The LCR technique also provides the possibility to detect slowly formingradicals, including those which are evolving from a radical reaction. Radicalswill be observed even when a Mu precursor has a lifetime of a gus, as long as thetransition frequency r is high enough to produce a significant LCR signal in theremaining muon lifetime. The loss of polarization during the precursor stage isnegligible in high longitudinal fields.LCR studies on muonated radicals show that it is a powerful spectroscopictechnique. Its spectra can give extra information about non-muon spin interactions and can readily be used to determine nuclear hyperfine couplings in paramagnetic spin systems. LCR complements conventional .tSR by providing additional information which should be useful in identifying radicals and exploringelectron spin distributions of muonated free radicals.Another remarkable feature of LCR is that it can be used to determinemuonated radical yields. The radical yield PR (the fraction of muons whichform muonated radicals) is given by [28]A 7 / A r\21p — I1mp4.LL)) i714 — 7k)2Abfv,.Chapter 2. Background and Experimental 32where Ampi and B are the amplitude and linewidth of the LCR signal, respectively; Abf is the absolute backward-to-forward asymmetry (which can bedetermined experimentally with pure benzene as standard) under the actual operating conditions.In many cases, Mu can react with the same substrate forming a number ofdifferent radical isomers. Since the LCR signals from different muonated radicalisomers normally do not overlap, this provides a convenient way to determinemuonated radical isomer distributions. This is what this thesis is mainly concerned with.2.4 Experimental set-up2.4.1 Set-up for TF-1SR experiments with backward muonsFig.2.7 depicts the experimenta.l set-up for TF-1tSR measurements with a backward muon beam. The apparatus ‘SFUMu’ was used for this set-up at the M2OAexperimental site. This apparatus provides uniform magnetic fields of up to 4kG perpendicular t.o the muon beam via, a Helmholz coil H. The sample S understudy sits at the center of this external transverse magnetic field. The beamsize at the sample site can be adjusted with a set of collimators C of desiredsizes. Normally, a muon comes through the hole in lead shielding A and thebeamline window, penetrates the remotely adjustable water degrader DEG andpasses through a set of collimators C, then penetrates the muon ‘start’ countersTM and M2, passes through the hole of veto counter Ml, enters and stops in thesample S. For such a muon, the muon start counters TM and M2 will produce amuon arriving signals, hut the veto counter Ml will show no response. Therefore,the logic signa.ture for a muon stopped in the sample is defined by a signal fromChapter 2. Background and Experimental 33TM and M2, and none from Ml, ie., TM.M2•Ml. This signal designates a mounhas reached the sample and is called a ‘start’ signal.In the figure, the magnetic field produced by H is perpendicular to the paper,so that the longitudinally polarized backward muons in the sample will precessin the plane of the paper. Ui, U2, Di, D2, Fl and F2 are plastic scintillatorcounters placed in the muon spin precessing plane and in the up, down andforward directions relative to the muon beam, respectively. They serve as decaypositron detectors. For example, an emitted positron in the up direction willproduce coincident signals from Ui and U2 counters. These gives a ‘stop’ signalwith the logic signature UlU2.Chapter 2. Background and Experimental//— HOU2/C T1iM2 UIDEDl U\ 0234Figure 2.7: The experimental set-up for a. backward muon beam on SFUMu.A—lead beam shielding, DEG—water degrader, C—beam collimator, TM, M2,Ml, Fl, F2. Ui. U2. Dl and D2—plastic scintillator counters, S—sample cell,H—Helmholz coil.\II///‘I— —Chapter 2. Background and Experimental 35The principal layout of the electronic detection scheme for TF-1iSR is depictedin Fig.2.8. The signals from muon arid positron counters are first transformed tostandard Nuclear Instrument and Measurement (NIM) pulses of -s20 ns widthand then input to various electronic units. A good muon decay event requiresthat within a certain time interval after a muon stop, a positron is detected. Thisperiod is called the data. gate and extends usually over several muon lifetimes.The data gate is produced by a gate generator triggered by the muon stop signal.A good decay positron is then identified by a coincidence of the positron signalwith the data. gate. A clock is started by the muon stop signal and stopped by agood decay event signal. The measured time interval then forms the address of ahistogram memory. and the content of the corresponding time channel is incremented by one. The process is repeated until sufficient. statistics are obtained.In this way, a pSR time spectrum is formed.In practice the electronics has to check for a number of further details, suchas pile-up rejection. A second muon event represents a stopped muon whichfollows a previously stopped first muon within the time interva.l defined by thepile-up gate. There are now probably two muons in the target and a subsequentlyemerging positron cannot be related unambiguously to the correct parent muon.Such ill-defined events must be rejected. This is achieved by requiring that theclock can only be started by a muon signal which is in coincidence with thenon-busy signal () from the pile-up gate. A more detailed explanation of theelectronics and computer logic can be found elsewhere [29].CDCa)C’)H1-.a)a)0Ua)a)U01-4Ua)a)a)4-4C0CC-iL:“4c’z0C--iU,Chapter 2. Background and Experimental 372.4.2 Set-up for LCR experiments with surface muonsFig.2.9 shows a block diagram of the experimental set up on HELlOS for LCRstudies using surface muons. The superconducting solenoid provides a longitudinal magnetic field up to 70 kG. The surface muons coming along the beamlineare about 100% polarized with spins antiparaflel their momentum direction (negative helicity). Because of the low energy of the surface muons, a snout is usedas an extension of the beamline so that the low energy surface muons can bebrought, under vacuum, to the sample a.t the center of the magnet. These muonsemerge from the beamline, penetrate the muon thin counter M, enter and stop inthe sample S, associate chemically, then start to decay. Their asymmetric decaygives a higher rat.e in the cylindrical backward counters BL and BR than in theforward counters FL and FR. In the absence of any relaxation of spin polarization, their ratio remains constant. However, at. the specific resonance field BR, asharp reduction in muon polarization occurs due t.o mixing of degenerate statesand polarization transfer from muon to other nuclei (with a non-zero spin) of themuonat.ed radical.In LCR. the integrated count rates in the forward (F) and backward (B) direction are recorded as a function of the longitudinal magnetic field. An integratedmuon decay asymmetry. A, is used, given by(299B+FThere is no theoretical limit on the incoming muon rate since it is not requiredthat there be only one muon in the target. at a time as in t.he TF-pSR techniques.Chapter 2. Background and Experimental 38SC SuperconductingsolenoloMC Field modulotioricoilS : SampleM : Thin counterBR.8L : BackwardCountersFR.FL : ForwordCounters4FR & FLLOGIC1(MEMORY IFigure 2.9: The block diagram of the experimental set-up for LCR studies usingsurface muons.ScFRBR & BLMajDetk Field/TChapter 2. Background and Experimental 39NOT ES—Preset on Prt mode, preset mode, timer of f, NIM pulses.-nputs 0 & 1 on Coin. Buffer (212) come from outbor of fon (true)Must flit continue on menu to stortFigure 2.10: A block diagram of the electronics for LCR studies.Chapter 2. Background and Experimental 40A block diagram of the electronics used for LCR experiments is shown inFig.2.10. In order to reduce systematic errors, data were accumulated only whilethe beam rate was within a given tolerance (normally 20%). Also, the magneticfield is modulated with a small square-wave field (about 50G) at a frequencyof the order of 1 Hz, dependent on the preset count required (106) before fieldshift. Baseline shifts were minimized by displaying and analysing the spectrumas (A+ - A—) vs. field, where the + and - signs refer to the directions of themodulation field. Therefore, the LCR spectrum is actually the difference of twoLorentzian lines of muon polarization separated by twice the modulation field.If the resonance linewidt.h is greater than the modulation field amplitude, theresulting lineshape is approximately field differential [26].Data were acquired over 5 to 20 modulation cycles (toggles) before the mainfield was stepped’. Examples of LCR spectra as recorded under these experimental conditions are shown in Fig.2.11.Precise values of magnetic field are essential for LCR experiments. By measuring the frequencies of diamagnetic signals at different fields (TF-1SR method),the fields can be determined, via Eq. 2.4, to be directly proportional to diamagnetic precession frequencies. The following equation was used to calibrate themagnetic fields,B = ,n(DAC — DAC0) (2.23)where B is magnetic field, DAC is the current set for the superconducting coiland m and DAC0 are constant experimental parameters..li35<• rcz2.:4 2.I 2.I l. 2 tI 2.3agec PeId/TFigure 2.11: Typical LCR spectra: (a) from neat benzene. (b) and (c) from13.9mM benzonitrile in water.chapter 2. Background and Experimental 41at-a-mam am am am am am ti zu Lu1.5 1.51 1.52 L53 1.54 1.55 1.56 I.!? 1.55 1.55 2CCC2.isChapter 2. Background and Experimental 422.4.3 Data analysisThe on-line computers in the TRIUMF counting rooms (PDP-11/60, more recently VMS workstations) were used for data. acquisition and for monitoring theexperiments. Most of the experimental data analysis was performed off-line onthe TRIUMF computers. The main software used is a package of multiparameterchi-squared minimization routines called MINUIT.For the muonium kinetics studies described in chapter 3 and 4, the raw hist.ograms were fitted to Eq.2. 7. The muonium decay rate AM is the parameterof central interest. The data from the up and down histograms are analysedindependently, and the average values of k1 are reported.For MRSR studies, the pSR histograms were transformed to frequency spacevia a FFT computing program to determine precession frequencies of the muonspins in the radicals.LCR spectra were fitted by theoretical lineshape (the difference between twoLorentzian functions corresponding to the opposite directions of the modulationfield), and the resonance position (BRL linewidth (B0b3)and amplitude (Ampi)of the signal thus obtained.2.5 Chemicals and sample solutionsSolutes were purchased as ‘Reagent Grade’ chemicals or better. All aqueoussolutions were prepared with triply distilled water.Two types of sample cells were used in this study. For TF-pSR experimentswith backward muons, an ordinary 50 mL round bottomed glass cell with arubber septum on its opening was used. The samples were bubbled with pureN2 gas to eliminate 02 before exposure to the muon beam. The other cell ischapter 2. Background and Experimental 43newly designed for LCR studies with surface muon beams. It is cylindrical inshape with thin mylar windows compressed by 0-rings to avoid 02 intrusion.The size of the cell was optimized within the cylindrically arranged countersfor maximum exposure to the muon beam, and the sample temperature couldbe adjusted through a thermostatically-controlled water-bath. A closed cyclepumping system was designed to allow changing deoxygenated samples withoutmoving the cell. A flow of pure N2 gas through the front compartment of thecell also prevented 02 diffusion from the air into the sample during experimets.Fig.2.12. shows the schematic arrangement of this pumping system.ha.pter 2. Background and Experimental 44IC : Terr,eroture controF : flowrneterS :SonIe0 Gi’erfbwP PumpSC Somple ornportmentCC : Gos comportmentAfter bubblerFigure 2.12: The schematic arrangement of the pumping system for LCR studiesChapter 3Muonium Reaction with Some Substituted Benzenes3.1 IntroductionIt is well known that the hydrogen atom (H) reacts with benzene and manyof its derivatives by free radical addition, forming cyclohexadienyl type radicals[30,31,32,33]. The proton hyperfine coupling constants (Ar) of many such radicalswere determined by ESR methods. Pryor et al.[34] measured the distributions ofortho-, meta- and para-addition radical isomers by product analysis for tritiumreaction with various substituted benzenes, and found that the partial reactionrate constants and the substituent parameters follow the Hammett relationship.It was concluded that the H atom behaves as a weak electrophile.The overall rate constants of Mu reactions with benzene and some of itsderivatives in dilute aqueous solutions were measured by low field TF-pSR technique (MSR) [35]. Muonated cyclohexadienyl radicals were observed by MRSRstudies [9,36] on neat benzene and various substituted aromatics in neat or concentrated organic solutions. These muonated free radicals were identified viadeuteration and their muon hyperfine coupling constants, A, were determinedwith FFT technique. Recently, it was shown by our group that in dilute aqueoussolutions of some aromatics, muonium atoms can also add to the aromatic ring,forming muonated cyclohexadienyl type radicals [37]; but no muon hyperfinecoupling and radical yield studies on substituted benzoic acids have ever been45Chapter 3. Muonium Reaction with Some Substituted Benzenes 46reported.In the present work, Mu reactions were studied in dilute aqueous solutions.The difference between dilute aqueous solution and neat or concentrated organicsolution is that: in neat and concentrated organic solutions, hot atoms andions play an important role [38]; however, in dilute aqueous solutions, the onlyreaction precursor to the muonated radicals is the thermalized Mu atom.Two sets of chemicals were chosen for this purpose: mono-substituted benzenes and para-substituted benzoic acids. The substituents chosen are -OH,-NH2, -COOH and -CN groups. The MSR technique was used to measure thereaction rate constants of Mu with benzene and benzoic acid and to determinethe muon hyperfine coupling constants for muonated benzoic acids whenever it isapplicable. Besides, the LCR technique was also utilized to detect the muonatedradicals formed in dilute aqueous solutions and to study their hyperfine couplinginteraction and isomeric radical yield distribution. Partial rate constants (seelater) were estimated and correlated to HMO parameters. Only some kM andA1 values were taken from the literature.In this chapter a new type of isotope effect on the hyperfine coupling constantsis defined and used in this analysis of data.3.2 Results3.2.1 Reaction rate constantsThe reaction rate constant of Mu atoms with benzene in aqueous solution wasmeasured at room temperature and found to be 3.0x109M’s1, and the rateconstant of Mu reaction with benzoic acid was measured as 7.4x109 M’s’.These rates are in good agreement with the reported values [35].Chapter 3. Muonium Reaction with Some Substituted Benzenes 473.2.2 Muon hyperfine coupling constantsThe TF-1tSR technique at high field was invoked to determine the hyperfinecoupling constants, A, for the muonated radicals formed by Mu formally addingto the substituted benzoic acids. Because of low solubility, the experimentswere conducted only with para-hydroxy and para-amino benzoic acids in basicaqueous solutions. Measurement for benzoic acid (BA) at high pH (as sodiumbenzoate) was also taken for comparison. The concentrations of all samples werehigh enough (1 to 2 M) to avoid initial phase incoherence of muon spins. Theexperiments were done at several magnetic fields. From the FFT power spectra,the As were obtained via Eq.2.11.As an example, Fig.3.1 shows the FFT spectra of aqueous solutions of 1M paminobenzoic acid at pH 10 and 1M p-hydroxybenzoic acid at pH 8 at magneticfields of about 3.9 kG. Table 3.1 lists the computer fitted frequencies of the FFTspectra and the A values thus obtained.Chapter 3. Muoniurn Reaction with Some Substituted Benzenes 481.B. ES6.E-54.E502. E5CS. E-S7. E-56. £-55.E-54.E53.E-52. E-SI.0100 150 200 250 300Frfquency (MHz)350 400Figure 3.1: The FFT of the jiSR spectra of of the aqueous solutions of (a) 1Mp-aminobenzoic acid at pH 10 and (b) 1M p-hydroxybenzoic acid at pH 8. Bothat about 3.9 kG.100 (50 200 250 300 350 400Chapter 3. Muonium Reaction with Some Substituted Benzenes 49Table 3.1: Parameters obtained from the FFT anaiysis of high field TF-pSRspectra of benzoic acid, p-hydroxy and p-amino benzoic acids (as benzoates)*.Sample pH Field/kG z4/MHz v/MHz AJMHz2M BA 12 2.4 209.4 292.2 501.6216.4 300.8 517.2197±4 277 474±52M BA 12 3.9 193.0 307.8 500.8179.4 295.3 474.7200.4 316.4 516.81M p-OH-BA 8 3.9 200.0 318.0 518.0178.1 294.8 472.91M p-OH-BA 8 5.1 185.1 333.0 518.0164.1 305±4 469±51M p-NH2-BA 10 2.4 189.1 268.7 457.8218.8 303±4 522±51M p-NH2-BA 10 3.9 171.9 286.7 458.6201.6 320.3 521.9* Fields are approximate experimental settings. Unless otherwise indicated, errors on VR are estimated as about ±1—1.5 MHz, and that on A, are about ±2—3MHz.Chapter 3. Muonium Reaction with Some Substituted Benzenes 503.2.3 LCR experimentsThe LCR technique was used to observe the muonated radicals formed when Muatoms reacted with the selected mono-substituted benzenes and para-substitutedbenzoic acids in acidic and/or basic aqueous solutions. With recorded spectra,the LCR parameters were obtained by a MINUITX2-minimization fitting prograin. From the A. values and the resonance positions (BR), the correspondingproton hyperfine coupling constants (AH) and the radical yields were estimatedvia Eq.2.15 and Eq.2.21, respectively. The results are given in the sections tofollow. Benzoic acid and benzoateLCR experiments were conducted with benzoic acid in both acidic and basicaqueous solutions. The LCR spectrum for 10mM benzoic acid at pH’2 wasrecorded from 18.2 to 21.5 kG and it consists of three resonance signals at 18.837,19.952 and 20.946 kG. The LCR spectrum for 15mM sodium benzoate at pH 9.5was recorded from 18.4 to 21.5 kG and the spectrum also shows three peaks atslightly shifted fields. Table 3.2 presents these resonance positions (BR), amplitudes (Ampl) and linewidths ( B03). Fig.3.2 shows the LCR spectrum of10mM benzoic acid in water at pH—’2.Chapter 3. Muonium Reaction with Some Substituted Benzenes 51Table 3.2: The resonance positions, linewidths and amplitudes of the LCR spectra of 10mM benzoic acid at pH2 and 15mM benzoate at pH 9.5 in aqueoussolutions.*compound BR/kG zB0b3/kG Ampl(%)Benzoic acid 18.837 0.111 0.24919.952 0.222 0.44920.946 0.136 0.191Benzoate ion 19.079 0.0862 0.19020.288 0.0972 0.44320.914 0.0898 0.153* Errors for BR are estimated as ±10 G. Errors for linewidths are about 10-30%and that for amplitudes are about 10%.—.00 1—.002—.003—.004— .005—.006—.00?—.00810 mM Benzoic acid in ‘water1.8 1.85 1.9 1.95 2 2.05 2.1 2.15Longitudinal Magnetic Field /T52Chapter 3. Muonium Reaction with Some Substituted Benzenes1<+Figure 3.2: The LCR spectrum of 10mM benzoic acid in water at pH-’.2: shownas the normalized forward-to-backward asymmetry difference (A+, with a smallmodulation field applied with the main field, A-, with it opposed) as a functionof longitudinal magnetic field (in Tesla, 104G). The solid line is the computer fit.Chapter 3. Muonium Reaction with Some Substituted Benzenes 533.2.3.2 Terephthalic acidBecause of low solubility of the protonated form, the LCR experiment for terephthalic acid (TPA) was carried out only at high pH. The field regions from 19.65to 21.15 kG and from 26.9 to 29.1 kG were scanned. Fig.3.3. shows the recordedLCR spectrum of 20mM TPA in aqueous solution at pH 12. At a field of 20.095kG, there is a strong resonance signal. Two weaker peaks were found at muchhigher fields (27.737 and 28.427 kG, respectively). Table 3.3 presents the computer fitted resonance positions, linewidths and amplitudes for these signals.Table 3.3: The resonance positions, linewidths and amplitudes of the LCR spectrum of 20mM terephthalic acid in aqueous solution at pH 12*.BR/kG zB03/kG Ampl(%)20.095 0.121±0.006 0.724±0.0227.737 0.0312±0.006 0.17±0.0328.427 0.0385±0.01 0.305±0.03* Errors for BR are about 10 G.Chapter 3. Muonium Reaction with Some Substituted Benzenes—.114—.111CC54Figure 3.3: The LCR spectrum of 20mM terephthalicat pH 12.acid in aqueous solution.IlI—.12I I I I I I I I I.11 1.S7 i.I I.S 2 2.I 2.12 2.13 2.14 2.SS 2.062.715 2.775 2.715 2.115.tttg Fj,J.l 1)Chapter 3. Muonium Reaction with Some Substituted Benzenes 553.2.3.3 Other substituted benzenes and benzoic acidsLCR experiments were conducted on aqueous solutions of benzonitrile, p-cyanobenzoic acid (p-CN-BA), phenol, p-hydroxybenzoic acid (p-OH-BA), aniline andp-aminobenzoic acid (p-NH2-BA). For benzonitrile, two LCR spectra of 13.9and 15mM benzonitrile in water were recorded during two separate beamtimes.Totally three resonance peaks at 19.510, 20.970 and 18.626 kG were found in thefield region scanned from .—18.3 to -21.4 kG. For p-cyanobenzoic acid, the LCRspectrum was recorded with a 20mM solution at pH 9 and two peaks at 19.239 and20.138 kG were found in the same field region. The LCR measurements for phenolwere taken with 15mM solute in water during two beamtimes. Totally threeresonance peaks at 18,697, 20.977 and 20.189 kG were found in the field regionof 18 to 22 kG. For p-hydroxybenzoic acid (p-OH-BA), LCR experiments wereconducted with 20mM aqueous solutions at pH 1.7 and 8, respectively. For theacidic sample, two peaks at 19.233 and 20.934 kG were found. For the sample atpH 8, two peaks at 19.022 and 20.913 kG were recorded. The LCR experimentsfor aniline were conducted with 15mM samples at pH 2 and 8, respectively.Resonance signals were searched for in fairly broad field regions (from 15.5 to21.5 kG) for acidic solution and from ‘-15.5 to 19.3 kG for pH=8 solution.In both cases, only one signal was found. In the former case the LCR peak wasat 18.115 kG. In the latter case the peak was at 18.087 kG. For p-aminobenzoicacid, experiments were done with 20mM aqueous solutions at pH 10 and 2. Forthe basic sample, magnetic field was scanned from —16.5 to —p22.5 kG and twoLCR peaks were found at 18.485 and 21.124 kG. For the acidic sample, field wasscanned from 16.5 to -.i24.5 kG, one strong peak and one weak peak were found.Table 3.4 records the computer fitted resonance fields, linewidths and amplitudesChapter 3. Muonium Reaction with Some Substituted Benzenes 56of these signals. Fig.3.4 shows the LCR spectra obtained for p-hydroxybenzoicacid at two pHs as an example.Table 3.4: The resonance positions (BR), linewidths (zB0b8) and amplitudes(Ampi) of the LCR spectra of the substituted benzenes and benzoic acids inaqueous solutions studied here.*Compound Conc.(mM) jW BR/kG LB0b3/kG Ampl(%)Benzonitrile 13.9 7 19.510 0.118 0.37520.622 0.118 0.173Benzonitrile 15 7 18.626 0.0856 0.296p-CN-BA 20 9 19.239 0.149 0.31820.138 0.111 0.278Phenol 15 7 18.697 0.135 0.48320.977 0.130 0.20620.189 0.101 0.190p-OH-BA 20 8 19.022 0.145 0.39020.913 0.125 0.325p-OH-BA 20 1.7 19.233 0.120 0.35520.934 0.166 0.310Aniline 15 8 18.087 0.105 0.524Aniline 15 2 18.115 0.19±0.05 0.139p-NH2-BA 20 10 18.485 0.114 0.47221.124 0.0933 0.298p-NH2-BA 20 2 19.922 0.153 0.36317.195 0.041±0.024 0.056±0.022* Errors for BR are about 10 0. Unless otherwise indicated, errors for areabout 15-20% and that for Ampi are about 10%.Chapter 3. Muonium Reaction with Some Substituted Benzenes.112—.014—.115• —.116S•.111.IIS.014—.815& .016& —.11,—hO—.019—.022.05 2.06 2.8 2.06 2.09 2.1 2.11 2.12 2.13 2.14 2.15Mpetc PeIdfTa 657Figure 3.4: The LCR spectra of 20mM p-hydroxybenzoic acid in aqueous solutions. (a) at pH 1.7 and (b) at pH 8.a.12III 0.59 0.5 1.51 0.12 0.11 1.) 1.1$ 0.11 0.17 I. 85 1. 67S I.! 0.525 0.55 .075—.514.11I.111.II5.02l2 2.025 2.05 2.075 2.1 2.I 2.15MagDetic Pkld/TChapter 3. Muonium Reaction with Some Substituted Benzenes 583.3 DiscussionIt is well known that in aqueous solutions the thermalized Mu atom is the precursor of many reactions, and it is expected that Mu atoms react with aromaticsolutes by ‘addition’ forming muonated free radicals.In this section, the resonance peaks of the LCR spectrum of benzoic acidin acidic aqueous solution will be assigned to the particular protons of specificradicals based on the muon hyperfine coupling constant reported in the literature, and other criteria. The assignments of the resonance signals of other LCRspectra will simply be reported and the procedures for these assignments are presented in Appendix B. Radical isomer yields will be estimated and their relativedistributions calculated from the LCR spectra. Using the overall reaction rateconstants of Mu (kM) with these compounds, the partial rate constants (kb) willbe obtained from the o-, m-, p- distribution. Correlation between these partialrate constants and HMO parameters will be discussed. Finally, some conclusionswill be drawn.3.3.1 Benzoic acid and benzoate3.3.1.1 Resonance peak assignmentThe observed LCR spectrum of 10mM benzoic acid in aqueous solution at pH s2consists of three resonance signals as shown in Fig.3.2. The resonance positionsand amplitudes of all these three peaks are typical for the methylene protons(—CHMu—) of muonated cyclohexadienyl-type radicals [37]. Therefore, it seemsreasonable to assume that these three LCR peaks are due to the methyleneprotons of three different Mu-containing carboxylated cyclohexadienyl radicalsformed by Mu addition to the aromatic ring at o-, m- and p-positions relative toChapter 3. Muonium Reaction with Some Substituted Benzenes 59the carboxylic group. With regard to muon hyperfine coupling constants of theseradicals, no significant solvent effect on A has so far been reported.’ Therefore,the A,, values reported by Roduner et aL[36] for these three types of radicalsin an organic solvent were taken to apply here in water. The values taken areshown in Table 3.5. In order to assign these resonances, first, all possible protonhyperfine coupling constants AH for the methylene protons are calculated fromEq.2.15. The corresponding theoretical linewidths (IBth) of each LCR spectrumis also evaluated by Eq.3.1 [26,40],2[v + Po/27r)2j’/= (3.1)(7t—where ii,. is the LCR transition frequency, ) is the intrinsic muon decay constantwhich is the reciprocal of its mean lifetime and 7’s are the magnetogyric ratiosof muon and proton. All these calculated values are also listed in the table.Table 3.5: Hyperfine data and calculated radical yields of 10mM benzoic acid inwater at pH 2; method of the LCR peak assignment.AJMHz BR/kG AH/MHz f2 zBth/kG LB0b8/kG Ampl(%) PR497.1 18.837 145.0 1.08 0.1478 0.111 0.249(ortho) 19.952 124.3 1.26 0.1200 0.222 0.449 0.316*20.946 105.9 1.47 0.09781 0.136 0.191 0.077514.0 18.837 161.8 1.00 0.1703 0.111 0.249(meta) 19.952 141.1 1.15 0.1405 0.222 0.449 0.22920.946 122.7 1.32 0.1167 0.136 0.191 0.054*467.8 18.837 115.9 1.28 0.1117 0.111 0.249 0.051*(para) 19.952 95.22 1.54 0.08612 0.222 0.44920.946 76.82 1.91 0.06774 0.136 0.1911Although in the case of acetone, A, shows a shift due to a different muonium (hydrogen)bonding as the solvent is changed [39], for Mu-radicals with Mu directly attached to a carbonatom, no significant solvent effect on A,A has been observed.Chapter 3. Muonium Reaction with Some Substituted Benzenes 60The observed linewidth should never be less than the theoretical one becauseother muon spin relaxation processes (eg., chemical reactions of muonated radicals) may be involved which Eq.3.1 does not take into account. Comparing allpossible LBh with i.B068 for the resonance at the lowest field, this peak canonly be assigned to the Mu-radicals formed by para-addition. Assignments ofortho-and meta- radical signals will be done in the next section. Hyperfine coupling isotope effectColumn 3 in Table 3.5 records all possible methylene proton coupling constantsAH for the Mu-adducts. Here the symbol AH is used in order to make a distinction with A which is reserved for the proton hyperfine coupling constant of theH-addition analogues. The A,, values of carboxylated cyclohexadienyl radicalsformed by H adding to 0/rn/p-positions of benzoic acid were not measurableby ESR [31]. However, the AH values should not be far from the A,, values ofthe radicals formed by H-atom a.ddition. In the literature,A1.L7,,/A,,7, representsthe isotope effect on hyperfine coupling constant [36]. We now call this the‘hyperfine coupling isotope effect of the first kind (f,)’. By analogy, it seemssuitable to call AP-1,,/AH-P the ‘hyperfine coupling isotope effect of the secondkind (ff2)’. Fig.3.5 depicts these two kinds of isotope effects. As an example, A,,for cyclohexadienyl radical is 134.1 MHz [41], A and AH of the methylene proton for muonated cyclohexadienyl radical are 514.6 and 126.1 MHz, respectively.One gets ft1 of 1.206 and f:2 of 1.282 for the methylene muon and proton.When the nucleus involved in LCR is a proton, Eq.2.15 can be rewritten asbelowchapter 3. Muonium Reaction with Some Substituted Benzenes 611 f12-r — - fi27 + 7;’BR=—AM — (3.2)2 fi7(7s7p) fi27M7eTherefore, when the resonance field, BR, is known, from the hyperfine couplingisotope effect of the second kind, f:2, one can estimate the AM, and vice versa.Figure 3.5: An example showing the meaning of hyperfine coupling isotope effectsof the first kind (f) and the second kind (f2). f,1=AM,p/Ap, fi2=AMp/AH.Chapter 3. Muonium Reaction with Some Substituted Benzenes 62Table 3.5 lists all possible vaiues of f12. The f:1 values for the methylene muonand proton of cyclohexadienyl-type radicals are in the range of 1.15 to 1.21 [36j.Comparing these values with those f2 in Table 3.5, it is clear that the assignmentfor para-addition already made to the peak at 18.837 kG is consistent since itgives fi2 of 1.28.The peak at 19.952 kG can now be assigned to the ortho-radical with a f2value of 1.26, and the peak at 20.946 kG to the meta-radical with f2 of 1.32.All possible radical yields, PR, are then calculated by Eq.3.3 [28]A 7 fAD \21.-im.pL i’-1Jobs)AR— 2A&ii/rThese calculated values are listed in the last column of Table 3.5. The assignedyields are starred. One can see that ortho-addition dominates. It was foundthat ortho-addition was also the most favored one for saturated benzoic acid inethanol where other precursors contribute [36]. Partial rate constantsBased on the possible resonance assignments of Table 3.5 and Eq.3.2, five isomericyields of Mu-containing carboxylated cyclohexadienyl radicals were calculated.The final assignments made are starred in Table 3.5. When these are summed,a total muonium-radical yield of 0.42 for 10mM benzoic acid in acidic aqueoussolution at pH --p2 was thus obtained. This value is a bit higher than 1- PD forwater (PD of water is 0.62 [7]); but. the overall experimental error here may be ashigh as ‘-.25%. The relative o/m/p-radical yields are 75, 13 and 12% respectively,or 37.5, 6.5 and 12% per site.The rate constant of Mu reaction with benzoic acid was determined as 7.4x109M’s1,which is in good agreement with the reported value of 7.0x109M1 s1Chapter 3. Muonium Reaction with Some Substituted Benzenes 63[35]. The measured reaction rate constant is invariably the overall value. Inthe literature, the magnitude of reactivity at any one position in a substitutedbenzenoid compound as compared with that at one position in benzene is calledthe partial rate factor [34]. It seems suitable to call the reaction rate constantat particular site of the aromatic ring as the partial rate constant (kb). For Muaddition reactions into benzoic acids, the following equation should holdkT_9k0 9km-’-k 34M MT MT Mwhere k1 is the overall observed rate constant, with k, k and k as the partialrate constants at each ortho, meta and para site, respectively. With radicalisomer distribution obtained from the LCR results, k can now be broken downinto its partial rate constants. These values were estimated as 2.8x109,O.48x109and O.89x109Ms1 for ortho-, meta- and para-addition respectively.As far as the precursor of the Mu-radicals is concerned, it is well establishedthat in such a. dilute aqueous solution, the precursor should be the thermalizedMu atoms. The dramatic directional effect of ra.dicai formation in this case alsosupports the above statement, since hot or epithermal muonium (Mug) wouldadd to the ring less selectively and with a ratio much nearer 2:2:1 for o:m:paddition. Also should add at the met.a position preferentially, and e wouldbe picked up by 10mM benzoic acid only after 10_8s by which time ionswould have become MuOH in the water.Benzoic acid in basic solution exists as the benzoate anion. The TF-1iSRmeasurement implies that when Mu reacts with benzoat.e, three types of Muradicals were also formed. The LCR spectrum of 15mM sodium benzoate inaqueous solution at pH 9.5 has three resonance peaks in the field region of 18.4Chapter 3. Muonium Reaction with Some Substituted Benzenes 64to 21.5 kG. These are typicai signals from aromatic ring methylene protons,which implies that when the Mu atom reacts with benzoate, it also adds to thering site ortho-, rneta- or para- to the —COO- group. With the measured AL.values and the computer fitted LCR parameters given in Tables 3.1 and 3.2, andgoing through the same procedure as for the LCR peak assignment in benzoicacid case, one can assign the peak at 20.288 kG to the methylene protons of theradicals with Mu attached to the ortho position with A of 501.6 MHz, the peakat 20.914 kG to the meta radical isomers with AL. of 517.2 MHz, and the peak atthe lowest field (19.079 kG) to the para-radical isomers with AL. of 474.0 MHz.Table 3.6 lists these assignments and the deduced hyperfine data and radicalyields.Table 3.6: The hyperfine data and radical yields of 15mM benzoate in aqueoussolution at pH 9.5Ra.dical k/MHz BR/kG AH/MHZ f12 PRortho 501.6 20.288 122.6 1.29 0.081meta. 517.2 20.914 126.5 1.29 0.022para 474.0 19.079 117.5 1.27 0.027(a) Position of Mu relative to -C00 group.Chapter 3. Muonium Reaction with Some Substituted Benzenes 65Comparing these data of benzoate with those of benzoic acid, one can see thefollowing:i) The muon hyperfine coupling constants change by a few MHz when thesolution changes from acidic to basic. However, the A, for the meta-isomerchanges least. This is in line with Roduner et al.’s results [36] on various substituted aromatics which show that the substituent effect on A is the smallest forrn-addition isomeric radicals.ii) The hyperfine coupling isotope effect of the second kind (ft2) are fairlyclose: all in the range of 1.26 to 1.32.From the measured A,s, one can estimate the substituent effect of -C00group on muon hyperfine coupling constant via Eq.3.5 [41].= A°(1 — LIX) (3.5)where A refers to the radical under consideration, A is for muonated cyclohexadienyl radicals (i.e., 514.6 MHz from benzene [25,42]), and Lx is the ‘substituenteffect’. Table 3.7 lists the values of Lx for the muonated benzoate radicals deduced in this work. These Lx values will be applied to the substituted benzoicacids at high pH for the —CO group.Table 3.7: The substituent effect of —COO- group on muon hyperfine couplingconstant of muonated benzoate radicals.radical isomer(a) x(%)ortho 2.41meta -0.62para 7.78(a) Position of Mu relative to -COO- group.Chapter 3. Muonium Reaction with Some Substituted Benzenes 663.3.2 Terephthalic acidAs mentioned in section, the LCR spectrum of terephthalic acid (TPA)was recorded with a 20mM aqueous solution made at pH 12 due to low solubilityof the protonated molecule. At such high pH, TPA exists as doubly chargedanions (TPA2). Experience tells one that the resonance peak at the field of20.095 kG is due to aromatic ring methylene protons. In order to estimate theradical yield and abstract AH, one needs the A value of the radical. The TF1iSR technique could not be utilized for this purpose because the pure materialis solid and solutions are not concentrated enough. Therefore, one has to rely onan indirect method.Since only one radical is possible, these three LCR peaks must be due tothree different protons of this same muonated radical (MuTPA2). Its yield isdetermined to be 21.3±2.0% using Eq.3.3. Assume that Mu is at C(2) in TPAand at C(1) in Bz muonated radicals. the assignments are made and listed inTable 3.8. Details for these assignments are presented in Appendix B.2MuTPA MuC6H0 M CD 0 CDCDCDno n 0 (j)0 a)::C)’ )-CD•4L’.)t’t’en01)-1—ibL’3C3CO-1Cl),._C)31k)(‘.3C.3CDl-1CJ1C).3eJ’;—3;-- ‘—-.--c’c’jnL’3Ci-CD (I) IChapter 3. Muonium Reaction with Some Substituted Benzenes 683.3.3 Other mono-substituted benzenes and p-substituted benzoicacidsIt is deduced that all resonance peaks of LCR spectra recorded for other mono-substituted benzenes and para-substituted benzoic acids studied are due to methylene protons of the corresponding rnuonated radicals. Some assignments for theseobserved peaks along with hyperne parameters and radical yields are reportedin Tables 3.9 and 3.10. Details for these LCR peak assignments are presented inAppendix B.Table 3.9: The hyperfine data and isomeric radical yields for 13.9 and 15mMbenzonitrile in waterRadical(a) Conc.(mM) AJMHz(b) BR/kG AH/MHZ f12 PRortho 13.9 485.8 19.510 121.3 1.26 0.102meta 518.2 20.970 126.4 1.29 0.044para 15 463.2 18.626 115.3 1.26 0.035(a) Position of Mu relative to the -CN substituent.(b) From TF-pSR studies of pure benzonitrile [36].In the case of 20mM p-CN-BA in aqueous solution at pH 9, the LCR peakat 20.138 kG is due to the methylene proton of the radical with Mu at C(2) (I),and the peak at 19.239 kG due to the methylene proton of the radical with Muat C(3) (II). The radical yield of the former, (I), is about one half of the yield ofthe latter, (II).I HMuChapter 3. Muonium Reaction with Some Substituted Benzenes 69In all structures of muonated cyclohexadienyl radicals with one or two substituents studied here, C(i) will be the ring-C to which the substituent is attached,and when there are two, C(i) will be that carrying COOH or COO-. Typicalradicals are shown as (I) and (II) above for p-CN-BA.The LCR spectra of 15mM phenol in water recorded during two beamtimesindicate that there are three resonance peaks in the field region from ‘18 tokG. It is expected that these signals are due to the methylene protons ofortho-, meta- and para-rnuonated radical isomers. With the reported A,, valuesfor these radicals in pure phenol [36], the peak assignment was made and theradical yields estimated. These data along with f2 and PR are listed in Table3.10. Here again, one sees that Mu addition to the ortho position dominates.Table 3.10: The hyperfine data and radical yields of 15mM phenol in waterRadical(a) A,,/MHz(b) BR/kG AR/MHz f PRortho 467.4 18.697 117.6 1.25 0.181meta 517.4 20.977 125.2 1.30 0.064para 493.0 20.189 115.3 1.34 0.044(a) Position of Mu relative to -OH substituent.(b) A,, from TF-1tSR studies of neat phenol [36].In the case of 20mM p-OH-BA in aqueous solution at pH 8 the peak at 19.022kG is due to the radical with Mu at C(3) and A,. of 471.1 MHz, and the peak at20.913 kG due to the radical with Mu at C(2) and A,. of 518.1 MHz. The radicalyield of the latter is about one half of that of the former.For 20mM p-OH-BA in acidic solution (pH 1.7) the peak at 19.233 kG is dueto the radical with Mu at C(3), and the peak at 20.934 kG due to the radicalwith Mu at C(2). In this case, the radical with Mu attached to the C ortho toChapter 3. Muonium Reaction with Some Substituted Benzenes 70-COOH group dominates.The LCR peak of 15mM aniline in aqueous solution at pH 8 can be assignedto the methylene proton of the ortho-radical isomers with A of 441.3 MHz [36).In acidic solution, aniline exists as a protonated cation. The observed LCRpeak at 18.115 kG of 15mM aniline at pH 2 is probably due to the ortho-additionradical isomer.The LCR spectrum of 20mM p-aminobenzoic acid in aqueous solution at pH10 consists of two resonance peaks in the field region of r16.5 to 22.5 kG, asexpected. These peaks are taken to be due to the methylene protons of tworadical isomers. The peak at 18.485 kG is most likely due to the radical withMu at C(3) and the peak at 21.124 kG due to the radical with Mu atIn the case of 20mM p-NH2-BA at pH 2 the LCR peak at 19.922 kG is mostlikely due to the radical with Mu atThe details are provided in Tables B.1 through B.9 in Appendix B.3.3.4 Correlation between the partial rate constant and HMO parameters3.3.4.1 HMO resultsAs mentioned in the introductory chapter, Hückel Molecular Orbital theory(HMO) is a simple but useful tool. In many cases, particularly for aromatics, the molecular orbital energy levels, ir-electron density distribution, radicallocalization energy etc. can be obtained by HMO method to a good approximation. In this study, the ir-electron density distribution of the neutral substitutedbenzenes studied and the radical localization energy of these aromatics whenthey react with free radicals were calculated with the Hückel Molecular OrbitalChapter 3. Muonium Reaction with Some Substituted Benzenes 71method. The HMO computing program was provided by Dr.D.P.Chong [44].For hetero-atom (0) and the bonds C—O and C=O, the h and k,.3 values forEq.1.1O and Eq.1.11 were taken from literature [16]. The results obtalned arepresented in Table 3.11. Corresponding parameters for benzene are also given.Here, numbering of ring-C’s is the same as in the previous section.Table 3.11: The r electron density distribution and radical localization energy as calculated by HMO for benzene, monosubstituted benzenes andp-hydroxy-benzoic acid.Compound C-site( i) ir-electron radical localizationdensity energyBenzene 1.000 2.5359benzoic 2,6 0.976 2.3890acid 3,5 0.992 2.54504 0.978 2.4371phenol 2.6 1.023 2.46253,5 1.007 2.54264 1.018 2.4961aniline 2.6 1.048 2.33993,5 0.998 2.54094 1.037 2.3729benzo- 2,6 0.988 2.3940nitrile 3,5 0.996 2.54444 0.989 2.4401p-OH-BA 2,6 0.941 2.38933,5 1.039 2.4113(a) In units of tI.Chapter 3. Muonium Reaction with Some Substituted Benzenes 723.3.4.2 Partial rate constantsIt has been shown in previous sections that these aromatic solutes undergo Mu-addition at the C-sites ortho-, meta- and para- to the substituent. With radicalisomer distributions obtained from the LCR results and k values measured inthis study or from the literature, partial rate constants were estimated. Thesevalues are presented in Table 3.12.Table 3.12: The overall and partial rate constants of Mu reactions with themonosubstituted aromatics studied here (plus benzene).Solute k/l08M1s C-site(i) k/108M’s’benzoic acid 74 2,6 283,5 4.84 8.9benzonitrile 72(a) 2,6 193,5 8.84 14phenol 70(a) 2,6 223,5 7.74 11aniline 88(a) 2,63,54benzene 30 — 5.0(a) from Ref.[35].(b) Since only one LCR peak was found, these are limits based on the estimationthat the relative yield of the ortho-radical isomer is 80%.Chapter 3. Muonium Reaction with Some Substituted Benzenes 733.3.4.3 Correlation between rate constants and HMO parametersThe two parameters calculated by HMO methods are (i) ir electron density and(ii) Radical localization energy Lr. It is interesting to try to interpret the muonium rate constants in terms of the calculated HMO parameters.(I) ir electron densityFor benzoic acid and benzonitrile, the partial rate constants seem to relateto ir electron density distributions over the ring, ie., the partial rate constantis larger at the lower ir electron density site. However, this is not the case forphenol, where k is the largest but the ir electron density at the ortho-positionis also the highest, and in aniline too. Therefore, it does not look as if the Muaddition rate to the aromatics studied here is governed by the ir electron densityon the aromatic ring of the original molecule.(ii) Radical localization energy L,.When one compares these partial rate constants with the radical localizationenergies, one sees there is a trend: the lower the radical localization energy,the higher the partial rate constant. Fig.3.6 presents the plot of log k vs.L/I/ for benzoic acid, benzonitrile and phenol. It can be seen that there isfairly good linearity between these two sets of parameters, and the computerfitted line has a substantial negative slope. This implies that when Mu attacksa substituted benzene molecule to form a transition state, the local ir electrondensity may have some effect, but the reaction rate is mainly controlled by theradical localization energy (Lr). Evidently, the smaller the localization energy,the easier the transition state is reached. This is also true for the case of pOH-BA in which Mu adding to the lower Lr C-sites (ortho to -COOH group)dominates, although the partial rate constants are unknown.Chapter 3. Muonium Reaction with Some Substituted Benzenes 749. 69. 49. 299. 88. 68. 42.362.56L.Figure 3.6: The plot of log k, vs. L. for (x) Phenol. (.) benzoic acid and(o) benzonitriie. k\1 in units of M1s, L in units of I/I• The solid line is thecomputer fit.2. 4 2. 42 2. 46 2. 5 2. 52Chapter 3. Muonium Reaction with Some Substituted Benzenes 75This correlation seems qualitatively reasonable and provides an explanationfor the fact, that for H addition reactions to these monosubstituted benzenes,ortho-addition also dominates [34] regardless of the different nature of the substitutents. But Fig.3.6 shows more than that: it suggests a direct proportionalitybetween log k and -L..3.4 ConclusionIn retrospect it should not be too surprising to find a direct correlation betweenthe rate constant for addition of a free radical (looking for one unpaired electronto bond with) and the energy required to localize one electron from delocalizedaromaticity at a particular point.Chapter 4Muonium Reaction with N-Heterocyclic Compounds4.1 IntroductionNitrogen heterocyclic aromatic compounds have long been interesting subjectsfor study by chemists, biochemists and theorists since some of them, particularlypyrimidine derivatives, are of biological importance. The reaction rate constantsof some N-heterocyclic compounds with the primary radicals produced whenionizing radiation interacts with water, i.e., hydrated electrons (e;q), hydrogenatoms (H) and hydroxy radicals (OH), have been reported and some reactionproducts identified [46,47.48]. The presence of nitrogen atom(s) in the aromaticring affects these rate constants in different ways which seem related to the type ofreaction and the nature of the attacking radicals. Muonium is the lightest isotopeof hydrogen and one of the simplest free radical species. It is, therefore, of interestto know how the presence of N atom(s) in the ring affects Mu reactivity. Pyridine(Py), and the three diazines, pyrazine (Pz), pyrimidine (Pm) and pyridazine (Pd)were chosen for such investigation since all these compounds are commerciallyavailable and soluble in water which is the best media for studying Mu reactions.The structures and the numbering of these compounds are presented in Fig. 4.1.In this chapter the reactions of Mu with the four N-heterocyclic aromaticcompounds are studied in a similar manner to those described in Chapter 3. PDvalues for neat Py and Pd are measured with water as a standard. Overall kM76Chapter 4. Muonium Reaction with N-Heterocycic Compounds 77vaiues are determined, isomeric radicai yield distributions deduced from LCRspectra using A as measured, then k determined. These partial rate constantscorrelate nicely with radical localization energies obtained by HMO calci.ilations.4 45 561 1Pyridine Pyrazine4 46Pyrimidine Pyridazine1Figure 4.1: The structures and numbering of the N-heterocyclic compounds.Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 784.2 Results4.2.1 Reaction rate constantsAll muonium reactions with these four N-heterocyclic compounds were conductedin aqueous solutions at room temperature and neutral pH. In the case of Py, thereactions were also carried out in acidic solutions. The bimolecular rate constantof the reaction (kM) is determined by Eq.2.8 ( k = (A-A0)/[S] ). Data for Pmis given in full as representative, and the data for Pd were used to describe thetechnique in Chapter 2 as Fig.2.4.Table 4.1 gives the concentrations of Pm used and the measured Mu decayconstants A. Fig.4.2 shows the plot of A vs. [Pm] based on these data.Table 4.1: The concentrations of pyrimidine and muonium decay constants inaqueous solutions at room temperature and neutral pH for up and down counters.[Pm]/mM A(a)Up Down0 0.24+0.02 0.25±0.010.11 0.54+0.06 0.69+0.070.23 0.99±0.13 1.34±0.140.34 1.25+0.15 1.57±0.200.45 2.19±0.21 1.91±0.31(a) The errors given are the computer-generated standard deviations from thestatistical fits.U,0(Pm] (all)Chapter 4. Muoniurn Reaction with N-Heterocyclic Compounds 792.521.5.50Figure 4.2: The plot of Mu decay constant . V3. pyrimidine concentration atroom temperature. Slope equals kM. Data are from the up (x) and down (D)counters. The solid line is the computer fit.0 .05 .1 .15 .2 .25 .3 .35 .4 .45 .5Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 80From the slope of Fig.4.2, the bimolecular rate constant of the reaction between Mu and Pm was determined to be 3.7(±0.2)x109M1s’. This rate constant and those for other N-heterocyclic compounds are recorded in Table 4.2.The Mu reaction rate constant with benzene(Bz) is also listed in the table forcomparison.Table 4.2: The bimolecular rate constants of muonium reaction with theN-heterocyclic compounds and benzene in aqueous solutionssolute pH kM(109M’s’)Bz 7 3.0±0.3Py 7 5.8±0.4Pz 7 7.7±0.5Pm 7 3.7+0.2Pd 7 5.0+0.3Py 1.2 7.4± Diamagnetic yield measurementIntermediate field TF-1tSR experiments were conducted in order to determinethe yield of diamagnetic states. This type of experiments was conducted for neatpyridine and pyridazine. Pure water was used to calibrate the asymmetry. Theexperimental results are recorded in Table 4.3, together with that of benzene.Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 81Table 4.3: Diamagnetic yields of neat pyridine, pyridazine, water and benzene.Sample Field/G PDH20 110 0.62*Neat Py 110 0.30Neat Pd 93 0.42Neat Bz 0.15** From Ref. [7].4.2.3 Muon hyperfine coupling constantsMuon spin rotation experiments in high transverse field (1.5 to 5 kG ) wereperformed in order to detect all muonated free radicals formed by the reaction ofMu with these N-heterocyclic compounds, and to determine their muon hyperfinecoupling constants (AM). These experiments were done on aqueous solutions atneutral pH to ensure that the thermalized Mu atom was the precursor. Due tothe requirement for initial phase coherence in the precession of muon spins, therate of formation of the radicals detected must be very high, 50 1 to 2 M solutionsof N-heterocycles were used. The computer-fitted frequencies of the FFT spectraand estimated A values (via. Eq.2.11) are summarized in Table 4.4.Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 82Table 4.4: Experimental values of frequencies obtained by FFT analysis of highfield ttSR spectra of N-heterocycles in water and adopted A vaiues*Sample Field/kG z4/MHz u/MHz A,JMHz An/MHz adopted1M Pz 2 200.0 276.6 476.6 476.6±0.54.8 169.5 307.0 476.52M Py 4 191.2 310.5 501.7 501±26 162.4 337.9 500.34 195.8 313.6 509.4 512±36 170.0 343.9 513.94 204.3 321.5 525.8 526±36 176.4 350.8 527.22M Pm 2 211.3 265.2 476.5 475±61.5 215.6 257.6 473.22 217.3 274.8 492.1 494±42.5 212.3 283.4 495.72 232.2 287.9 520.1 520±32.5 226.3 292.9 519.22M Pd 2.3 222.0 306.0 528.0 529±31M Pd 3 216.0 313.0 529.0* Fields are approximate experimental settings. Because of the smallest of thepeaks, errors on are probably ±2—6 MHz for all except Pz where it is ±0.5MHz.Chapter 4. Muonium Reaction with N—Heterocyclic Compounds 832M Pz gave FFT spectra with one pair of frequencies at both the fields used,2 and 4.8 kG. The computer fitted frequencies are given in Table 4.4. Thesesum togather as in Eq.2.11 to give A,=476.6±O.5 MHz. Fig.4.3 shows the FFTspectra for 1M Pz in water at 2 and 4.8 kG as a representative.For the diazines, with at least 2 or 3 pairs of peaks expected, the FFT spectraare much more complicated, the intensities of individual peaks much weaker andthe pairing can only be done by selecting frequencies that move according tothe changed field (as in Eq.2.1O with i’D cc field). The FFT spectrum of 2MPy at 4 kG shows three pairs of frequencies. The FFT spectrum at 6 kG alsoshows three peaks (t4) which shifted to the lower frequencies relative to thecorresponding peaks at 4 kG. The other three related peaks (va) are shifted tothe higher frequencies as expected. These three high frequency peaks are ratherweak and can barely be distingushed from the noise. The FFT spectra from Pmand Pd solutions are rather noisy. The FFT spectrum of Pm at 2 kG shows fairlyclearly three pairs of peaks, but the other FFT spectra of Pm at magnetic fields1.5 and 2.5 kG do not show all these frequency signals. Only one pair of peaksfrom the 1.5 kG FFT spectrum and two pairs of FFT frequencies from the 2.5kG spectrum can match the three pairs of FFT frequencies observed at 2 kG.For Pd sample, only one pair of frequencies could be clearly seen.The best pairedfrequencies are given in Table 4.4 with their summed A values at two fields.Chapter 4. Muonium Reaction with N-Heterocyclic CompoundsFrequency/MHz84Figure 4.3: The FFT of the pSR spectra. of 1M pyrazine in water, presented asFourier power against frequency: (a) at about 2 kG; (b) at. about 4.8 kG.a2015to$20aA.0V.ciLlIs10thZ,-1—L.a-——100 150 201 251 300 350 4001 1 1-S0100 150 201 251 300 350 400Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 854.2.4 LCR experimentsThe LCR technique was used to search for the radicals’ resonance signals whenMu reacted with the selected N-heterocyclic compounds in aqueous solution atneutral pH. In the case of 20 mM Pz solution, the magnetic field was scannedfrom -49 to 21 kG and from 26 to .s28 kG. A strong resonance signal at19,545G was found and two weaker signals appeared at higher fields (26,646 and27,628G ). These experiments were carried out in duplicate during two differentbeamtimes and good reproducibility was achieved. LCR experiments were alsoconducted in the low field regions of 0.1 kG to 5 kG, and no resonance signalswere found. The recorded LCR. spectra are presented in Fig.4.4.In the case of 20mM Py, resonance signals were searched from 20 to 22kG, and three strong peaks were found at 20,752G, 21,378G and 21,599G, respectively. In the case of Pm, a more concentrated solution (0.3M) was used inorder to record LCR signals. The magnetic field scanned covers from -‘18 to22 kG. The spectrum observed is a bit complex due to facility instability. Bycareful inspection, three resonance peaks at 20.011, 21.347 and 22.347 kG can berecognized. In the case of Pd, 20mM solution was used. Resonance signals weresearched in field regions from -.48 to —P19.5 kG and from 20.5 to 22.1 kG. Twopeaks at 18,897G and 21,248G were found.These LCR spectra were fitted with the computer fitting program and the corresponding resonance positions (BR), linewidths (B0b3)and amplitudes (Ampi)were obtained. All these fitted parameters are listed in Table 4.5.Chapter 4. Muonium Reaction with N-Heterocyclic Compounds+.0l.D120—.Dll.0175-.02•.11I02021-.122Magnetic Field/T86-. 12251.01 1.02 1.03 1.04 1.00 1.00 in i.p. III 2 2.01—. 1222.02 2.02 2.04 2.01 2.00 2.6 2.00 2.02 Z 2.71Figure 4.4: The LCR spectra of 20 mM pyrazine in water.Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 87Table 4.5: LCR positions(BR), linewidths (B0b), amplitudes (Ampi) and calculated radical yields (PR) for the N-heterocyclic compounds in water.compound Conc./mM BR/kG zB0b8/kG Ampl(%) PRPz 20 19.545 0.1214 0.676 0.24±0.0326.646 0.033 0.16 0.23±0.0527.628 0.050 0.25 0.24±0.05Py 20 20.752 0.06215 0.323 0.113±0.0221.378 0.05540 0.243 0.070±0.0121.599 0.05722 0.143 0.036±0.01Pm 300 20.011 0.07064 0.1436 0.066±0.0221.347 0.04285 0.2094 0.042±0.01522.347 0.07280 0.2006 0.10±0.03Pd 20 18.897 0.02364 0.3237 0.08±0.0321.248 0.04577 0.3004 0.086±0.03** estimated fromChapter 4. Muonium Reaction with N-Heterocyclic Compounds 884.2.5 HMO resultsThe four N-heterocyclic compounds studied are aromatics, each molecule hassix r electrons delocalized over the whole ring (each N atom contributes one relectron and has one lone pair of electrons lying in the ring plane). The HMOmethod was used to calculate: (i) the Lowest Unoccupied Molecular Orbital levels(LUMO), (ii) 7T electron density distribution and (iii) radical localization energies for these four N-heterocyclic compounds. The parameter h of the Coulombintegral for the N atom (Eq.1.12) and the parameter kr3 of the resonance integralfor the aromatic bonds connecting N and C atoms (Eq.l.13) were taken as 0.5and 1.0, respectively [16,17]. These HMO results, along with that of benzene,are presented in Table 4.6.Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 89Table 4.6: The LUMO, ir-electron density distribution and radical localizationenergy of benzene and N-heterocyclic compounds calculated by HMO methodCompound LUMO site(i) ir-electron Radical Localizationdensity energy L*Py 0.841 1 1.195 2.58512,6 0.923 2.51243,5 1.004 2.53804 0.950 2.5373Pz 0.686 L4 1.147 2.72562.3,5,6 0.926 2.5004Pm 0.781 1,3 1.199 2.58942 0.845 2.53824,6 0.874 2.53645 1.009 2.5391Pd 0.727 1,2 1.124 2.68343.6 0.923 2.53744,5 0.953 2.5245Bz 1.000 1 to 6 1.000 2.5359* in units of 3j.Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 904.3 Discussion4.3.1 LCR peak assignment and yields of individual radicals4.3.1.1 PyrazineFig.4.3 shows that the FFT spectrum for a Pz solution has only one pair offrequencies, which implies that when Mu reacted with Pz in aqueous solution atneutral pH, only one type of muonated radicals was formed.Mu reacts with many aromatics by addition to the ring and that seems tobe the case with Pz. There are two ways for Mu adding to this 6-memberedaromatic ring: to the N site or C site. Experimental results in this study showthat Mu prefers to add to the C site.The reasons for drawing this conclusion are based on the hyperfine parameters, and on yields of the muonated radicals formed. (i) First, the very high muonhyperfine coupling constant, A,, = 476.8±0.5 MHz, is characteristic of muoniumaddition to C in aromatic rings, which has the ‘out-of-plane’ structure, i.e., the Catom attached to Mu has four bonds of sp3 geometry with the Mu and H atomsplaced at the opposite sides of the ring plane. The overlap between the odd electron orbital of the radical and Mu’s nucleus (1c) is thus rather large, thereforeleading to large A values. Muonated cyclohexadienyl radicals themselves haveA1. value of 514.6 MHz, and with NH2, OH, CN, COOH, etc. groups at ortho,meta or para positions relative to Mu, the A1. values all lie in the range 460to 530 MHz [41]. These differ from corresponding H-adducts (Ar) by the ratioof nuclear moments (3.18-fold favoring ) and by a factor of 1.2, which is atypical isotope effect (of the first kind) arising from enhanced hyperconjugationbecause the C-Mu bond is longer than the corresponding C-H bond due to theChapter 4. Muonium Reaction with N-Heterocyclic Compounds 91higher vibrational zero point motion of Mu relative to H [9,7,41]. Our value of476.8 MHz for Pz thus falls in the very range one would anticipate for an aromatic radical with Mu attached to C and out of plane. The fields of the LCRsignals, being in the 20kG region, also show that A1, must be in the the 460 to530 MHz range for the only radicals observed. In addition, no resonance signaiswere found in the low field region (0.1 to 5 kG) where the resonance due to a Nnucleus would be expected if Mu was added to the N site.The high A1, value is also in sharp contrast to the proton hyperfine couplingconstants of planar heterocyclic free radicals with H adding to N [58-62]. Sincethe H atom lies in the ring plane, the overlap between the radical’s odd lr*electron and the H nucleus (p+) is very small. Therefore, these A values aretypically only 15 to 25 MHz, as found by ESR in acidified pyrazine [49,50) andin picolines and pyridines [51,52,53]. If our 476.8 MHz coupling constant wereto be attributed to >N-Mu, we would have to try to explain an unreasonablylarge isotope effect of 7 (rather than the usual —‘1.3). Furthermore, for neataliphatic compounds containing -N=N- groups, where only N-bonded Mu atomswere possible, the Mu-radicals observed by zSR had A1, values of only 21-35MHz [54]. Such low A1 may be understood by Mu addition to the double bond,breaking the ir bond so that Mu can freely rotate about the N-N a bond left.Consequently we conclude that Mu attaches to C in Pz.(ii) Second, confirmation of this comes from the LCR data through the internal consistency of its assignments and yields, as follows. When the parametersof the three peaks of Fig.4.4 are each analysed according to Eq.2.21 using A1,476.8 MHz (and the AH values assigned later), the values of PR given in the lastcolumn of Table 4.5 were obtained. The fact that each peak has the same yieldvery strongly suggests that all three correspond to different proton resonancesChapter 4. Muonium Reaction with N-Heterocyclic Compounds 92because its fractional yield of 0.24 accounts for a large fraction of available Muatoms. Specifically, with kM = 7.6 x iO M’s’ (some three-fold less than thediffusion controlled limit [7]), 20 mM Pz allows Mu in water a mean lifetimeof 7 ns — by which time a significant ‘missing fraction’ (‘..‘0.07) has occurredfrom the initial Mu yield of 0.38, due to nonhomogeneous track effects [55]. Theaddition reaction observed thus arises from a fractional yield of 0.24 of the 0.31scavengable muonium atoms available (ie. .s78%).Assignment of these LCR peaks to specific protons utilizes Eq.2.15BR = 0.5[(A11— — 7k) — (A — 2MA)/7e( — Ak)]where k stands for ‘another’ nucleus ( ‘H or ‘4N here). Consequently, we haveAH values of +111.5, -20.0 and -38.2 MHz for the three LCRs for three of the Hatoms of this radical. They are assigned, as in Table 4.7, from their closeness tothe AR values of the H atoms in muonated cyclohexadienyl radicals [43]. (Wepresume that. the weak couplings expected with ‘H meta to Mu, and both ‘4Nnuclei, are not observable in our dilute aqueous solutions of Pz.) Fig.4.6 showsthe structures and numbering of MuBz and MuPz radicals.The strongest and lowest-field peak, at. 19.5 kG, is thus attributed to the Hattached to the same C as Mu (the only H, see Fig.4.6) with AH = 111.5 MHz.One can now calculate the hyperfine coupling isotope effect of the second kind,f2, to be 1.34. (Note that a very similar isotope effect for Mu compared to H,on the same C of a given radical, was found forthe meta-muonated free radicalof benzoic acid in chapter 3).Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 93MuPzFigure 4.5: The structures and numbering of MuBz and MuPz radicalsTable 4.7: The proton hyperfine coupling constants of MuBz and MuPz radicalsand LCR peak assignment for the latter radicalradical BR(kG) site AH(MHz)1 126.1MuBz 2,6 -25.13,5 +7.54 -36.219.545 2 111.5MuPz 26.646 3 -20.027.628 5 -38.24MuBzChapter 4. Muonium Reaction with N-Heterocyclic Compounds 944.3.1.2 PyridineThe high-field TF-1iSR experiments show that when Mu reacted with pyridinein aqueous solution, three types of muonated free radica’s were formed, withmuon-electron hyperfine coupling constants (A,) of 501.0, 511.7 and 526.5 MHz,respectively. HMO results show the r electron density at the N site of Py is1.195, significantly higher than unity, and at all the three types of C sites, lowerthan or about unity (see Table 4.6). Based on Pz’s results, it seems reasonableto assume these radicals were formed by Mu’s nucleophilic addition to the threetypes of C sites in the Py ring.The LCR spectrum of 20mM Py in aqueous solution shows three fairly strongresonance signals at the fields about 20 to 22 kG. By comparison with aromatics,we believe all these resonances are due to methylene protons of three types ofmuonated radical isomers.Based on three A values and the computer fitted LCR. parameters (resonancepositions. linewidths and amplitudes), and going through the same procedure asfor the benzoic acid case in chapter 3. one could assign the resonance at 20.752kG to the methylene protons of the muonated radicals with A, of 501.0 MHz,the resonance at 21.378 kG to the radicals with A, of 511.7 MHz and the oneat 21.599 kG to the radicals with A of 526.5 MHz. The corresponding isomericradical yield, PR. and the hyperfine coupling isotope effect of the second kind(ff2) are listed in Table 4.8.Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 95Table 4.8: The hyperfine coupling constants (Au), LCR resonance positions (BR),radical yields (PR), the hyperfine coupling isotope effect of the second kind (fi2)and the LCR peak assignment for 20 mM pyridine in waterBR/kG AJMHz PR f2 P/site(%) site(i)20.752 501.0 0.113 1.39 26 2,621.378 511.7 0.070 1.43 16.0 3,521.599 526.5 0.036 1.35 16.4 4If one assumes the relationship between log k and the radical localizationenergy obtained by the HMO method (L) for aromatics also holds for Py, thenone may further assign these LCR peaks to the methylene protons of particularradical isomers. The LrS (in /I units) are listed in Table 4.6. One sees that atthe ortho position (relative to the N atom), the radical localization energy is thelowest, therefore Mu adding to this position is expected to have the highest isomeric yield. Evidently, this corresponds to the resonance at 20.752 kG. Similarly,one could assign the resonance a.t 21.378 kG to the radicals with Mu attached tothe meta position to the N atom, and the peak at. 21.599 kG to the para-additionra.dicals. These assignments are shown in the last column of Table 4.8.It wouid be more convincing t.o assign these LCR signals if one could conductexperiments with deutera.ted and substituted pyridines at particular sites. PyrimidineThe FFT spectra of 2M pyrimidine in water at high fields show three types ofmuonated radicals formed when Mu reacted with Pm in aqueous solution. Theseradicals have A. values of 475.1, 493.9 and 519.6 MHz which are all in the rangefor aromatic radicals. There are three types of C sites in Pm molecules. HMOcalculations indicate that at sites 2, 4 and 6, the r electron densities are less thanChapter 4. Muonium Reaction with N-Heterocyclic Compounds 96unity, but at site 5 (also a C site), the ir electron density is slightly higher than1 (1.009). However, the r electron density at the N-site is much higher (1.199).Besides, the free radical localization energies at all these C sites are fairly closeand that at the N-site much higher (see Table 4.6). Therefore, these muonatedradicals are taken to be those formed with Mu attached to the three differenttypes of C sites in the Pm ring.The LCR spectrum of 0.3 M Pm in water shows three fairly strong resonancesat 20.011, 21.347 and 22.347 kG. Similar to the peak assignment for Py, onecould assign the peak at the lowest field (20.011 kG) to the radical with A of475.1 MHz, the peak at 21.347 kG to the radical with A,1 of 493.9 MHz and thepeak at the upmost field to the radical with A,, of 519.6 MHz. By Eq.2.21, thecorresponding isomeric radical yields were estimated as 0.066, 0.042 and 0.10,respectively. These data are recorded in Table 4.9.Table 4.9: The hyperfine coupling constants (An), LCR resonance positions (BR),radical yields (PR) for 0.3M pyrimidine in waterBR A,,/MHz PR - P/site(%) site(i) -20.011 475.1 0.066 32 221.347 493.9 0.042 20 522.347 519.6 0.100 24 4,6Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 97Similarly, one might make more detailed peak assignment with the relationship between the log k and the L obtained from HMO calculation for aromatics.Since radical localization energies at all C sites are fairly close to each other, onecould easily assign the resonance peak at 22.347 kG to the methylene protonsof the radicals with Mu attached to site 4 or 6. For the other two peaks, thereis no strong evidence to make the assignment, but it seems reasonable to assignthe peak at the lowest field to the radicals with Mu adding to site 2, since thecorresponding yield is a. bit larger than another, which is in line with the slightlysmaller L.No resonance signals were found in the low field region (1 to 3 kG) where theresonance due to the N nuclei would be expected if Mu did add to a N site. Thisgives additional support to the assignment given above. PyridazineThe FFT spectra of 2M pyridazine in water show only one evident pair of frequency peaks which leads to A of 529 MHz. However, The LCR spectrum of20mM Pd in water consists of two resonance peaks at the fields of 18.897 and21.248 kG. The Pd molecule has two different types of C sites as shown in Fig.4.1.Based on these facts and all reasoning made so far, it is most likely that Mu reacts with Pd forming two types of C-centred radicals, one with Mu adding to site4 or 5, the other to site 3 or 6. Perhaps FFT spectra failed to show two pairs ofpeaks because of high instrumentral noise.Similar to the peak assignment for benzoic acid and other N-heterocycles, onecould assign the LCR peak at 21.248 kG to the radicals with A,. of 529 MHz.The observed linewidth is somewhat smaller than the theoretical linewidth. Inorder to estimate the isomeric radical yield, Bh was ta.ken instead of B03Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 98for Eq.2.21, and a PR of 0.08 for the corresponding radical isomer was obtained.For another LCR signal, a value of 1.3 as f2 for the corresponding muonatedradicals was assumed. (This assumption was based on the results for aromaticsand other N-heterocycles). Thus, an A value of 466 MHz was obtained for theradicals which show the LCR resonance at 18.897 kG. The observed linewidth forthis peak is smaller than the theoretical one. Resonance signals were searchedfor through a rather wide magnetic field region, but no other signals were found.Therefore, it is assumed that this is the right one and /.Bth was also used toestimate the isomeric radical yield (0.086). Thus a total yield P of 0.17 wasobtained. These assignments and data are recorded in Table 4.10.Table 4.10: The BR, A,, PR and the LCR peak assignment for 20mM pyridazinein waterBR/kG AJMHz PR P/site(%) site(i)18.897 465.7 0.086 26 4,521.248 529.0 0.080 24 3,64.3.2 Reaction rate constantFrom Table 4.2, one can see that the presence of one nitrogen atom in the aromatic ring (Py) almost doubles the Mu reaction rate constant at neutral pH. Theeffect of the second N atom in the ring is dependent on its position. The rateconstant for Pz (with two N atoms at 1,4 positions) is the highest, but the rateconstants for Pm and Pd are lower than for Py. The rate constants are in thefollowing order:Pz>Py>Pd>Pm>BzChapter 4. Muonium Reaction with N-Heterocyclic Compounds 994.3.2.1 Partial rate constantBased on the isomeric radical yield distributions obtained from LCR results,these overall rate constants, k, can be broken down into partial rate constants.these values are presented in Table 4.11. For the convenience of discussion below,the corresponding r electron densities and radical localization energies given inTable 4.6 are also listed in the table.Table 4.11: The partial rate constants of Mu reactions with mono- and diazinesCompound site(i) k(108M’s’) 7r-e density L’)Py 2,6 15 0.923 2.51243,5 9.2 1.004 2.53804 9.5 0.950 2.5373Pz C 19 0.926 2.5004Pm 2 12 0.845 2.53824,6 8.9 0.874 2.53645 7.4 1.009 2.5391Pd 3,6 12 0.923 2.53744,5 13 0.953 2.5245(a) L in units of /• Correlation between rate constants and HMO parametersAs discussed for rate constants of Mu reactions with aromatics in chapter 3, rateconstants of muonium reactions with N-heterocyclic compounds will be analysedin terms of HMO parameters here.(i) LUMOFrom Table 4.6 one sees that the LUMO levels for the four N-heterocycliccompounds and benzene are in the following order:Pz<Pd<Pm<Py<BzChapter 4. Muonium Reaction with N-Heterocyclic Compounds 100It is clear that k values do not show a complete correlation with LUMO.It is interesting to see if the rate constants of e;q with the selected N-heterocycliccompounds correlate with LUMO parameters. Table 4.12 records these ks andLUMO levels. It is clear that the presence of one N atom in the ring dramaticallydecreases the LUMO level and increases the rate constant ke by about two ordersof magnitude. Adding another N atom in the aromatic ring decreases the LUMOlevel further in all cases studied here. At the same time, it enhances the ratefurther by a factor of about 20. This feature is significantly different from Muatom reactions. It is also different from H reactions (see later), despite e;q, Muand H all being simple reducing agents.Fig.4.6 shows the plot of log ke VS. LUMO energy levels for these compounds.If one notices the rate constants k of diazines are in the diffusion controlledregion, then one would agree that there is fairly good linear relationship betweenlog ke and LUMO levels. This implies that these e;q reactions are simple electronattachment reactions — the electron goes into the LUMO of its reaction partner.(The LUMOs are the lr* orbitals of the parent molecules. Electron addition inthese cases does not change the aromaticity of the molecules, but Mu additiondoes).N.—.CD(D(DCD08CDt,)CDI-., (DCDCD C)—.±c-p,-•CD CD CD ‘1 0 C) C) C) C) 0 C Ii U)9NNC——•1—1—1;- C’‘•!!‘!‘‘•3:•v<><v-I-I-I—I—000b--ic.L’0)0)-.II-•C)I•-cCD C) IChapter 4. Muoniurn Reaction with N-Heterocyclic CompoundsFigure 4.6: The plot of log ke vs LUMO level for Py, Pz, Pm, Pd and Bz.ke in units of Ms’, LUMO in units of IflI.102010. 5109.598. 587. 576. 50.65 0.7 0.75 0.8 0.85 0.9 0.95LUMO1 1.05Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 103(ii) 7 electron densityTable 4.6 shows that the highest ir electron density in each N-heterocycliccompound is located at the N site. No Mu addition to the N site was found.Fig.4.7 shows the plot of log k vs. ir electron density for the four N-heterocydiccompounds studied here. It seems that the Mu atom adds to the site of lower relectron density faster as the computer fitted line (with a linear fitting program)has negative slope. These are in line with Mu’s nucleophilic nature. However,data in the figure are very scattered.(iii) Radical localization energy L,.Fig.4.8 shows the plot of log k vs. L/I/3I. It can been seen that there isfairly good linearity between these two sets of data. This could be understoodif one accepts that the Mu reactions with these four N-heterocyclic compoundshave similar mechanistic features, ie. Mu attacks the low electron density sitesand its reaction rates are mainly governed by the radical localization energy. Itsuggests an Arrhenius-like relationship with the activation barrier scaling withLr.Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 1049. 49. 39. 29. 1S8. 39. 88. 70. 94 0.86 0.98 0.9 0.92 0.94 0.96 0.99p1 eie ctr on dnsjt y1• 02Figure 4.7: The piot of log k vs. r electron density for mono- and diazines. k,in units ofI1s.I I I II I I I I105Chapter 4. Muonium Reaction with Nfl’eterocycliC Compounds9. 49. 39. 2- 5.1S8. 98. 88. 72.495 2.5 2.505 2.51 2.515 2.52 2.525 2.53 2.535 2.54Figure 4.8: The plot of log k, vs. L. for mono and diazines. k) in units ofM’s’, L in units of /31.Chapter 4. Muonium Reaction with N-Heterocyclic Compounds 1064.3.2.3 Comparison of Mu with HIt is interesting to compare the reactivity of Mu with those of H toward benzeneand these mono- and diazines.It was reported 146] that the reaction rate constant of the H atom with benzene is 1.1x109M’s’, and the presence of N atom(s) in the ring dramaticallyreduces the rate ëonstants for H reactions [47]. It was explained by H being electrophilic. In sharp contrast to H reactions, this study shows that the presence ofN in the aromatic ring enhances the Mu reaction rates.Mu and H atoms react with Bz both via adding to the ring carbon. If onecompares the rate constant of Mu with H for Bz, one finds Mu reacts withBz about three times as fast as the H atom does. This isotope effect on therate constant is understandable, since Mu’s mass is only one ninth of that ofprotium, it diffuses in the solution three times faster than the H atom, so theencounter frequency is about three times that of H. The corresponding ratios forN-compounds are much larger. It implies that Mu and H atoms may undergodifferent reactions with these N-heterocyclic compounds. Indeed, ESR. studiesreveal that the H atom a.dds to the ring N [49,50], but the present 1iSR. and LCR.studies show Mu a.dds to the ring C.4.4 ConclusionWhen Mu reacts with mono- and diazines, it prefers to add to the points of lowelectron density (the C atoms). This finding is particularly interesting since itgives strong support to Mu being nucleophilic [56], whereas published studiespoint to H being electrophilic. The reasonably good linearity between log k1and L. shows that the HMO method is a good approximation in these cases, andChapter 4. Muonium Reaction with N-Heterocyclic Compounds 107the radical localization energy is the important factor which governs Mu reactionrates. Based on the Arrhenius reaction rate model this suggests the activationbarrier is directly proportional to L.Bibliography[1] C.D.Anderson and S.H.Neddermeyer; Phys. Rev., 51, 884 (1937).[2] J.I.Friedman and V.L,Telegdi; Phys. Rev., 106, 1290 (1957).[3] V.W.Hughes, D.W.McColm,K.Ziock and R.Prepost; Phys. Rev. LetL, 5, 63(1960).[4] P.W.Percival, H.Fisher, M.Camani, F.N.Gygax, W.Rüegg, A.Schenck,H.Schilling and H.Graf; Chem.Phys.LetL, 39, 33 (1976).[5] D.G.Fleming, D.M.Garner, L.C.Vaz, D.C.Walker, J.H.Brewer andK.M.Crowe; Adv. in Chemistry series, 175, 279 (1979).[6] V.W.Hughes, D.W.McColm, K.Ziok and R.Prepost; Phys. Rev., Al, 595(1970).[7] D.C.Walker; Muon and Muon.ium Chemistry, Cambridge University Press,Cambridge, 1983.[8] A.M.Brodskii; Zh. Ezp. Teor. Fiz., 44, 1612 (1963).[9] E.Roduner, P.W.Percival. D.G.Fleming, J.Hochman and H.Fisher; Chem.Phys. Lett. , 57, 37 (1978).[10] R.L.Garwin, L.M.Lederman and M.Weinrich, Phys Rev., 105, 1415 (1957).[11] J.L.Friedman and V.L.Telegdi, Phys. Rev., 105, 1681 (1957).[12] C.S.Wu, E.Ambler, R.W.Hayward, D.D.Hoppes and R.P.Hudson; Phys.Rev., 105. 1413 (1957). -[13] A.Abragam; C.R.Acad.Sc.Paris, 299, series II, 3, 559 (1984).[14] S .R.Kreitzman, 3 .H.Brewer, D .R.Harshman, R.Keitel, D .L.Williams,K.M.Crowe and E.J.Ansaldo, Phys. Rev. LetL, 56, 181 (1986).[15] R.F.Kiefl, R..Keitel. S.R.Kreitzman, G.Luck, J.H.Brewer, D.R.Noakes,P.W.Percival, T.Matsuzaki and K.Nishiyama, uSR Newsletter, 31, 1794(1985).108Bibliography 109[16] A.Streitwieser,Jr., Molecular Orbital Theory for Organic Chemists, JohnWiley and Sons, New York, 1961.[17] C.A.Coulson, Brian O’leary and R.B.Mailion, Hickel Theory for OrganicChemists, Academic Press, New York, 1978.[18] V.W.Hughes, Bull. Am. Phys. Soc. II, 2, 205 (1957).[19] A.Schenck, in Nuclear and Particle Physics at Intermediate Energies, ed.J.B.Warren, Plenum Press, New York, 1975.[20] J.D.Bjorken and S.D.Drell, in Relativistic Quantum Mechanics, p.261,McGraw-Hill, New York, 1964.[21] 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).[22] J.H.Brewer, and K.M.Crowe, Ann. Rev. Nuci. Part. Sci., 28, 239 (1978).[23] S.F.J.Cox, J. Phys. C: Solid State Physics, 20, 3187 (1987).[24] D.G.Fleming, D.M.Garner, L.C.Vaz, D.C.Walker, J.H.Brewer andK.M.Crowe, (Muonium Chemistry—a review) in ‘Positronium and MuoniumChemistry’, Advances in Chemistry Series 175, 279 (1979).[25] E.Roduner and H.Fisher, Chem. Phys., 54, 261 (1981).[26] R..F.Kiefl, Hyperfine Interactions, 32, 707 (1986).[27] M.Heming. E.Roduner, B.D.Patterson, H.KelIer and I.M.Savic, Chem.Phys. Lett., 128, 100 (1986).[28] K .Vankateswaran, M.V.Barnahas, R.F.Kiefl, J .M. Stadlbauer andD.C.Walker, J. Phys. Chem., 93, 388 (1989).[29] D.M.Garner, Ph.D. Thesis. Univ. of British Columbia, 1979.[30] H.Fischer and K.H.Hellwege, eds., Magnetic Properties of Free Radicals,Landold-Bornstein, New Series, Vol.2, Part 9b, Springer, Berlin, 1977.[31] K.Eiben and R.H.Schuler, J. Chem. Phys., 62, 3093 (1975).[32] M.B.Yim and D.E.Wood, J. Am. Chem. Soc., 97, 1004 (1975).[33] S.DiGregorio, M.B.Yim and D.E.Wood, .1. Am. Chem. Soc., 95, 8455(1973).Bibliography 110[34] W.A.Pryor, T.H.Lin, J.P.Stanley and R.W.Henderson, J. Am. Chem. Soc.,95, 6993(1973).[35] J.M.Stadlbauer, B.W.Ng, R.Gaiati and D.C.Walker, .1. Am. Chem. Soc.,106, 3151 (1984).[36] E.Roduner, G.A.Brinkman and P.W.F.Louwrier, Chem. Phys., 88, 143(1984).[37] K.Venkateswaran, M.V.Barnabas, Z.Wu, .1 .M.Stadlbauer, B.W.Ng, andD.C.Walker, Chem. Phys., 137, 239 (1989).[38] E.Roduner, Hyp. InL, 17-19, 785 (1984).[39] K.Venkateswaran, R.F.Kiefl, M.V.Barnabas, J .M .Stadlbauer, B .W.Ng,Z.Wu and D.C.Walker, J. Phys. Chem., 93, 388 (1989).[40] R.F.Kielf, 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,34, 681 1986).[41] E.Roduner, The Positive Muon as a Probe in Free Radical Chemistry, inLecture notes in chemistry, 49, Springer-Verlag, Berlin, 1988.[42] E.R.oduner, G.A.Brinkman and P.W.F.Louwrier, Chem. Phys., 73, 117(1982).[43] 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., 133, 465 (1987).[44] D . P. Chong, private communication.[45] K.Venkateswaran, M .V.Barnabas, Z.Wu, J .M.Stadlbauer, B .W.Ng andD.C.Walker, Chem. Phys. Letters, 143, 313 (1988).[46] G.V.Buxton, J. Phys. Chem. Ref. .Data,17, 513 (1988).[47] P.Neta and R.H.Schular, J. Am. C’hem. Soc., 94, 1056 (1972).[48] P.Neta, Chem.Rev., 72, 533 (1972).[49] B.L.Barton and G.F.Fraenkel, J. Chem. Phys., 41, 1455 (1964).[50] H.Zeldes and R..Livingston, J. Phys. Chem., 71, 3348 (1972).Bibliography 111[51] T.Rakowsky and J.K.Dohrmann, Ber. Bunsenges. Phys. Chem., 79, 18(1975).[52] J.K.Dohrmann and W.Kieslich, J. Mag. Res., 31, 69 (1978).[53] J.K.Dohrmann and W.I{ieslich, J. Mag. Res., 32, 353 (1979).[54] P.W.F.Louwrier, G .A.Brinkman, C.N.M.Balcker and E.Roduner, HyperfineInteract, 32, 753 (1986).[55] K.Venkateswaran, M.V.Barnabas, Z.Wu and D.C.Walker, Can. J. Phys.,68, 957 (1990).[56] J.M.Stadlbauer, B.W.Ng and D.C.Walker, Hyp. mt., 32, 721 (1986).[57] J.W.T.Spinks and R.J.Woods, Radiation Chemistry, 2nd edition, John Wiley & Sons. Inc., 1976.Appendix ACollaborative work already publishedAll the work presented in chapters 3 and 4 stems from experiments conductedwith the candidate as primary investigator. In this appendix, however, variousother projects are presented which were of a collaborative nature. The major investigators, besides my research supervisor, were Drs. K. Venkateswaran,J. M. Stadlbauer and M. V. Barnabas, and other collaborators included Drs.R. F. Keifi, G. B. Porter and B. W. Ng. Most of this work has now been published in various journals as listed below and Xerox copies of reprints are attachedat the end of this thesis. These projects are included as a part of my thesis inthis appendix because of my full involvement in the design and conduct of experiments, in the data analysis, and, in paper 6, in writing the first draft of thepaper. Due to the nature of the TRIUMF beam-time system — one in whicheach group of experimenters is given on average two weeks of experimental timeevery half year — all projects must be done in close collaboration, with 4 to 6people involved.1. Muonium Atoms Compared to Hydrogen Atoms and Hydrated ElectronsThrough Reactions with Nitrous Oxide and 2-propanol. K.Venkateswaran,M. V. Barnabas, Z. Wu, and D. C. Walker, RadiaL Phys. Chem., 32, 65(1988).112Appendix A. collaborative work already published 1132. Micelle-induced Enhancement of the Reactivity of Muonium Atoms in Dilute Aqueous Solution. K. Venkateswaran, M. V. Barnabas, Zhennan Wu,J. M. Stadlbauer, B. W. Ng and D. C. Walker, Chem. Phys. LeiL, 143(3),313 (1988).3. A Level-Crossing-Resonance Study of Muonated Free-Radical Formation inSolutions of Acetone in Hexane, Water and Dilute Micelles. K. Venkateswaran, R. F. Kiefi, M. V. Barnabas, Z. Wu, J. M. Stadlbauer, B. W. Ngand D. C. Walker, C’hem. Phys. LetL, 145(4), 289 (1988).4. Muon level crossing resonance study of radical formation in allylbenzene,styrene and toluene. K. Venkateswaran, M. V. Barnabas, Z. Wu, J. Stadibauer, B. W. Ng and D. C. Walker, Chem. Phys., 137, 239 (1989).5. Loss of Muonium in Nonhomogeneous Processes Studied by Level crossingResonance. K. Venkateswaran, M. Barnabas, Z. Wu and D. C. Walker,Can. J. Phys., 68, 957 (1990).6. Ortho-, Meta-, Para-Directional Effects in Muonium Addition to BenzoicAcid. J. Sta.dlba.uer, M. Barnabas. Zhennaii Wu and D. C. Walker, Hyperfine Interact. 65. 939 (1990).7. Comparison of Muona.ted Free Radicals in Pure Liquids with Those inDilute Solutions: Origins of Radicals. M. V. Barnabas, K. Venkateswaran,.1. Stadlbauer, B. W. Ng, Z. Wu, A. Gonzales and D. C. Walker, HyperfineInteract, 65. 945 (1990).8. Contrast between Ura.cil and Thyinine in Reaction with Hydrogen Isotopesin Water. M. V. Barnabas, K. Venkateswaran, J. M. Stadlbauer, Z. WuAppendix A. collaborative work already published 114and D. C. Walker, J. Phys. Chem., 95, 10204 (1991).Appendix BLCR peak assignmentB.1 Terephthàlic acidThe three peaks of the LCR spectrum of 20mM TPA in aqueous solution at pH12 can be assigned via indirect methods.One way to approach this is to use the hyperfine coupling isotope effect ofthe second kind, f12. From the result of benzoate, one knows that the f, forboth o- and m- radical isomers are 1.29. Compared with benzoate, TPA2- hasone more -C00 group at the para position. The Mu in the MuTPA2 radicalis at the position ortho to one substituent and meta to the other. Thereforeit seems reasonable to assume that f:2 for MuTPA2 is 1.29. In general, onemight assume that the following approximation holds:(B.1)where f2 is the value taken from the average of the two relevant radical isomers.From the observed resonance field BR and the isotope effect f12, one can estimateA via Eq.3.2. This yields A for the MuTPA2 as 496.4 MHz. With the otherobserved LCR parameters for TPA listed in Table 3.3, the radical yield PR of0.21 was obtained.115Appendix B. LCR peak assignment 116Another approach is based on the substituent effect on muon hyperfine coupling constant as shown in Eq.B.2 [41]A,.1 = A. 11(1 — zx)(1—(B.2)where,is an additional correction term which reflects a position-dependentinteraction between two substituents X and Y. Other terms are the same as inEq.3.5. Usually, i, is fairly small [41]. If is negligible, then Eq.B.2 can berewritten asAA°.fJ(1—Lx) (B.3)where the muon hyperfine coupling constant (At) is daggered in order to distinguish it from that of Eq.B.2.With this approach and the benzoate results, one gets A of —500 MHz forthe MuTPA2 radicals, which agrees with the first approximation.At the higher fields, there are two weaker LCR peaks. Comparing these withmuonated cyclohexadienyl radical’s data [43,41], one can assume that these tworesonances are from the same radical. If one takes A of 496.4 MHz, one canestimate the corresponding radical yield for the peaks at 27.737 kG and 28.427kG as 0.205 and 0.222, respectively. Within experimental error, these values arethe same as the value obtained from the peak at 20.095 kG, which gives strongsupport to the assumption that they all come from the same radical.By comparison with MuC6H,one can make assignment for the two resonancesignals at higher fields: the peak at 27.737 kG to H(s) and the peak at 28.427kG to H(5). The resonance signal due to the H(6) of MuTPA radicals was notdetectable. This can be understood if one notices that the AH for the metaprotons of the MuC6H is only 7.5 MHz, therefore the LCR signal due to theAppendix B. LCR peak assignment 117H(6) should be very weak.B.2 Benzonitrile and p-cyanobenzoic acidThe LCR spectrum of 13.9 and 15mM benzonitrile in water totally consists ofthree resonances in the field region from ‘-48 to 1-.d21.5 kG. Again, these peakscome from the aromatic ring protons of muonated radicals. With the A values reported in the literature for neat liquids [36] and going through the sameprocedure of LCR. peak assignment as for benzoic acid, one can assign the peakat 19.510 kG to the ortho-radical isomer, the peak at the highest field to themeta-isomer and the remaining one to the para-isomer. The corresponding proton hyperfine coupling constants, PR and f,2 can also be estimated as before. Thevalues obtained are listed in Table 3.9.These assignments are supported by the reasonable f2 values, total radicalyield, P, of 0.20 and the normal order of the resonance positions of the LCRpeaks, ie., the larger the A. the higher the BR. In addition, ortho additiondominates as seen in other aromatic cases.The LCR spectrum of 20mM p-CN-BA in aqueous solution at pH 9 consistsof two peaks in the field region around 20 kG. This is expected since there aretwo different types of ring sites in the molecule where Mu can add. In order tomake peak assignment, one needs A,s for these two radicals. Since no A. valueshave been reported and we could not determine these values experimentally, someapproximation had to be made as in the TPA case.Table B.1 presents the hyperfine coupling data, radical yields and the corresponding muonated radicals based on the average fj2 approximation. TableB.2 presents the hyperfine data, radical yields and the corresponding muonatedAppendix B. LCR peak assignment 118radicals based on the A1. approximation.Table B.1: The observed values of BR for 20mM p-CN-BA in aqueous solutionat pH 9, the assumed values of ft2 and the deduced values of A1., AR, PR and PRadical f(a) BR/kG A1./MHz AR/MHZ PR PJ(I) 1.29 20.138 497.6 121.3 0.067 31(II) 1.275 19.239 477.2 117.7 0.147 69(a) values are obtained with average f:2 approximation.(b) P is the relative radical isomer yield.Table B.2: The observed values of BR for 20mM p-CN-BA in aqueous solutionat pH 9, the assumed values of A and the deduced values of AH, PR and PRadical At/MHz BR/kG AH/MHZ PR P%(I) 505.1 20.138 (128.8) 0.058 33(II) 488.1 19.239 (128.6) 0.118 67It is expected that these two approximate approaches give somewhat differenthyperfine data and radical yields. However, both approaches assign the peak atthe higher field to the radical with Mu attached to the ring C ortho to the -CO 0group, (I), and the peak at the lower field to the radical with Mu attached to thering C meta to the -COO- group, (II). In both ways, the radical yield of (I) isabout one half of the yield of (II). The closeness of the parameters deduced withthe two approximations gives support to the assignment made above.B.3 p-Hydroxybenzoic acidThe LCR spectrum of 20mM p-OH-BA in aqueous solution at pH 8 shows tworesonance peaks in the field region from .‘19 to -.21 kG, as expected. The A1.Appendix B. LCR peak assignment 119values of the two types of muonated radicals were directly determined by TF1SR measurement as 471.1 and 518.1 MHz, respectively, since this compound wassufficiently soluble in water. The peak assignment can be made by comparisonof these measured A4, values with the approximate A values. From the closenessof the corresponding vaiues, the peak at 19.022 kG can be assigned to radical(IV) with A4, of 471.1 MHz, and the peak at 20.913 kG to the radical (III) withA of 518.1 MHz. The parameters determined are listed in Table B.3.Table B.3: The observed values of A and BR for 20mM p-hydroxybenzoic acidin aqueous solution at pH 8, the assumed values of A and the deduced valuesof Ajj, fi2 PR and P.Radical At/MHz An/MHz BR/kG AH/MHZ PR P%III 504.9 518.1 20.913 127.4 1.28 0.091 34IV 470.3 471.1 19.022 115.7 1.28 0.177 66The LCR spectrum of 20mM p-OH-BA in acidic solution (pH 1.7) also showstwo resonance peaks in the field region around 20 kG. These two peaks arebelieved due to the methylene protons of the radicals (V) and (VI). A4, couldnot be determined directly due to low solubiity; but, based on both A and f2approximations, one can assign the peak at 19.233 kG to radical (VI) and thepeak at 20.934 kG to radical (V). The relevant results are listed in Table B.4 andUI IvAppendix B. LCR peak assignment 120B.5, respectively.Table B.4: The observed values of BR for 20mM p-hydroxybenzoic acid in aqueous solution at pH 1.7, the assumed values of A and the deduced values of AH,fi2, PR and P.Radicai At/MHz BR/kG AH/MHZ f22 PR .P%V 499.2 20.934 108.2 1.45 0.228 63VI 466.3 19.233 107.0 1.37 0.136 37Table B.5: The observed values of BR for 20mM p-hydroxybenzoic acid in aqueous solution at pH 1.7, the assumed values of f:2, and the deduced values of A,PR and P.Radical f12 BR/kG AJMHz PR P%V 1.28 20.934 518.5 0.152 58VI 1.28 19.233 476.2 0.109 42V VIAs in the case of p-CN-BA at pH 9, two approximate methods give somewhatdifferent results. However, both assign the peak at 20.934 kG to radical (V) andthe peak at 19.233 kG to radical (VI). In addition, both indicate that radical (V)with Mu attached to the C ortho to -COOH group dominates.Appendix B. LCR peak assignment 121B.4 Aniline and p-arninobenzoic acidThe LCR experiments for aniline were conducted with 15mM aqueous solutionsat pH 2 and 8. In the basic solution, aniline exists as a neutral molecule. Unlikethe TF-iSR results, in the fairly broad field region of 16 to 22 kG, only onestrong LCR resonance peak was observed. It occurred at a field of 18.087 kG.Since should be larger than IBth, this peak can only be assigned to theortho-radical isomers with A,, of 441.3 MHz [36]. Its yield is 0.163 andf12.35.These results are given in Table B.6. Here, ortho-addition also dominates, whichis in line with other aromatics.Table B.6: The observed value of BR, deduced values of AH, f12 and PR for 15mManiline in aqueous solution at pH 8.Radica1 A,,/MHz’) BR/kG AH/MHZ f2 PR%ortho 441.3 18.087 102.9 1.35 0.163(a) Position of Mu relative to -NH2 group.(b) From Ref. [36].In acidic solution, aniline exists as protonated cation. No correspondingmuonated radicals have been observed before. The LCR spectrum of 15mManiline at pH 2 shows one resonance peak in the field region as for the one athigh pH. If one assumes this peak is also due to the ortho-radical isomer andthat fi2 does not change significantly when pH drops from 8 to 2, then one canestimate the hyperfine parameters and the radical yield. These estimated valuesare listed in Table B.7.Appendix B. LCR peak assignment 122Table B.7: The observed BR, assumed f12 and deduced A, AH and PR for 15mManiline in aqueous solution at pH 2.Radical(a) BR/kG f An/MHz AH/MHz PRortho 18.115 1.35 441.4 102.8 0.146(a) Position of Mu relative to-NHt group.(b) f12 is taken the same as for the basic form.The LCR spectrum of 20mM p-aminobenzoic acid in aqueous solution atpH 10 consists of two resonance peaks in the field region of 18 to 21 kG, asexpected. These peaks are taken to be due to the methylene protons of radicalswith Mu atta.ched to C(2). (VII). and to C(3), (VIII).vmTwo A vaiues were obtained by TF-jtSR measurement (Table 3.1) for thesetwo radical isomers. In order to decide which A,. for which radical isomer, onemay invoke the A approximation. With the x values for the -COO- and -NH2groups, one gets A of 510.7 MHz for radical (VII), and 444.0 MHz for (VIII).By closeness, it is most likely that A, of 521.8 MHz is for radical (VII), and458.2 MHz for radical (VIII). With these data, one can assign the peak at 18.485kG to radical (VIII) with yield of 0.139, and the peak at. 21.124 kG to radical(VII) with yield of 0.047. These data along with their hyperfine parameters areMuVIIAppendix B. LCR peak assignment 123presented in Table B.8.Table B.8: The observed values of A and BR and deduced values of AR, f2, PRand P for 20mM p-aminobenzoic acid in aqueous solution at pH 10.Radical AJMHz BR/kG AH/MHZ f12 PR P%VII 521.8 21.124 127.2 1.29 0.047 25VIII 458.2 18.485 112.9 1.28 0.139 75For protonated p-aminobenzoic acid in acidic solution, only one LCR peakat 19.922 kG was observed. With f2 and A approximations, this peak can beassigned to the methylene proton of radical (IX). The relevant data are presentedin Table B.9.Table B.9: The observed BR, assumed f2 and deduced A, AH and PR for 20mMp-aminobenzoic acid in Aqueous Solution at pH 2TXBR/kG f12 AJMHz AH/MHZ PR19.922 1.28 493.4 121.2 0.166


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